Introduction
Independent researchers investigating the disappearance of MH370 today released a new technical report to guide the next search for the debris field on the floor of the Southern Indian Ocean (SIO). The report provides the scientific and mathematical foundation that was used to define the recommended search area that was disclosed last month. The authors of the report are Bobby Ulich, Richard Godfrey, Victor Iannello, and Andrew Banks.
The full report, including all appendices, is available for download. What follows is a brief summary of the important results.
The flight of MH370 was analyzed from takeoff to impact in the SIO using a comprehensive, fully integrated model. The model was developed using exhaustive data sets and technical documentation available from both public and confidential sources, and includes:
- radar data collected by military and civilian installations in Malaysia
- timing and frequency measurements collected by the Inmarsat satellite network
- aircraft performance data for Boeing 777-200ERs
- historical performance data for airframe 9M-MRO
- navigation and speed modes for automated flight
- drift analysis of debris that floated and was recovered in East Africa
- aerial search results from March and April 2014
- weather data along the flight path
A total of 2,300 possible flight paths were evaluated, and an overall probability metric was defined that incorporates the information from all the data sets. The highest probability flight path was identified as due south from waypoint BEDAX, which is about 185 km (100 NM) to the west of Banda Aceh, Sumatra, and an impact in the SIO near S34.2342° E93.7875°, which is 4380 km (2365 NM) from BEDAX.
The work included the development of an accurate fuel consumption model, and well as a statistical metric for the expected random noise inherent in the recorded satellite data. These improvements allowed the rejection of hypothetical flight paths that were previously believed to be possible.
Turnback Across Malaysia
After takeoff, the climb was normal, and the aircraft leveled at a cruise altitude of FL350 (35,000 ft standard altitude), tracking towards waypoint IGARI in the South China Sea. After flying by waypoint IGARI, the transponder was disabled as the aircraft turned towards waypoint BITOD. On passing the FIR boundary between Malaysia and Vietnam, the aircraft began turning back towards the Malay peninsula, and flew towards Kota Bharu airport, as shown in the figure below.
The civilian radar installation at Kota Bharu captured MH370 as it flew towards and then away from Kota Bharu. An analysis of this radar data shows that the aircraft climbed from FL350 to about FL385 (true altitude of 40,706 ft) and accelerated to near its maximum operating speed of Mach 0.87 as it passed to the north of Kota Bharu. It then flew across the Malay peninsula and towards Penang Island, where a civilian radar installation at Butterworth Airport captured the radar targets. As it passed to the south of Penang Island near Penang Airport, it slowed down to a speed closer to Mach 0.84, and turned to the northwest over the Malacca Strait.
Flight over the Malacca Strait and Around Sumatra
The flight over the Malacca Strait was captured by Malaysian military radar, as disclosed in a briefing to family members in Beijing in March 2014. After passing Penang Island, the aircraft proceeded on an exact course to waypoint VAMPI, and intercepted airway N571. The last radar target was captured at 18:22:12 about 10 NM after passing waypoint MEKAR on N571. The flight over the Malacca Strait, around Sumatra, and towards the South is shown in the figure below.
In the report, it’s deduced that soon after the aircraft was beyond Malaysia radar coverage, MH370 began a “lateral offset” that would position the aircraft about 15 NM to the right of N571, possibly to ensure separation from other traffic. Once this offset was completed at around 18:29, a descent began, and when the altitude reached FL250 (well below the minimum altitude of FL275 for traffic on N571), the aircraft turned directly towards waypoint IGOGU on a westerly course.
On reaching IGOGU, it’s deduced that the aircraft continued its descent and turned due south, flying along the FIR boundary between Malaysia and India. It leveled at around FL100 (10,000 ft standard altitude), and continued south until reaching the FIR boundary of Indonesia. It then turned to the west, away from Indonesia, and flew along the FIR boundary.
It’s further deduced that the final course change was due south towards waypoint BEDAX. After passing BEDAX, a climb to FL390 began at around 19:24, ending at around 19:41. The aircraft continued on a due south course at LRC speed towards the South Pole until fuel exhaustion occurred in the SIO at around 00:17.
The authors observe that the trajectory last covered by Malaysian radar was to the northwest along N571. Only when beyond Malaysian radar coverage was a descent to a lower altitude initiated, which was followed by turns to the west and south. It’s hypothesized that the intention was to lead the searchers into believing the trajectory continued along N571 to the northwest, as the transit at low altitude would have been below the radar horizon of Indonesian and Thai radar installations. It is only because of the analysis of the satellite data first performed by Inmarsat that we know the flight path continued into the SIO. Very likely, the party responsible for the diversion was not aware that this data set was recorded and could be later used to deduce a path.
The entire flight path is summarized in the figure below.
Possible MH370 Sighting by Kate Tee
Kate Tee was on a sailboat on 7th March 2014 southeast of Great Nicobar Island and northwest of Sumatra. She reported seeing a large aircraft coming towards her from the north, flying at an unusually low altitude. At around the same time, she reported that the sailboat gybed accidentally. This gybe event and the track of the sailboat were recorded on the GPS system on board, and serves to define a position and an approximate timestamp for her sighting. In this time interval, the sailboat was close to waypoint NOPEK along the FIR boundary between Malaysia and India, which may help to explain her sighting.
The figure below depicts the path of MH370 at 18:55:57 and the GPS track from the sailing boat every five minutes from 18:25 to 19:25. The GPS track from the sailing boat and the deduced flight path of MH370 appear to align.
Probability of Various Paths to the SIO
In order to rank the likelihood of various reconstructed paths to the SIO, the available data sets were compared to predictions from the mechanistic models, and the match between the measured data and the models were used to develop probabilities for each path. For each path, probabilities were calculated for four classes of measured data:
- Measured satellite data compared with model predictions for navigation, weather, and data statistics
- Observed fuel endurance with model predictions from fuel consumption models
- Observed location and timing of recovered debris with predictions from drift models
- Failure to find floating debris compared with the areas targeted by the aerial search
The overall (composite) probability for a path was calculated as the product of the of the probabilities of the four classes of data and then normalized to produce a probability density function (PDF) in which the cumulative probability across all latitudes is unity.
Each panel in the figure below shows the probabilities for each class of data, followed by the overall probability. If only considering the match to the measured satellite data presented in the first panel, the probability is highest for the path ending near 34.3°S latitude. However there are many other prominent peaks for paths ending along the 7th arc to the north and south of 34.3°S, so further discrimination is required using the other three data sets.
Peaks corresponding to end points to the south of 34.3°S are rejected because of low probabilities of matching the observed fuel endurance and the reports of the recovered debris in East Africa. On the other hand, end points to the north of 34.3°S are rejected because the impact would have produced a floating debris field that would have been detected by the aerial search with a high probability. What remains is a single prominent peak at 34.3°S, which represents a due south path from a position near waypoint BEDAX towards the South Pole.
Search Area Recommendation
The analysis presented above suggests that MH370’s flight path in its final hours followed E93.7875° longitude, corresponding to a great circle path between waypoint BEDAX and the South Pole. Using this result, the last estimated position (LEP) is S34.2342° E93.7875°. Although some of the subsea was previously searched in this vicinity, the terrain is challenging, and the debris field might have been not detected, or detected and misinterpreted. There is also the possibility that there was a controlled glide after fuel exhaustion, and an impact well beyond what was previously searched.
To define the search area near the LEP, three cases were considered, each with an associated search area. The highest priority search area, A1, of 6,719 NM2 (23,050 km2), assumes there were no pilot inputs after fuel exhaustion. The search area of next highest priority, A2, encompasses 6,300 NM2 (22,000 km2), and assumes there was a glide towards the south after fuel exhaustion. The lowest priority, A3, is the controlled glide in an arbitrary direction with an area of around 48,400 NM2 (166,000 km2). The three search areas are shown in the figure below.
Discussion
A new report is now available that suggests that MH370’s flight path in its final hours followed E93.7875° longitude, corresponding to a great circle path between waypoint BEDAX and the South Pole. The report concludes that an impact near S34.2342° E93.7875° is most likely.
The technical details are included in the report so the analytical results can be evaluated, reviewed, and replicated by other investigators.
Three end-of-flight scenarios were considered, and a recommended search area for each scenario was defined and prioritized. As parts of the recommended search areas were already searched by GO Phoenix and Ocean Infinity, we recommend a thorough review of the existing sonar data, recognizing that the quality of the data in that vicinity varied due to challenging terrain.
As there are no ongoing MH370 search activities, the authors of the report believe the new technical results provide credible evidence that justifies a new search.
Update on March 9, 2020 – Civilian Radar Data
A newer version of the civilian radar data is now available as an Excel file. This data set represents the raw data from the Kota Bharu and Butterworth radar heads before the data was processed and stored by the radar network. This data set was used for the calculations in the report. Also included in the Excel file is the methodology for converting the raw data to latitude and longitude.
Update on March 12, 2020
The best estimate of the point of impact (BE POI) has been renamed the last estimated position (LEP), which is a more accurate description. The location is unchanged.
Update on January 7, 2021 – Links for CSIRO Drift Results
Some contributors are performing their own drift studies using the results from the CSIRO calculations. The following links can be used to download the results as MATLAB data files. The calculations were performed for floating particles that are considered “generic” and for floating particles that are hydrodynamically and aerodynamically similar to the flaperon.
Generic particles: http://www.marine.csiro.au/~griffin/MH370/data/br15_MH370_IOCC_tp3l1p2dp_arc7_4408_15_tracks.mat
Flaperon particles: http://www.marine.csiro.au/~griffin/MH370/data/br15_MH370_IOCC_tp3l1p2dpf10_20_99_arc7_4408_15_tracks.mat
Great post Victor! Many thanks!
Well we have a lot of reading to do before we post.
I thank all involved for the incredible work effort, and I am confident that there are many important new ideas disclosed. I am semi-convinced myself of the 180S start of the flight path.
@Paper authors. Thanks for this work. A couple of quick technical queries if I may.
You mention that Butterworth primary radar record runs up to 18:00:51. I thought this was 18:01:21 (ref “pure RHP clock” version)?
You say (page 11/12) we can use channel C6 BFO at 1840 because it aligns with an adjacent R4 value. But we can’t use C6 BFO at 2314 because we don’t know C6 offset. I don’t understand how you can hold those positions simultaneously. Why can’t we use the 2314BFO with whatever C6-specific offset (or offset range) that you have deduced from 1840?
Related to the last point, were there no C6 BFO observations from MH371 (or other accessible datasets) that permit empirical validation of a C6 channel BFO offset?
@paul smithson said: You mention that Butterworth primary radar record runs up to 18:00:51. I thought this was 18:01:21 (ref “pure RHP clock” version)?
In Section 5.2.1, it says Between 17:46:23 and 18:01:23, using the PSR data from the Butterworth radar data, a similar analysis was performed to calculate the ground-speed for various altitudes.
We’ll correct other times so they are consistent.
Why can’t we use the 2314BFO with whatever C6-specific offset (or offset range) that you have deduced from 1840?
This is a bit confusing. The routes were prioritized without regard to the BFO values at 23:14 because we don’t know the C-channel offset a priori. However, once the best route is selected, we can calculate the channel offset at 23:14 (for that route), and then apply that same offset at 18:40.
Thanks
Victor: Re: BFO C6 Bias
I haven’t been through the whole paper yet, so maybe the answer is in there…but how does your C6 bias value compare to what was estimated in 2017 (146.71 Hz)? Source here: http://bit.ly/2LaHqTq
@airlandseaman: Bobby would know the exact value of the channel offset, but using a linear fit at 23:14 should not be very different than the value calculated from the “best” route.
If plane turned a few times, it could have turned many times more, maybe doing a holding pattern. BTO/BFO with hourly gaps are just not enough to exclude pilot inputs in-between. Beating a dead cat. If any Australians are here, file a FOI request to your military to disclose raw acoustic data from Zenith Plateau search (which even included an oil slick sampled, chromatography should exist somewhere?)
@Kirill Prostiakov said: BTO/BFO with hourly gaps are just not enough to exclude pilot inputs in-between.
That’s correct. We can’t be absolutely sure that there were no pilot inputs after 19:41.
And yet, the BTO and BFO values after 19:41 have the same signature of an automated flight at Long Range Cruise (LRC) speed and a due south course between waypoints BEDAX and the South Pole.
What do you think the probability is that there were pilot inputs that just happened to match these automated settings?
@paul smithson
Victor states in his post “The model was developed using exhaustive data sets and technical documentation available from both public and confidential sources”.
The Butterworth RHP data goes to 18:01:23.203 UTC, a bit further than we wanted to publicly state. But you have now done that for us.
The DSTG Western Hill military radar data goes to 18:01:49 UTC, even a bit further still.
Neither data set changes the MH370 flight path in the Malacca Strait.
@All: As Richard has noted, we do have access to civilian PSR data that is slightly different than was publicly shared in a previous blog post. We believe this data set is more accurate, as there is less processing by the system before it was stored, and there are some additional points not included in the first data set. That said, the data sets are very similar.
I have received permission to share the updated data set so we’re all on the same page. I’ll update the article with a link to the most recent PSR data shortly.
@Bobby, Richard, Victor, Andrew
Many thanks for sharing the paper. An enormous amount of work and thinking has gone into this, so I’ll study with care. I started with some basic checks. The first is to run FL390 LRC in my tool with same 19:41 position. So far so good: I get a 00:11 lat of 33.40S which seems pretty close (note a small typo in your fig. 4, 00:11 lat), however I should check for implications of “air packs off” for the FF model. How much would that differ?
Could you indicate where to look for detailed parameters in relation to fig. 4, is that the fig. 35?
Many thanks for this analysis, to all the authors. You have come a long way over time, and this report contains the most plausibly constrained area I have seen so far. Well done.
Gents,
Once again an enlightening read.
@Victor et. al.
Had a viftually all day medical schedule today. So I did not put a lot of time into your excellent report.
At first blush, I am inclined to go with Figure 38.
@Niels
Many thanks for spotting the typo in Figure 4. I have fixed that in the link to the full report available for download. Victor will fix that in his post above in due course.
You ask: “I should check for implications of “air packs off” for the FF model. How much would that differ?”
The difference to the fuel flow when the air conditioning packs are switched off is described on pages 20, 36, 42 and more fully in the appendix pages 77 to 79.
You ask: “Could you indicate where to look for detailed parameters in relation to fig. 4, is that the fig. 35?”
Yes, Figure 35 gives the detailed flight parameters for the SIO flight route constrained to waypoint BEDAX and with Air Conditioning Packs off.
The text and figures of the downloadable .pdf are searchable: “packs” is found on 14 pages and “00:11:00” is found on 9 pages.
The video presentation of the new paper to the next of kin at the MH370 6th Remembrance Event on Saturday 7th March 2020 was well received, according to the family members who organised the event.
Here is the YouTube link: https://youtu.be/MgEDB36h_iA
Anthony Loke (former Malaysian Minister of Transport) was present at the event and promised to visit his successor, following the Government change in Malaysia, and push for a further MH370 underwater search.
Meanwhile, the video has been viewed 388 times.
@DennisW
You stated: “At first blush, I am inclined to go with Figure 38.”
When I read that comment, I could not stop laughing for several minutes.
Very drôle!
Figure 38 is the “Route Probability of Matching the BTOs and GDAS Data (not using BFOs)”.
Of course, I prefer Figure 39.
@All,
I appreciate all the hard work that has gone into this, but I fear it is another case of making the maths fit your preferred scenario. Just as CAPTIO came up with a route ending near CI.
Isn’t it becoming clear that this mystery could be just a random, meandering route(autopilot off-direct mode)? If this the case then multiple routes, perhaps even more than 2300 could be made to fit the maths.
@Tim: The route from 19:41 to fuel exhaustion shows evidence of automated flight. The probability of a “random, meandering route” matching a great circle path at LRC speed and FL390 is practically zero. On the other hand, the route between 18:28 and 19:41 was selected to match the beginning and end point in location and time, which also matching the BFO values at 18:40. It is true that we can’t prove that this part of the path is unique, but it doesn’t affect the end point.
On the other hand, the CAPTIO path requires multiple changes in course, speed, and altitude to fit the data after 19:41.
A B777 flying with autopilot disengaged and in direct mode would not fly the path recorded by the military and civilian radar, including the intercept with N571 at VAMPI, if that is your claim.
@Richard
Thanks a lot!
@Tim
You asked “ Isn’t it becoming clear that this mystery could be just a random, meandering route(autopilot off-direct mode)?”
No, it is becoming clear that this mystery is a carefully planned and perfectly executed diversion. There was nothing left to chance. There was no random!
We are not fitting our scenario to the maths, we are fitting a large number of independent data sources to the scenario.
@Henrik Rydberg: Thank you. The report represents an accumulation of knowledge and data gained over a period of nearly six years. You had an integral role in that.
ET302 interim report released:
http://www.aib.gov.et/wp-content/uploads/2020/documents/accident/ET-302%20%20Interim%20Investigation%20%20Report%20March%209%202020.pdf
@Richard
“… a carefully planned and perfectly executed diversion…”
Minor inconsistency.
If the perpetrator was not aware of BTO BFO then there was no perfection in this plan. However, if he knew about it, what was the plan?
Overall a great report.
@Richard said: Many thanks for spotting the typo in Figure 4. I have fixed that in the link to the full report available for download. Victor will fix that in his post above in due course.
The updated figure should now appear in the post above.
Hishammuddin Hussein, who at the time of the disappearance of MH370 was the Malaysian Minister of Defense and Acting Minister of Transport, has been appointed the Foreign Minister for the newly formed government.
https://www.nst.com.my/news/nation/2020/03/573172/foreign-minister-appointment-huge-trust-says-hishammuddin
@airlandseaman,
To expand on Victor’s answer to your question about the C6 BFO bias:
1. We did not find other instances of C6 besides the two phone calls during MH370. Apparently this channel is only used during phone calls.
2. The most accurate means of determining the C6 bias is to interpolate the 19:41-00:11 R4 BFOs at 23:14, and then find the channel frequency offset for C6 relative to R4.
3. The BFO at 18:40 cannot be independently estimated, because the flight path is unknown.
4. We found the 23:14 C6 bias by interpolating the R4 BFOs. You can use a linear fit to the 19:41-00:11 R4 BFOs, or you can use a 2nd order fit. The two methods differ by < 1 Hz.
5. We found a BFO bias of 148.9 Hz for C6 using a 2nd order interpolation and assuming the R4 bias is 149.86 Hz.
6. We applied that C6 bias to the 18:40 BFOs used in fitting the FMT Route.
DrB wrote “We did not find other instances of C6 besides the two phone calls during MH370. Apparently this channel is only used during phone calls.”
‘C6’ is a Channel Unit, a GES module that provides multiple separate channel CODECs, not a discrete channel.
The GES Log shows that three discrete channel CODECs were used for voice signalling, #3730, #3737 and #373E.
and “The most accurate means of determining [C-channel] bias is to interpolate…”
I wouldn’t characterise that as “the most accurate means”. It’s a method. Can one be confident that the performance of a demod/decoder for a continuously modulated channel be reliably compared to the performance of a demod/decoder operating on a packet data/burst channel?
As a check, would the interpolation reliably predict BFO for a T-ch burst from a preceding R-ch burst?
@Victor
Concerning Hishammuddin Hussein, plus ça change.
@Victor et. al.
Seriously, a great report. It will take me several days to digest it. One thing I find a bit strange is the “probability” ordinate. I was expecting a “probability density” ordinate. I am not sure how to get the probabilty that the wreckage is between 34.2S degrees and 34.4S degrees (34.3S +/- 0.1 degree).
@Don
You asked “As a check, would the interpolation reliably predict BFO for a T-ch burst from a preceding R-ch burst?”
The attached table shows 5 pairs of T-ch and R-ch from MH370 on the ground in Kuala Lumpur, adjacent in time, from the same Channel Unit 8. The minimum difference in BFO is 0 Hz and the maximum difference is 3 Hz.
https://www.dropbox.com/s/pfylb0grwzptp8h/Channel%20Unit%208%20T%20vs%20R%20BFOs.png?dl=0
The 29 Channel Unit 6 BFOs at 23:14/15 UTC are all CODEC #3737 and vary between 216 Hz and 222 Hz.
The 51 Channel Unit 6 BFOs at 18:39/40 UTC are either CODEC #3730 or #373E and vary between 86 Hz and 90 Hz.
Variations of 3 Hz, 6Hz and 4 Hz are all within the expected range.
I would characterise the data as reliable and accurate.
@Richard,
Thank you, I’m more than familiar with the observed and recorded data.
It is the process of interpolation, described by DrB, about which I expressed the interest.
@Don
Your “interest” in the process of CU6 interpolation in our paper is actually criticism.
You stated: “I wouldn’t characterise that as “the most accurate means”.”
Your criticism was based on the fact that the CU6 data comes from different CODECs.
Since you are so familiar with the data, then you could have pointed out that the data at 23:14/15 is all from one and the same CODEC and that there was only a small variation in the data within the expected bounds.
Just correcting the record.
@DennisW said: I am not sure how to get the probabilty that the wreckage is between 34.2S degrees and 34.4S degrees (34.3S +/- 0.1 degree).
My co-authors might disagree, but I don’t put a lot of weight on the value of the peak probability at 34.3S latitude. Rather, what is significant are the low probabilities at other latitudes.
I asked the co-authors what they thought the success probability was for A1 or A2. I’ll leave it to them to disclose what they said [if they so desire]. I put the probability of success at around 50% because we don’t know what we don’t know. If the modeling is accurate and the measured data has the errors we assumed, the probability of success would be much higher.
@DennisW
I think the probability for A1 is 90% and A1 + A2 is 97%.
@Richard. Thanks for sticking your neck out. Out of the residual 3%, how much of that is A3 – by implication, how much of it is “none of the above” aka probability that 180S is not the correct solution?
Dr. B: Re your March 10, 2020 at 11:43 am response:
On Page 148, it was stated:
Using R4 as the reference for a BFO Bias of 150.0 Hz, these channel offsets ranged from +1.0 Hz for C6 to -5.0 Hz for T12.
But above, you wrote you found a BFO bias of 148.9 Hz for C6 using a 2nd order interpolation and assuming the R4 bias is 149.86 Hz. To be consistent, shouldn’t “…+1.0 Hz for C6 …” be -1.0 Hz, not +1.0 Hz?
But I believe there may be more than a sign error in the paper. I did exactly what you stated (I used a linear fit of the R4 data) back in 2017. Using that technique, I found the exact same same R4 average (149.86 Hz), but an average of the 40 C6 samples = 146.71 Hz, not 148.9 Hz. See the summary page and page 14 in particular in that 2017 paper: http://bit.ly/2LaHqTq
Dr. B: Correction: Page 148 should read Page 143.
@airlandseaman,
There is no sign error. When you compute a predicted BFO for the phone calls using a 150 Hz BFO bias, the result is about +1 Hz too high, compared to measurements Thus the BFOR, which is predicted minus measured, is + 1Hz for the phone call BFOs when using a 150 Hz bias. The “offset” I use is the correction to be added to the raw BFO so that the predicted BFO, using a 150 Hz bias, equals the measured BFO. A +1 Hz correction puts the 2nd order trendline halfway between the high and low BFO values during the phone call. If you use the mean of the twenty-seven 23:14 BFOs, which I am not sure is more accurate because of the sawtooth errors, the correction is a little larger, about +2.7 Hz. So, in that case, the BFO bias would be about 150 – 2.7 = 147.3 Hz.
@DennisW,
You said: “I am not sure how to get the probability that the wreckage is between 34.2S degrees and 34.4S degrees (34.3S +/- 0.1 degree).”
The route probability is precisely defined in the paper. It represents the percentage of random trials (i.e., using random BTORs and BFORs), that fit no better than the current trial. It is legitimate, in my opinion, to consider the route probability as a relative value of a probability density function for the route probability alone.
The same may not be true of the composite probability we showed. The composite probability in the paper is simply the product of the route, fuel, debris drift, and aerial search probabilities. This product may not be the optimum method of combining those 4 separate statistics. One could use the Fisher method, for instance, and that result would probably be a reasonable estimate of an overall probability density function, and better than the simple product. It is desirable, as your question implies, to obtain a composite probability density function. Work is underway on this question.
@Don Thompson,
You said: “It is the process of interpolation, described by DrB, about which I expressed the interest.”
Do you have any alternate methods to suggest for estimating the frequency offset of the 23:14 phone call BFOs?
The “Combined Overall Probability” graph at the bottom of Figure 5, which is what determines the new search zone, is almost entirely driven by the “Fuel Probability” graph (2nd from top) and the “Aerial Search” graph (4th from the top). In fact, one could have ignored the BTO and BFO data entirely and still arrived at the bottom graph.
However, I am very confused by the Fuel Probability graph (repeated in Figures 15 and D-3). The only section of the paper to describe how this graph was derived appears to be Appendix D.5. Is that correct? In particular, it is stated:
“We did trade studies of SIO Routes over a wide range of LNAV true track angles. The best-fit route at each track angle intersected the 7 th Arc at a particular latitude. We evaluated the probability of each route according to fuel, debris drift, aerial search, and route fitting statistics. Therefore, we can plot any probability measure, or a combination of probabilities, as a function of 7 th Arc latitude. This is a convenient way to display and understand these results.”
So I interpret this graph as being the probability that there was sufficient fuel on board to fly a particular LNAV route, and those LNAV routes are some subset of the thousand or so routes that were part of the grid search. Is that correct? In other words, all other possible autopilot modes (true track, magnetic track, true heading, magnetic heading) are excluded? And since the particular LNAV routes do depend on the BTO and BFO data, we haven’t actually ignored them. Is that correct?
To the authors of the new report – It is a phenomenal effort from all of you and as Victor mentions – it combines everything we have read and some new analysis from the past six years. Thanks for your continued efforts in trying to solve this unparalleled aviation mystery.
Reading this report multiple times would still not suffice as each time you read it something else sticks or resonates with the reader than the previous read.
Just one query – Since this is available as a report format now on this blog, would the link to the research paper also be available on this blog? I guess it is early days but could not find the link to the research paper online yet.
@the authors
I’m also mainly looking at the fuel probability graph at the moment as it is main responsible for the “cut-off” to the south. An additional question: I assume that several routes used to construct it have different 19:41 positions. So, how are then “pre-19:41” and “post-19:41” connected / what was assumed for “pre-19:41” for the different cases?
@paul smithson
Regarding my comment “I think the probability for A1 is 90% and A1 + A2 is 97%.”
You asked “Out of the residual 3%, how much of that is A3”?
My answer is A1 + A2 + A3 is 98.9%.
We have made a number of assumptions and considered a number of sources of error. We have estimated error budgets and these are used in determining a probability estimate, whilst making some more assumptions about the randomness and potential correlations among the error sources. I am mindful of Victor’s comment that “we don’t know, what we don’t know”!
The key assumptions are:
1. Auto-Pilot engaged and LNAV mode selected, therefore navigation errors are negligible.
2. Air conditioning packs switched off for a large part of the flight, therefore an inactive pilot towards the end.
3. An ultimate waypoint of the South Pole was selected and therefore no lateral manoeuvres after 19:41 UTC.
4. LRC Fuel Mode was selected and Flight Level 390 was maintained after 19:41 UTC (no step climbs).
The key error sources are:
1. The available and required fuel, fuel speed modes selected during each leg, flight levels during each leg, the ZFW, the R/L Engine FF ratio, the PDA, Packs On/Off times, Cross-Feed Valves Open/Shut times, Fuel Balancing performed or not, Fuel Tank FQIS sensor accuracy, Engine FF sensor accuracy, …
2. The FMT route timing and distance, descent, turns, climb, R Engine INOP, …
3. GDAS air temperature and wind data accuracy, precision, interpolation, …
4. BTO and BFO accuracy, precision, offset, cabin temperature effect, eclipse effect, variation over time, …
5. End of Flight path, roll, spiral, engine restart, APU fuel, aircraft attitude, …
5. Debris predicted transit times, reporting delays, windage, buoyancy, …
6. Aerial Search estimates, detection rates, debris size, debris number, debris separation, …
@VictorI and All,
It’s clear that many man-years of work went into developing that impressive report.
I think everything is consistent and unbiased up to the 18:40 FMT. The plane appears to be flying between waypoints, even with sudden changes.
I am surprised to now see two 90 degree dogleg turns added that follow radar boundaries. That bakes in the bias of pilot intent to hide the plane, which should not be necessary. You then go back to a single waypoint BEDAX, and with the next point presume that the pilot implemented a suicide plan to the south pole.
(There was a 20 km ice floe much closer to aim for, BTW!).
Passing by the Tee witness sighting is fine, but she said she saw the plane after the gybe, not before. Timing that flyby to the minute confers more accuracy than her recall. (Though she may well have seen the plane at low altitude, and before the event that woke up her crew.) Including waypoint NOPEK right by Tee matches her estimation that the plane made a turn just after it passed.
I prefer a much simpler waypoint route to NOPEK, BEDAX, and then on to ISBIX, which is an exact low altitude match for the 2nd arc BTO, and that waypoint route is exactly tangent to the arc as shown by curve fitting.
In recent comments there has been disparagement about the probability of an arbitrary multiturn route fitting the BTO/BFO vs this suicide path and glide. That may have been asserted about the CAPTIO approach of fitting to BTO+BFO, but it’s not how I arrived at the full waypoint path.
I started with early hydrophone detections of an event near the 7th arc, but too far north for ATSB to consider.
I then used seismometers to confirm that it was directly on the 7th arc at a specific spot.
With IG search projections then heading farther north on the arc, a flyby of Cocos Island seemed feasible.
Using seismometer data, I found good evidence of a close flyover at about the right time.
Later, I checked Christmas Island, and found a weaker but isolated signature of a flyby there, too.
Now it was a matter of connecting the dots. I found intervening waypoints between ISBIX, Cocos, and Christmas Island airports. The timing of the flyovers and BTO points where arcs crossed the path determines the speed of the plane. I ignored the BFO in selecting the waypoints.
The only fudging was picking a waypoint that crossed the last arcs with reasonable speeds.
I then calculated the speed profile and BFOs, finding that the fit was still good.
The BTO tangent curve is unchanged.
What are the odds of that match?
Probably astronomical if it was random, but the path is defined by verifiable evidence.
If the evidence matches up, especially for a very narrow area that has not yet been searched, that seems like a high probability place to look.
I don’t expect to change the momentum of your collected efforts, but as you advise OI and Malaysian authorities, please keep open the possibility of additional low cost search zones. Of course the plane can only be in one place, but I would appreciate any help with FE matches and confirming my BFO calc.
I also thought I had the FE chart downloaded and bookmarked just weeks ago, along with a dropbox doc full of pointers to Victor’s papers. My browser history now has many dropbox 404 errors.
Could you please repost the VI papers link?
Would you be willing to share your fuel model spreadsheet for experimenting with other scenarios?
Thanks for tolerating my 370Location.org scenario and evidence on your site. I do try to behave.
I believe you did say when I arrived that you thought it merited more discussion!
@370location said: I am surprised to now see two 90 degree dogleg turns added that follow radar boundaries. That bakes in the bias of pilot intent to hide the plane, which should not be necessary. You then go back to a single waypoint BEDAX, and with the next point presume that the pilot implemented a suicide plan to the south pole.
The 90-degree turns follow FIR boundaries. If this route was followed, my guess is the pilot skirted Indonesian airspace to avoid both detection and interception until traveling south and away from Sumatra. There was never an intention to reach the South Pole. It was a convenient waypoint to enter that was well beyond the fuel range and would ensure the plane was as far south as possible into the SIO and remained in LNAV mode.
In any event, the route between 18:28 and 19:41 was not used to construct the route between 19:41 and 00:19. It was the opposite. Our intention was to create a feasible path between 18:28 and 19:41 that satisfied the data constraints but also could be logically justified. There is no guarantee that the proposed path between 18:28 and 19:41 is unique.
Passing by the Tee witness sighting is fine, but she said she saw the plane after the gybe, not before.
There are some unexplained circumstances surrounding her statements, and we debated whether to reference the sighting in the report. We decided to not use her sighting to discriminate among paths, but we did point out that the approximate timing and exact location of her sighting match our low altitude fly by of waypoint NOPEK, which is on the FIR boundary. We leave it to others to decide whether or not she saw MH370.
I prefer a much simpler waypoint route to NOPEK, BEDAX, and then on to ISBIX, which is an exact low altitude match for the 2nd arc BTO, and that waypoint route is exactly tangent to the arc as shown by curve fitting.
Exact tangency is not a requirement for a route. What is required is a statistical match to the BTO (and BFO) data. For relatively straight paths of nearly constant speed, the path will be nearly tangent to the 2nd arc because the BTO values reach a minimum value in that time frame.
In recent comments there has been disparagement about the probability of an arbitrary multiturn route fitting the BTO/BFO vs this suicide path and glide. That may have been asserted about the CAPTIO approach of fitting to BTO+BFO, but it’s not how I arrived at the full waypoint path.
I am sorry if I am wrong, but I believe your path requires multiple changes in speed to match the BTO values and you ignored some large BFO errors. That was not our approach.
With IG search projections then heading farther north on the arc, a flyby of Cocos Island seemed feasible. Using seismometer data, I found good evidence of a close flyover at about the right time. Later, I checked Christmas Island, and found a weaker but isolated signature of a flyby there, too.
A flyover of Cocos Island accompanied by unambiguous infrasound or seismometer data would be interesting. Previously, I wrote an article about a possible automated path over Cocos Island, and some of us (notably @David) investigated the infrasound data looking for a match. My recollection is the results were not conclusive.
Frankly, I haven’t fully explored your results. However, I do appreciate your expertise in these matters, and I was hoping that others here would take the time to understand your reports and either support or refute your analyses.
As I said in a previous comment, I cannot profess that there is near certainty that the plane is where we predict. It’s our best estimate based on our predictive models combined with a number of assumptions.
Could you please repost the VI papers link?
Here is a link for some relevant papers. It also appears at the top of the page (“Papers”).
Would you be willing to share your fuel model spreadsheet for experimenting with other scenarios?
At this point, Bobby has the most detailed fuel model. Perhaps he can respond.
@Richard
“My answer is A1 + A2 + A3 is 98.9%.”
That is very compelling.
@DennisW
You stated “ That is very compelling.”
Let us ask your daughter to organise an event in San Francisco at her University.
I will fly over and we can hold a joint presentation.
You can talk about the importance of the BFO,
I will talk about the rest! 😳
@Richard
I have been unable to ellicit any interest at all in MH370 from my daughter or my better half. Both are “coin operated” with respect to getting them to think about anything.
@370Location,
It’s not possible to put everything needed to predict fuel flow into one spreadsheet, because of the need to interpolate the GDAS data base in 4-D and the need for numerous speed and fuel flow tables for different speed settings. My program uses several dozen worksheets, and it is not user friendly. However, Appendix A contains all the equations you need to create a useful fuel model. Tables C-2 and C-3 are spreadsheet tables showing our predicted fuel flows during the entire flight. These may be used to check your calculations.
@Niels,
We fit all the 19:41-00:11 SIO Routes before we attempted to ascertain the 18:22-19:41 FMT Route. In fitting the SIO Route, nothing was assumed prior to 19:41, except that the 19:41 position be reachable from the 18:22 position in the time available. We found this was possible for all the SIO Routes we studied.
After we obtained an excellent SIO Route fit, we next worked on demonstrating the feasibility of a FMT Route that connected seamlessly in time and space at 19:41. We were able to do that for our BEDAX 180 degree route. We have not directly demonstrated the feasibility of connecting a plausible FMT route to all SIO route fits, but I think this is quite likely to be possible. In broad terms, either a descent is needed, or a Holding pattern up to 29 minutes in duration is needed prior to 19:41, to avoid arriving at the 19:41 location too early.
@sk999,
After exploring all lateral navigation methods, we concluded that LNAV was a better fit (i.e., higher in route probability) at all bearings than the other navigation methods. Therefore, the fuel model probability is based just on the LNAV routes, because they were always the superior fit to the satcom data.
@all
So I updated my comments on the MH370 search to include the Iannello et. al. new paper. (Appended at the end of the previous Bayesian commentary). The Cliff notes version is that if one accepts the new search analytics, it is best to search 33S to 35S even if BFO is discarded.
https://docs.google.com/document/d/1ayLc-x_uLo5W5uj_r5QnOhxkXsUGQ0GufY1Flxv5xSo/edit?usp=sharing
@DrB
My question was meant as follow up on @sk999 (I’m sorry, indeed you can read it differently).
In other words: So what would you assume for the fuel remaining at 19:41 (and why so), for the different LNAV routes used for constructing the fuel model probabilities, thinking they would have different 19:41 positions.
DrB said:
“After we obtained an excellent SIO Route fit, we next worked on demonstrating the feasibility of a FMT Route that connected seamlessly in time and space at 19:41. We were able to do that for our BEDAX 180 degree route. We have not directly demonstrated the feasibility of connecting a plausible FMT route to all SIO route fits, but I think this is quite likely to be possible. In broad terms, either a descent is needed, or a Holding pattern up to 29 minutes in duration is needed prior to 19:41, to avoid arriving at the 19:41 location too early.”
This remains the weakest aspect of your case. For 5 years, explaining this gap has required creativity. The time to arrive at 19:41 in your preferred case is driven by the parameters of the route to 180T. So, you are effectively working back from the 7th arc location. I believe that this is a source of confirmation bias, but does not mean that you are wrong.
(I had not intended to make a comment until I have thoroughly assimilated your paper, but decided to make this comment so as to participate in the discussion.)
@Niels,
The available fuel at 19:41 is estimated using nine cases. Three of those are the “no-descent” FMT route with various aircraft configurations. The fuel used in these cases is time-based. That is, we figure the fuel remaining at 19:41. This is virtually independent of the assumed 19:41 location. We know that all LNAV SIO Routes are reachable at their 19:41 locations. So, for all LNAV routes, there is at least one case of estimated available fuel at 19:41 that can match its 19:41 location, although it may fall short of the fuel required at 19:41 to fly to latitudes south of 36S. In addition, many of the LNAV SIO Routes will have a fuel requirement at 19:41 that will match one or more of the “descent” cases of the FMT Route.
@Sid Bennett,
Referring to the time gap between the end of the radar track and the 19:41 position (i.e., the FMT Route), you said: “This remains the weakest aspect of your case. For 5 years, explaining this gap has required creativity. The time to arrive at 19:41 in your preferred case is driven by the parameters of the route to 180T. So, you are effectively working back from the 7th arc location. I believe that this is a source of confirmation bias, but does not mean that you are wrong.”
Our unique solution for the SIO Route is independent of what the aircraft did prior to 19:41, and a definitive solution of what occurred prior to 19:41 is not essential (or even helpful). What we have proved is that our 19:41 location, which is the starting point of our SIO Route, is reachable in 4-D with either of two FMT Routes (“descent” and “no-descent”). Furthermore, either of those FMT Routes provides sufficient fuel to fly our SIO Route and achieve MEFE at 00:17:30.
I don’t see how this can be characterized as a weakness. We have shown two FMT Routes that demonstrate the complete feasibility of the SIO Route in terms of starting location, starting time, starting altitude, starting speed, starting bearing, and endurance. It seems to me this is a great strength which enhances the credibility of our SIO Route.
One statement you made is not quite correct. You said “The time to arrive at 19:41 in your preferred case is driven by the parameters of the route to 180T. So, you are effectively working back from the 7th arc location.”
That statement is untrue for the “no-descent” FMT Routes.
Our goal for both the “descent” and the “no-descent” FMT Routes was to demonstrate the feasibility of our 180 degree SIO Route. We have done that. The “no-descent” FMT Route also demonstrates the feasibility of meeting up with all the LNAV Routes, not just the one at 180 degrees. So, none of the LNAV SIO Routes can be discarded because it is impossible to fly the aircraft between the last radar contact and the 19:41 starting location of a LNAV SIO Route, but some can be eliminated because of a large fuel shortfall at 19:41, and others can be eliminated due to poor fits to the satcom data.
To the Authors,
BRV and Andrew,
QUOTE: “Figure 18 is a plot of Ground Speed Error versus time for … (Trial 854). In this case the GSEs are even smaller.”
Figure 18 is impressive. Pretty good evidence of a good fit.
You should be complimented.
@DrB
Thank you, Bobby, for explaining. The nine cases correspond to fig. 29. I’ll study that part and the appendices first more in detail before further detailed discussion.
A final question for now: what would be the estimated effect on available fuel at 19:41 if the descent to FL100 would have commenced say 15 minutes later?
@Richard, other authors
I’ve ran the FL390 LRC 180degrees route with my tool. I used 72 kg/hour per engine less fuel for packs off and a FFF of 1.015, I hope that is reasonable. The differences seem to be small if I compare to your fig. 35: Less than 5 km for the 00:11 position when starting at the same latitude as you.
https://www.dropbox.com/s/82vxjqqzl9z8uvs/check180degFL390.pdf?dl=0
I have slightly lower temperatures, which I have to check.
I’m currently using 3D interpolation. I do not interpolate for the latitude as we step rather fast through many different latitudes.
Note that the mean BTOR can be easily reduced to virtually zero by shifting the 19:41 some km’s north:
https://www.dropbox.com/s/hnokwd0dfm1r286/check180degFL390_lowmean.pdf?dl=0
oops..run..
Update
The best estimate of the point of impact (BE POI) has been renamed the last estimated position (LEP), which is a more accurate description. The location is unchanged.
@DennisW: That’s an interesting result. Thanks for diving in.
@Niels,
You said: “Note that the mean BTOR can be easily reduced to virtually zero by shifting the 19:41 some km’s north.”
Of course that can be done, but it degrades other statistics. When the route probability is maximized, the mean BTOR is not zero.
You asked: “. . . what would be the estimated effect on available fuel at 19:41 if the descent to FL100 would have commenced say 15 minutes later?
If two engines were in use at Holding speed at FL100, the FF is almost identical to LRC at FL390. So, purely from a time perspective, the fuel burned at low altitude and at high altitude are equal in the same amount of time. There is a small loss in descending and climbing, so the descent route has a bit less available fuel at 19:41 (maybe a couple of hundred kg). That difference does not depend on the length of time spent at low altitude nor on when that occurs. Of course, if one flew at LRC with the descent delayed by 15 minutes, the aircraft would be further south by about 60 NM at the bottom of the descent, which is roughly 20 NM south of NOPEK.
@Victor
Congratulations on introducing LEP
@DrB
Regarding FF FL100 vs FL390: Thank you; I am thinking about a turn south around 18:35 and a descent just after the first phone call.
In my most recent calculations I get best-fit LRC and ECON paths slightly south of S34.5 with FLs in the 330 – 350 range. Would be interesting to see if there could be scenario’s where available fuel would allow such paths.
Bravo pour votre travail, on se rapproche enfin des images satellite que j’ai relevées le 25 mars 2014 lat 42S LON 97, en tenant compte de la dérive de surface vos calculs sont cohérents
@Patrick Tissot: Salut! Ça fait longtemps. Est-ce que vous croyez toujours que les images sont mal localisées?
@Richard et al,
Congratulations on an outstanding piece of work.
I have to say that it is very encouraging to note that my rough and ready speed determination, first hypothesised in 2014, using only very limited data available at the time, is in close agreement with the new report.
In a later paper [April 2015] I tested some issues relating to the final 15 minutes of the flight and concluded that a final turn to the left, developing into a spiral dive seemed most likely. The resulting point of impact could very well lie inside the 7th arc. Victor reviewed some of these issues too, and the Boeing flight sim test results.
Hence I was also very interested in the last 15 minutes of the best-fit SIO route parameters, in table G1 of the report. I note that the required average speed over the final Leg 6 is 363 knots. But the Ground Speed Error is shown as -107 knots.
It seems me that a little more work might clarify that result. The GSE results from the modelled TAS of 483 knots and a modelled GS of 470 knots. But we know that the TAS following the right engine flame out will reduce. Indeed the discussion earlier in the report shows that the left engine will automatically go to full power, but the speed [and altitude] will gradually decrease to just above the stick shaker speed. It should be possible to estimate the deceleration over that leg and hence reduce the apparent GSE.
Actually the result may also help eliminate the possibility of a turn to the right after the left engine fails, as I hypothesised, and improve the probability of a final impact within area A1.
@Niels,
Matching the 18:40 BFOs requires a track near 215 degrees at LRC and FL385, so the route moves westward rather quickly.
Reducing the SIO altitude from FL390 to FL340 increases the FF by 1.2% and reduces the Mach by 3.3%. Range is certainly an issue at such low FLs.
@Brian,
Yes, I agree. It is an impressive piece of work.
I remain skeptical of using BFO as a route qualifier, but the authors provided a “BFO out” option for which I am grateful. It certainly looks like 33S to 35S is the best place to resume a search.
@Dr B. In your Wx interpolations in time and space, can you comment briefly on the time interpolation method? For example, does 1800Z weather pertain from 1800-2100, or for 1800 +/- 1.5 hours? Do you splice the times with hard time boundaries, or blend across the boundaries (eg 2000hrs is 2/3 weighting of 21000 and 1/3 weighting of 1800)?
@paul smithson.
To find the GDAS values, I first do a bilinear interpolation in latitude and longitude between the four corners of the nearest integer coordinates. I do this for each time and at five GDAS standard flight levels in the data base (with at least two higher and two lower). Then I do a bicubic interpolation over time and flight level.
This works well but requires a lot of computations.
Richard does a linear interpolation in all 4 parameters. To save time during runs, he pre-calculates some of the intermediate steps.
We have extensively compared our results. The agreement is generally excellent. I don’t think it matters which of these two methods you use. Both are sufficiently accurate that the dominant error is in the values in the data base, not in the interpolation method.
Thanks Dr B – I’m inclined to agree that “I don’t think it matters which of these two methods you use. Both are sufficiently accurate that the dominant error is in the values in the data base, not in the interpolation method.” But could you also clarify: for 1800 Wx in your GDSS database, is 18.00 the temporal mid point of 16.30 – 19.30, or does 18.00 refer to 18.00 – 21.00 with a mid-point of 19.30?
@paul smithson
You asked “But could you also clarify: for 1800 Wx in your GDSS database, is 18.00 the temporal mid point of 16.30 – 19.30, or does 18.00 refer to 18.00 – 21.00 with a mid-point of 19.30?”
The GDAS data is available every 3 hours from midnight 00:00 UTC each day.
Both Bobby and I use the GDAS data on 7th March 2014 at 15:00 UTC, 18:00 UTC, 21:00 UTC and on 8th March 2014 at 00:00 UTC and 03:00 UTC. We cover the entire solution space of MH370 both spatially and temporally.
So the GDAS data at 19:30 UTC is a temporal interpolation at a given latitude, longitude and altitude, in my case between the data at 18:00 UTC and 21:00 UTC, in Bobby’s case considering the wider trend between the data at 15:00 UTC, 18:00 UTC, 21:00 UTC and 00:00 UTC.
For the MH370 route based on a BEDAX LNAV 180° South Pole at FL390, the wind direction reverses between 22:17 UTC and 22:25 UTC. This is the only critical phase in the temporal interpolation, but since we recalculate all flight parameters every minute, even these 8 minutes are well determined. Figure 17 in the paper shows the SAT, Wind Speed and Wind Direction en-route.
@Richard
Is the ROC at 19:41:03 included in the BFOR calculation in fig. 35 / how much would be the contribution?
@Richard. Thanks for that clarification. I see also that the basic GDAS model is run x4 per day and so the 3-hr interval outputs are presumably an interpolation from the 6-hourly.
Have either you or Bobby, by any chance, had an opportunity to test your route with an alternative weather model wind/temperature field, eg ECMWF or the one that the DSTG used (ACCESS-G)? Of course, no model is going to be perfect and I understand that your error/noise modelling accounts estimates uncertainty in the weather model. Nonetheless, it would be informative to see how the solution path performs under different weather models.
@DrB,
Thank you for the details on your fuel model. I was hoping for a simpler solution, of course. It sounds like recreating your model with GDAS could be a graduate thesis in itself.
The largest uncertainty in FE appears to be the 1.4% 2-sigma error for the initial fuel load. I recall an email discussion with Tom of LANL from 2016 (after I first found a loud southern event) about the possibility that the plane might have had more fuel than indicated. Don had provided info that the crew gets ultrasonic tank level readings, but they have discretion when entering the values that are used by the FMC and reported by ACARS.
Tom ran some estimates on the climbout performance based I think on an assumption of accurate FF. His conclusion was that the initial fuel load was in the ballpark. With improved performance and FF history, I wonder if refining the departure fuel weight is possible, if not already done. I’m assuming that the plane has no load sensors on the gear to measure the true weight and COG, but that it’s all calculated.
@VictorI,
Your Cocos Island scenario is a fascinating read. The big surprise was that the KIAS was reduced to 210 for landing, but the plane never left FL320 and flew on at that KIAS with a ground speed of 354kt. I looked up the YPCC charts and it’s weird that the runway 15 magnetic headings are both 151 and 152, and deviation varies between 2 and 3 deg. I used the distance from the outer approach waypoint and your fuel spreadsheet to figure your flyover time would be 22:18:41 UTC. My detection is centered around 22:22:22 UTC.
I also figured the time to your FL350 7th arc at your groundspeed from my flyover, and get an arrival at 00:21:22 UTC. Using a lower altitude 7th Arc makes it almost right on. BUT, that’s probably to be expected at any flight heading if the speeds are based on the arc timing.
I note that the currents would carry heavy flotsam SSW away from the aerial search coverage around the ULB pings, and the winds going NW would bring lighter debris to where it could have been detected.
There are no good hydrophone detections there, but beam-forming the Pilbara seismic array last year showed a possible arrival at 00:23:30 from bearing 272.8 just N of the ULB ping search (but distance unknown).
Sorry to be so late to reviewing your report!
@Niels
The ROC is not included in the BFOR calculation in Figure 35 at 19:41:03 UTC, which shows a BFOR of -6.5 Hz.
To zeroise the BFOR at 19:41:03 UTC requires a ROC of ca. 320 fpm.
The climb model predicts a ROC of ca. 400 fpm at 19:41:03 UTC.
@paul smithson
We have done spot checks between GDAS and other weather models and are generally satisfied with the GDAS accuracy.
As mentioned in G.4.1 on page 156, we did perform a comprehensive check between the ACARS Position Reports and the GDAS weather model for 57 positions of MH371 during the flight from Beijing to Kuala Lumpur for various altitude between 27,600 feet and 40,000 feet.
We concluded the temperature differences were about 1-2 ° C. The wind differences were about a knot in speed and several degrees in direction.
The average temperature predicted – actual difference over 57 measurements was +0.9 °C.
The average wind speed predicted – actual difference over 57 measurements was -0.7 knots.
The average wind direction predicted – actual difference over 57 measurements was -11.4 °T.
The large wind direction average difference during the MH371 flight is again due to the wind reversing direction between 05:29 UTC and 05:49 UTC, whilst MH371 was over the South China Sea and Vietnam. Removing that 20 minute timespan from the calculation, changes the average difference from -11.4 °T to +2.4 °T.
When passing through the eye of a cyclone or anti-cyclone, the spatial and temporal GDAS accuracy cannot match the accuracy of the actual measurements from an aircraft’s FMC, for a short period of time.
@Richard
Thank you, Richard. I’m currently checking if both the path curvature I typically see in the first hour after 19:41, as well as the 19:41 BFOR can be explained in a certain way. The hypothesis I’m checking is that the climb occurred between 19:41 and 20:41. It would not necessarily mean that the 00:19 position would change, but it’s clear it would impact fuel considerations.
The combination of LRC FL350 with 00:19 position around 35.5S, with a long (over an hour) low flight level (FL100) will not work. The 19:41 position will be too far north to connect the parts.
I’m now looking at FL350 from 19:41 onwards; my best fit LRC path leading to S35.4 has a 19:41 latitude around N1.4, which might be achievable through an early (18:30 – 18:35) turn south.
@DrB might be right that the fuel is an issue for such path: Around 27.9 tonne fuel needed at 19:41.
@Richard et al,
Referring again to table G1 in your report . . where the final leg shows a GSE of -107 knots.
To test the suggestion I made a day or so ago, I have done some elementary calculations to determine if a significant improvement can be made to the Leg 6 GSE by incorporating a deceleration in the TAS following the REFE.
I am not able to determine from DrB’s analysis exactly when the REFE occurred in his most likely scenario, which I think is 7B1, but based on much earlier work we did on fuel flow I will assume that this time is 2 minutes before 00:11 utc.
We also know, based on the sim tests carried out by Mike, that the deceleration immediately following REFE is approximately linear at 19 knots/minute, presumably down to just above stick-shaker speed if the left engine continues to operate. In our case this lower speed may not have been reached before the LEFE occurred.
So, making some broad assumptions, if the REFE occurred at 2 minutes before 00:11 utc, then the TAS at 00:11 is likely to be 445.6 knots [483.6-38]. The average speed for Leg 5 will change only an insignificant amount, so the GSE for this leg remains as in Table G1.
Then, continuing the deceleration through Leg 6, until the LEFE at 00:17:37, the TAS at that time will be 445.6-6.5*19, or 322.1 knots.
If I then assume, because the flight trajectory from that point is indeterminate, that there is no further deceleration, and that the track remains straight, then the new average distance travelled is 52.3 nm, and the average speed is 369.3 knots.
The resulting GSE of -6.2 knots looks like a significant improvement to me.
In this elementary calculation I have not incorporated the wind vector. It is a lot easier for you to do that in your model, but a quick check suggests that this will improve the result even further.
@George G
Many thanks for the corrections you spotted in the paper. The download link in the post has been updated with the correct references on page 36, 122 and 123 as well as a clarification on page 120.
@370location
RE: “…the possibility that the plane might have had more fuel than indicated. Don had provided info that the crew gets ultrasonic tank level readings, but they have discretion when entering the values that are used by the FMC and reported by ACARS.”
The fuel quantity indicating system (FQIS) uses ultrasonic sensors to measure the fuel height at various locations within each fuel tank, and a densitometer in each tank to measure the fuel density. The fuel quantity determined by the FQIS is displayed on EICAS and is also used by the FMC until engine start.
The FMC fuel quantity may be overwritten by the crew, but that is not the normal procedure. Further, if the FQIS is operating normally, a manual entry will be deleted at engine start, at which point the FMC sets its fuel quantity equal to that determined by the FQIS. The FMC then uses fuel flow to determine a calculated fuel remaining.
Given the checks that are performed after refuelling, it’s unlikely the aircraft had more fuel than indicated. An independent check of the fuel quantity is
@Andrew,
Thanks for filling in the details on the fuel measurement procedure. I may have misunderstood how much discretion the crew had. If ground crew were informed of the post-fueling checks, then I suppose there would be a paper trail. It sounds like it would take a manual override after engine start to create altered FMC readings.
I’m not advocating that anyone would have done that, but if other deceptions like radar avoidance are part of the new scenario, then I thought it should be considered.
Your last sentence appears to be truncated, leaving me
@370Location
There certainly is a paper trail after refuelling. The fuel uplift (as recorded by the fuel truck) is added to the fuel quantity before refuel and the result compared to the fuel quantity indicated by the FQIS. Any discrepancy outside the allowed tolerance is investigated, by dipping the tanks if necessary. The figures are recorded on a refuel record document, a copy of which remains with the maintenance engineers when the aircraft departs. Unfortunately, a copy of MH370’s refuel record was not included in the SIR or the leaked RMP documents.
The crew would not normally enter a fuel figure in the FMC unless there were a problem with the FQIS, in which case the fuel on board would need to be manually entered in the FMC.
@Richard
Because of possible fuel issues for LRC paths ending further south, I started looking at ECON mode. I found a potentially interesting path, see link:
https://www.dropbox.com/s/td9aos8g39pxw2d/ECON_FL350_v1.pdf?dl=0
In your “matrix”, have you checked FL350 for ECON_CI52 in the vicinity of 180 degrees?
Could you perhaps run the path with your tool? (I haven’t cross-checked any ECON paths so far)
It might need some minor optimization of the initial position because of small differences between tools.
@DennisW said: One thing I find a bit strange is the “probability” ordinate. I was expecting a “probability density” ordinate.
We agree. This has been changed in the article and in the paper.
@Niels,
Figure 22 shows our best result for a 180 degree path at ECON with CI = 52. It occurs at FL380, but its route probability is only 1/3 of the LRC value
Figure 23 shows that tECON with CI = 52 is the best speed mode for initial bearings from 173.0 to 177.5 degrees.
@Brian Anderson,
I also think a left turn after MEFE is more likely than a right turn. That would favor placing a higher priority on searching the eastern half of Search Area A1 before the western half.
Looking at Figure 29, you will see the predicted REFE and LEFE times for 9 Cases. Generally, when there is no fuel balancing and the cross-feed valves are closed, REFE occurs 6:22 before LEFE. So, if LEFE were at 00:17:30, then REFE would be at 00:11:08. For Case 8, when there is a manual fuel rebalancing, after which the cross-feed valves are closed, REFE is only 2:43 before LEFE. In this case REFE would occur at 00:14:47.
I agree that a significant deceleration would occur during the interval between REFE and LEFE, but that intreval is not likely to be longer than 6:22, and it could have been as short as 2:43. I think the cases with the cross-feed valves opened near the end of the flight are quite unlikely, because the air packs being off after 19:41 (which we believe is quite likely), would render that impossible to perform.
@370Location,
After many calculations and much discussion, we have determined that it is highly likely that the value of ZFW entered by the pilot at the gate was 174.4 tonnes. This is in accordance with standard practice. The reported fuel quantities after that appear to be consistent with the accuracy of the sensors.
@DennisW,
See the new Appendix J for a description of the PDF calculation.
@Andrew
@370Location
Fuel density also would be important to know, but as far as I know we have no reported data for it. Unless someone thinks some of the FQIS data such as fuel height has been reported in the ACARS or engine reports. So far nothing on fuel density or other qualities.
@Richard
You said: “Many thanks for the corrections you spotted in the paper.”
Not a problem from this end. I was getting slightly confused concerning some of the referenced Scenario numbers on Page 123. Please see my updated comment concerning Scenario 6A.
Unfortunately my previous query re Scenario 6D referenced on Page has snowballed. In particular this now concerns Scenario 7B1. Compare the text on Page 123 with the content of Table D-4.
@George G
You would not believe, how many times this paper has been proof read, by how many people.
The problem is some corrections have consequences, that are not readily evident elsewhere in the paper.
Please take a look at the latest download.
@TBill
The FQIS calculates volume from multiple sensors (each tank) as well as density (each tank) and temperature (one tank only), but reports fuel weight via ACARS as TOTFW for each tank.
@Richard
It is virtually impossible to get things all correct even after multiple passes. I had a running $50 bet with my staff that when they produced a first draft of a new product manual that I could find 50 mistakes in a day read. I never had to pay up, and I am not counting things like typos. I also liked to go to shipping from time to time, grab a product packaged and “ready” to go, and take it to my office while pretending to be a customer. More often than not I could find something to complain about including a product that was defective in some manner.
@George G,
You said: “Figure 18 is impressive. Pretty good evidence of a good fit.”
I, too, was surprised by how small the GSEs were for the best fit. Initially, I was seeing 3-5 kts with less-than optimum fits and with crudely estimated GDAS weather parameters. It’s hard to know independently what the GDAS accuracy really is when averaged over an hour and about 500 NM. As it turns out, part of the few knots of GSE was due to an initially inadequate GDAS interpolation method, and part was due to imperfect route optimization. Of course, these go together, in the sense that one cannot fully optimize the route until one has an accurate GDAS interpolation method with adequate sampling along the route. Improvements in the GDAS interpolation accuracy and sampling were key in achieving enhanced route optimization.
Richard said:
March 14, 2020 at 12:01 pm
@George G
“You would not believe, how many times this paper has been proof read, by how many people.”
Answer: Yes I probably can
“The problem is some corrections have consequences, that are not readily evident elsewhere in the paper.”
Answer: I’m beginning to think that is and was what lead to part of my initial confusion.
“Please take a look at the latest download.”
Answer: Yes, I have been doing that, and I have been trying to reconcile my confusion and after a (short) sleep and other matters I hope to return to continue and when I have reconciled my confusion concerning “7B1” and “6D”, then I will attempt to be clear in a single comment.
In the meantime, would you please kindly review my updated comment on Scenario 6A, the one with the highest fuel probability with the bleed air ON. It may make sense.
@DennisW
I offered my kids a bottle of champagne for the first one to find our deliberate mistake!
That would have been easy picking ….
@DrB
In fig. G9 the ECON 180 degrees route FL380 seems to have a probability quite close to the LRC route.
In any case: thank you. I failed to get a good fit for FL380. I then spotted a problem in my M(FL, weight) 2D function for ECON. It is a recent implementation which, as mentioned, has not been cross checked yet vs. another tool.
I’ll come back to my 7:37 am posting later.
@DrB
I found the problem in the M(Fl, weight) function and can indeed find a reasonable fit for FL380, ECON_CI52, 180 degrees with a RMS BTOR of 42 microseconds and a 00:11 lat of S33.21. Could you please share the details of your particular path calculation for me to compare/cross check in detail?
@George G
You must be losing patience with me and yet another cut and paste error!
The paragraph now reads “The highest fuel probability with the bleed air on during the SIO Route, allowing pilot survival until MEFE, is Scenario 6A. It has the bleed air off for two hours after diversion, the right engine is off for an hour prior to 19:41, and the cross-feed valves are always closed. The fuel probability of Scenario 6A is only 21%. Therefore, we can say that the probability of having a functioning pilot at MEFE is significantly less (by about 4X) than the probability of having an incapacitated pilot at MEFE.”
@DrB, Richard,
Thank you for directing me to Figure 29.
My aim, in testing the deceleration issue, was to see if including that in the the best fit route parameters [Table G1], resulted in an improvement in the GSE. It does, and to quite a significant degree. Hence it also ought to help in discriminating between routes, and enhancing the probability of the preferred route.
@Richard
😊
@Brian Anderson,
You said: “My aim, in testing the deceleration issue, was to see if including that in the the best fit route parameters [Table G1], resulted in an improvement in the GSE. It does, and to quite a significant degree. Hence it also ought to help in discriminating between routes, and enhancing the probability of the preferred route.”
We do not use the GSE from 00:11 to 00:19 as a figure of merit in fitting SIO routes. Once a route was selected, we thought it might assist in determining which direction the initial turn might have taken. However, there seemed to be too many unknown factors to make a definite selection. It might also allow one to determine whether it was more likely that REFE was at 11:08 or at 14:47. That appears possible only if some turning (or not) scenario is assumed, and this may render all conclusions suspect.
@Authors and All,
One could also suppose that additional fueling details weren’t included in the investigation reports because there was no discrepancy with the ACARS.
Thank you for carefully considering the accuracy of the initial fuel weight.
@370Location
The Malaysian SIR states there was a discrepancy between the estimated take off fuel of 49,100 kg and the ACARS transmitted take off fuel of 49,200 kg (page 51 section 1.6.6).
All the more reason to include a copy of the Fuel Log and Refuel Record in the SIR.
We used the ACARS TOTFW at 17:06:43 UTC as our baseline.
Also I thought check of jet fuel quality was supposed to be one of the first steps after an accident.
Since flight duration is very important, we should have basic jet fuel analysis, which probably exists somewhere. If there is a detailed data download for each flight in the archives, perhaps the prior day MH370 flight, if the FQIS data is downloaded, we could determine approx density for both Beijing and KLIA jet fuels. Also of course there may be lab records.
If the new Malaysia government is going to facilitate search, I believe this is one detail that should be further examined. Not that I expect any earth shattering discovery, but who knows, just crash analysis 101.
@TBill: The heat value of the fuel (per unit mass) should be fairly independent of the density. As Richard says, the FQIS accurately calculates the fuel mass in each tank using both volume and density measurements. The flowmeters also measure mass flow, not volumetric flow. It is extremely unlikely that the diversion occurred due to fuel contamination. What benefit is there to further investigate the fuel quality?
@Victor
I think mainly energy content but boiling range and other parameters could be helpful. The normal reason for immediate checking jet fuel is to make sure the other flights taking off are not getting bad jet fuel, which is rare but nonetheless important to rule out fuel quality as accident cause.
In this case mainly secondary interest as energy content is important. I am not an energy content expert but in years past USA jet fuels were heavier because the refineries tended to max out gasoline. Presumably Malaysia/China jet fuel energy content could be lower, due to paraffinic crude sources etc, but I have no info on typical KLIA jet fuels at all.
In the complete lack of info, I recently estimated jet fuel qualities and did some vaporization calcs based on that.
https://twitter.com/HDTBill/status/1222935727492751365?s=20
@TBill: Again, the heat energy per unit mass is not likely to vary much, even if the density does.
In Appendix J, Bobby Ulich implicitly presumes that the fuel constraint (Figure 5, 2nd panel) is statistically independent of the route model (Figure 5, top panel.) However, given the way that the fuel constraint is constructed, that is simply not true – the fuel probability is derived entirely from those LNAV routes in the top panel that best fit the data. My understanding is that the LNAV routes are constructed by first finding the best fits to the data (BTO, BFO and other constraints), one route per heading, and then the fuel endurance is determined for that route after the fact. If that is not correct, then ignore the rest of this post.
However, if that is the case, then there is an insidious bias built into the fuel constraint. Consider an LNAV route that terminates at 37S. In my model calculations (not necessarily matching anyone elses, but good enough for the present purpose) the best constant mach route that fits the BTO and BFO data is at FL410, mach 0.846, and, at 19:41, passes latitude 0.03 degrees. However, it runs out of fuel at 00:01, sixteen minutes too early. The fuel constraint in Fig 5 likewise rates the probability of this route being viable as less than 10%. However, if one dropped the speed to mach 0.835, the altitude to FL400, and shifted the 19:41 latiude South to -0.358 degrees, the fit to the data is slightly worse (BTO rms increases from 28 to 36 microsec) but still acceptable, and the fuel now lasts 16 minutes longer due to the lower speed. The distance from the crossing of the 1st arc to the 19:41 point is small enough that there is plenty of time for the aircraft to have reached this position with an eary FMT.
What this says is that fuel performance should be an integral part of the figure of merit and not tacked on later. Small degradations in the quality of the BTO fit can be traded for improvements in fuel efficiency. These tradeoffs will not be evident when BTO rms (and the other figures of merit)
are used standalone.
Does this make sense?
@sk999,
You said: “In Appendix J, Bobby Ulich implicitly presumes that the fuel constraint (Figure 5, 2nd panel) is statistically independent of the route model (Figure 5, top panel.) However, given the way that the fuel constraint is constructed, that is simply not true – the fuel probability is derived entirely from those LNAV routes in the top panel that best fit the data. My understanding is that the LNAV routes are constructed by first finding the best fits to the data (BTO, BFO and other constraints), one route per heading, and then the fuel endurance is determined for that route after the fact. If that is not correct, then ignore the rest of this post.”
Perhaps you intended something different than how I am interpreting what you wrote. First, the fuel probability is not “derived entirely from those LNAV routes in the top panel.” The emphasis here is on “entirely”. One cannot determine a fuel probability with only a calculation of “required” fuel at 19:41, which depends on the SIO Route and also on the post-19:41 aircraft configuration. You also need estimates of the “available” fuel at 19:41 for various FMT routes and pre-19:41 aircraft configurations. What we have done is to produce a matrix of 36 combinations of available and required fuel at 19:41. From that matrix we select the maximum fuel probability. Thus, for each LNAV route, we pick the best possible case and option.
It is correct that we have (1) optimized the route probability at each initial bearing, and then (2) assessed its fuel probability. We did not fit the route by maximizing the product of the route and fuel probabilities. In fact, when we found the route probability curve, we had not yet finalized our FMT Route and our method of computing the available fuel. So, we were not concurrently calculating the fuel probability. That was done later.
Maximizing the product of the route and fuel probabilities MIGHT very slightly change the shape of the composite PDF. For LEPs north of 34.3 S, the effect will be negligible. For LEPs south of about 37 S, the effect will be negligible. But what about LEPs between 34.3S and 37S? Consider first the region between 34.3S and 35.5 S. Here both probability curves have similar large slopes, declining rapidly with increasing S latitude. I would not expect this region to be changed noticeably by a different method of optimization. If the two probabilities are anti-correlated, as one might expect, then one rising and one falling is unlikely to change the product significantly. The last region is from 35.5 S to 37 S. Here the route probability is high and slowly declining. The fuel probability here is quite low (< 15%).I would not expect it to be possible for the fuel probability to be increased by a factor 2-3X or more without a large reduction in the route probability. So, here again, I would not expect a different optimization procedure to produce a significantly different composite PDF.
I would also caution against drawing conclusions about the acceptability (i.e., probability) of any route based on a single FOM like RMS BTOR. Other factors must also be considered, especially the correlation coefficients and the GSEs. In addition, any route fit that does not use numerous samples of 4-D interpolated GDAS temperature and wind data along each leg will suffer large errors in predicted ground speed, rendering the fit useless.
One final point is that an assumption of "statistical independence" of the fuel probability from the route probability is not required to derive the same formula for the composite PDF. In fact if one assumes the fuel probability is conditional upon the route being probable, one obtains the same product of probabilities. Or, one could assume the route probability is dependent on there being sufficient fuel (otherwise the route is not flyable). So, whether they are independent, or one is conditional upon the other, the formula is the same product of the two probabilities.
@Dr B, Richard, Victor, Andrew. Having so far got to your Appendix D I attach another contribution on your paper to there. Despite its nature as a critique I join others in congratulating you all on the paper and its clarity.
https://www.dropbox.com/s/t0bedutgz7w4hof/Comments%20on%20the%20BRVA%20paper%2016th%20March%2C%202020.docx?dl=0
Some results from over the weekend:
https://www.dropbox.com/s/pcaajw97ohnp19c/LRCandECON_paths_around_180degrees_v3.pdf?dl=0
A thought: what looks like a peak when scanning parameters one by one, might be a ridge/crest in parameter space. So it could be important to vary parameters in combination (for example bearing in combination with FL).
@DrB, Richard
I do not fully understand how your path generators/fitters operate, but a question regarding the GS based on lat/lon: how do you exactly calculate this, at the WGS84 surface or above?
Every time I compare my distance traveled with yours I have a few km extra over the total 4k km.
@Niels,
The average leg ground speed derived from the lat/lons is simply the distance traveled divided by the elapsed time. I use the full Vincenty method for calculating distance, which is good to about a mm. I also make a modification of the Earth parameters to give, to a very good approximation, the correct distance at the geometric altitude. This last step is necessary to achieve the required accuracy.
Victor, Richard, and I have compared our range calculations. They always agree within a fraction of the length of the aircraft.
The predicted leg-averaged ground speed is found from the Mach, SAT, track, and wind. The Mach is converted to KTAS, and the vector sum of the KTAS in the heading direction and the wind “to” vector gives the ground speed vector in the track direction. This ground speed estimate is then averaged over numerous points along each leg.
The ground speeds calculated by the two methods must agree within about 1 kt for the True Route. This is essential. Ground speed errors (GSEs) > 1 kt indicate a route error.
When fitting an arbitrary route, it is always possible to find handshake locations which satisfy the condition that the GSEs must be smaller than 1 knot. The second test is whether or not the satcom and other statistics are acceptable.
I will repeat to you the same advice I gave to @sk999: “I would also caution against drawing conclusions about the acceptability (i.e., probability) of any route based on a single FOM like RMS BTOR. Other factors must also be considered, especially the correlation coefficients and the GSEs. In addition, any route fit that does not use numerous samples of 4-D interpolated GDAS temperature and wind data along each leg will suffer large errors in predicted ground speed, rendering the fit useless.”
So, in order fopr a route to be “acceptable” as a True Route solution, it must first have GSEs < 1 knot, and secondly it must have multiple (9) statistics which are consistent with the expected values for the True Route within the expected noise levels.
Of course, just as it is always possible to satisfy ONLY the GSE requirement, it is always possible to satisfy ONLY the RMS/STDEV BTOR requirement. In many cases it is also possible to satisfy ONLY the multiple statistics when ignoring the GSEs. However, the TRUE Route must simultaneously satisfy the GSEs and the multiple statistics used in the route probability. We believe the very sharp peak in Figure 19, which is the highest route probability, demonstrates the True Route was at exactly 180 degrees true bearing.
You said: "So it could be important to vary parameters in combination (for example bearing in combination with FL)."
Our Figure 23 proves this is the case. For each bearing, we found the best combination of speed setting and Flight Level.
@DrB
Thanks for explaining. Although the range errors I see are 1 ppt or below I realize it’s too much for doing the extended FOM; it is one of the reasons I’m trying to find the cause.
Regarding the GSE: in the vector addition procedure that I apply (with 3D interpolation applied every 10s time step) it would always be zero following your definition, so that’s good 🙂
@DrB
“Our Figure 23 proves this is the case. For each bearing, we found the best combination of speed setting and Flight Level”
It would be interesting to make a 3D plot for fig. 23, with the route probability on the z-axis. Maybe just for LRC. And then compare to fig. 19.
@DrB et al. I have made some minor amendments to my comments.
@David,
Our responses to your critique of our most recent paper are available HERE .
We appreciate your taking the time to ask questions and make suggestions for improvements.
DrB et al. My thanks for those responses. Altogether not very fruitful for the collective effort entailed.
My comments on what you have said are below, though I seek no further response.
https://www.dropbox.com/s/f54wv1b07p86j73/Response%20to%20BRVA%20comments%20on%20my%20critique%2018th%20March%2C%202020.docx?dl=0
@All, @David
I have made the following changes in the paper available in the download link in the article above:
1. Page 20 clarification as per response document to @David, regarding fuel reduction with air conditioning packs switched off. Many thanks @David for pointing this out.
2. Page 32 and Table E-1 correction of the typo @David kindly pointed out, regarding the time the power was restored to the SDU.
3. Page 119 changed “7 cases in Table D-1” to “9 cases in Table D-1”.
4. Page 119 correction of the typo @David kindly pointed out, regarding Option B2.
@David,
With regard to the lateral offset, the MH370 FL was already offset by at least 500 feet from the traffic in both directions on N571. So, it was not necessary to perform a lateral offset to avoid a collision. The lateral offset would assist in avoiding any visual detection by other N571 air traffic, both before and during the descent.
With regard to reaching the LEP with a functioning pilot, we think that is unlikely, based solely on our fuel model predictions. However, if our fuel model in fact has an error outside our estimated accuracy, then perhaps the LEP could be reached. We allow for this possibility by providing search areas A2 and A3 at a low priority.
@Dr B. With reference to your post above, would it not be useful to specify how much of A1 actually remains to be searched? By my reckoning, it’s about 20% of it (the inner-most strip). Plus any confirmed data-holidays. Or are we saying that we are so utterly convinced of the path that the whole of A1 should be searched again before proceeding to A2 and A3?
With respect to the debris, I recall that there were numerous potential debris signings. But when they were investigated by surface vessels nothing was found. Do you consider this data potentially useful in conjunction with the other indicators?
@Richard. Thank you for the amendments.
@DrB. My thanks for those further explanations.
Your Fig A -3 remains controversial. I attach the previous TM page to illustrate why I persist in my belief that those two graphs do not relate directly. It describes how schedules 1,2 & 3 are set by cabin altitude. Schedule 4 is set by altitude. They separate the two.
https://www.dropbox.com/s/4qsys3lwx0qtsh0/Pack%20airflow%20scheduling.png?dl=0
@paul smithson.
My personal opinion is that the entire A1 should be scanned anew before moving on to A2 and A3. First, cover the data holidays. Second, revisit all areas with suspect data and difficult terrain. Third, if necessary, re-scan the remainder so new data are obtained for the entire A1.
Ocean Infinity’s recent experience with initially missing the ARA San Juan due to a human classification error should have taught us a valuable lesson. That submarine was eventually located very close to its planned course and within the uncertainty of the hydroacoustic location error ellipse.
@DrB
ARA San Juan is a poor example as I have previously pointed out. It came to rest on the seafloor largely intact. The debris from MH370 is highly fragmented with many pieces literally acting like specular reflectors. IMO, the MH370 debris field will be much harder to miss than the San Juan.
If one uses the Metron estimate of detection probability of 90% you derive about a probability of finding the wreckage in A1 of about 13%
@DennisW: IMO, the MH370 debris field will be much harder to miss than the San Juan.
The San Juan was not “missed”. The contact was detected and incorrectly classified.
In addition to the parts of A1 where we have either no or bad data because of terrain avoidance or shadows, we also have other parts of A1 of questionable data quality due to imprecise positioning of the GO Phoenix towfish. That’s why I’ve been a strong advocate of a thorough review of the existing data instead of assigning arbitrary numbers to the detection probability.
@Victor
“missed” and “misclassified” amount to the same thing in my vernacular.
The fact remains that MH370 should have a sizable debris field. Link below to AF447 wreckage.
https://docs.google.com/document/d/13uvE68f2YS6q70jfWdtiwx-NHxLwHChesiyBjWFRGvI/edit?usp=sharing
Oh, THANK YOU, David !
Below is what I had written last night, and I was about to calculate whether or not the higher than 22, 000 feet altitude section of the lower part of Figure A-3 was for a constant volumetric flow, then …. SO, I have.
My writing started out:
DrB, David,
A little over three days ago I told Richard that “I will attempt to be clear in a single comment”.
Unfortunately that single comment has developed into an “Addendum Report” titled “Case ID and Resolution, and Options”.
Mainly it concerns Appendix D and fuel probability. It now looks like I won’t complete it even tonight.
David’s comments discuss some related aspects.
Bleed Air:
David, like you I thought the approach taken by BRVA to calculate the packs-off fuel savings “novel” (your terminology).
But my approach to that was along the lines of: “So what ? It makes allowances for the effect of Bleed-Air On or Off in a manner seemingly suitable for our purposes and provides for a basic comparison”.
David, you say: “Whereas you have applied “Airplane Altitude in Feet” to flow schedules 1-3 I believe the top graph in your Fig A-3 is unrelated to the bottom and those schedules are dependent just on cabin altitude. Schedule 4 alone varies with the aircraft altitude.” I fully agree here with your opinion, yet DrB clearly contradicts this: “Our understanding, after discussion” etc.
Note that Schedules 1, 2 and 3 show a reduction in MASS flow with increase in CABIN altitude. At “first glance” the schedules look to be scheduling constant VOLUMETRIC flow. A simple check of the mass flow ratios between that indicated on Figure A-3 for 8000 feet cabin altitude and that indicated at sea level for Schedule 2 satisfactorily confirms this. Using the pencil and ruler and paper printout method for Schedule 2 the ratio of mass flow at 8000 feet to that at sea level is 75.9%. ( 245 / 323 ) whereas the standard atmosphere pressure ratio is 75.9%. Satisfactory agreement for the purposes intended with the method used.
[Perhaps it might be appropriate to schedule the same volumetric flow within the cabin so the flow velocities within the cabin around the human passengers do not change significantly as cabin altitude varies.]
I do not know just what Schedule 4 is intended to show, but it might even be the Outflow Valve Control Schedule ?
The constant mass flow at aircraft altitudes below 20,000 feet may simply indicate those are altitudes where a sea level, or comfortably near sea level, CABIN altitude may be achievable. THAT is WITHOUT exceeding the 8.6 psid limit. The outside standard pressure at 22,400 feet altitude is nominally 6.1 psia (Thank you Messrs P&W) which is 8.6 psi below standard sea level atmospheric pressure.
In more detail DrB’s comment on Figure A-3 reads: “Our understanding is the cabin altitude and airplane altitude scales are related. The maximum cabin altitude of 8,000 ft provides a pressure differential of 8.6 psi at the aircraft’s certified maximum altitude of 43,100 ft.” The latter sentence is mathematically correct. But how are the upper and lower sections of Figure A-3 related ?
Does the lower chart of Figure A-3 shows an attempt to maintain cabin pressure at sea level, or comfortably near sea level, for approximately the first half of the ascent to cruise, followed by a transition period and then operation close to the 8.6 psid structural limit, or some cabin pressure below but close.
At 22,000 feet altitude the standard atmospheric pressure is 8.5 psi below standard sea level pressure.
At 22,400 feet altitude the standard atmospheric pressure is 8.6 psi below standard sea level pressure.
The aircraft MUST have a lower cabin pressure at higher altitudes.
IF, as DrB’s comment implies, the cabin altitude progressively reduces from sea level through to 8,000 as the aircraft climbs from sea level through to 43,000 feet, then the cabin pressure when the aircraft reaches 22,000 feet altitude will be equivalent to the pressure corresponding to 4,093 feet altitude. This is ….
__________________________________________________
AND Then I was going through the procedure of calculating whether the outflow valves began to choke at around 20,000 feet and whether the schedule was for a progressive increase in pressure differential from approximately 6.4 psid (at 22,000 feet through a maximum of 8.6 psid at 43,100 (say 43,000) feet. (Also at a constant volumetric flow rate.)
[the “approximately 6.4 psid” is the difference between the standard atmospheric pressure of 12.65 psia at 4093 feet and 6.21 psia at 22,000 feet]
My estimate from Figure A-3, using the pencil and paper printout method, of mass flow at 22,000 feet was 173 lb/min and at 43,000 feet was 153 lb/min. The cabin altitude at the latter is 8,000 feet, 10.92 psia. Calculating (173/153)x(10.92) gives 12.35 psia which equates to the standard atmospheric pressure at about 4750 feet.
SO, for the intent of the purpose of the training manual (as represented by Figure A-3), this is not too far off 4,093 feet.
__________________________________________________
@DennisW,
You said: “IMO, the MH370 debris field will be much harder to miss than the San Juan.”
I disagree. The MH370 debris field is likely to have more pieces on the bottom, all of which are smaller than the several chunks of the ARA San Juan hull. This will make it undoubtedly more difficult to detect, because the maximum acoustic signal reflected from each piece will be much smaller. In addition, the height of the MH370 debris from the surrounding terrain is much less, and it will be more difficult to detect the shadows caused by the opaque proud debris. The ability to discriminate (i.e., to classify) MH370 debris from the natural roughness of the terrain will depend on the density and size of the natural features, boulders, etc. That will vary from place to place on the sea bottom. Not all sea bottom is flat and featureless, and where there are natural features about a meter or two in size, the search will require significantly better resolution in order to discriminate targets effectively.
Correction:
Using the pencil and ruler and paper printout method for Schedule 2 the ratio of mass flow at 8000 feet to that at sea level is 75.9%. ( 245 / 323 )
whereas the standard atmosphere pressure ratio is 74.3%.
Satisfactory agreement for the purposes intended with the method used.
74.3% = 10.92 psia (at 8,000 feet) divided by 14.70 psia
@DrB
The ATSB does not appear to share your view.
https://docs.google.com/document/d/1m6-an5v44EzDPomtUrcShYJA0mwkMetuj13cDSvATGM/edit?usp=sharing
@DennisW,
Which view is that? The ATSB graphic simply proves they quit before they finished the task at hand. Why didn’t they get high-quality data for 100% of the search zone? In this endeavor, close is not good enough. In addition, our search area is larger and contains unsearched territory.
The first thing I would have done is to put test targets on the bottom in the search area, but not tell the search crew where they were, just that they are some number of them deployed in the search area. Then you have a controlled experiment with quality checks on the whole process. If the search crew can demonstrate they have covered the whole area with quality data, and if they find ALL the test targets, and if all other detected objects are demonstrated not to be aircraft debris, then you can prove you have conducted an effective search and ruled out the presence of the target of the search, with a high probability.
Calibration targets near port are also useful to avoid a long round trip just to find out you have technical problems. However, that does not test the search effectiveness end to end. Only known targets at unknown locations in the search area can do that.
I am generally a fan of ATSB, but, in the underwater search, they came up empty. To be fair, this was outside their normal realm. I have also spent 20 years finding meter-sized objects in the sea and on the sea bottom for the U.S. Navy and others agencies. You can only clear an area of targets with a rigorously controlled and constantly validated system. We used to drop targets into the sea so we could make a return pass and verify it was automatically detected and properly classified with a CFAR sensor system I designed and built. ATSB could have done the same thing. Proving something is NOT there is actually quite a difficult task.
@DrB
Some 97%+ of the A1 area is classified as “high probability” by the ATSB meaning a greater than 95% detection probability.
I respect the analytics you and your collaborators have done, but I think you are beating on a dead horse relative to convincing anyone to search A1 again.
I also disagree with your earlier comments relative to the debris field, size of wreckage, terrain… You obviously disregarded the sonar scans of AF447. They were literally a blizzard of returns.
@DrB
Said another way, it take takes about 10 minutes of analytics to show that your thousand+ hours of analytics are very very questionable.
Give it up.
@George G. Yes the page I posted at 2:33 notes that schedules 1-3 provide air at constant volume, mass flow therefore reducing with cabin pressure decrease.
Regarding your comment, “I do not know just what Schedule 4 is intended to show, but it might even be the Outflow Valve Control Schedule “, cabin pressure is independent of the airflow delivery, being controlled by the outflow valves. I gather schedule 4 is used in the descent. Maybe that is stated is in the BRVA paper though I cannot locate it.
The paper does note that schedule 3 is used when one engine is providing the bleed air for both packs, at page 78 paragraph 12.
You ask, “But how are the upper and lower sections of Figure A-3 related ?” If they are directly related as per the BRVA Fig A-3 then with both the abscissae being linear and the end point of 8,000 ft cabin altitude being at 43,000 ft aircraft altitude, cabin altitude rises at a constant 1,860 ft per 10,000 ft increase of aircraft altitude, or 0.186:1.
Also, cabin air flow rate, linear with both abscissae, will fall from about 323 lb/min at sea level to 238 at 43,000 ft, that is by a constant 19.76 lb/min per 10,000 ft increase in aircraft altitude.
If on the other hand they are not directly related, then they will need to be elsewhere in a table. There is a trade-off between cabin altitude being low, to provide more comfort, and the cost of doing that. The lower it is held the higher the airflow (from the top graph) so the higher the fuel cost. Though the cabin altitude reaches both its maximum and minimum limit of 8,000 ft at 43,000 ft, beneath that I speculate that airlines might have flexibility, like they do with the cruise cost index.
I do not think that the designers of the outflow valves would envisage choking. At low altitude there will be little pressure differential yet they discharge up to 323 lb/min scheduled flow under schedule 1 minimum and that can rise to 390 at the schedule 1 maximum should the aircraft take more passengers. On top of a discharge approaching that the outflow valves may be designed to cope with another 268 lb/min, that is should the pilots forget to turn on the recirculating fans for some reason, though there pressure relief valves also.
On the pressure ratio of your ‘correction’ being about equal to the mass flow ratio, Boyle with his Law might give a nod to that.
@DrB. About targets, my reservations about those have been that while supposed to replicate the volume of a wrecked engine, some looked to be flat sided steel, ie of sonar reflectivity that might be quite unrepresentative.
These test targets themselves could have been calibrated against a junked wrecked real article. As I have mentioned before, the modified flaperon tested by the CSIRO drifted quite differently from their earlier replica and also the French CFD model.
Then there was the flat hard bottom of the test site.
Did you utilise realistic shapes and materials as targets for calibration in your searches?
@Andrew. The ‘Thrust Derate Switch’ in the climb EHM. I do not suppose it is relevant but in case it is do you know what it is for please? It appears to be all-over-the-place.
https://www.dropbox.com/s/wz4bn3wpe2uja6h/Thrust%20Derate%20Switch%2C%20EHM%20climb%20report.png?dl=0
@David
There is an error in the Malaysian SIR – Appendix 1.6B – EHM Climb Report for the Thrust Derate Switch.
In the ACARS data the Thrust Derate Switch Status Word is only one byte, not two as they incorrectly show in the SIR. They are repeating the last digit of the EPR Actual – Right data in the previous data item, as an analysis of the raw data below shows.
For MH370 the Thrust Derate Switch Status Word ACARS data is HEX “8” for all 3 data entries and for MH371 the Thrust Derate Switch Status Word ACARS data is HEX “C” for all 3 data entries.
Here is a link to the relevant part of the ACARS data for MH371 and MH370:
https://www.dropbox.com/s/3o1nhr4junlsgws/EHM%20Climb%20Reports%20MH371%20and%20MH370%20Data.png?dl=0
Here is a link to the relevant part of the the raw SU Log for MH371 and MH370:
https://www.dropbox.com/s/t503kcniihg2yp8/EHM%20Climb%20Reports%20MH371%20and%20MH370%20Raw.png?dl=0
@David,
Targets intended to test search effectiveness, not just basic sensor function, must be realistic. We used two types. The crude (and cheap) disposable targets were used to test sensor function. We knew where they were, so you look at those at the start of every sortie. The realistic targets generally were inert actual devices. In this case one could use actual pieces of aircraft wreckage – engine cores, main landing gear, etc., or even crushed small automobiles. Sure, it costs money to put these out, but a “blind” experiment is the best means I know of to demonstrate actual search effectiveness.
@DennisW,
You said: “Said another way, it take takes about 10 minutes of analytics to show that your thousand+ hours of analytics are very very questionable.”
No amount of analytics can supply data that were never taken. That includes the data holidays in the previously searched areas and the new unsearched areas we are recommending.
So, the current MH370 coverage is less than 100%. I will also point out that the coverage in the ARA San Juan search was 100%, and yet they still missed it.
In addition, the effectiveness of the ATSB-reported “high confidence” areas cannot be proven with the data at hand. Things could go wrong which are not apparent in the data stream. Actually finding test targets at previously unknown locations is by far the best proof of effectiveness. Analytics can only go so far, and it won’t test everything.
David,
I can assure you the outflow valves will be choked in the second stage of Schedule 4 flow.
At aircraft altitudes above 22,000 feet the ratio of cabin pressure to outside pressure ensures this.
Example: 30,000 feet, 4.37 psia; Estimated Cabin Altitude 5581 feet, 11.97 psia;
Ratio: Cabin Pressure to Outside = 2.74 > 1.89; Outside to Cabin = 0.365 < 0.528
And below 20,000 feet they should not be.
The transition region in between will depend on the actual cabin pressure schedule when passing through/between 20,000 and 22,000 feet.
Andrew, We need your help, or that of some of your colleagues, in reconciling the following:
I interpret the upper chart of Figure A-3 (transposed from the Training Manual, Page 37 of 21-51-00) as being the TOTAL air flow through the air conditioning packs, INCLUDING Recirculated Air.
Subsequent to David's putting up a link to the previous Page 36 (of 21-51-00) I now interpret the lower chart Schedule to be the air THAT THE ENGINE/S supply to the air conditioning system. QUOTE: "The minimum flow to pressurize the airplane and to operate the air cycle machine."
Does this give more information :
1. Four Recirculating Fans make up the difference between Schedule 1 (Min) and Schedule 4;
This is 240-157=83 lb/min at 39,000 feet "read" off the charts
2. Loss of one Recirculating Fan incurs a make-up loss of 83/4=21 lb/min;
3. Fuel Flow penalty for loss of that one fan: 0.3%
4. Using the average value, the FF increases by 1.3% with four inoperative recirculation fans. Quoted from the BRVA Report Paragraph 7 of Section A.11.
Can we interpret that 83 lb/min Engine Bleed Air Flow means 1.3% Fuel Flow at cruise ?
In other words the loss of recirculated air is made-up for by bleeding more off the engine ?
If we can make this assumption, Then I propose that you can allocate normal (Schedule 4) Engine Bleed cost as being 1.3% x 157/83 = 2.5% of Cruise Fuel Flow.
Hence doing away with the cabin air conditioning provides us with an additional 2.5% Fuel Available in comparison to the 1.16% derived in Paragraph 11 of Section A.11. If we interpret the charts as I do.
And to add confusion, Schedule 3 is below Schedule 1 (Min) by an amount of 79 lb/min, which is what what one engine normally provides.
Are you able to find out the information. I have no access to manuals or other relevant information here.
Whilst writing the above I have been more and more "certain" that the upper chart of Figure A-3 refers to Total Air Flow passing through the air conditioning packs, including the recirculating flow.
Hoping you can confirm/deny, or have means to determine, as making my assumption affects a critical factor.
@DennisW
You stated “The ATSB does not appear to share your view.” and point to the ATSB report dated 3rd October 2017 Figure 73.
You also stated “Some 97%+ of the A1 area is classified as “high probability” by the ATSB meaning a greater than 95% detection probability.”
A 10 minute analysis shows, that both your statements are simply not true and misleading.
Overlaying Figure 51 from our paper showing our Recommended Search Area A1 depicted in green, on the ATSB Figure 73 from their report dated 3rd October 2017, shows that only 34.2% was previously covered by the ATSB.
28.4% of our search area A1 area was covered at a high confidence of 97.8% by ATSB (depicted in yellow).
5.8% of our search area A1 area was covered at a high confidence of 91.5% by ATSB (depicted in orange).
65.8% of our search area was not covered at all by the ATSB and the rest to a confidence level of 96.7%.
https://www.dropbox.com/s/3gzjwktmdpjhc2k/Search%20Area%20Coverage.png?dl=0
A zoom in on our recommended search area reveals, that even in the area previously searched by ATSB, there a large number of shadow zones (depicted in blue), a few equipment failures (depicted in magenta) and a few low
probability detection areas (depicted in green).
https://www.dropbox.com/s/gqf7lsquwidm1vw/Search%20Area%20Coverage%20Zoom.png?dl=0
As we point out in our paper in Figure 48, Ocean Infinity covered a further area beyond the ATSB area, but still only between 25 NM and 32 NM from the 7th Arc. We are recommending 37 NM either side of the 7th Arc.
Ocean Infinity did not cover the original ATSB area a second time.
ATSB and Ocean Infinity did not cover all our recommended search area A1.
Our recommended search areas A2 and A3 have also not been covered.
@David
@George G
RE: “Your Fig A -3 remains controversial. I attach the previous TM page to illustrate why I persist in my belief that those two graphs do not relate directly. It describes how schedules 1,2 & 3 are set by cabin altitude. Schedule 4 is set by altitude. They separate the two.”
We do not dispute the mass air flow for schedules 1, 2 & 3 is related to cabin altitude and the mass air flow for schedule 4 is related to aircraft altitude. That much is evident from the charts and the text.
The question is whether the cabin altitude scale is related to the airplane altitude scale. I had a long talk with one of our Boeing technical training instructors about this topic. These guys are specialists and they are very knowledgeable. I was told the two scales are related. The relationship is dictated by the pressurisation schedule, which controls the cabin altitude linearly with airplane altitude, so that the cabin reaches a maximum of 8,000 ft at the aircraft’s maximum certified altitude of 43,100 ft. At that point the cabin also reaches its maximum differential pressure of 8.6 psi.
We have used a methodology to estimate the fuel flow changes based on the best available information. It may not be perfect, but it’s all we can do with the available information.
RE: “I do not know just what Schedule 4 is intended to show, but it might even be the Outflow Valve Control Schedule ?”
Schedule 1 is the usual flow schedule and is the relevant schedule for our purposes. The other schedules provide less air to the packs and are used when necessary to reduce the engine bleed air load, or to make more air available to other systems. For example, schedule 2 is used during take-off (for 10 minutes); and during descent or when there is a single bleed source with two engines operating, AND the APU does not supply air. Schedule 4 is used when a variety of conditions apply, including engine start, the first two minutes of take-off, descent with a single bleed source and wing anti-ice on, amongst others. There is a logic diagram in section 21-51-00, page 39 of the 777 Training Manual if you care to check. As stated in the text: “Flow schedule 4 gives the minimum flow to pressurize the airplane and to operate the air cycle machine.”
@David
RE: “The ‘Thrust Derate Switch’ in the climb EHM. I do not suppose it is relevant but in case it is do you know what it is for please?”
Richard has already explained that the data for the Thrust Derate Switch in Appendix 1.6B of the SIR is incorrect. As for its purpose, I don’t know. The engines have several climb thrust settings that are automatically selected by the FMC, depending on the take-off thrust setting. The climb thrust settings are CLB, CLB 1 or CLB 2, where CLB is the rated climb thrust; CLB 1 is a 10% derate of CLB thrust to 10,000 ft, increasing linearly to CLB thrust at 30,000 ft; and CLB 2 is a 20% derate of CLB thrust to 10,000 ft, increasing linearly to CLB thrust at 30,000 ft. The Thrust Derate Switch might indicate which climb thrust setting was in use.
@Richard. Your point is made that ATSB search “effectiveness” estimates pertain to the stuff that was seached under their watch, not OI. Are you of the view that OI’ search technology is inferior to the preceding searches? If not, the broad conclusion would still stand.
I previously (twice) asked for an estimate of how much of A1 has not been searched. This seems to me to be rather important, unless you advocate disregarding null sub-sea search result altogether for the purpose of predicting aircraft location.
I interpret your comment above to mean that unsearched area comprises a 7NM strip on one side and 5NM strip on the other, total width 12NM, out of A1 total width 54NM. By that rough estimate, about 78% of A1 has already been searched. Is that about right?
@DrB
In reference to your response to @David, why would the bleed air be off for the trip south, whereas I think you are suggesting the strategy is probably other than fuel conservation.
@PaulS
Here is a search area graphic courtesy LabRatSR (Kevin Rupp) on Reddit. This graphic may be slightly outdated as far as 34.4S “hot spot” vs. 34.2S. In the Magenta you see GoPheonix coverage areas, whereas the darker purple represents OI extent of search. As shown, and if I recall, when OI originally searched 34S there was a preference for the searching outside beyond Arc7 rather than inside Arc7. So if the aircraft was uncontrolled and flying circles it could conceivably have gone inside Arc7 into an unsearched portion of A1 zone, in addition to any data gap/obstructed areas.
https://i.imgur.com/hQLaacc.jpg
Thanks, Tbill.
@paul smithson
You asked “ Are you of the view that OI search technology is inferior to the preceding searches?”
I think OI has great technology and as I stated in my recent video to the NOK, the OI technology gets better all the time.
My earlier comment was in answer to @DennisW and I pointed out, that each of our Recommended Search Areas A1, A2 and A3 have not been searched fully by either ATSB or OI.
If you insist, I will calculate the exact percentages for each area.
But, it is already clear, that job is not complete.
@Richard. The point that I am making is that your reasoning (to search A1 regardless) appears to rank the criteria used in filtering your search zone more highly than the null result of the undersea search. I would have placed the latter right at the top of my criteria – meaning that if an area has been searched it should be excluded from the recommended search zone. The only exception being data holidays or any other demonstrable reason to believe that the search “null result” is unreliable. If you counter this by saying … well there’s a 5% chance that it was missed, then my point still stands. Except the null search result should be given 95% weighting rather than 100%.
@paul smithson
I am just following the data.
I disagree that because an area was searched, it should be excluded.
Bobby has tried to make this point twice:
(1) ARA San Juan.
(2) Blind tests in the Search Area.
Please do not presume, what the results of my future analysis (not yet published) might be.
Like everyone else here, I am working on this subject on my own unpaid time, not your demands.
@richard. enough, already.
@paul smithson
Thank you!
@TBill,
You asked: “In reference to your response to @David, why would the bleed air be off for the trip south, whereas I think you are suggesting the strategy is probably other than fuel conservation.”
Possibly the bleed air was turned off a second time to depressurize the aircraft and commit suicide.
@paul smithson
Our Recommended Search Area A1 was searched 34.16% by ATSB and 79.97% by ATSB and OI.
Our Recommended Search Area A2 was searched 4.98% by ATSB and 6.02% by ATSB and OI.
Our Recommended Search Area A3 was searched 6.04% by ATSB and 9.49% by ATSB and OI.
https://www.dropbox.com/s/4qsz0f2ilggx33q/Search%20Area%20Coverage%20ATSB%20and%20OI.png?dl=0
It is the original 34.16% of A1, that concerns me, more than the additional 45.81% of A1 or even the remaining 20.03% of A1.
I believe MH370 was more likely missed in A1 in the original ATSB search.
@Richard. Thanks for the clarification.
@sk999,
You previously said: “What this says is that fuel performance should be an integral part of the figure of merit and not tacked on later. Small degradations in the quality of the BTO fit can be traded for improvements in fuel efficiency. These tradeoffs will not be evident when BTO rms (and the other figures of merit) are used standalone.”
To which I replied: “Maximizing the product of the route and fuel probabilities MIGHT very slightly change the shape of the composite PDF.” and ” I would not expect a different optimization procedure to produce a significantly different composite PDF.”
I have done a comparison of fitting the route by (a) maximizing the route probability and (b) by maximizing the product of the route and fuel probabilities. The results are available HERE .
Figure 1 is the product of the route and fuel probabilities plotted versus 19:41 bearing. It demonstrates that the two fitting methods produce nearly identical results, as I had predicted. The differences are less than a few tenths of a percent.
Figure 2 compares the resulting route probability using the two fitting methods. Again, the differences are quite small – a few tenths of a percent.
Figure 3 is like the first figure but plotted versus S latitude of the LEP instead of bearing. Note the rapid decline in fuel probability as the LEP moves west and south. It is important to appreciate that the LRC speed schedule slows down quite a bit (from M0.84 to less than M0.80) as the aircraft gets lighter, and this cuts the fuel flow late in the flight. However, the fixed-Mach speed schedules at 0.84 and 0.85 don’t slow down as the plane gets lighter, so the fuel flow reduction is less late in the flight. That effect contributes to the rapid increase in the 19:41 fuel shortfall past 36 S.
These figures demonstrate the following:
1. The best overall probability occurs at 180 degrees bearing, ending on the 7th Arc at a LEP of 34.3 degrees S.
2. The fuel is sufficient at 180 degrees, within the estimated 1-sigma model error.
3. Bearings greater than 180 degrees require higher KTAS and therefore higher fuel flows.
4. The fuel probability declines very rapidly at bearings greater than 180 degrees.
5. At bearings of 186 degrees and larger the fuel probability is essentially zero. This corresponds to LEPs south of 37 degrees S.
@Richard. The Thrust Derate Switch data being all over the place.
Thank you for that explanation. I do not know what it does but at least it is not erratic.
@George G. Outflow valve choking. I think we have different interpretations as to what ‘choking’ means. For my part, wide open, flow rate is unresponsive to pressure differential.
With the differential at altitude being high and flow less, the outflow valves need to be open much less. As I look at it while they are restricting flow the valves are not choked.
@George G. My second line should read please.
“For my part, wide open, flow rate is unresponsive to increased pressure differential.”
@David
RE: ” Your Fig A -3 remains controversial. I attach the previous TM page to illustrate why I persist in my belief that those two graphs do not relate directly. It describes how schedules 1,2 & 3 are set by cabin altitude. Schedule 4 is set by altitude. They separate the two.”
It is patently obvious from the charts and the text that mass air flow for schedules 1, 2 & 3 is related to cabin altitude and that mass air flow for schedule 4 is related to airplane altitude. We do not disagree. The question is – how is cabin altitude related to airplane altitude?
I spoke with one of our Boeing technical training instructors about this topic. They are specialists and they are very knowledgeable. I was told the cabin altitude and airplane altitude scales in the chart are related. The relationship is determined by the pressurisation schedule, which controls the cabin altitude linearly with airplane altitude, to ensure the cabin reaches a maximum of 8,000 ft at the aircraft’s maximum certified altitude of 43,100 ft.
The methodology we used to estimate the packs off fuel flow is based on the best available information. It may not be perfect, but it’s all we can do with the available information.
RE: ” The ‘Thrust Derate Switch’ in the climb EHM. I do not suppose it is relevant but in case it is do you know what it is for please? It appears to be all-over-the-place.”
Richard showed that Appendix 1.6B is wrong and that the Thrust Derate Switch did not change during the climb. The FMC automatically selects one of several climb thrust settings (CLB, CLB 1, or CLB 2) depending on the take-off thrust setting. CLB is the full rated climb thrust, while CLB 1 and CLB 2 are de-rated climb thrust settings that begin to wash out when the aircraft climbs above 10,000 ft. The three thrust settings are equal above 30,000 ft. I’m guessing, but I assume the Thrust Derate Switch shows which climb thrust setting was in use.
@George G
RE: ”I do not know just what Schedule 4 is intended to show, but it might even be the Outflow Valve Control Schedule ?”
Flow schedule 1 is the usual flow schedule and is the relevant schedule for our purposes. Schedules 2, 3 & 4 provide less air to the packs for one or more of the following conditions and are not relevant in this case:
· The amount of bleed air available is less than usual.
· More than the usual number of bleed air user systems are on.
· Takeoff or single engine operation.
Schedule 4 provides the least flow to the packs and is in effect when a variety of conditions are met, including engine start, wing anti-ice It provides the minimum flow required to pressurise the aircraft. The logic diagram for the pack flow schedules is on page 39 of section 21-51-00 of the 777 Training Manual.
RE: ”Whilst writing the above I have been more and more ‘certain’ that the upper chart of Figure A-3 refers to Total Air Flow passing through the air conditioning packs, including the recirculating flow.
Hoping you can confirm/deny, or have means to determine, as making my assumption affects a critical factor.”
Cabin air is NOT recirculated through the packs, which are always supplied by ‘fresh’ bleed air taken from the pneumatic system, ie the engines or APU. Recirculated cabin air is fed back into the distribution ducts AFTER the packs.
David,
@George G. My second line should read please.
“For my part, wide open, flow rate is unresponsive to increased pressure differential.”
Choking has a very specific meaning.
Flow goes sonic at the throat.
Flow through the nozzle (valve) is then only dependent on pressure at the inlet, the inlet fluid temperature, and the area.
In the case of a pressurised and temperature controlled aircraft cabin the only variables we are interested in are the pressure and area. Temperature is controlled within a reasonably small range.
Flow through the valve can be controlled by varying the area.
Pressure control is actioned by balancing the flow into the cabin (controlled by another valve, or valves, for the air from the engine compressors) and the outflow control valve/s.
For air the critical ratio of the downstream pressure to the upstream pressure at which the flow in the throat of the nozzle becomes sonic is 0.528.
Or alternatively, more sensibly or easier to comprehend in my view, the critical ratio of the upstream pressure to the downstream pressure above which the system upstream of the throat “couldn’t care less about what is going on downstream” is 1.89, the reciprocal of .528.
@David said: I think we have different interpretations as to what ‘choking’ means. For my part, wide open, flow rate is unresponsive to pressure differential.
More accurately, when the flow is choked, the flowrate is independent of the back pressure. For air, this occurs when the pressure ratio exceeds 1.893. Increasing the upstream pressure will increase the mass flowrate.
With the differential at altitude being high and flow less, the outflow valves need to be open much less. As I look at it while they are restricting flow the valves are not choked.
You cannot look at a valve and determine if the flow is choked. The flowrate would be proportional to the upstream pressure and the flow area. Changing the position of the louvers effectively changes the flow area, and hence the flow rate.
Flow through the valve can be controlled by varying the area.
Pressure control is actioned by balancing the flow into the cabin (controlled by another valve, or valves, for the air from the engine compressors) and the flow out of the cabin by controlling the area of the outflow control valve/s.
Andrew,
Thank you very much for your answer/s to my query re Air Pack Scheduling.
In particular, thank you for detailing the purpose of, or reason for, all 4 schedules, AND also detailing that “Cabin air is NOT recirculated through the packs, which are always supplied by ‘fresh’ bleed air taken from the pneumatic system, ie the engines or APU. Recirculated cabin air is fed back into the distribution ducts AFTER the packs.”
Re: Choked or Sonic Flow
Here is the calculator I use and with 7.5-in orifice diameter to approximate both outflow valves 100% open:
https://www.tlv.com/global/US/calculator/air-flow-rate-through-orifice.html
@Andrew, George G, Victor. I stand corrected, thank you.
@DrB
Could you perhaps share all route probabilities for best fit (bearing&FL) LRC routes used in fig. 23 ? So relating to the orange dots in that figure.
DrB said:
March 19, 2020 at 6:00 pm
“The best overall probability occurs at 180 degrees bearing” and “The fuel is sufficient at 180 degrees, within the estimated 1-sigma model error.”
Your Figures 1,2,3 only served to highlight a matter which has been niggling me for some time (months):
You chose to include the data point for 176 degrees LNAV Bearing, 31.9 degrees South LEP Latitude (intersection with Arc 7).
Refer to Figure 15 of “The Final Resting Place”.
This is “Figure 15 – Combined Overall Probability vs Last Estimated Position Latitude” for the purposes of clarity.
“Figure 5 – Summary of Results” is the same chart for the record for anyone else reading this.
Please note that were the consideration of the “Probability of the Aerial Search Not detecting the Floating Debris Field” removed from the considerations which are used to derive the final “Probability Density Function of Being the Correct Route”,
then the result would be noticeability different.
Part of what has been niggling me is both Richard and yourself are adamant that the 180 degree flight south is the one and only solution, yet I’m not too sure that you have satisfactorily demonstrated discrimination between one candidate flight path south and another. I have no doubt that all your work over the last year or two has made that discrimination, but is it really evident ?.
In Section G.5 of “The Final Resting Place”, when discussing Route Parameter Sensitivity you state:
QUOTE:
We also explored other regions of Interest using constant track and constant heading navigation.
None of these came close to matching the route probability of the LNAV 180° route.
END Quote.
So, please consider the following as a test case.
Concerning your use of the “Probability of the Aerial Search Not Detecting the Floating Debris Field”. I ask did it become necessary to use this to weed out (discriminate) one potential path from another ?
Or are you simply putting the icing on the cake ?
Consider your recent use of the data point for 176 degrees LNAV Bearing, 31.9 degrees South LEP Latitude (intersection with Arc 7).
Were it not for the use of “Probability of the Aerial Search Not Detecting the Floating Debris Field” then your Combined Probability for this data point would be much greater.
The product of the remaining three probabilities would be 0.54. I have not made any attempt to normalise this estimate.
For the “180 Degree Bedax Route (LRC at FL390)” the corresponding number would be 0.79.
The simple difference in these numbers does clearly indicate preference for the route you have determined as THE ONE AND ONLY route over the 176 degree route, but the question still stands: Did it become necessary to use Probability of the Aerial Search Not Detecting the Floating Debris Field to weed out (discriminate) one potential path from another ? Or are you simply putting the icing on the cake ?
With respect to the use of this method it does seem a little contrary that you have been providing argument for consideration that the aircraft wreckage on the sea floor may have been missed during previous searches (which argument I have no argument with) and that basically [in my terms] one can never be certain of where something is if you can’t or haven’t yet detected (found) it.
This approach conflicts somewhat with ruling out an area (on the sea surface) because nothing was seen there.
As part of preparation for the requested test case:
Refer to Figure 73 of the ATSB Report “operational-search-for-mh370_final_3oct2017” for which Richard recently provided a link.
[Comment-27393 March 19, 2020 at 8:52 am]
The 31.9 degrees South Latitude intersection with Arc 7 has some interesting underwater topography (bathymetry if you wish).
Refer to Figure G-8 (and/or Figure 23) of “The Final Resting Place”. The fit of the 176 degree route is certainly not as “nice” a fit as is the fit of the 180 degree route and LRC at FL390, but is it statistically close to the Flight Plan ECON which you have shown (also at FL390) ?.
Refer to Figure G-9, your Speed Setting Sensitivity Study. Here you have tabled (i.e. plotted) Flight Plan ECON at FL380. I’m sure I don’t quite understand why the results differ ?
BUT, perhaps the following sentence answers that.
QUOTE:
To study the speed setting further, we performed additional route fits at 180 ° with the complete
variety of speed settings, allowing the flight level to be optimised for each speed setting. The result
is shown in Figure G-9.
END Quote.
If there were to be conducted Sensitivity Studies done for the 176 Degree ECON FL390 Route what would be the results ?
Or have you already done this which I guess you have ?
If so would they placate Doubting George’s like myself ?
Concerning your “19:41 Initial Bearing Sensitivity Study” you state: “We believe this narrow central peak at exactly 180.00 ° proves this was the MH370 LNAV bearing.” Please note that a large contributor to this being a narrow peak is the use of the Probability of the Aerial Search Not Detecting the Floating Debris Field method.
https://www.dropbox.com/s/sxx5650dapcd79x/Product%20of%20the%20Probabilities%20of%20Route%20Fuel%20Drift%20Models.docx?dl=0
@Niels,
You asked: “Could you perhaps share all route probabilities for best fit (bearing&FL) LRC routes used in fig. 23 ?”
I have made a table, and it is available HERE .
@All,
Bill posted an image of the OI Seabed Constructor track.
Courtesy of SeisIntel, which specializes in tracking seismic surveys and mapping their coverage, here is a .kmz file:
https://www.dropbox.com/s/wh9fb7zkdrtw249/180611-SeisIntel-tracks-Ocean-Infinity-Seabed-Constructor-2018–18AU_01148XX1X.kmz
They also made a tracking demo before the OI survey was complete:
https://portal.seisintel.com/resources/demo/Seabed_Constructor_20180413.mp4
For more details, see: https://370location.org/?s=SeisIntel
The OI coverage swath in the .kmz that I have been using is 150km wide near 34S.
I assume that their technology is more advanced than what ATSB got, with multiple passes over the A1 area.
(Even if it took two tries with ARA San Juan).
I no longer consider my candidates in areas that OI searched as priority sites, even though there is still acoustic evidence to pursue if future searches turn up empty.
The ATSB and GeoScience Australia set up a site to display their scanning data on the web:
https://www.ga.gov.au/about/projects/marine/mh370-data-release
Their interface was hard to reference to my candidates, so to visualize the ATSB seafloor coverage I cobbled together a Google Earth network interface to the online ga.gov.au arcgis datafiles. I shared it with Don about a year ago, but was worried that a public release might overload their servers. I doubt that is a major concern now, but please don’t enable all eleven layers at once:
https://www.dropbox.com/s/rhckh5ec7z5hnvl/190404-Geoscience-Australia-MH370-Survey-Data-Overlays.kmz
What I see for the new IG candidate site is very good coverage, on a relatively flat seabed.
p.s. When talking about the one True Path, I wish that could be qualified as fitted to a straight heading, with the acknowledgement that waypoint or more complex paths could provide good fits.
Also, “following the data” would hopefully include three items of acoustic evidence that were not in the SIR.
@DrB
Thank you, Bobby. I made a plot of both fig. 19 and values from the table you provided (in steps of 0.25 degrees) related to fig. 23 (LRC). They perfectly overlap, probably because the optimal FLs near 180 degrees bearing are very close to FL390. I find the relative high probabilities in the S35.5 – S36.0 range worth a closer look. They are “lost” in the combined probability because of the sharp drop in your “fuel/endurance” probability.
https://www.dropbox.com/s/vtocr1lcprx5mrz/Figs19and23.pdf?dl=0
@George G,
You asked: “Did it become necessary to use Probability of the Aerial Search Not Detecting the Floating Debris Field to weed out (discriminate) one potential path from another ? Or are you simply putting the icing on the cake ?”
Our identification of the True Route does not depend on the aerial search probability, so I would say it was more of the latter (icing on the cake).
You also asked: “Refer to Figure G-8 (and/or Figure 23) of “The Final Resting Place”. The fit of the 176 degree route is certainly not as “nice” a fit as is the fit of the 180 degree route and LRC at FL390, but is it statistically close to the Flight Plan ECON which you have shown (also at FL390) ?”
Figures G-8/23 do not indicate anything at all about the “nicety” of the fit (other than the fact that the best fit at each bearing is a flyable speed setting and altitude). It simply illustrates how the optimum speed setting and altitude vary across the range of possible bearings.
You asked: “Refer to Figure G-9, your Speed Setting Sensitivity Study. Here you have tabled (i.e. plotted) Flight Plan ECON at FL380. I’m sure I don’t quite understand why the results differ ?”
The results don’t “differ”. Figure G-8 shows the optimum speed setting, altitude, average air speed, and average ground speed at each bearing. It shows that at 180 degrees, the best speed setting is LRC and the the best flight level is FL390. Figure G-9 is a separate study, at 180 degrees only. It shows how the route probability varies with speed setting, when the flight level is optimized separately at each speed setting. It also shows that LRC at FL390 is the best speed/altitude combination for 180 degrees initial bearing at 19:41. Figures G-8 and G-9 are consistent with one another.
You also asked: “If there were to be conducted Sensitivity Studies done for the 176 Degree ECON FL390 Route what would be the results ?”
We have not done as many speed combinations at all bearings as we did at 180 degrees in Figure G-9 (which was for illustrative purposes). Clearly, at each bearing there is a value of average KTAS which fits best, and there are usually only a couple of speed settings at high altitude which can provide that true air speed. So, with some practice, it is straightforward to find the best speed/altitude combination by running two or three test cases (i.e., try several speed settings and let the altitude be optimized in each test case). Even when straightforward, it is not quick. Each trial run requires 1-2 hours of work. So, we are talking about 4 or more hours per bearing, with more than 100 bearings. Figure 8 represents a huge amount of time and effort, because the speed and altitude were individually optimized, by trial and error, at each bearing, as they must be to obtain reliable comparisons.
You said: “Concerning your “19:41 Initial Bearing Sensitivity Study” you state: “We believe this narrow central peak at exactly 180.00 ° proves this was the MH370 LNAV bearing.” Please note that a large contributor to this being a narrow peak is the use of the Probability of the Aerial Search Not Detecting the Floating Debris Field method.”
We were referring the the sharp peak in route probability in Figure G7. This has nothing to do with the fuel or aerial search or debris drift probabilities. We believe this unique and extremely sharp peak in route probability is the “fingerprint” of the True Route. It is also apparent that the other probabilities, when considered separately from the route probability, indicate a narrow region at 180 degrees. Thus, the two independent results (route probability and the product of fuel, debris drift, and aerial search probabilities) consistently agree on 180 degrees.
The PDF without considering the route probability is available HERE .
@DrB,
Thank you for your reply.
( Your PDF without considering the route probability clearly shows high dependence on reliance that the aerial search was sure to find signs of debris in the rough seas below. )
I am highly inclined to consider reliance on the route probability combined with the available-fuel to required-fuel comparisons providing limits on reasonable endurance as the main determinants as to where to search in future.
@Richard. In case this has not been brought up before, the Table H-2 3rd “Reporting Date” years look to be based on 2010 rather than 2014.
“….3rd column…” that is.
@370Location said: What I see for the new IG candidate site is very good coverage, on a relatively flat seabed.
That’s simply not true. Please re-read the section from the last article (or Section 8.3 of the report) entitled “Terrain Near the LEP”.
There were definitely holes in the GO Phoenix coverage, some of which were partially covered by Seabed Constructor. Also, the tracks of Seabed Constructor only give a rough notion of the seabed scanned. I’ve relied on the work of Richard Cole to better estimate the path of the AUVs.
@David
The error in Table H-2 has been fixed.
Many thanks for spotting that error.
@all
More blathering as a result of having too much time on my hands “sheltering in place” in commiefornia.
https://docs.google.com/document/d/1S0MAb5aL_mLv-wbSSiaV6saZumqb6_kivMKLJf4lmV0/edit?usp=sharing
@VictorI,
What I meant was that to my untrained eye, it APPEARS from the scans to be well covered.
If you will load up the .kmz I provided, zoom to 34.25S and enable the “sidescan sonar 2014-2015 2k” layer, you will see some holes. Then enable “Fugro Deep Tow Sonar 5m 2k” and “AUV sidescan SONAR 1k”. They went back and covered those gaps.
There remain a few small dropout areas less than 250x750m, which are on smooth seafloor sections. I suspect that someone decided that the time spent revisiting those would not be fruitful.
Visually, the limitation seems to be the mismatched contast of the towed sidescan vs the array that fills the gap below the towfish. I suspect that the computational photography tools used for panoramic stitching could have improved that a lot, without introducing artifacts. But, then again, doctors don’t trust them for enhancing X-Rays.
I must admit that I have no experience with seafloor recovery operations, and defer to true experts.
FYI, in my own research area, I’ve come up with a method of using the CTBTO hydrophone triads to analyze signals below 4 Hz with relatively good bearing discrimination. (Not using wave correlation, but phase differential correlation, similar to instantaneous frequency coherence but without angular unwrapping noise). I believe I am seeing reflections of various events as they traverse the Antarctic coastline, the 90 Degree East ridge, and Broken Ridge. Unlike the proposed Acoustic Gravity Waves proposed by Kadri for finding MH370 at these frequencies, I believe what’s going on is that VLF waves around 1-3 Hz travel farther outside the SOFAR channel, especially in warmer waters. This technique should also work with the restricted data from French OHASISBIO SWAMS triad array near Amsterdam Island, which has wider hydrophone spacing.
@370Location: I am fully aware of the Geoscience Australia data, which I access via their WMS as layers with Google Earth. The steep slopes I reference were covered neither by the GO Phoenix towfish, nor by the AUV excursions. How much of the southern slope was covered by Seabed Constructor and its team of AUVs remains unclear, and cannot be inferred by the path you supplied.
What I have been calling for (both publicly and privately) is an expert review of the existing data in the vicinity of the LEP to assess data gaps and the quality of the existing data, so we are not relying on perceptions from untrained eyes to make decisions.
Authors,
The word “parameter” is used extensively but sometimes inconsistently in the report.
Page 7 introduces “… seven parameters that determine a possible MH370 flight path …” Later there is reference to “route parameters” – presumably these are one and the same?
Page 24 introduces “… flight parameters …” which seem to be the same as the route parameters. On p. 165, there is the phrase “Route Flight Parameters,” which also seem to mean the same thing. However, on p. 81, the term “flight parameter” is used in the disucssion of radar and fuels models, and in this case it seems to refer to the instantaneous state of the aircraft.
Finally, on p. 12, there is the statement that BTOs have random read noise which is uncorrelated with all other “parameters”. Normally, one talks about correlations amongst measurement errors in the data or between those errors and independent variables such as time, not between errors and, say, the route parameters (although one could do so, I suppose). What is intended in this sentence?
I am baffled by Section G.5 – Route Parameter Sensitivity Studies. All of the “best estimate” route parameters are correlated amongst themselves, some quite highly. Yet the only correlation that is discsussed in this section is that between air speed setting and flight level (since it is the combination that determines the ground speed.) Why are other correlations ignored? I have never seen anyone rely on figures such are shown in G-5 to G-7 to study sensitivities when the parameters are correlated. Instead, one normally employs a Fisher information matrix type calculation. If one wants to demonstrate the sensitivity to a particular parameter, that is normally done by “marginalizing” over all of the hidden parameters. You can’t just keep them fixed. Figure G-5 to G-7 give the illusion that the route parameters are tightly constrained, whereas the reality is that they are not, or at least not as tightly as these figures seem to indicate.
@Richard,
I have been considering one of the conflicts in Appendix D between Table D-1 and Tables D-3 and D-4 to be simple text or transposition errors in Tables D-3 and D-4.
For the Pre-19:41 Case 7 Bleed-Air-Off duration, Table D-1 (and Figure 29) and all text mentions within Appendix D have the duration for Case 7 as 1.96 or two hours.
Tables D-3 and D-4 have the Pre-19:41 Bleed-Air-Off duration for Case 7 as 1.1 hours.
I have been considering the use of “1.1” in D-3 and D-4 to be the error. For the Fuel Shortfall of Table D-3 for Scenario 7B1 of only 95 kg (and the probability of 82% in Table D-4) the “1.96 hours” of Table D-1 has to be correct.
I was writing the following:
“Scenario 7B1 differs from Scenario 9B1 only in that the Pre-19:41 Air Packs Off Period is almost 55 minutes (54 mins 50 secs) longer. The tabled difference in Fuel Available is 58 kg. This difference takes the aircraft closer to the estimated time at MEFE by ….” when I guffawed and then wrote:
“… BUT IF HE WAS AT FL385 (or 390) FOR 2 HOURS WITHOUT PRESSURISATION THEN HE WOULD BE NOT IN A GOOD CONDITION BY THE … WHY EVEN ATTEMPT TO CALCULATE ..”
The implication is that if Table D-1 is correct concerning the Bleed Off time Pre-19:41 being 2 hours, then why would the pilot even bother re-starting the air supply for another measly 17 minutes, only to turn it back off again (as proposed by Case 7 and Scenario 7B1) ?
Kate Tee may have seen the aircraft after all.
A hypothesis, as you and your co-authors discuss in your report, is that the pilot shut off the air to the cabin and ascended to (probably) the highest level he could take the aircraft given the aircraft weight at the time. Afterwards, descending to a reasonably low level for a time, say 10,000 feet, makes even more sense if his intent was to proceed until he could send the aircraft on it’s way south. His survival was simply necessary so long as he could negotiate through or past “obstacles”, re-start the engine he had earlier shutdown, for whatever reason, re-balance the fuel in the tanks, and start the aircraft on it’s ascent to a pre-programmed high altitude route. His presence at the top of the climb was not required.
A person planning such a course of action might have quite valid reasons for running simulations before conducting the final flight.
Richard, I suggest you not bother to update the report at this time. I would, however, like someone to produce a set of back-up calculations of the fuel implications of my proposed variation on your FMT Route.
The links should be self-explanatory.
https://www.dropbox.com/s/qgy9wv8v9abne4w/Table%20D-1%20Case%207.pdf?dl=0
https://www.dropbox.com/s/apmp67axny1o8nf/Scenarios.pdf?dl=0
@George
(1) Table D-1 Error and Typo
Thank you for picking up the error in Table D-1 Case 7.
We will change “End of Lateral Offset” to “Cruise at FL385 continues”.
There is another typo, which you did not pick up in Table D-1 Case 6.
We will change “Start of climb o FL385” to “Start of climb to FL385”
(2) Table D-1 Clarification
We will change Table D-1 by adding an option column.
In general 9 Cases/Options are covered in Table D-1 versus 27 Cases/Options in Table D-3 and D-4.
There are no general “transposition errors” between Table D-1 and Table D-3 and Table D-4.
(3) Table D-3 Typo
We will change the typo in the pre-19:41 case 7 bleed air off from “1.1” to “2.0” in Table D-3.
(4) Option B2
An active pilot is needed to function for the 17 minutes to balance the tanks in all options B2.
(5) Case/Option 7B1 vs 9B1
You point out that the difference between 7B1 and 9B1 is 58 kg of fuel. The difference between the two scenarios is that 7B1 has the bleed air off pre-19:41 for 1.96 hours, whereas 9B1 has the bleed air off pre-19:41 for 1.06 hours.
You ask why bother to even calculate case 9B1.
In our view 7B1 and 9B1 are reasonable scenarios to run, as they are the closest to zero fuel shortfall.
We will change D.4.6 from “In Scenario 7B1 the pre-19:41 bleed air off time is consistent with the cabin being depressurised from turn-back to the end of the traverse at 19:24.” to “In Scenario 7B1 the pre-19:41 bleed air off time is consistent with the cabin being depressurised from turn-back to circa 19:24.”
(6) What-If Case/Option 10B3
You suggest a variant 10B3. This differs from Case 8 by having the bleed air off after 17:26 for the whole flight. You have not considered engine restart and fuel balancing requires an active pilot.
We are not a “what if” scenario service provider to the MH370 community.
If a new scenario or variant make sense and we wish to check it out, then we will.
@Richard
Thank you.
10B3 : Point taken, thank you.
You say: “You ask why bother to even calculate case 9B1.”
Sorry, that came across wrong. I was asking myself why calculate the expiration time of 7B1 compared to 9B1 if for 7B1 the pilot or person in the pilot’s seat was expected to last for two hours. Seemed unlikely.
The green box in Figure 51 defines search area A1; this area extends for about 1 degree of latitude, -33.75 to -34.75, when measured along the 7th arc. The box is based on the premise that the LEP is a single point rather than a range of latitudes. However, the bottom panel of Fig 5 shows that there is, indeed, a range in possible latitudes for the LEP. Suppose I convolve that distribution with a boxcar in latitude of width 1 degree, then compute what fraction of the probability is inside the green box. It is only 48%. If I use the probability distribution function that excludes the aerial search results, the fraction of probability in the green box drdops to 35%. The search will need to be extended considerably outward in latitude from the green box in order to achieve coverage of 90% or more.
@sk999,
A “parameter” is defined as a constant, a variable, or a statistic, depending on the context in which it is used. Within its definition, it is not used inconsistently in our paper.
In general, there are seven flight parameters which determine the aircraft trajectory in four dimensions. More particularly, the trajectory during a particular “route” is determined by the “route flight parameters”. This is not a complicated concept.
In addition, it is obvious that instantaneous values of the flight parameters define the “instantaneous state of the aircraft”. There is nothing inconsistent about doing this, either.
The meaning of the statement that the BTO read noise is independent of all parameters besides itself (i.e., all “other” parameters) is obvious. This means the correlation coefficients with all other parameters will have an expected value of zero. This includes the satellite data, the weather data, and the route parameters. This property of the BTO read noise allows one to add multiple statistics to figuring the route probability. Without doing this, unique features like that shown in Figure 19 would be undetectable.
You said: “I am baffled by Section G.5 – Route Parameter Sensitivity Studies. All of the “best estimate” route parameters are correlated amongst themselves, some quite highly. Yet the only correlation that is discsussed in this section is that between air speed setting and flight level (since it is the combination that determines the ground speed.) Why are other correlations ignored?”
There is nothing baffling about it. They are only “correlated” by the (one) data set being fitted. The route parameters are all independent variables which may be set individually by the pilot. The only thing that will “correlate” them is a route fit to a particular set of satellite data, and that correlation will vary from route to route and from data set to data set. The concept of sensitivity studies by adjusting one variable at a time is not a new concept. It is quite useful, whether or not the variables are “correlated” by the data set being fitted. The degree of “independence” of each variable is graphically displayed by the sensitivity studies, wherein one variable is allowed to change while all others are fixed. This is plainly stated, and it should not mislead anyone. Within small ranges, they are essentially independent, but over larger ranges they may not be. These graphs immediately identify which variables are the most critical in optimizing the fit to the data, and what ranges of values can provide an acceptable fit. Correlations among the flight parameters for the MH370 data set were not pursued beyond what we did because they are not predictable and therefore add nothing to finding the best-fit route for the one data set we have. Some of the best-fit route parameters vary systematically with bearing because of the geometry of the problem, and it makes sense in this case to methodically step through the full range of bearings one trial at a time. This assures optimized route fits and illustrates the variations of air speed and fuel for LEPs along the seventh arc. At a fixed bearing, the only remaining significant trade-off among the other fitted route parameters is the one between altitude and flight level, and we devoted a huge amount of time (and two figures in the paper) to understanding this dependence and, in fact, finding the optimum combinations.
You are welcome to try any technique you want, but we don’t see any benefit to doing more complex information studies when we only have one data set. We don’t think there is additional useful information to be had, and therefore what we did is sufficient for the problem at hand.
@George G,
The myriad variations of aircraft configuration we used in the tables in Appendix D were intended to explore the a wide range of fuel options. You have suggested a new “descent” case with right engine shutdown, wherein the bleed air was off from 17:26 onward, and was never turned back on. It is very similar to 8B2, the only exception being the bleed air being off from 18:29 to 19:41. That would save another 80 kg or so in fuel. Based on inputs from our pilot co-author, we think the fuel re-balancing would not begin until the right engine was re-started at the end of the traverse circa 19:24 and just before the climb began. We figured that from 19:24 to roughly 19:41 the left engine would be drawing fuel from the right tank. Near the top of the climb, the tanks would be balanced, and the cross-feed valves would be closed. A difficulty arises during the climb from 19:24 to circa 19:41, if the bleed air were off. We can see that perhaps at FL100 the bleed air could be off but the pilot could breathe more or less normally anyway because of the low altitude. During the climb from FL100 to FL390 the cabin pressure would drop quickly, and the breathing would become labored again, even with the positive pressure oxygen mask. Perhaps that was endured, but it could have been avoided by simply closing the outflow valves and turning the bleed air back on, at least until the level cruise was established at FL390. Your scenario is possible, but we really don’t know what happened.
@SK999
My take on the probability of the wreckage being in A1.
https://docs.google.com/document/d/1S0MAb5aL_mLv-wbSSiaV6saZumqb6_kivMKLJf4lmV0/edit?usp=sharing
@Dennis. And that number doesn’t take into account that the unsearched portion of A1 (the strip most distant from the arc) is also the least likely.
@Paul
I did not weight the probabilty by distance from the arc. I debated it, but did not feel comfortable with a model for that. I do agree that closer to the arc is more likely.
Bobby Ulich,
Parameters are correlated when computing contours of constant chi square (or whatever your figure of merit) in the multi-dimensional parameter space. The correlations are expressed (at least in a linear approximation) by the covariance matrix, which is the inverse of the Fisher matrix (if I have my terminology straight). The square roots of the diagonal elements are the 1-sigma uncertainties in the parameter estimates, properly marginalized. The correlations are not dependent upon the actual measurements, only their statistical errors.
Figure G-5 implies that the start longitude has an uncertainty of about 0.08 degrees 1-sigma; the actual uncertainty is about 0.4 degrees 1-sigma. Figure G-6 implies that the start latitude is known with an accuracy of about 0.1 degrees 1-sigma. The actual value is about 1.2 degrees 1-sigma. Figure G-7, initial bearing, does not have enough dynamic range to estimate the initial bearing uncertainty (although you state that the peak is less than 0.1 degrees wide) but I find that the uncertainty is 2.2 degrees 1-sigma. Of course, none of this really matters. All that matters is the uncertainty in the final latitude along the 7th arc. I find an uncertainty in this latitude of 1.2 degrees 1-sigma. To check this, I ran 1000 simulations where I assumed that the true route was the one derived in the report and generated 1000 sets of random errors to be added to the true BTO and BFO values, then solved for the maximum likelihood route (LNAV mode only). The scatter in the final latitude was 1.1 degrees 1-sigma.
For the record, my maximum likelihood LNAV route using the actual data is essentially the same as the route given in the report, passing very close to BEDAX.
@sk999
“.. then solved for the maximum likelihood route (LNAV mode only)”
Is that with a certain speed setting constraint / only LRC?
@DrB
Thank you.
As I understand it the pilot or person in the pilot’s seat did not to have survive to the top of the climb in a functioning condition.
All that was required was to restart the engine so the climb could be initiated and then re-balance the fuel tanking.
It was also necessary to ensure the Autopilot was be set to climb to FL390 on a pre-determined (simple 180) course.
Your pilot co-author may wish to confirm/deny this.
@sk999. If they were giving out prizes for the most erudite contribution to this blog, then I think yours takes the biscuit. For the rest of us mere mortals (to borrow a phrase from Mick Gilbert) its a bit like a dog watching TV. Chapeaux.
… also necessary to ensure the Autopilot was set to climb to FL390 …
Niels,
I have been using constant Mach, not LRC. For the particular LNAV routes in question, the differences are small, although I am not prepared to say that they are negligible.
@sk999
I have now done both and can say the difference is (as we say) “in the noise”.
I have now updated the paper in the download link in the article above:
1. New Section 8.8 Search Area Coverage.
2. Revised Appendix D with corrected Table D-1, D-3 and D-4.
3. Typo in Appendix F.3 “19:01:03” changed to “19:41:03″.
4. New Appendix G.10 Alternative Objective Function for Route Fitting.
5. New Appendix J.1 Alternative Composite Probability Density Function.
@sk999
You stated “I have been using constant Mach, not LRC. For the particular LNAV routes in question, the differences are small, although I am not prepared to say that they are negligible.”
@Sid Bennett
You stated “I have now done both and can say the difference is (as we say) “in the noise””.
Sid, it is important to appreciate that the LRC speed schedule (used at 180 ° bearing) slows down considerably (from M0.84 to less than M0.80) as the aircraft gets lighter due to fuel consumption, and this reduces the fuel flow late in the flight. However, the fixed-Mach speed schedules at 0.84 and 0.85 don’t slow down as the aircraft gets lighter, so in these cases the fuel flow reduction is less late in the flight.
This effect contributes to the rapid increase in the 19:41 fuel shortfall past 36 °S, because the larger ranges to those locations on the 7th Arc require higher air speeds than LRC. These higher speeds require more fuel, especially so nearing fuel exhaustion.
@Sid Bennett,
The difference in Mach between LRC and M0.84 depends on both weight and Flight Level.
For example, at FL390, the difference is quite small. At 220 tonnes, LRC is M0.840 and at 180 tonnes it is M0.839. So, at FL390 the difference between LRC and M0.84 is small in both air speed and in fuel flow.
At FL350, the story is quite different. Here at 220 tonnes, LRC is M0.840, but at 180 tonnes it is only M0.796. So, at FL350 there is a significant difference in air speed and fuel flow between LRC and M0.84 late in the flight as the weight drops below 210 tonnes.
The 186-degree LNAV route is best fit at FL360 and M0.84. At FL360 the LRC Mach drops from M0.841 at 220 tonnes to M0.810 at 180 tonnes. Therefore, there is a significant difference in air speed and fuel flow between LRC and M0.84 for bearings > 180 degrees when the optimum altitude drops below FL390 down to circa FL350-360.
At 180 degrees, the difference between LRC and M0.84 is small in KTAS and in required fuel. This is demonstrated by our Figure 22, which shows that M0.84 is not far below LRC in route probability.
Richard is correct when he points out the fuel required increases for LEPs past 36 degrees S, because those routes must be flown below FL390, where LRC drops below M0.84 when the weight falls below 200 tonnes. This occurs several minutes after 19:41, so virtually all of the SIO Route is affected.
@sk999,
You said: “For the record, my maximum likelihood LNAV route using the actual data is essentially the same as the route given in the report, passing very close to BEDAX.”
It is good to hear your best route agrees with ours. What is your FOM for determining “maximum likelihood”? Are you using our route probability or something else? If something else, does it include fuel or debris drift or aerial search contributions?
@DrB
Why do you say those (further westerly) routes have to be flown below FL390? just curious.
@sk999,
Does your “maximum” likelihood FOM take into account 4-D interpolated GDAS weather along the route, and have you applied any conditions on the GSEs?
@Authors
I’m still struggling with the GSE concept. For the model ground speed it is mentioned in fig. 35:
“ = Magnitude of vector sum of model TAS (in heading direction) + GDAS wind vector in “To” direction”
What is exactly the “To” direction here?
@Niels: Meteorologists (and aviators) refer to wind direction by where the wind is coming from. We analysts tend to think in terms of the wind vector, i.e., where the wind is blowing towards. To avoid confusion, we sometimes specify whether we are talking about the “from” (meteorological/aviation) direction or the “to” (vector) direction. They are 180 degrees apart.
@DrB
you said:
“Richard is correct when he points out the fuel required increases for LEPs past 36 degrees S, because those routes must be flown below FL390, where LRC drops below M0.84 when the weight falls below 200 tonnes. This occurs several minutes after 19:41, so virtually all of the SIO Route is affected.”
you also said :
“For example, at FL390, the difference is quite small. At 220 tonnes, LRC is M0.840 and at 180 tonnes it is M0.839. So, at FL390 the difference between LRC and M0.84 is small in both air speed and in fuel flow.”
In comparing paths at about FL390, the difference between the two is no difference M.001). Further, I have seen no cogent argument against using FL390 and LRC or CM on the entire route after the FMT.
@TBill,
You asked: “Why do you say those (further westerly) routes have to be flown below FL390? just curious.”
The more westerly the route, the longer is the range.
The longer the ranger, the higher is the KTAS with fixed handshake times.
The higher the KTAS, the higher is the Mach for a given Flight Level.
When the higher Mach is less fuel efficient, then the higher KTAS can be achieved at the same Mach by flying at a lower altitude, where the air is warmer and the Local Sound Speed is higher.
It turns out that once you get past 180 degrees bearing, it requires less fuel to descend several thousand feet to gain the extra KTAS than to stay circa FL390 and fly at a higher Mach.
Routes even further to the west require M0.85, and at decreasing altitudes.
This is illustrated in Figure 23, which displays the optimum combinations of Mach and Flight Level.
Bobby Ulich,
My best fit route does a full nonlinear least squares fit to the BTOR rms, the BFOR rms, and (new to the party), the fuel exhaustion time. My fuel model for this round of fits uses approximations that I made incorportating Boeing’s performance data from the SIR, appendix 1.6E. I note that the fuel burn from these approximations are not entirely consistent with the previous tables that you unearthed up, so caveat emptor.
The adjustable parameters are the start longitude, latitude, Mach, flight level, initial heading, BFO offset, and three wind speed offsets for the last 3 legs. (I assume that the offset for the first leg is accounted for in the initial Mach setting.) These last 3 are, I believe, entirely equivalent to your GSEs.
I have LRC fits that are just as nice as the the constant Mach fits but they run out of fuel too early. However, these were run before I included the fuel exhaustion time constraint, and I haven’t tried rerunning them with the constraint.
My 00:11 position (without any accounting for early right engine fuel exhaustion) for the maximum likelihood route is latitude 33.15S, 93.98E. That is about 16 nm NE of your Figure 16 position. Pressure altitude is FL402. Mach 0.8344. BTOR rms is 36 microsec (you have 34). BFOR rms (after accounting for the BFO bias offset) is 1.7 hz. I think this should be compared to your stdev, which is 2.0 (and I don’t account for n v. n-1). Heading at 19:41 is 179.6 deg. Fuel exhaustion is 0:17:00. The wind speed offsets are all less than 1 knot.
And yes, I do full 4-d interpolation in the GDAS tables (linear only).
@VictorI
Regarding groundspeed calculation
Thank you for clarifying. I’m doing the “reverse” vector calculation as I have a GS available (and bearing), and use this together with wind data to calculate TAS. If this TAS deviates from the targeted TAS, feedback control modifies GS. Initially I had this control loop implemented to follow the BFO curve.
I’m currently comparing my results in detail with your fig. 35. It appears largest deviations develop going from TAS to GS. Possibly through the read-out of wind data (interpolation method?). I have moved to 4D (linear) interpolation, though interpolation for latitude seems less essential for the mainly southerly tracks.
@Sid Bennett,
You said: “In comparing paths at about FL390, the difference between the two is no difference M.001). Further, I have seen no cogent argument against using FL390 and LRC or CM on the entire route after the FMT.”
Our Figure 22 shows the SIO route probability is higher for LRC than M0.84, by about 8%. The fuel required is virtually identical. So, there’s not a large difference after 19:41, but the route probability does favor LRC after 19:10 (as we have predicted for the FMT). There is evidence that the altitude was low circa 18:54, which conflicts with a FMT happening before then.
@sk999,
I have some questions related to your calculations of fuel exhaustion time (MEFE).
1. Are you assuming the bleed air is on or off after 19:41?
2. What FFFs are you assuming for L and R engines?
3. What fuel tank difference are you assuming at 19:41?
4. Are you correcting for single-engine INOP FF for some minutes before MEFE?
5. Are you assuming the fuel cross-feed valves are closed or opened near MEFE?
Other questions are:
6. Why are you using RMS BFOR as a fitting FOM instead of the 1-hour BFOR differences?
7. Are you assuming the Mach is unchanged throughout the whole SIO Route (for non-LRC routes)? If not, how do you allow it to change?
I would also remark that you cannot fly a B777 at M0.8344. The only available speed modes I am aware of being used generally are ECON, MRC, LRC, and fixed Machs in 0.01 increments. So, it would be better to only allow flyable Machs in your fits. The Mach speed setting is not arbitrarily adjustable.
Bobby Ulich,
I am considering none of the effects you mentioned w.r.t fuel consumption. I am only taking the numbers straight out of Appendix 1.6E (which claim to account for the PDA of this particular aircraft) and applying TAT corrections only.
Take differences of 1-hour BTORs? If I understand you correctly, then the differences would have correlated errors that need to be removed, and in doing so you would end up back with the original BTORs by themselves.
Mach is constant. The quantization of Mach is worth noting – thanks. At the high Mach end of the performance charts, small changes (even 0.01) have a significant impact on fuel consumption. Flight level is another troublesome parameter – the least squares fitter will merrily send the plane to unachievable altitudes. All of the adjustable parameter have both priors and constraints, so that is how some degree of control is achieved, but it is partly art and far from perfect.
@sk999, @DrB: The Mach resolution of the MCP speed is 0.001, not 0.01.
Victor,
Thanks. The Qatar FCOM says:
The display range is:
• 100 – 399 KIAS
• .400 – .950 Mach.
So the implication is 3-digits for either mode of speed indication – thus a resolution of 1 knot for indicated air speed or .001 for Mach.
I do not own a 777-200ER, so can’t immediately check and verify.
Victor,
Apologies if the last line of my previous post appeared out of line. Not intended to be so.
@victor
Is this discussion really going anywhere?
The fact remains that the probabuity of the wreckage being in A1 is around 0.3. Do you really expect OI (or anyone else) to search at that probilitity level?
@sk999
@DrB
@Victor
RE: “So the implication is 3-digits for either mode of speed indication – thus a resolution of 1 knot for indicated air speed or .001 for Mach.”
It is possible to select speeds in increments of 1 knot or M0.001, via the MCP or the FMC. However, pilots normally select Mach speeds in increments of M0.01, eg M0.82, M0.83, M0.84, etc.
@DennisW
You asked “Do you really expect OI (or anyone else) to search at that probability level?”
Yes!
OI, ATSB, the NOK and the former Malaysian Government have told us that they are taking our latest paper seriously.
We shared our paper with OI in advance of publishing, at their request. OI are wanting to search again, including our recommended search area A1. OI are willing to review the previous search data from A1. OI have appointed a project manager, who is collaborating with us.
The former Malaysian Minister of Transport promises to visit his successor, following the change of Government in Malaysia and push the case to resume the search and point out the findings from our latest paper. Anthony Loke (former Malaysian Minister of Transport) was present at the 6th remembrance event organised by the NOK and watched the video presenting our findings, which was prepared at the request of the NOK.
When you ask “Is this discussion really going anywhere?”
My answer is, that there are a lot of analysts from the MH370 community, contributing to this blog, who are taking the discussion seriously, running their own models, asking pertinent questions, contributing their relevant expertise and clarifications and all supporting the goal of helping to solve the world’s greatest aviation mystery. Please continue to contribute to the discussion.
@DennisW said: The fact remains that the probabuity of the wreckage being in A1 is around 0.3.
The data in the vicinity of the LEP should to be reviewed. We need input from experts to determine if the data holes and the quality of the data merit another search in that vicinity.
@DrB
“There is evidence that the altitude was low circa 18:54, which conflicts with a FMT happening before then.”
OK I’ll bite. What is the evidence?
Kate Tee might have seen the Singapore AWACS/radar aircraft. Also she saw an aircraft smoking for some reason. PS- Thank you for FL390 explanation.
@George G
RE: “As I understand it the pilot or person in the pilot’s seat did not to have survive to the top of the climb in a functioning condition. All that was required was to restart the engine so the climb could be initiated and then re-balance the fuel tanking. It was also necessary to ensure the Autopilot was be set to climb to FL390 on a pre-determined (simple 180) course.”
Having initiated the climb, the pilot could certainly set the autopilot to climb to FL390 on a pre-determined course; however, fuel balancing requires a conscious pilot to start the process and to stop it once the tanks are balanced.
Fuel balancing is achieved by first opening a cross-feed valve and then switching off the boost pumps in the tank with the lower fuel quantity. Fuel from the opposite wing tank is then used by the operating engine(s). Fuel is not transferred between the tanks and the time it takes to balance the tanks is entirely dependent on the fuel flow of the operating engine(s). When the fuel tanks are balanced, the process is stopped by selecting the boost pumps on and then closing the cross-feed valve.
In scenario 8B2, we assumed the pilot commenced fuel balancing when the aircraft commenced its climb. Given the two-engine fuel flow during the climb, the fuel imbalance would have been corrected at about the time the aircraft reached FL390. The pilot would need to be conscious at that time to reconfigure the fuel system and stop the fuel balancing.
@DrB
” There is evidence that the altitude was low circa 18:54, which conflicts with a FMT happening before then.”
What is said evidence of low altitude?
In defense of @sk999 (who needs no defense) only if our temperature models of the atmosphere are exactly correct is an 0.84 Mach model really 0.84 Mach.
Thank you for the above FL390 explanation of fuel consumption.
@TBill,
You said: “only if our temperature models of the atmosphere are exactly correct is an 0.84 Mach model really 0.84 Mach.”
The GDAS temperatures appear to be accurate to better than 0.5 C, based on comparisons with radiosonde data and our flight model fits. That temperature error corresponds to 0.001 Mach. So, M0.84 should appear to be between M0.839 and M0.841 due to temperature error alone. M0.8344 is 4 times farther away from M0.83 than can be explained by temperature error.
The Kate Tee sighting is evidence of MH370 being at a low altitude circa 18:54. You can decide for yourself how credible it is. I am convinced she saw an aircraft at an unusually low altitude, and this could have been MH370. As far as I know, reports of other planes being at that location at that time are just rumors and suppositions, unaccompanied by data.
@sk999,
You said: “Take differences of 1-hour BTORs? If I understand you correctly, then the differences would have correlated errors that need to be removed, and in doing so you would end up back with the original BTORs by themselves.”
You may have mis-read my comment. I referred to BFORs, not BTORs. Yes, the BFORs are indeed correlated, as a result of OCXO drift. That correlation is mostly removed by taking the 1-hour differences. So, one can use a random number generator to create sets of (uncorrelated) 1-hour BFOR deviations (not to create sets of uncorrelated BFORs, which don’t mimic the real case).
There are two ways in which inserting random BTORs and random BFOR differences can be helpful in understanding the precision of route fitting.
The first thing one can do (and which we both have already done) is to find the best-fitting set of route parameters using the actual BTO/BFO data. Our 7th Arc locations are quite close. That best fit gives you a value for the Figure of Merit (FOM) which is optimized using an Optimization Function (OF). In my case, the FOM is the route probability (or the product of the route and the fuel probabilities). My OF, which is to be minimized, is simply OF = 1 – FOM. So, minimizing the OF maximizes the FOM.
Your OF is some (weighted?) combination of RMS BTORs, BFORs, and a MEFE time error. I will note that minimizing these parameters is, in general, not optimum. One should instead try to make them match their expected error statistics (mean, standard deviation, etc.). It would be helpful in understanding your results to show the exact equation you use for the OF.
The next logical step is to hold the route parameters fixed, and vary the BTORs and delta BFORS using random values with the appropriate statistics. Then one observes the variation in the FOM. In my case, it should have a mean of 50% and a standard deviation of 29% (when using just the route probability for the FOM). It does match that. This result confirms that my probability calculations behave as expected. However, it does not, by itself, tell me anything about the precision or accuracy of the route parameters. That can be done in a next step by observing the route parameter sensitivity curves. How fast the FOM falls off away from the peak value tells me how sensitive the route fit is to that parameter. This sensitivity is related to the precision and the accuracy of the route fit. That relationship depends on the FOM being used.
My FOM involves 9 or 10 statistics, whereas yours uses only 3. Therefore, comparing the sensitivity results must be done with caution, because comparing sensitivities based on different FOMs is comparing apples to oranges. In general, the sensitivity of a given route parameter to the FOM will depend on the FOM. Using more statistics in the FOM leads to better discrimination of the route parameters (and therefore better rejection of non-True Routes). That is, an expanded FOM becomes more sensitive to each route parameter. We see that occurring when comparing your “sensitivities” to mine. I am not surprised my FOM leads to greater sensitivity, and therefore smaller allowable ranges, for each of the route parameters. That is to be expected as a direct result of my using more statistics in the FOM.
The second thing one can do is to actually fit the route parameters to each set of random BTORs and delta BFORs. You have already done this. I have not, because of the slowness of my route fitting method. In this case, we are primarily interested in just one parameter based on the route fit – the 7th Arc latitude. The sensitivities of the other route parameters are interesting to know, but they don’t directly affect a search area recommendation. Your result for the variation of the LEP latitude seems reasonable for the FOM you are using, but I would expect the more complex FOM I am using to have a smaller variation in the LEP latitude. The point is that you can’t legitimately apply individual route parameter sensitivities based on one FOM to the fits based on a different FOM, other than to say the your 3-parameter FOM sensitivities will represent an upper limit on my 10-parameter FOM sensitivities.
@Richard
You said in response to my search expectation query:
“Yes!
OI, ATSB, the NOK and the former Malaysian Government have told us that they are taking our latest paper seriously.”
I too take it seriously, very seriously. Does that mean that I would make a funding decision involving several million USD based on the paper? That is the question I am asking this group and myself. At this moment I do not have an answer.
@DennisW said: Does that mean that I would make a funding decision involving several million USD based on the paper? That is the question I am asking this group and myself. At this moment I do not have an answer.
There is no answer at this point.
We have provided a new methodology to discriminate paths that incorporates a very accurate route reconstruction model along with statistical metrics related to the randomness of the implied measurement errors associated with each reconstructed path. This has led to a fairly small recommended search area. We’ve also provided extensive documentation of all methods and assumptions so that the report can be peer-reviewed.
We’ve also called for a review of all existing and missing seabed data in the vicinity of the LEP.
Most of us believe it is unlikely that Malaysia will read the report and independently call for a new search. There is a higher probability that OI will approach Malaysia, along with the NOK, and negotiate the conditions for a new search. So the possibility of a new search at this point really rests with OI’s assessment of risk and reward.
I expect that within the coming months, OI will be gathering more inputs, and will have a better estimate of whether it’s possible the debris field is in A1 (or A2). Until then, we just have to wait. Any pronouncements of what OI will or will not do is premature.
@Victor
Thx. That is my take on it as well.
@Andrew
Thank you.
You said: “Given the two-engine fuel flow during the climb, the fuel imbalance would have been corrected at about the time the aircraft reached FL390.”
This, the time to balance taking about the same as the climb, explains why in the report you considered that the pilot may have chosen to restore the aircraft pressurisation to normal during the climb.
You said: The pilot would need to be conscious at that time to reconfigure the fuel system and stop the fuel balancing. (Agreed, no argument,)
But, please, let’s consider:
We have a person who previously endured a hypothesised period of just over an hour (63 minutes) at FL390 and survived by using “a large supply of supplemental oxygen and a mask which is effective” [Section D.4.6].
The pilot and aircraft then descended to 10,000 feet, the descent taking virtually a quarter of an hour and flew at 10,000 feet for 40 minutes.
It is considered reasonable that the pilot continued to use oxygen during the descent, and possibly continued to do so whilst at 10,000 feet.
Would that person need to restore the aircraft pressurisation to normal during the climb (17½ minutes) and completion of the fuel balancing (say 20 minutes altogether) ONLY to then switch it off again. ?
@Sk999 Can say what the start time, start location and FL are you using for your simulation?
@VictorI Getting significant figures right (of the decimal point 😉 ) has been my problem since being an undergraduate.
>>>>
Some of us have found that setting a fixed FL and varying the M was a convenient approach to absorbing any small errors in the met model so as to see if the error on a route minimizes and to make quantitative comparisons. That does not mean that the simulation exactly duplicates the physical environment at that time. For the nonce (Br.) all of my comments, except when stated, refer to LRC. The difference with respect to constant M, at FL390, is nil.
@DrB
The statement that the FMT occurred later than circa 18:54 conflicts with your Fig 3 where the path at 18:43 is 180T. Moreover, this line of argument presumes that your path from NILAM to IGOGU is accepted (including the descent). So far as I am aware, there is no evidentiary basis for that assumption during the period from 18:22 to at least the FMT.
@Sid Bennett,
You said: “The statement that the FMT occurred later than circa 18:54 conflicts with your Fig 3 where the path at 18:43 is 180T. Moreover, this line of argument presumes that your path from NILAM to IGOGU is accepted (including the descent). So far as I am aware, there is no evidentiary basis for that assumption during the period from 18:22 to at least the FMT.”
There is no conflict. We believe it is most likely that the FMT occurred circa 19:10. There were probably two turns after 18:43. See the Events Table E-1. Just because the track was at 180 degrees at 18:43 does not mean the FMT occurred before then.
The evidentiary basis is that our FMT Route is consistent with the radar track, with the Kate Tee sighting, and with the practice shown earlier in the flight to turn at and to follow FIR boundaries. This includes the path from IGOGU to NOPEK, which is a FIR boundary. Our FMT Route also arrives at the best-fit 19:41 location on time and at the correct track with no Holding Pattern. If you have an alternate FMT Route that does the same things, please show it.
@DrB
Only if the (initial) FMT at IGOGU is to 180 is it on a FIR boundary. The second turn along a FIR boundary is arbitrary.
For 5 years, the term FMT has been understood to be “Final Major Turn”. Re-purposing it creates confusion. I suggest that you find another neologism for your zigzag path.
Prior to the FMT, the only coincidence noted with FIR boundaries is that at IGARI when the plane first diverted. But it does not follow the convoluted FIR boundary over land. The route seems to me to be direct Penang. It is well off any published air route.
I have not followed the Kate Tee conversation for years, but if this is the newly applied evidence, we need to return to the previous discussions to see why it was previously discounted.
As to an alternate route, I proposed 186 at 18:39:30, LRC @ FL390 (no further maneuvers). I have published my example spread sheet. It does not run out of fuel providing that you do not attempt to join it to your post 19:41 route starting point.
I have also recomputed the paths surrounding the 186 path, increasing the BFO_sd value from 1.0 to 2.0Hz to be consistent with your model and of course this improves the fit.
I am in the process of digitizing you Fig. 17 so that I can compare the temps, wind direction and speed that I use for plausibility.
@DennisW
You asked “Does that mean that I would make a funding decision involving several million USD based on the paper?”
OI, prior to their previous search in 2018, invited us to London on 7th/8th December 2017 for a conference before spending several million USD on a further underwater search for MH370, on a no risk basis for the Malaysian Government. Unfortunately, that search was unsuccessful.
If OI return to the underwater search and this time find MH370, then they will have demonstrated to the world, that they are the unrivalled leaders in the seabed search and salvage business in a multi billion dollar market. The deep sea mining business alone is set to grow to $15.3B by 2030.
Why wouldn’t you make the funding decision?
@Richard
My comfort zone for taking on financial risk is low. I think OI is already highly regarded in the search and salvage business, and taking unnecessary risk might not be in their best interest.
@Richard
Also, when I looked at the OI/Malaysia previous agreement I concluded that OI’s expenses were not tax deductible if they did not find the wreckage.
@DrB
Bobby and team, congratulations on the extraordinarily comprehensive effort.
Re: ‘… with the practice shown earlier in the flight to turn at and to follow FIR boundaries.‘
You’re on very shaky ground with that claim. The aircraft most assuredly did not follow a FIR boundary earlier in the flight. As Sid has noted subsequent to the turnback the aircraft tracked pretty much directly towards Penang. That track was roughly coincidental with what was then a published and well trafficked airway, B219. As has been noted any number of times, B219 (being straight) crossed the Golok River (being serpentine) and therefore the Thai-Malaysian FIR boundary at four places. However, there was never any confusion as to responsibility for traffic on B219; it fell under Malaysia’s ATC Sector 5 Area of Responsibility.
The contention that an aircraft would deliberately track along FIR boundaries to avoid attention is frankly somewhat flawed. To avoid attention you would seek to do what is usual or normal; you would avoid doing the unusual or abnormal. It is not usual or normal for air traffic to track along FIR boundaries; doing so would only serve to draw rather than avoid attention.
Separately, in the paper you make the unconditionally declarative statements ‘The Indonesian Military Radar at Sabang was not operational on 7th March 2014‘ (p.5) and ‘The Indonesian military radar at Sabang was not operational on the night of 7th/8th March 2014.‘ (p.18). How do you know that?
You refer to the possibility of radar detection on p.5 but address it in more detail on p.34 where you state,
‘If unexpectedly, a radar detection was made by Sabang, then MH370 would be deemed as no threat, by following the FIR boundaries and turning due west away from Sabang and Indonesian airspace, at the critical point of possible detection.‘
Surely, this misses the point. If radar detection was made by Satrad 233 Sabang then the entire south-west-south sequence from ANOKO to south of BEDAX would have been observed. The target may not have been deemed a threat but that utterly bizarre manoeuvring would have been at the very least noteworthy, particularly to the military.
And that manoeuvring, all performed under the potentially watchful gaze of a military radar station, is the key element of the old switcheroo from an otherwise unremarkable transit north-west along the Strait of Malacca to the final, ostensibly deceptive track into the Southern Indian Ocean. It’s somewhat akin to a bank robber planning to switch get away cars just outside a police station.
@DennisW. In your 11th March “Additional Commentary” on search probability you found the probability of a find in the A1 searched and unsearched areas was 31%. On 19th March on lifting the search detection probability from its previous 0.8 to 0.9 you arrived at 22.4% probability of a find in those areas.
In the attached I describe another approach using those most recent 0.6 & 0.9 probabilities. That comes up with 39%.
Also, if a priori probabilities of 0.95 & 0.95 were assumed, representative of the ATSB figures, the a posteriori probability of it being in that total area would be about a half, the other half lying outside. The probability of it being in that particualr A1 searched area would be about 8%, though if a high weighting were given to that area it might rise to 80%. Again this is using the ATSB probabilities.
https://www.dropbox.com/s/0srojs876gbpc9w/Bayesian%20search%20probabilities.docx?dl=0
@Richard, DennisW. Enter stage left Covid-19. Ships (and I might add submarines) will need to be careful in screening and what ifs.
Bobby Ulilch,
I stand corrected – difference of BFORs. You state, “Yes, the BFORs are indeed correlated, as a result of OCXO drift. That correlation is mostly removed by taking the 1-hour differences.” That depends on the type of drift. A step-function in the bias offset would, indeed, be largely removed, and that is one application where I have seen differencing is used. A linear drift would result in a constant, non-zero mean value for the differences and so would not be removed. A quadratic drift (such as is introduced by routes that end at the northern limit of the ATSB search zones) would result in a linear drift in the differences. I actually looked at that case some 3-4 years ago. However, differencing also introduces correlations between successive differences due to read noise (+contribution in the 1st difference, -contribution in the 2nd.) As they say, pick your poison.
“Your OF is some (weighted?) combination of RMS BTORs, BFORs, and a MEFE time error.” Weighted – yes. Can’t combine them sensibly otherwise.
“The next logical step is to hold the route parameters fixed, and vary the BTORs and delta BFORS using random values with the appropriate statistics. Then one observes the variation in the FOM.” Actually, the next logical step is to run a maximum likelihood analysis, just like what was done in the report, and determines the final latitude. But you do note that later in your comment.
“Therefore, comparing the sensitivity results must be done with caution, because comparing sensitivities based on different FOMs is comparing apples to oranges.” Agreed in general. But the tall pole is and alway will be the BTORs. They are the best route discriminant. But I haven’t looked in detail at all the other statistics you include. If you have others that are materially useful (and not just repetitive of what we already have), I would be interested to know which ones.
“The second thing one can do is to actually fit the route parameters to each set of random BTORs and delta BFORs. You have already done this. I have not, because of the slowness of my route fitting method.” That is what I bring to the table. I gather that your algorithms are implemented in Excel. I am amazed at what folks are able to accomplish with that tool, but at some point you hit a wall. My algorithms are implemented in code. Getting the algorithms correct is all important, but once you do, code is easy to run fast and in parallel.
“Your result for the variation of the LEP latitude seems reasonable for the FOM you are using, but I would expect the more complex FOM I am using to have a smaller variation in the LEP latitude.” Agreed. But by how much?
@Dennis W. Two changes please. 3rd line should conclude, “….22.4% probability of the wreckage being in those areas.”
3rd para second line should read, “….in that total ATSB area…”
@Sid Bennett,
You said: “For 5 years, the term FMT has been understood to be “Final Major Turn”. Re-purposing it creates confusion. I suggest that you find another neologism for your zigzag path..”
We are not re-purposing it. You are very confused.
The FMT is the LAST major turn made by MH370. We follow that meaning exactly, as the last turn in our proposed route is a 90 degree left turn at 19:10 at 6.0N 93.8E That puts MH370 on a 180 degree true track through BEDAX and then toward the South Pole.
You also said: “Prior to the FMT, the only coincidence noted with FIR boundaries is that at IGARI when the plane first diverted. But it does not follow the convoluted FIR boundary over land. The route seems to me to be direct Penang. It is well off any published air route.”
The diversion and turnback occurred exactly at the FIR boundary, as shown in our Figure 2. The path back to Penang does not follow the (wiggly) FIR boundary exactly, but it does follow it in an average sense when over land and then leaves it when nearing Penang.
You also said: “As to an alternate route, I proposed 186 at 18:39:30, LRC @ FL390 (no further maneuvers). I have published my example spread sheet. It does not run out of fuel providing that you do not attempt to join it to your post 19:41 route starting point.”
Your route turning once to 186 degrees does not match the 18:40 BFOs at LRC. In addition, there is insufficient fuel to fly a 186 degree route, ending near 37.5S, as we have demonstrated in great detail in our paper. The fuel probability is 0%. You cannot get an acceptable fit to the satellite and GDAS data with LRC at FL390 at 186 degrees. A higher air speed is needed at and after 19:41. The best combination is M0.84 at FL350. The significantly higher FF needed to fly significantly faster than LRC at FL350 (as I discussed previously) makes it impossible to achieve MEFE at 00:17:30.
You are beating a dead horse.
@sk999,
You said: “But I haven’t looked in detail at all the other statistics you include. If you have others that are materially useful (and not just repetitive of what we already have), I would be interested to know which ones.”
You will find a list of what we use in Appendix G.1. They all appear to be useful.
Also: ““Your result for the variation of the LEP latitude seems reasonable for the FOM you are using, but I would expect the more complex FOM I am using to have a smaller variation in the LEP latitude.” Agreed. But by how much?”
I’m working on running a limited number of random trials to get a handle on the dispersion of LEP latitudes with my FOM. I now have random BTO and BFO generators in my program that I can switch in to use instead of the satcom data. I have also verified that the statistics and route probability estimate they produce match the expected values (mean, standard deviation, etc.).
I will ask again, what is your equation for the FOM used in your fits?
@DennisW. My regrets. One correction made also to the dropbox expansion, at its para 5.
@David
All good.
@Mick Gilbert said: The contention that an aircraft would deliberately track along FIR boundaries to avoid attention is frankly somewhat flawed.
I’ll let the other co-authors speak for themselves, but my opinion is that MH370’s path was selected to minimize the occurrence of military interception, in addition to providing deception for the final trajectory.
Over the Malay peninsula, it flew at maximum speed as it tracked an inbound path towards Penang Airport that would have been similar to what would be needed for an instrument approach to Penang’s RWY 04, and therefore deemed “friendly” by military radar operators. The active runway at the time was RWY 22, but the approach to that runway would have come much closer to Butterworth, and would therefore be more likely deemed hostile.
Over the Malacca Strait, the plane remained in Malaysian airspace until it reached the boundary between Malaysian and Indian airspace at IGOGU, and turned south. It then traversed the Indian-Malaysian boundary, posing no threat to the Andaman and Nicobar Islands, and then west along the Indonesian-Indian boundary, posing no threat to Sumatra, before turning south and crossing into Indonesian airspace, but on a non-threatening, southern trajectory away from Indonesia.
The low altitude around Sumatra made radar detection difficult, which both minimized the probability of an interception, and also helped to hide the final southern trajectory to the SIO.
@Mick Gilbert
I agree with Victor’s assessment. It was all about deception and avoidance of interception.
Here are a few more detail points in response to your comments.
(1) Diversion at the FIR boundary between Kuala Lumpur (Singapore) and Ho Chi Minh.
You say we are on shaky ground with our claim concerning FIR boundaries, but the Malaysian SIR documents the confusion caused between the Vietnam and Malaysian ATC in full detail. That part of the plan worked very well.
(2) Turnback over Malaysia along the FIR boundary between Kuala Lumpur and Bangkok.
You say the aircraft “most assuredly did not follow a FIR boundary earlier in the flight.” I agree that MH370 followed close to the former flight route B219. I apologise that we did not include this flight route in Figure 2, but we used the current SkyVector chart and the flight route is no longer in use. B219 was used between 2011 and 2017 initially for flights between Kota Bharu (VKB) and Penang (VPG) and later also for en-route traffic to Penang from Vietnam, Hong Kong and China.
Here is a link to the old SkyVector chart from 2015, that shows flight route B219. As you can see it follows the FIR boundary between Kuala Lumpur and Bangkok. To state otherwise, as you do, is misleading.
https://www.dropbox.com/s/vk48a14qup2olyl/Malaysia%20Airspace.png?dl=0
(3) Malaysian Military Radar.
The Malaysian Military Radar data has not been published. But the DSTG were given the data and state that MH370 was tracked every 10 seconds from 16:42:27 UTC to 18:01:49 UTC. The Malaysian Military were aware, if they were watching, that MH370 diverted and crossed Malaysia, but they claim that they did not try to intercept MH370. That part of the plan worked as well.
(4) Indonesian Radar at Sabang.
Regarding the operational status of Sabang radar, you ask “How do you know that?” The answer is that it was confidential information under a private non-disclosure agreement from an official source. We know that Sabang was not operational and there is circumstantial evidence, that ZS knew that fact as well.
You further state “The target may not have been deemed a threat but that utterly bizarre manoeuvring would have been at the very least noteworthy, particularly to the military.” The first problem with that statement is, that the Indonesian military were not watching. The second problem is that the route is not “utterly bizarre”, it fits the timing and BTO at the 2nd Arc, it fits the fuel used, it fits the BFO data during the first call and all without a holding pattern. Please show me your FMT route that fits the BTO, timing, fuel and BFO data!
Bobby Ulich,
The figure of merit (actually, chi square) that goes into the least squares is the weighted sum squares of the BTOR and BFOR, with weights of 29 microsec and 2.8 hz respectively, plus the time of fuel exhaustion (I’ve been using 17:00). Iniitially I used an rms scatter on that time of 3 minutes (to account for all the possibilities that you have enumerated) but then found I could reduce it to 1 minute and still find a good solution. Additionally, for each adjustable parameter in the fit, I add a term that is effectively a prior “measurement” of that parameter with its own weight. The prior “measurements” for the route parameters, which are the starting values for the least squares, come from a previous grid search of those parameters and are simply there to keep the least squares fitter from sending them off to nonsensical values. The weights are kept loose (e.g., the starting longitude is 93.3 degrees, with a “standard deviation” of 30 degrees.) The one exception to diffuse priors is the flight level (which I parametrize as the index of the pressure altitude in the GDAS table) which is assigned a small standard deviation to keep it from reaching unphysical values. (The starting value is about FL400). The wind speed error parameters are given priors of 0 with a standard deviation of 2 knots.
I do not include either the mean of the BTOR or the mean of the BFOR as statistics in the FOM. The offset bias of the BTOs is known from the value when the plane was at the gate in KL and is thought to be stable for a flight, so there is no reason to allow it to float. The offset bias of the BFOs is accounted for by including it as yet another parameter in the fit with a prior given by the value at the gate in KL and with a standard deviation of 2.3 hz. This latter is derived by examining the in-flight shifts in the BFO bias for both the MH371 and Mumbai flights, where we have gate values both before and after the flights.
@sk999
I would not reference the Mumbai flight as an example of the advisability of using BFO as a flight path metric.
@sk999,
Thanks, Steve, for the explanation of your FOM for route fitting.
I do a similar thing in EXCEL as your “prior measurements”. For instance, the EXCEL nonlinear minimization algorithm often starts with a 10% step in non-zero parameters. Sometimes that is far enough that one of the calculations blows up. So, for a number of the sensitive parameters (FL, longitude, etc.) I fit a delta to a nominal value. This keeps the calculations valid and without errors, so it can converge. By the way, the EXCEL nonlinear minimization routine is finicky and very slow to converge. That’s the kindest thing I can say about it. Usually I can can get there faster by running several fits of parameter subsets. You really can’t just tell it to adjust all the parameters and walk away. It’ll never get there in many cases. It seems to get stuck, perhaps at a shallow local minimum, but sometimes it is clearly not at any minimum, local or global. It just stps converging. Usually I can see which parameter is off, and a manual iteration gets it moving again. So, I have to run each fit in multiple stages, and this is time consuming for me to do. It usually takes several hours per trial. If I could start over, I wouldn’t use EXCEL, although I have to say it is very handy for doing the simple subroutines, but poor for fitting 10 or more parameters.
@sk999: Have you looked at the correlation factor of the BTORs to see if there is a trend near the peak and away from the peak?
@Richard
Re: Sabang- A person on Reddit is trying to say there is also civil radar at Sabang that would pick up approx. 60-nmile radius…I gave up arguing with the guy. I realize they may have other radars (WITT etc) but we do not think they were up and running, right?
@DrB
I am preparing a summary of the my current position and hope to complete it in a few days or less.
I do not have to accept your premise that the route to 180T identified as starting at 19:22 (your table G-1) is the only such route that can be found. I assure you there is a similar route starting at 19:22 (at a different lat/long of course)that reaches the 186T intersection with the 6th arc. Moreover, it joins exactly to a LRC route at 186 starting at IGOGU at 18:30:30. My horse lives!
When we discussed this some months ago, the problem was that I did not care what the FL was, and adjusted the M for minimum error. The that the intersection of the path with the 6th arc is required at 00:11 is a defacto constraint on maximum range as we know that the fuel is exhausted prior to 00:19. This determines the ground speed. Having been criticized for not having used a fuel model per se, I ran cases for Barry’s LRC fuel model and found that somewhere between 390 and 410 would give the appropriate ground speed and endurance.
I have provided bits and pieces of this before, but I see that it is necessary to provide a more extensive discussion and I am preparing that.
With respect to the radar data. Richard says that Indonesian radars were inoperative and that a private source indicated that ZS knew it.
If the Indonesian radars were operating during the times in question, the plane would have been observed over the Straits of Molocca. No such observation was reported. So we should not expect any detections at a later time, unless the Indonesian radar data was entirely suppressed.
Sid
“With respect to the radar data. Richard says that Indonesian radars were inoperative and that a private source indicated that ZS knew it.”
Richard did not say that.
@Sid Bennett,
You said: “I do not have to accept your premise that the route to 180T identified as starting at 19:22 (your table G-1) is the only such route that can be found. I assure you there is a similar route starting at 19:22 (at a different lat/long of course)that reaches the 186T intersection with the 6th arc. Moreover, it joins exactly to a LRC route at 186 starting at IGOGU at 18:30:30. My horse lives!”
I never said our FMT Route was the ONLY route to get to the 19:41 position for the SIO Route.
However, I have been unable to find any route which turns directly off N571 (offset or not) to 186T and matches the necessary (to match the 19:41 to 00:11 satcom data) 19:41 location at 186T without additional turns or a holding pattern in between. You are welcome to try.
Please provide the positions and altitudes versus time to back up your claim. While you are at it, please show how the 18:40 BFOs are also matched by your route.
@Mick Gilbert, @Sid Bennett, @DennisW, @TBill
Indonesian Radar
What we can say is that we have talked with a former official who was part of the MH370 investigation, who believes the Indonesian radar records were blank, because the radar was not operating, when MH370 passed near Sumatra.
@DrB
Richard did say “Regarding the operational status of Sabang radar, you ask ‘How do you know that?’ The answer is that it was confidential information under a private non-disclosure agreement from an official source. We know that Sabang was not operational and there is circumstantial evidence, that ZS knew that fact as well.”
If I quote, I quote. If I paraphrase, I paraphrase.
For the nonce, since it suites my view, and since I respect Richard’s need for protection of confidential information, I take the statements as factual.
@DrB said:
“Please provide the positions and altitudes versus time to back up your claim. While you are at it, please show how the 18:40 BFOs are also matched by your route.”
I have shared versions of this spread sheet before with Richard and others. However, there are multiple modes of operation of which this is the LRC at 39000ft, starting at 18:22 with a PDA=1.0. It is not intended to be used without some understanding of one or two quirks when actually using the spread sheet, which have been left in for code stability purposes and which I work around.
https://www.dropbox.com/scl/fi/s4i4rjhpqn4dzv6mhzvv0/186BSMv7-10-4-1-rFMT186LRCtest1.0pct-PDAadjFMT1_work-copy.xlsx?dl=0&rlkey=1ook1t4tojttpc22u3ry6w92d
Your paper strongly implies that there is only one last leg from 19:22 that, when joined to the path at an earlier time, meets the fuel criteria and the error criteria for a plausible route.
I cannot agree with you based on the spread sheet referenced above.
@Sid Bennett
You state: “I have shared versions of this spread sheet before with Richard and others.”
That statement is true, but misleading. I have not seen this version of your spreadsheet before and it is quite different.
I have already responded to you in private and on this blog with my critique of previous versions of your spread sheet. I will now respond to the latest version of your spreadsheet.
You incorrectly set the PDA to 1.0% and the ZFW to 174,000 kg. You do not account for the fact that the right engine uses 1.5% more fuel than the left engine.
You show fuel exhaustion at 00:12:15 UTC and not 00:17:30 UTC, demonstrating that there is insufficient fuel for your proposed flight path, even with your incorrect settings.
Correcting the PDA to 1.5% and the ZFW to 174,369 kg in your model, results in fuel exhaustion at 00:09:15 UTC, which is an even worse fuel shortfall of 741 kg, according to your own calculations.
Bobby, Victor and I have each built models independently of each other. Our 3 models agrees very very (repeat intentional) closely with each other. These models have been validated with a number of test cases. Bobby and Victor have both previously pointed out to you, that there is insufficient fuel to reach your end point of 37.67°S 88.98°E. Your own model shows you there is insufficient fuel to reach your end point.
In addition, your model is inaccurate and inadequate for the purpose:
1. Your model only includes the weather data to the nearest integer latitude and longitude and does not interpolate to the exact latitude and longitude.
2. Your model does not interpolate the GDAS data for time between 15:00, 18:00, 21:00, 00:00 and 03:00 UTC and only considers GDAS data at 00:00 UTC.
Our models perform a quadrilinear interpolation in 4D on the GDAS data.
Our models do not assume any particular start time, start latitude, start longitude, altitude, navigation mode, speed mode or Initial bearing. We have tested all combinations.
We have simulated over 2,300 different flight paths and the LNAV180 LRC FL390 is unique.
You are stuck on one flight path based on an inadequate model, which even according to your own model does not have sufficient fuel.
To use @DennisW terminology “you are beating on a dead horse”.
CORRECTION:
@Sid Bennett
Your model includes the weather data to the nearest integer latitude and longitude and now includes a linear interpolation to the exact latitude and longitude, but only at each pressure altitude from 150 hPa, 200 hPa and 250 hPa and only at 00:00 UTC.
@Richard
As I mentioned yesterday, I am preparing a paper which tries to place the studies I have done in context. I am responding to you now so that the readers of the blog may better follow the arguments when reading it.
Richard said ,and my responses are interspersed [ ]:
@Sid Bennett
You state: “I have shared versions of this spread sheet before with Richard and others.”
That statement is true, but misleading. I have not seen this version of your spreadsheet before and it is quite different.
[On March 16, 2020 I posted the link to the spread sheet using the LRC and PDA =1.0 to the IG mailing list. All of the authors of your paper are included.]
I have already responded to you in private and on this blog with my critique of previous versions of your spread sheet. I will now respond to the latest version of your spreadsheet.
[Ultimately I concluded that you would not appreciate the results computed at a constant M, so I finally performed the computations for LRC referred to above, even though the granularity of ground speed would be greater. Fortunately the 39kft altitude (about 200hPa) the ground speed at M=.84 turns out to be satisfactory.]
You incorrectly set the PDA to 1.0% and the ZFW to 174,000 kg. You do not account for the fact that the right engine uses 1.5% more fuel than the left engine.
[Well, if the right engine uses 1.5% more fuel, what does the left engine use? I believe our PDA is for both engines. It is a little less precise than your model.]
You show fuel exhaustion at 00:12:15 UTC and not 00:17:30 UTC, demonstrating that there is insufficient fuel for your proposed flight path, even with your incorrect settings.
Correcting the PDA to 1.5% and the ZFW to 174,369 kg in your model, results in fuel exhaustion at 00:09:15 UTC, which is an even worse fuel shortfall of 741 kg, according to your own calculations.
Bobby, Victor and I have each built models independently of each other. Our 3 models agrees very very (repeat intentional) closely with each other. [And therefore redundant. The use of multiple models serves as a check on a possible computational error but does not improve the accuracy if the models are substantially the same.] These models have been validated with a number of test cases. Bobby and Victor have both previously pointed out to you, that there is insufficient fuel to reach your end point of 37.67°S 88.98°E. Your own model shows you there is insufficient fuel to reach your end point.
[In Fig. 29 of your paper ,case 9, for example, you state the predicted fuel at 19:41 as 26,507kg. At cell R11 of the main tab of the spread sheet, the FOB is 26,591. Starting with the ZFW as a standard of comparison is not as precise as your computed FOB for the various cases.]
In addition, your model is inaccurate and inadequate for the purpose:
1. Your model only includes the weather data to the nearest integer latitude and longitude and does not interpolate to the exact latitude and longitude.[In a later post you acknowledge that Barry’s spread sheet does do interpolation. So far as I am aware, it has had this capability for years.]
2. Your model does not interpolate the GDAS data for time between 15:00, 18:00, 21:00, 00:00 and 03:00 UTC and only considers GDAS data at 00:00 UTC.
[I have prepared a comparison of the winds and temperature that you use in Fig. 17 with the spread sheet data and show the comparison in a document availible here:
https://www.dropbox.com/s/s093bjfzoh4fvlb/comparison%20with%20Fig.%2017_032620.pdf?dl=0
Note that since the 186T path is further South than the 180T path at 19:40, the plane experiences the effect of the environment at a later time for the 180T case.]
Our models perform a quadrilinear interpolation in 4D on the GDAS data.
Our models do not assume any particular start time, start latitude, start longitude, altitude, navigation mode, speed mode or Initial bearing. We have tested all combinations.
[Nor did ours assume a particular location except for the position of the plane at 18:22]. The path is the result of hundreds (probably thousands..I never counted) of trial paths so as the refine the current path estimate.
We have simulated over 2,300 different flight paths and the LNAV180 LRC FL390 is unique.
You are stuck on one flight path based on an inadequate model, which even according to your own model does not have sufficient fuel.
To use @DennisW terminology “you are beating on a dead horse”.
I expect to post a draft of my findings in several days.
@Sid Bennett said: Well, if the right engine uses 1.5% more fuel, what does the left engine use? I believe our PDA is for both engines. It is a little less precise than your model.
2.25% for the right and 0.75% for the left would be a good place to start. The average PDA would be 1.5% and the difference would be 1.5%.
@VictorI
A quick adjustment of the PDA to 1.5% changes the FOB estimate at 00:11 from +125kg to -65kg. Such precision would seem to be unnecessary unless we were using the results to inform our understanding of the behavior after fuel exhaustion.
@Sid Bennett: You were discarding 0.5% of fuel flow because you didn’t understand how the average PDA for the two engines could be 1.5% coincident with a difference of 1.5%. Now you say a refinement of 0.5% is “unnecessary” instead of accepting the correction.
A wise man once told me that there is no use in trying to persuade somebody that doesn’t want to be persuaded.
@Sid Bennett
Fuel exhaustion was at 00:17:30 UTC and not 00:11:00 UTC.
A quick adjustment of the PDA to 1.5% changes the FOB estimate at 00:17:30 UTC according to your spreadsheet from -548 kg to -741 kg.
We discarded all flight paths with a fuel shortfall of greater than the 2σ fuel prediction error, which is 427 kg (please see Appendix D and Table D-2 in our paper).
@VictorI
Sorry if I read your post too literally. But in order to be exactly comparable, isn’t the use of 1.5% for both engines a reasonable estimate.
The fuel consumption at 00:11 is about 107kg/min with both engines. You estimate the maximum continuous thrust of the left engine at 74kg/min (para A.12).
If I had anticipated this attack on the details of the fuel model, I would have run the model at 41kft and somewhere around 185.8T and had about 90 kg fuel remaining at 00:11. So, the additional 6 minutes of fuel to get to 00:17 would be about 370kg and we would predict a shortfall of about 280kg.
You are insisting that all of the parameters match those which you use in order to be credible. I realize that you have devoted an enormous effort to the paper, and it provides me with a wealth of detailed information to better place my study in context.
If you really are open to the possibility that there is more than one plausible path, you should look at this more carefully. You have all of the parameters that I use and the only question seems to be the altitude of the flight if it indeed was at a fixed FL. You should compute it yourself.
I am lazy, Did you consider the discrepancy total arising from using a fixed passenger weight? 🙂
@Sid. I have a lot of sympathy with the your affinity for paths towards the southern end. What I cannot understand is why you have settled on 186 in particular. As IG, ATSB, DSTG showed way-back-when, there is a whole spectrum of more or less equally good paths from a BTO fit perspective. I also don’t understand why you favour a theory that ends up in a zone that has been thoroughly searched.
@paul
You might well ask the same question of the boosters of 180T or other areas that have been suggested. ATSB/DSTG defined the search area statistically, whereas Richard I and some others of the have studied discrete plausible paths.
I did not settle on 186 in particular. The spread sh3eet did after a consensus was reached that the plane flew on N571 until it turned south. The spread sheet indicated that the turn needed to occur between 18:35 and 18:40. Using that result, the solution space of times and azimuths were computed to determine the path and FMT time with the least error.
I realize now that using a constant M at an arbitrary altitude solely to obtain the required TAS did not satisfy others, but the selection of a reasonable altitude (e.g., 39kft made the difference between LRC and M=.84 to obtain that TAS minimal.
A number of other paths have been suggested and I have studied fragments thereof, just as Richard did in his broad survey. But the proponents of the other paths have not been able to make a convincing argument starting at 18:22.
Implied in my stubbornness is a belief that the crash site lies further from the 7th arc than has been searched. I have held this view for a long time and argued it on the IG mailing list years ago. I may be wrong, but then again….
Do you have a particular path to suggest? If it is reasonably doable with Barry’s spread sheet I will try it.
I have spent the day answering comments on this blog rather than working on my paper, but will attempt to proceed as rapidly as possible.
You may well ask why I am making my comments now. I made them before, but I did not have the wealth of detail that the recent paper provided. What was it they used to say in English classes? “compare and contrast”.
If I have made an error or unfounded assumption, let me know. If there are two plausible paths to the 7th arc, there may be more.
@DennisW. Your, “..all good..”.
Thanks and I note that you have adjusted your March 21st probability of the wreckage now being in A1 area from 31% to 46%.
That was drawn from the probability of it being in the search area of 0.6 and the probability of it being found if there of 0.8, 80% of the search area being searched.
A continuing problem with that is that solution overlooks the remaining area, with a prior probability of 1 – 0.6 = 0.4. A posteriori that would become 0.4/(1 – 0.6*0.8) = 77%. That plus 46% makes a total post probability of greater than 100%, at 123%.
After further head scratching, herewith I believe is a satisfactory solution. I use your 21st March probabilities.
Points:
• As you had them, prior, the probability of it being in the searched area of 80% of A1 was: 0.8*0.6 = 0.48; in the 20% unsearched A1 area a quarter of that at 0.12, those two adding to the 0.6 probability in total.
• Outside A1, the remaining unsearched area had the remaining prior probability of 0.4 as above.
• Post, the probability that of it now being in the 80% searched area still would be: 0.48*(1 – 0.8)/(1 – 0.48*0.8) = 0.15584
• The prospect of it being in the 20% unsearched area would be; 0.12/(1 – 0.48*0.8) = 0.19480
• The prospect of it being in the remainder of the unsearched area would be; 0.4/(1 – 0.48*0.8) = 0.64935
• 0.15584+ 0.19480 + 0.64935 = 0.99999.
• QED?
In summary, the new search prospects for the different areas are:
• The 80% of A1 searched area, 16%.
• The unsearched A1 area, 19%.
• All the area outside A1, 65%.
So, an A1 search probability of 35%.
Even so, I am confused. As I understand it you established a 60% probability for A1 from your histogram of Dr B’s route then as I see it you calculate what the probability would be that the wreckage was there after a search, as if Dr B’s probability applied before the last search.
@Sid. There are a great many plausible paths to the 7th arc – and that is the nub of the problem! We have a positive embarassment of solutions.
Since you ask, my preference is similar to yours but based on an earlier FMT. Depending on exactly when and where, you end up somewhere between 39.3S and 39.8S when you reach the 7th arc. I have come to the view that neither debris drift models nor BFO preclude a solution this far south.
Fuel inadequacy (using Dr B’s model) is a greater challenge – there seems to be an unbridgeable shortfall. I am currently chewing this aspect over to see whether I can come up with any possible explanation (apart from a straight-line drift-down, which I guess might do it).
@David
Yes, I am assuming DrB’s et. al. probability does not include adjustments for previous searches.
@DennisW. Then your (and my calcs) are looking at the probability that the wreckage is in the A1 area should a further search there fail.
@David
I am not sure about you statement. My probability calculation is for the probability of finding the wreckage should a new search be undertaken.
@DennisW. On second thoughts I withdraw it.
35% I believe.
@paul
If you take an approach such as DSTG did, there are certainly many paths, but most of them are not coincident with any physical path. If you have a proposed path with a specific turn to the SIO, I will try to simulate it.
As for the fuel model, I contend that the difference between my calculation and one which DrB would have made for the same route is minimal. I explained that previously today. The spreadsheet fuel model assumes that the two engines have the same PDA. The fuel consumption after about 00:11+ is shown for two engines and my post adjusted it for one engine at max continuous power.
My preference for 186 and a single FMT goes back to the original IG calculation of a recommended hot spot and my earlier calculations were a part of the ensemble used.
@paul
If you have a specific path that you are interested in, I will attempt to simulate it with the same spreadsheet.
@David
We have had a long history of analytical predictions – some six years worth now. The latest is indeed a Herculean effort, but it is hard to ignore history. Especially for an old guy like me.
Having said that, my inclination is to continue the search North along the 7th arc from 25S.
I have read some compelling arguments for a more Southerly location, but they are difficult to entertain considering fuel range.
@Sid, that is kind of you to offer but no need. I am also using Barry Martin’s model but have adapted it to operate in 5 second steps with time-interpolated Wx for specific flight levels, plus some other minor tweaks.
@ paul smithson
I was looking for your old report – had a copy but can’t find it in my computer. Do you have a link please.
@DennisW. Mr Bayes can help with a couple more questions.
As previously, using your 0.8 probability that the wreckage would have been found if in the area of the previous search, the probability of it being found in a search now of A1 would be 35% by my estimate. But supposing that 0.8 were 0.95, ie indicative of what the ATSB expected, what difference would that make?
By my estimate (workings available) the 35% would drop to 26%.
Also, if a search of A1 were conducted now with that same 0.95 prospect but unsuccessfully, the probability of the wreckage being in A1 remaining your estimate of 0.6, what would be the likelihood that it would be in A2 or A3?
The likelihood of it being outside A1 would be 98%. Were then it assumed that the prospect of it being in A2 or A3, rather than elsewhere, is 90%, that translates to an 88% probability of it being in one or the other.
However I think you would take issue with that assumption.
Again, in the above there is neither weighting nor consideration of probability density (ie per unit area) but these simple formulae and analyses do add some insight all the same I think, thank you.
@David
I am not ready to embrace a terminus very far from the 7th arc. The data simply does not support that conclusion. I regard it as a creation by the authors of the latest report to justify (the wreckage not being found) and expand their terminal predictions.
I used 80% detection probability as a conservative number to recognize Victor’s claims of terrain masking.
@ Dr B.
https://mh370.radiantphysics.com/2017/02/16/more-analyses-of-mh370-data/#comment-213
In the post referenced above, you introduced the requirement to compensate for temperature in calculation of fuel flow at the rate of +3% per 10C TAT and that this is a matter of physics rather than specific engine design. Could you please provide a citation for this?
In the same post, you go on to note that the combined effect of the temperature adjustment and PDA renders latitudes 37S-38S unreachable. In fact at this point you concluded that endurance to 00:17:29 was impossible except at best holding speed, although your figure also suggests that MRC at FL390 could get you there for a PDA of 1.5%.
However, in ATSB’s “MH370 – Flight path analysis update, Oct.2014” p9/15 Figure 2 indicates that the MRC boundary intersects the 7th arc at 38S. Similarly, in “MH370 – Definition of underwater search areas Dec. 2015 pp20-21/28 we are told that (assuming constant altitude MRC, BTO-compliant path models, prevailing winds, historic engine efficiencies) “The Boeing analysis gave a series of ranges and time intervals for different cruise altitudes. It was noted that a constant altitude of FL350 or higher gave sufficient range to reach the region on the arc corresponding to the DST Group analysis.”
Regrettably, we can’t see the details of the Boeing models and predictions. However, considering the remarks above, it is clear that their model must be several percentage points different in predicted fuel flow.
I realise that since then you have put in many more hours on refinement and validation of the fuel model. But as far as I’m aware, this fundamental difference in predicted endurance/range capability remains. How could this difference be accounted for?
@Sid Bennett
You shared your worksheet MAIN on:
March 25, 2020 at 3:40 pm.
Your fuel usage shows remarkable agreement with that of the BRVA report.
Remarkable in that your estimate FOB [RR] at 19:41:30 at Line#337 is tabled as: 26536 kg. Compare this with 26565 kg at 19:41:21 for Case 7 and Scenario 7B1 of the BRVA report, which produces the best (lowest) fuel shortfall of the Scenarios of that report. Refer Table D-3.
You run out of fuel just after 00:12:15. Refer MAIN Line#1420 87135 (secs) FOB [RR] at Column#GJ where just 5 kg is remaining. Compare this with Scenario 7B1 of the BRVA report, where the time at MEFE is approximately 00:16:32 (my estimate, not tabled in the report).
Even more remarkable that there is reasonable agreement between your fuel usage and the BRVA report considering that for the PDA for 9M-MRO you have only assumed 1.0%. Refer MAIN Cell FY16.
The word that Mick Gilbert used concerning the BRVA report, “comprehensive” is perhaps an understatement. The amount of gathering together of threads of information to produce the analysis and report is impressive. Concerning fuel usage by the aircraft, the reported use of historic records of previous flights and the initial part of Flight MH370 would seem unarguable. The use of 1.5% PDA (the two engines combined) seems unarguable.
Taking your tabled fuel flows or fuel tankage and applying the 1.5% PDA in lieu of 1% implies the following:
1. Initial fuel at time reported by the last ACARS message: 43,800 kg at 17:06:43
UTC; (for reference only, you have rounded this to 17:07)
2. Your estimate of fuel remaining at 19:41:30: 26536 kg;
3: Difference: 17264 kg consumed since time reported by last ACARS;
4: 17264 x 1.015 / 1.01 = 17349 so the revised estimate of fuel remaining at 19:41:30 is 26451;
5: Yes the revision only amounts to 85 kg equivalent to about 48 seconds flight time.
Applying similar arithmetic to consumption of the fuel remaining, or to all of the fuel consumed since 17:07, the overall reduction in endurance is approximately (just over) two minutes. This revised estimate for your analysis has the engine running out of fuel within a minute of, but before, the time of the sixth “arc” transmission.
@George G
Fuel exhaustion was at 00:17:30 UTC. Sid’s model shows a fuel shortfall of 741 kg (GJ1441), when you set the PDA to 1.5% (FY16) and the ZFW to 174,369 kg (GA6).
As I mentioned previously, we discarded all flight paths with a fuel shortfall of greater than the 2σ fuel prediction error, which is 427 kg (please see Appendix D and Table D-2 in our paper), with which you are intimately familiar, having spotted a number of typos!
@GeorgeG
Thank you for the careful assessment of the fuel modeling. Make a copy of the spread sheet as a working copy and change the PBA to 1.5 if you wish.
Yes, the correspondence with the UGIB paper is close (Do the authors prefer BRVA? If so I will alter my reference.). The only thing that has changed from the spread sheet that I have been using for years is to change from constant M to LRU and altitude from 350 to 390.
I don’t want to comment in detail as I am devoting my effort to the paper I mentioned previously.
I am computing the last leg of the 180T path so as to compare the two starting at 19:22). If they compare closely, the other last leg fuel models in UGIB can be adopted.
Our fuel model assumes that the two engines operate at the same PDA and would run out of fuel at the same time, without fuel balancing of some kind. In practice, taking account of the difference in PDAs, once the first engine fuel is exhausted, the fuel consumption of the second engine increases somewhat, but the overall time to complete fuel exhaustion increases.
Also, and I don’t know if it is significant, but the one engine could run out shortly before 00:11 without impairing the 6th arc ping.
Back to work on the paper….
@paul smithson,
You said: “I realise that since then you have put in many more hours on refinement and validation of the fuel model. But as far as I’m aware, this fundamental difference in predicted endurance/range capability remains. How could this difference be accounted for?”
I suspect that part of this difference lies in the assumed route between 17:07 and 19:41. After 19:41, we are using a Boeing LRC fuel flow table with the standard correction for TAT. So, it’s hard to see how our fuel flow calculations can be far off the mark. However, we have found, fairly recently, that the actual air speed after the turnback and until reaching Penang, was M0.87. This is based on our analysis of the civilian radar data. As far as I know, nothing like this air speed was assumed in Boeing’s calculations of the fuel available at 19:41. Therefore, the substantially higher fuel flows required crossing Malaysia will reduce the fuel we calculate as being available at 19:41, and this will noticeably reduce the range and therefore the latitude limit on the 7th Arc. Since no details sufficient to independently calculate the fuel following Boeing’s assumptions were given, it is impossible to compare their fuel at various points along the route.
In addition, Boeing’s fuel modeling was intended to bound the range problem. That’s why Boeing used MRC. Our goal is different – we predict the fuel required to achieve a best-fit route. West of 34S the air speed needed to match the satellite data is LRC and higher. That means that the there is at least a 1% lower SAR in our LRC (and higher) air speed than the MRC air speed in Boeing’s assumption. I am not ctiticizing the MRC choice back then. That was the appropriate choice to bound the problem when they had not yet assessed the probability that MRC could match the satcom data. Now we have determined that much higher speeds than MRC are required to the west of circa 180 degrees track.
So, our available fuel calculations at 19:41 are roughly 1% lower than Boeing’s, and our required fuel at 19:41 is at least 1-2% higher than Boeing’s because you can’t fit the satcom data there at MRC; it requires LRC and higher air speeds. So, there is at least a total 2-3% reduction in range in our fuel calculations compared to Boeing’s, with about a third of that occurring between 17:30 and 18:00 and the rest occurring after 19:41. In both both cases the cause is the need for higher FF because of the higher Mach needed to fit the civilian radar data and the satcom data.
You also said: “In the post referenced above, you introduced the requirement to compensate for temperature in calculation of fuel flow at the rate of +3% per 10C TAT and that this is a matter of physics rather than specific engine design. Could you please provide a citation for this?”
You can look at HERE ( or go to https://en.wikipedia.org/wiki/Thermal_efficiency ) for the equation for the Carnot efficiency of a heat engine, which is equal to [ T(H) – T(C) ] / T(H). Here T(H) is the temperature of the heat into the mechanical engine. For a turbofan engine this is the temperature of the air/fuel mixture after it is burned. T(C) is the environmental temperature into which the heat from the engine is exhausted (i.e., the air temperature). Now T(H) must be limited by the engine design and metallurgy to fixed value to maintain engine life. So, the engine efficiency (how much work it can do with the heat available) is proportional to a constant minus the air temperature. So, when the air temperature rises, the engine efficiency drops, and the lower efficiency must be compensated by a higher fuel flow to provide the required thrust. So higher air temperature causes higher required fuel flow. It seems intuitive that a heat engine is more efficient when the difference between the internal and external temperatures is greater. Warmer outside air reduces this temperature difference, and this reduces the engine’s efficiency, which must be made up by higher fuel flow to provide the required thrust.
You also said: “In the same post, you go on to note that the combined effect of the temperature adjustment and PDA renders latitudes 37S-38S unreachable. In fact at this point you concluded that endurance to 00:17:29 was impossible except at best holding speed, although your figure also suggests that MRC at FL390 could get you there for a PDA of 1.5%.”
That post was 3 years ago, and since then I have made many improvements in fuel modeling. I am still in agreement with the fact that there is insufficient fuel to reach 37S-38S, although the underlying reasons have changed somewhat.
Dr B. Thanks for the detailed response. From the above, it appears that you are saying the engine burns 3%/10C TAT more fuel to produce the same thrust (TSFC).
But are there not other variables at play here? With increased temperature we also get a (linear) reduction in air density. Drag, in turn, has a linear relationship to pressure (for a given Reynolds number). To make matters more complicated, I gather that the Reynolds number also changes with temperature.
On top of all this (for the purpose of kg/NM rather than kg/minute calculations), we have the change in local speed of sound with the sqrt of temperature, leading to higher TAS for given Mach, and drag being proportional to square of the speed. All of this is well outside my comfort zone and I am quite unsure how all of these factors combine together.
But, in short, if temperature changes are we not going to have a different thrust requirement? In which case it would not be correct to simply apply a TSFC correction factor for temperature while ignoring its effect on drag.
Above should read …Drag, in turn, has a linear relationship to pressure *density*
@DrB/Richard/Victor,
Philosophical musings.
I find the current situation very interesting relative to methodology. I have spent a quite bit of time over years reading about the “frequentist” approach to PDF versus “Bayesian”. In most cases the approaches converge, but the real statistical purists (savants) caution that they are quite different, and answer fundamentally different questions. I am not smart enough to follow their arguments and nuances.
I would characterize the recent paper as a frequentist approach as opposed to the DSTG Bayesian approach – both impressive pieces of work. However, the results truly are very different. Frankly, it would have never occurred to me to use a frequentist approach to the MH370 terminal PDF.
Anyway, good stuff, and very thought provoking.
@paul smithson: You are making this all too complicated. The 3% per 10K TAT increase in fuel flow (recommended by Boeing) includes the effect of density and viscosity changes from the standard atmosphere on both thrust and drag (including the Reynolds number effect). It is true that mileage decreases less than 3% per 10K TAT because TAS increases with temperature. But since we calculate TAS (using the OAT) and endurance (using the fuel flow), mileage is implicitly included in the analysis.
@victor. What I am trying to understand is what your “temperature-adjusted fuel flow” actually applies to. Is it TSFC? Mach? TAS?
The compensation makes an adjustment on the thrust side of things but that same temperature change also makes a difference to drag – and hence to thrust requirement to maintain a given speed.
@paul smithson: The LRC (and holding) tables list the value of fuel flow and Mach number(or IAS) for a given weight and pressure altitude. The 3% per 10K TAT deviation corrects the fuel flow when the OAT (and hence the TAT) deviates from the ISA temperature. That fuel flow deviation is due to changes in both TSFC and drag. The TAS of course will change for the same Mach number due to the temperature offset from ISA.
I suspect the response is “it simply increases LRC fuel flow, in kg/minute, period”.
But if that statement refers to LRC speed mode and the LRC selects mach according to weight/altitude, and that optimal mach will be affected by density/drag… you’ll see what I’m getting at.
So, do you think an LRC table for ISA+10 would look identical, except for the increased fuel flow 3%? Would the Mach/weight/FL relationships remain the same?
“except for the increased fuel flow 3%” – understood that this is per 10C TAT, not ISA delta
@paul smithson,
Yes, at non-ISA SATs, the LRC fuel flow table (for a given FL and weight), with 3% added per +10C in TAT, would be the only change. This corrects for both the TSFC and for the changed drag. The desired LRC Mach for a given FL and weight does not change with temperature, but the KTAS and the FF do.
Thanks Dr B. I shall pause and reflect!
@Paul
You said:
“Thanks Dr B. I shall pause and reflect!”
I think that is questionable… I still just “burst out” with anything I am thinking at the time. Pros and cons to each approach. I think forward progress is maximized by the “bursting out” mind set, and I encouraged it in my working career.
@Sid Bennett,
@Richard,
Sid, my intent was an independent reality check. If the 186 path you were proposing was not verifiable concerning available fuel, then there was no need to proceed with any other analysis, simple or in depth.
Sid, you wrote: “Our fuel model assumes that the two engines operate at the same PDA and would run out of fuel at the same time”
They don’t do that, sorry they didn’t, and in general they don’t. The likelihood of having two engines with identical fuel consumption is miniscule. [OK, my use of that word may be arguable.]
Hence it becomes necessary to make an estimate of the difference between the engines as well as of the overall fuel consumption. Fortunately, fuel consumption information for 9M-MRO was available.
The matter of individual fuel flows becomes of significance when estimating overall fuel endurance (i.e. when the second engine ran out of fuel) and in consideration of likely end-of-flight scenarios.
Sid, you also wrote: “Also, and I don’t know if it is significant, but the one engine could run out shortly before 00:11 without impairing the 6th arc ping.” It is significant. And I know [I think] the matter of when the SDU would run out of power has been thoroughly discussed previously in Victor’s blog/s, but I am not going to hunt for the information (I have not saved it) when someone (say Richard or Victor) could answer immediately. As I understand it, fuel runs out, engine runs down, AC power generation ceases during initial part of engine run-down, SDU becomes non functional.
Richard, Thank you. You wrote: “Sid’s model shows a fuel shortfall of 741 kg (GJ1441), when you set the PDA to 1.5% (FY16) and the ZFW to 174,369 kg (GA6).”. Comparison with my simple calculations shows the effect of the increase in ZFW from 174,000 to 174,396, resulting in increased drag and fuel flow, affects fuel consumed by about 50 kg in the time after 17:07 UTC on the 7th March (after having taken account of the PDA). The effect on estimated fuel exhaustion is significant. (Almost half a minute earlier). But any estimates of final fuel exhaustion for Sid’s model must now be tempered by “Our fuel model assumes that the two engines … would run out of fuel at the same time”.
Richard, yes the impact of the 2σ fuel prediction error, 427 kg, is clear in context of your report. As I said above, a reality check.
Richard, you write: “Fuel exhaustion was at 00:17:30 UTC.” In other words that is your estimate. In Section 5.4 the report reads: “the APU takes approximately 60 seconds to provide electrical power.”. Of interest might be the uncertainty in the time to start of the APU, but, admittedly, this should be a relatively minor factor.
@DennisW
Commendable approach. You had me “bursting out”
@Richard,
In your earlier discussion with Sid you mention that the “correct” zero fuel weight should be 174,369kg. This matches the value shown in SIR Table 1.6D Aircraft weights.
When we look at the ACARS messages 16:41 through 17:07 which provide aircraft gross weight (lbs) and fuel weight (kg) we find quite a variation in implied zero fuel weight, from 174,055 to 174,204; in all instances rather lower than the 174,369kg value.
Notwithstanding quantisation of the fuel weight estimate, I am puzzled why the ACARS-derived weights vary so much and why – on average – they imply a ZFW that is about 250kg less than the value in table 1.6D.
@Authors
Is it correct that you used the “Holding” Mach / FF values for FL100?
For the temperature do you use about 16 K above ISA conditions at FL100?
If so, one could “gain” some fuel available at 19:41 by descending to for example FL200 (in stead of FL100) and at the same time reach a 19:41 latitude slightly further south (0.6 – 0.7 deg further south). A quick estimate would suggest that subsequent 181 deg bearing LRC path should be feasible in terms of fuel available vs. fuel required. Possibly such approach could be followed to slightly higher FLs (200 – 300 range) and slightly larger post-19:41 bearings?
Furthermore, I’m looking at alternative routes, like turning directly towards BEDAX at 216 degrees track, from approx. 7.408, 95.217 at around 18:33, with and without a descent after 18:41. Main issue there seems to be to make the connection between pre and post-19:41 paths (for the “fuel feasible” candidates).
@George G
I agree with you that it is unlikely that the engines shut down at the same time. But right now the fuel model needs to be adjusted such that so that one engine needs to shut down first. That aspect needs further work.
Paper will be ready soon. (Different cultures have different meanings for “soon”, but I hope to post it today.)
@Sid Bennett said: I agree with you that it is unlikely that the engines shut down at the same time.
Actually, if there was a conscious pilot, manually opening the crossfeed valves when the fuel levels were low would ensure that the engines flameout at nearly the same time. This would also maximize the range, if that was the intent.
Note that, assuming no PF, unless both engines shut down within a few milliseconds, there would still be a residual rudder bias following MEFE due to the TAC function, surely causing a turning descent, decreasing in radius as it descended. Of course, a live PF could cause any kind of Post FE path.
@paul smithson
I agree with you that the ACARS data is difficult to align with the ZFW.
We are told that the ZFW was 174,369 kg in the SIR, but there is no evidence like a copy of the fuel log to support the statement.
We are given some of the fuel planning documents in the RMP report, but also not the actual figures from refuelling or fuel log.
The ACARS weight is to the nearest 100 lbs (45.36 kg) and the ACARS TOTFW is to the nearest 100 kg.
The ZFW entry in the cockpit was assumed to be 174.4 MT as only 1 decimal place is allowed.
But what the actual ZFW was, we cannot be sure given the lack of data.
We discussed this issue at length as co-authors and decided the only safe basis was to accept the ACARS TOTFW at 17:06:43 UTC as 43,800 kg ± 50 kg.
This is included in the fuel prediction error budget in Appendix D.
@ALSM
The descent kernal used by the DSTG linked below. You can bet they had a lot more input from Boeing than we ever had. It is one of the reasons I hold on to notion of terminus close to the 7th arc.
https://photos.app.goo.gl/8KsYdjxQcZAJYsTk8
https://www.dropbox.com/s/qrj6nx7xlhf78rz/MH370%20Report-0322920.pdf?dl=0
Here it is. It covers bot too little and too much, but I hope that it will lead to a useful discussion.
“bot” = both
@Sid
Did a first pass. It is an interesting read. You write well.
You did make some misallignments in your text references to figure numbers on pages 11-12, but it did not distract from understanding.
Your terminus agrees quite well with the DSTG terminus.
My assumption is that your cost function would have the same general characteristic if BFO was not used.
I am not qualified to comment on the fuel model you used.
@Ventus45. I think that the expiry of that domain has rendered my old report unobtainable. That is probably a good thing since I no longer subscribe to key aspects of the argument that I made at the time, or the conclusion advocated. In case there is something specific you were looking for, please holler. I don’t mind if Victor shares my email contact with you.
@DennisW
Thank you for reading the paper and for your comments. I will fix the problem if in a future draft.
I would say that it fits well with the IG terminus. If memory serves, we were there first.
You are correct that in the region of interest the cost model is much more sensitive to BTO errors than BFO errors. But, for paths that are not correct, the BFO error sticks out. So, if there are paths where the BTO would give a false result (if there are any) the BFO would be the safety net.
As for the fuel model, it gives similar results as UGIA for a base case. In the general area we are talking about, the variation with azimuth should be slow, and it effectively defines a range from, for example, IGOGU.
(As for the errors in the fig references, practice patent law as a “retirement” job and I tell inventors who point out mistakes that at least it shows that you read the specification I drafted for you 🙂 )
@Sid,thank you for providing your write up.
I am still uncomfortable with your preference for 186T on the basis that:-
1) there is a whole spectrum of paths that are not materially inferior from the point of view of BTO fit. So going for a precise “cost minimum” isn’t compelling if the optimum is quite shallow.
2) the zone around this has already been searched thoroughly.
A few other points:
1) The further one goes from 1822, the greater the uncertainty in time/lat/long introduced by the range of possible speeds and headings before the FMT. By the time you get to ~1839, how do you pick the right combination of lat/long/time to run your path models?
2) I am extremely dubious about the 1822 “last radar”. Firstly, it is completely implausible that there was a singular capture. As I understand it, a radar will normally need to sweep a target more than once before registering it. And why should it disappear again after a single sweep? The position is a good fit for an extrapolation of the LIDO path (never officially acknowledged) but arrives at the first arc about 100 seconds too early – requiring an exquisitely-timed “jink” (having followed N571 without a care in the world up to that point) to cross the arc at the correct time. I’m also intrigued by the fact that the penultimate “military radar” position perfectly matches Butterworth LKP plus 6 cycles @4 seconds (which I gather is the typical target coasting). I guess since Butterworth is a military airbase, they could call that PSR “military radar” even if most pundits take that to mean Western Hill. Even the Butterworth PSR LKP needs to be treated with caution unless the timestamps have been corroborated against other sources to confirm that they are zeroed against UTC.
3) If your model makes an instantaneous turn, you will end up at the turn exit approximately 60s later than turning through an arc to the same position. That kind of difference in “start time” makes a material change to the speed required to fit your path and possibly to the quality of path fit overall.
4) I don’t think it is legitimate to substitute TT for LNAV (or perhaps I misunderstood you?) except for 180 – where the two coincide. Otherwise, the bearing of a great circle path gradually changes, makes a material difference to BTO fit compared to true track.
I came to the conclusion that running paths from 1822 and simply looking for the best fit FMT was a fruitless task. There are just too many variables in the air to be able to pin it down. A “wrong” path solution can start to look right, or right enough, if you fool around sufficiently with a combination of azimuth/speed/start time, not to mention weather at different altitudes.
@paul smithson
RE: “I am puzzled why the ACARS-derived weights vary so much and why – on average – they imply a ZFW that is about 250kg less than the value in table 1.6D.”
In my opinion, the discrepancies you noted are probably caused by the different methods used to derive the weights in the ACARS reports. The gross weight is taken from the FMC, which uses the zero fuel weight entered by the crew during the preflight preparation and the fuel quantity calculated by the FMC. The fuel weight, on the other hand, is the weight reported by the fuel quantity indicating system (FQIS), ie the sensed fuel quantity.
At engine start, the FMC takes a snapshot of the sensed fuel quantity and then uses fuel flow to calculate the fuel quantity remaining. It is very common to see a difference of several hundred kilograms between the sensed and calculated fuel quantities, with the calculated quantity typically lower than the sensed quantity. The gross weight and fuel weight reported by ACARS cannot be used to reliably determine the zero fuel weight.
@Niels,
You asked: “Is it correct that you used the “Holding” Mach / FF values for FL100?”
Sort of. Both the Holding and INOP Holding speed tables we use are from Boeing, and they are in KIAS, not Mach. They are identical in KIAS values.
We also use Boeing FF tables for Holding and INOP Holding. Of course the INOP FF values differ from the Holding FF values.
You also asked: “For the temperature do you use about 16 K above ISA conditions at FL100?”
Figure E-11 shows the Delta SAT from 18:43 to 19:23 is just a bit over +15C.
You said: “If so, one could “gain” some fuel available at 19:41 by descending to for example FL200 (in stead of FL100) and at the same time reach a 19:41 latitude slightly further south (0.6 – 0.7 deg further south).”
This is true, but you could gain more fuel by not descending at all. I will say again that I don’t think any of the maneuvers were driven by saving fuel. If fuel saving was a prime motivator, why fly across Malaysia at MMO? Why fly out the Malacca Strait at LRC? Why descend and then climb back to cruising altitude? Indeed, why fly into the SIO at LRC instead of MRC? Nothing in the MH370 route after the diversion suggests fuel saving was a factor. Instead, avoiding interception, laying a false trail, and then hiding the turn south from radar detection were accomplished.
You also said: “Furthermore, I’m looking at alternative routes, like turning directly towards BEDAX at 216 degrees track, from approx. 7.408, 95.217 at around 18:33, with and without a descent after 18:41. Main issue there seems to be to make the connection between pre and post-19:41 paths (for the “fuel feasible” candidates).”
If a turn was made straight to BEDAX, then you will arrive at the 19:41 position far too early. You must either fly a zig-zag path before then or do a Hold for several tens of minutes.
@paul smithson
Understood, but I would still like to re-read it – if possible.
I am also happy for Victor to give you my email.
Re: ZFW
Several of us were recently studying ZFW offline (Ventus, David and I). We had some minor questions, but decided there was no major discrepancy. I had started to estimate fuel vaporized due to ascent, but did not complete the calc due to the small numbers. But that is now back on my to-do-list in case a smaller number is of interest. Just air pressure would be I think about 700-lbs difference from ground, but I do not know how that is factored into the equations.
@TBill: I would be careful about tinkering with the ZFW. Remember that the fuel factor (FF) corrections are calculated from historical data of fuel consumption, and those calculations include an estimated value of ZFW. Unless there is reason to believe that MH370 had an atypical weight profile (e.g., passengers and baggage were heavier or lighter than other flights), I’d accept the ZFW (and the FF) as correct.
@paul smithson
Please find my comments below. Your questions are helpful.
1) there is a whole spectrum of paths that are not materially inferior from the point of view of BTO fit. So going for a precise “cost minimum” isn’t compelling if the optimum is quite shallow.
**Please propose specific paths, including the BFO. The graph of fig 6 is the rms error of each of the parameters normalized by the expected measurement standard deviation. It is smooth and sharp, especially in the BTO with a LRC fuel model. Not much wiggle room there.**
2) the zone around this has already been searched thoroughly.
**Only within a fixed distance of the arc. Also coverage was not 100%. Completely excluded piloted flight. The same can be said for 180, but with a smaller area covered.**
A few other points:
1) The further one goes from 1822, the greater the uncertainty in time/lat/long introduced by the range of possible speeds and headings before the FMT. By the time you get to ~1839, how do you pick the right combination of lat/long/time to run your path models?
**A large number of simulations were run at regular azimuth and time spacings and the minimum cost for each time interval determined (at whatever azimuth). That led to the results recapitulated in:
https://www.dropbox.com/s/0zv2zivx0asbp47/Sept19Report.pdf?dl=0
starting at para [0020].**
2) I am extremely dubious about the 1822 “last radar”. Firstly, it is completely implausible that there was a singular capture. As I understand it, a radar will normally need to sweep a target more than once before registering it. And why should it disappear again after a single sweep? The position is a good fit for an extrapolation of the LIDO path (never officially acknowledged) but arrives at the first arc about 100 seconds too early – requiring an exquisitely-timed “jink” (having followed N571 without a care in the world up to that point) to cross the arc at the correct time. I’m also intrigued by the fact that the penultimate “military radar” position perfectly matches Butterworth LKP plus 6 cycles @4 seconds (which I gather is the typical target coasting). I guess since Butterworth is a military airbase, they could call that PSR “military radar” even if most pundits take that to mean Western Hill. Even the Butterworth PSR LKP needs to be treated with caution unless the timestamps have been corroborated against other sources to confirm that they are zeroed against UTC.
**The LIDO data have never been acknowledged. By the same token they have never been disowned. They have been ignored. I take this as confirmation. The slide looks like a time lapse replay of data selected for those tracks not having transponder tags. Only the time tag.**
3) If your model makes an instantaneous turn, you will end up at the turn exit approximately 60s later than turning through an arc to the same position. That kind of difference in “start time” makes a material change to the speed required to fit your path and possibly to the quality of path fit overall.
**Some years ago I modeled the turn in detail. It did not meaningfully affect the results. But I needed to reduce the number of data inputs to meet the spreadsheet format.**
4) I don’t think it is legitimate to substitute TT for LNAV (or perhaps I misunderstood you?) except for 180 – where the two coincide. Otherwise, the bearing of a great circle path gradually changes, makes a material difference to BTO fit compared to true track.
**It It would be expected if ISBIX were the last waypoint and should no be excluded as a possibility.It should be explored further**
I came to the conclusion that running paths from 1822 and simply looking for the best fit FMT was a fruitless task. There are just too many variables in the air to be able to pin it down. A “wrong” path solution can start to look right, or right enough, if you fool around sufficiently with a combination of azimuth/speed/start time, not to mention weather at different altitudes.
**My calculations as reported above lead to consistent results. Perhaps it is a question of methodology.**
**Let’s bound the problem. Due to fuel considerations any valid path has a maximum range which differs only slightly if the plane passes through a similar environment. The eyeball length of the 186 path from 18:22 to 00:11 is 2775nm. So go to GE and draw a direct path from the location at 18:22 to the 6th arc. I get:
38°40’3.23″S 85°25’29.10″E
I am sure that it can be done more accurately, but I see that location as the most furthest South possible location.**
It is interseting to observe the evolution of the analytics used to derive an MH370 terminus.
In the early Duncan days, the preferred method seemed to be a trial an error route selection based on minimizing the differences between modeled BTO and BFO and the recorded BTO and BFO data. Sid’s latest paper builds on that theme with a more formal use of a cost function. The fact that he derives a terminus near the early IG terminus is not sursprising.
A major departure was the work of the DSTG using a Bayesian approach. It also produced results similar to Sid’s and the early IG work. I am still struggling with the nuanced differences between Bayesian and frequentist analytics.
Along comes what I call the frequentist probability approach taken by the UGIB group. Their result is a major shift of the terminus to the North based on multiple path evaluations, a highly refined fuel model, and other data including debris drift and debris search observables.
There is a fourth approach not really appreciated by the hard core techies. I would call it the motive based terminus. I tend to lean in that direction. It is based on why the diversion was done, and what choices would be made on that basis. It leads to a terminus even further North than the UGIB conclusion based on the Cocos as a last resort bail out. In the past I also modeled a Christmas Island path with the same underlying attribute.
I have also noticed a shift to the consideration of a possible dive-glide-dive end of flight scenario which was not embraced by the cognoscenti in the past.
What a fun ride. Thank you, Victor.
@Paul Smithson
Continuing on the back of my envelope, I computed the intersection of a rhumb line originating at ISBIX at 185.98 and intersecting the 6th arc at 36deg 24 min 20 sec S and 89 deg, 33 min 47 sec E and found that the position was about 30nm further east on the 6th arc than my base case GCP. In addition the path length is 2210nm and I measured the base GCP case at 186T to be 2230. It would arrive at the 6th arc about 3.7 minutes earlier.
I am sure this can be done better.
@DennisW said: A major departure was the work of the DSTG using a Bayesian approach. It also produced results similar to Sid’s and the early IG work.
Inherent in all three models is the preference for paths with few maneuvers, which leads to a terminus around 37.5S latitude. (The Bayesian model allowed more maneuvers, but the a priori distribution for the number of maneuvers preferred a small number.) If the objective is to find the simplest path that results in BTO and BFO errors within acceptable limits, while ignoring fuel, drift, and aerial search results, we would today arrive at the same terminus as the IG did back in July 2014.
The problem is that terminus is not consistent with the available fuel, nor with the drift model results. I don’t see how that is overcome.
@DennisW said: What a fun ride. Thank you, Victor.
You’re welcome.
Although…the ride is slowing down. Contributors here might have some remaining questions about the report, but I don’t see a lot of new information or new insights surfacing. OI has our recommendations, and maybe the recommendations of others. Other than revisiting the sonar data near our LEP (or near other preferred locations), there is not a lot more to do.
@Sid Bennett
I have read your paper and have the following comments and questions:
1. FMT
You state you chose to terminate the lateral offset at IGOGU and start the FMT at 18:37:45 UTC at a position 7.6001°N 94.5468°E and an altitude of 39,300 feet, about 9.2 NM north east of IGOGU on a bearing of 057°T. The FMT is completed at 18:39:15 UTC, just 10 seconds before the call starting at 18:39:55 UTC. I find that too much of a coincidence.
You state that radar avoidance is not presumed, but at 39,300 feet the FMT is in full view of the Thai Military radar at Phuket and the Indonesian Military radar at Lhokseumawe. How do you explain that radar operators in two countries failed to see MH370 turning south near IGOGU?
2. Incorrect Model Comparison Start Altitude
You start your model comparison of our 180°T route near waypoint BEDAX at 19:22:45 UTC (not 19:22:52 UTC) at an altitude of 39,000 feet.
In our paper, we state, that there was a traverse at FL100 and the climb begins at 19:23:50 UTC after waypoint BEDAX was passed. At 19:22:45 UTC MH370 was at FL100, not 39,000 feet.
3. Incorrect Model Comparison Altitude from 19:41:21 UTC
Your model comparison of our 180°T route uses an altitude of 39,000 feet throughout.
In our paper, we state that the climb ends at 19:41:21 UTC at FL390 or a geometric altitude of 41,207 feet.
4. Incorrect Model Comparison Positions by 22:14 UTC
Your model comparison of our 180°T route states that MH370 position at 22:14 UTC is 17.8042°S 93.7600°E.
In our model, the MH370 position at 22:14 UTC is 17.5728°S 93.7876 °E.
Between 22:14 UTC and 22:24 UTC, your model shows the wind direction from changing from 83.8°T to 272.8°T and effectively reversing.
By 22:14 UTC you are already 0.24° of Latitude out, because you ignored the climb back up to FL390 and you use incorrect wind speed and wind direction calculations.
5. Incorrect Wind Speed and Wind Direction
Your model comparison of our 180°T route calculates the wind speed and direction for the position of MH370 at 22:14 UTC, but using the GDAS data at 00:00 UTC.
There is a significant difference between 22:14 UTC and 00:00 UTC.
There is a huge difference between the timespan from 16:41:43 UTC to 00:19:37 UTC and the timespan from 00:00 UTC to 00:00 UTC. In our model we interpolate the wind speed and direction for the position, altitude and time. You are ignoring the time dimension.
Between 22:14 UTC and 22:24 UTC, your model is out by 1.8 knots of wind speed, out by 48.7°T of wind direction and out by 3.75 minutes in the time of the reverse of the wind direction, because you use GDAS data only at 00:00 UTC.
In your view, what was the wind speed and direction at each minute between 22:17 UTC and 22:25 UTC for the LNAV 180 flight path from BEDAX between 18.0°S 93.787575°E and 19.0°S 93.787575°E?
In your view, did MH370 pass through the eye of the anticyclone slightly to the west (wind from the north giving a tailwind) or slightly to the east (wind from the south giving a headwind) on this flight path?
To say there is a match in your Figure 10 is nonsense. To say we have got the wind direction wrong, when you ignore the time dimension is hypocritical.
You show in your Figure 13 and 14 the Tailwinds from 18:00 UTC to 24:00 UTC for both paths, but these are based on the winds at 00:00 UTC only! Your model positions may be between 18:00 UTC and 24:00 UTC, but the wind is stuck at 00:00 UTC. These Figures are only correct at 00:00 UTC, a bit like an old broken pocket watch will show the correct time twice a day.
6. Incorrect Fuel Calculation
You claim that the fuel surplus is 119 kg as shown in MAIN S16 at 00:11:00 UTC.
In our model the fuel exhaustion is at 00:17:30 UTC (as I already pointed out to you) and not at 00:11:00 UTC.
00:11:00 UTC is the time at which MH370 passes the 6th Arc. This has nothing to do with fuel exhaustion, it is the time of a satellite ping.
Your model of our 180°T route does not account for the fuel required to climb back up to FL390.
In our model we account for the fuel required to climb back to FL390, which is 1,847 kg.
Once again you are trying to compare apples with oranges and flog a dead horse, but I enjoyed your mention of “satellite debris”.
@DrB
Thank you for your reply, and for clarifying.
I agree that nothing points at fuel saving as a prime motivator in choosing the path / maneuvers. The main reason I’m looking at fuel efficient scenarios between 18:30 and 19:41 is to check if there are plausible paths ending in the S35-S36 interval. Plausible in the analytical sense (high sat-data probability x high “fuel” probability). Follow that line and your suggestion:
What would be the 19:41 position and fuel remaining if we assume no descent at all?
“If a turn was made straight to BEDAX, then you will arrive at the 19:41 position far too early. You must either fly a zig-zag path before then or do a Hold for several tens of minutes”.
Yes, I see the issue there.
@Niels,
You asked: “What would be the 19:41 position and fuel remaining if we assume no descent at all?”
The 19:41 position depends on fitting only the 19:41-00:11 satellite data. Therefore, it does not depend at all on the FMT Route, including whether or not a descent occurred between 18:22 and 19:41.
The available fuel for the “no-descent” FMT Route is given in Table D-1. For example, the 19:41 available fuel for Case 5A is 26,397 kg. This assumes the bleed air was on through 19:41. Slightly more fuel is available if one assumes the bleed air was off prior to 19:41, as in Case 7A.
@Richard
You posed a number of questions and I am researching some points, but I posted graphs comparing your Fig. 17 with the results that would have obtained if the spreadsheet had been run at 41000ft starting at your 19:41 geographical location on 180T with LRC. So this is the equivalent of your final leg at high altitude from 19:41 to 00:11, which is common to all of your cases.
As you know I can only select 39000ft or 41000ft. The previous comparison was at 39000ft. In this data set, the rotation of the wind is clockwise, the wind speeds match well, but our temperature is lower than yours, which is the reverse of the previous comparison.
Well, dinner is served….
https://www.dropbox.com/s/7fkv0y00hxjzsmu/wind%20temp%20speed%20at%2041kft%20starting%20at%201941.pdf?dl=0
@Victor, TBill. The issue that Ventus, he and I were looking into was the ACARS gross weight versus fuel consumption discrepancy during the climb that has been discussed recently.
It looked to be of no consequence and Andrew’s explanation has confirmed that. Presumably the FMC calculates from the flow meters (readings as per the EHM report) though a remaining curiosity about that calculated fuel level is that when compared to the actual the difference (allowing for ±50kg for fuel and ±4.5kg for gross weight) is not random or linear but has a reversing trend.
Since the fuel measurement is accurate I can only suppose that the usefulness of the calculated is just an approximate standby.
The SIR ZFW of 174,369 kg is that of the load sheet, passed to the aircraft by ACARS at 16:06:32, as is the loading. That surely would reflect the actual figure from refuelling less a standard estimate for starting and taxying. In this instance this was an over-estimate.
The SIR states the basic weight (the aircraft will have been re-weighed and that recalculated periodically) as being 138,918.7 kg. Subtracting that plus the cargo and passengers-plus-crew combined weight of 31,086 kg from the ZFW, and also the basic weight, leaves 4364.3 kg unaccounted for. In presuming that consists of water, food, trolleys and other paraphernalia (possibly including passengers’ seats) I see no reason to query the ZFW or indeed the fuel load.
Since I take it that the ACARS gross weight is the sum of the ZFW and as-measured fuel remaining and the fuel consumption as measured has a nice linearity during the climb your choice of a fuel datum of 43,800 kg ± 50 kg five minutes past the top of the climb does look the best available.
Even so that does suppose that the consumption over the last five minutes of level flight, accelerating slightly, of between 3900 and 4500 kg/eng/hr is what could be expected though it may be on the high side. That does assume a 50 kg rounding error for the nominal as-measured 700 kg used over that 5 mins, though 100 kg is remotely possible.
@Victor,
You said:
“The problem is that terminus is not consistent with the available fuel, nor with the drift model results. I don’t see how that is overcome.”
The curriculum vitae of the DSTG authors is heavily biased towards math, physics, engineering,… No one on that team was an Andrew Banks or a DrB or a VI. They had to rely on information from Boeing on the fuel range. In affect you are asking us to disregard the manufacturer’s input in deference to your own.
3rd para. Second line. “That surely..” should read, “The fuel listed surely…”
5th para. First line, after ACARS replace “is” with “should be” please.
@DennisW: The DSTG fuel model was over-simplified. It simply limited the speed range to Mach 0.73 to 0.84 (and altitude between 25,000 ft and 43,000 ft). If Boeing provided input, it was only in a very broad sense. I strongly disagree that we are “asking [readers] to disregard the manufacturer’s input in deference to [our] own”.
Here are the relevant sections from “8.3 Assumptions”:
4. Infinite fuel: the fuel constraints on the aircraft can be applied to the pdf afterwards. In the simplest case, maximum reachable ranges could be used to censor impossible trajectories. However, analysis of candidate trajectories has indicated that the majority are feasible. Broad information about the fuel consumption rate of the aircraft has been used to inform the range of allowable Mach numbers.
7. The aircraft air speed is limited to the range Mach 0.73 to 0.84. Fuel consumption becomes very inefficient at speeds higher than this and at lower speeds the aircraft is not able to match the measurements. In practice it is likely that the viable range of speeds is actually much narrower than this.
@Victor
OK. Boeing’s lack of detailed input seems very strange to me.
@Sid Bennett
After having gotten back to your report late last night and finally realising that virtually any candidate path had similar fuel endurance issues and that with a little adjustment your fuel modelling and route would eventually come out virtually the same as for Richard’s, et al, I then realised the following basic matter. It had got so late in the morning that I HAD to go to sleep. So, today:
The Piece of String Analogy:
Refer to your Figures “Fig. 7 186T Path” and “Fig. 9 180T path, etc”.
You have chosen to draw both paths approximately or virtually tangential to a circle (or part of that circle). That enables the simple “Piece of String Analogy”.
Consider a piece of flat paper. One can draw any set of six arbitrary circles on that piece of paper with a common centre. Concentric circles. Let us now only consider five of those circles. For the time being we will remove one of those circles from our analysis. But we will NOT discard the inner circle.
At that inner circle let’s consider a cylinder placed concenctric with the circles and with outer diameter equal to the diameter of the inner circle. Now with one hand (say the left hand) hold a piece of string and with the other pull it tight around part of the cylinder. Note the measurements of the distance from where the string leaves the surface of the cylinder and crosses the outer four circles. Pull the string a little further around the cylinder and repeat the measurements. Notice something ?
In general, a line passing through all five circles and making the same chord-length across the inner circle (which chord-length tends to a minimum as the chord tends outwards towards the tangent) will be geometrically identical to any other similarly generated line.
We may wish to introduce an external reference to our set of circles and the theoretical chord-line. We may wish to draw a line through the common centre of the circles. We may wish to call this line “Equator”. Then we can discrimate between the infinite number of geometrically identical scenarios making the same chord-length across the inner circle. We may choose to use the angle between the chord-line and the “Equator” as the discriminator. We may even choose to call this angle the “Heading”.
Now consider our workpiece or template to be a spherical surface in lieu of a flat piece of paper. The same applies. For example consider someone, be it a little child playing or some supreme being, sitting on a satellite above the Equator, and drawing circles around the point immediately below using a laser pointer. A theoretical plane (a geometric plane, as distinct from an aircraft) passing through five of the circles so drawn will have properties analogous to the previously discussed chord-line.
We live on a not-quite spherical world. Within reason the above approach will also apply to that (this) world.
@Dennis W. You said, “There is a fourth approach not really appreciated by the hardcore techies. I would call it the motive based terminus.”
I agree that there could be merit in further consideration of motive. It seems to me that if you want to hide the wreckage and create a mystery, you must ‘hide’ the 37.5 ‘pinger’ signal and any floating debris. The deep south is a better choice than the Christmas Island region. Conversely, if you have some expectation an acceptable resolution and expect to land, then you don’t fly off to the deep south.
I think that the Malaysian officials did have early knowledge of the situation. Perhaps a note was left that was never published.
It would require solid knowledge of his (assuming ZS) personality and his personal situation to shed any light on his possible motivation. That would require a different skill set. I have been searching if anyone has approached the problem this way, but I can’t find much.
Also, I understand it, for a northerly terminus the analytics break down because the base assumptions (especially unpiloted flight) are likely not valid.
I have even imagined that the situation could have a few ‘twists of plot’. Perhaps somewhere just before the turn south there was a PAX intervention similar to the 9-11 Flt 93 scenario. The PAX took over the plane but no trained pilot was left. They could not even operate the radios but perhaps turned the plane around and wandered around the sky until the fuel ran out. Wild – but who knows?
I find it difficult to accept that ZS would commit suicide in this manner if his motivation was personal. If the motivation was political, then he failed totally. Perhaps he had put in place a means to make public his position and this feel apart.
In any case, as a frequent and interested reader, I greatly appreciate the effort and thought that has been given by the contributors to this blog. There are some very smart and capable people out there.
@Shadynuk
You stated “Perhaps a note was left that was never published.”
Following @DennisW’s philosophical exegesis on classical, Bayesian, likelihood and information criterion statistics, he concludes that our analysis has been frequentist and he promotes the consideration of the motive.
You agree that there could be merit in further consideration of motive. You point out that “it would require solid knowledge of his (assuming ZS) personality and his personal situation to shed any light on his possible motivation. That would require a different skill set. I have been searching if anyone has approached the problem this way, but I can’t find much.”
Sabine Lechtenfeld (@littlefoot), who is a criminal psychologist, has spent some time considering the psychological profile of ZS. I had the privilege to spend a weekend with Sabine going through the psychological profile of ZS. Another contributor to JW called Matt had also analysed all the online contributions from ZS and summarises his findings in a comment dated 16th September 2014.
ZS quoted a poem entitled “The Soldier” from “The Pilgrim and Other Poems” by Sophie Jewett dated 1896. The original text is headed with a quote in Italian from “The Divine Comedy” by Dante, taken from Paradise XXIX 91 “Non vi si pensa quanto sangue costa.” (You don’t think about how much blood it costs).
Here is the full text posted by ZS. The capitalisation is by ZS.
”The SOLDIER FOUGHT HIS BATTLE SILENTLY.
Not his the strife that stays for set of sun;
It seemed this warfare never might be done;
Through glaring day and blinding night fought he.
There came no hand to help, no eye to see;
No herald’s voice proclaimed the fight begun;
No trumpet, when the bitter field was won,
Sounded abroad the soldier’s victory.
As if the struggle had been light, he went,
Gladly, life’s common road a little space;
Nor any knew how his heart’s blood was spent;
Yet there were some who after testified
They saw a glory grow upon his face;
And all men praised the soldier when he died.”
Both Sabine and Matt conclude that ZS is identifying himself with the SOLDIER.
ZS had several Facebook accounts and Matt further points out that before and just after the Malaysian General Elections in May 2013, he was averaging 14 post per day and then suddenly stopped. Sabine notes that he may have moved from posting to planning.
Other sample posts by ZS shed further light:
“There is a rebel in each and everyone of us.. let it out! don’t waste your life on mundane life style. When is it enough?”
“General Elections 2013 are over, so its time they try to dismantle us. We are not going to be quiet.”
“If you are neutral in situations of injustice, you have chosen the side of the oppressor. – Desmond Tutu”
Matt explains in responding to Sabine, that he plucked the quotes directly from ZS’s rabid period of facebook posting (prior to the elections, and shortly thereafter). Then, after averaging approximately 14 posts a day over a period of 5-6 months, we have almost complete cessation of any posting whatsoever. He states that he points this out, because he feels and as Sabine correctly observes, that the cumulative effect of everything is beyond compelling, and points squarely to his culpability.
Sabine concludes that Matt’s observation that ZS went from frequent ravings to a total silence after the ‘stolen’ elections could be interpreted as a sign of an inner emigration. Maybe ZS became very busy with something else, like hatching a plan how he could use his aircraft against the political establishment.
Perhaps the “The soldier fought his battle silently” was the note, that was left.
@Richard. Thank you for that.
@Richard
@Sid
Richard said “In our model we account for the fuel required to climb back to FL390, which is 1,847 kg.”
>If we accept the 180 South flight path start, which I do, the key characteristic is that the aircraft shows up 2-3 degrees north of ISBIX at 19:41 for its appointment with Arc2.
The current team report essentially takes the most direct path to 19:41, which requires a descent down to FL100 to account for loiter time needed to make sure MH370 does not get to 19:41 too soon.
There is a hypothetical “non-descent” alternative to 19:41, where the pilot stays at altitude but does more distance to take up the loiter time.
What I would ask is, what is the fuel requirement for the non-descent alternative, and then that might bracket the range of possible fuel at 19:41.
@Richard,
I had many lengthy email conversations with Sabine.
At the end of the day I suppose I am also a techie i.e. a concert violist neighbor lady at our coast place refers to me as a propeller head. I had little useful to suggest to Sabine.
@TBill
You asked “what is the fuel requirement for the non-descent alternative?”
Bobby answered the same question from Niels above, please see the following link:
https://mh370.radiantphysics.com/2020/03/09/new-report-released-for-mh370-search/#comment-27611
@ George
Thank you for reading the paper and commenting.
You said:
“You have chosen to draw both paths approximately or virtually tangential to a circle (or part of that circle). That enables the simple ‘Piece of String Analogy’”.
I didn’t “choose to draw the paths that way for the 186T solution. That is the computed path from 18:22. The same cannot be said for the 180T solution where a start time of 19:22 is presumed, or for 19:41 where the final leg is asserted to start.
The IG has used the second arc as roughly the closest approach to the satellite of a simple path.
In my response yesterday to @Paul Smithson, I suggested that a conceptual boundary on allowable paths is defined (from at known position at 18:22) by estimating the maximum total path length to 00:11 under LRC or max endurance M, and drawing a circle of that diameter in GE, and a representation of the 6th arc. That defines the furthest South intersection.
I wonder if some other geometrical limit could be derived to further limit the domain of paths?
Once I have completed my response to Richard’s questions I am willing to use the spreadsheet tool to explore other paths (high altitude). I can’t do all of them, and prefer paths that have been documented by a paper that has been posted somewhere. Seems to me that I have weeks of time to devote to this.
@Sid Bennett
Your recent paper includes a Cost Function based on the BTORs, a standard deviation BTO of 30 µs, BFORs, a standard deviation BFO of 2 Hz (except for CU6, where the standard deviation BFO is 1.5 Hz).
You show the general equation:
Cost function = sum((BFO_pred – BFO_obs)/BFO_sd)^2 + sum((BTO_pred – BTO_obs)/BTO_sd)^2
In our paper we use an Objective Function based on 9 statistics for LNAV and 11 statistics for other navigation modes:
1. Mean BTOR (sample mean = μs = 0.0 μs, sample standard deviation = σs = 12.97 μs, N = 5 samples)
2. STDEV BTOR (μs = 29.3 μs, σs = 9.90 μs, N = 5 samples)
3. 1-Hour BFOR Deviation (μs = 2.19 Hz, σs = 0.90 Hz, N = 4 sample pairs)
4. Pearson’s correlation coefficient r for Leg Start BTOR to Leg End BTOR (μs = -0.237, σs = 0.447, N = 4 sample pairs)
5. r for Leg Start BFOR to Leg End BFOR (μs = -0.237, σs = 0.447, N = 4 sample pairs)
6. r for BTOR to Time (μs =0, σs =0.50, N=5 sample pairs)
7. r for BTOR to Along-Track Position Error (μs = 0, σs = 0.50, N = 5 sample pairs)
8. r for BFOR to Time (μs =0, σs =0.50, N=5 sample pairs)
9. r for BTOR to BFOR (μs =0, σs =0.50, N=5 sample pairs)
10. r for BTOR to Cross-Track Position Error (μs = 0, σs = 0.50, N =5 sample pairs)
11. r for Along-Track Position Error to Cross-Track Position Error (μs = = 0, σs = 0.50, N =5 sample pairs).
In these lists, the subscript “s” denotes “sample” statistical values, as opposed to “population” values. The sample standard deviations are always expected to be smaller than the population standard deviations. Generally speaking, there are 5 samples in the 5 handshakes from 19:41 to 00:11. In the two cases of autocorrelation (i.e., items 4 and 5 in the list above) there are 4 pairs of samples. We denote the expected values by “mu” (μ) and the standard deviations by “sigma” (σ). BFOR is the BFO residual (= predicted minus measured), and the BTOR is the similarly defined BTO residual.
We further consider the composite probability of these 11 statistics together with fuel, debris and aerial search results in order to find the overall result.
I find your cost function unable to fully discriminate between candidate flight routes and is essentially, what many of us were doing back in 2014.
Can you please explain, why the BFO cost function, at start times equal to or prior to 18:40, does not reference the CU6 BFO standard deviation for the BFO during the call in the PARAM table at B144 for the calculation at MAIN F4, F5, F6 and F7 and references PARAM B143 instead?
CORRECTION
“2. STDEV BTOR (μs = 29.3 μs, σs = 9.90 μs, N = 5 samples)”
should read
“2. STDEV BTOR (μs = 27.3 μs, σs = 9.90 μs, N = 5 samples)”.
The “population” standard deviation is 29 microseconds. That is found using a large number of samples.
The “sample” standard deviation, using only the five BTOs, is 27.3 microseconds. It is smaller because of the limited number of samples used. The sample standard deviation will always be smaller than the population standard deviation.
Richard said:
“I have read your paper and have the following comments and questions:
[Responses in brackets]
1. FMT
You state you chose to terminate the lateral offset at IGOGU and start the FMT at 18:37:45 UTC at a position 7.6001°N 94.5468°E and an altitude of 39,300 feet, about 9.2 NM north east of IGOGU on a bearing of 057°T. The FMT is completed at 18:39:15 UTC, just 10 seconds before the call starting at 18:39:55 UTC. I find that too much of a coincidence.
[You are right, I can put in a S-shaped return to 295T a little earlier and then begin the turn. Since the simulations are no being compared using a LRC fuel model, it is easier for me to put in the turn details and I will do so. Both models presume a turn at IGOGU and the path is merely being adjusted to conform to that presumption. But, in addition UGIA assumes that the turn which happens essentially coincident with the phone call was not observed, but that the BFO is consistent with a descent. There is no evidence for this.]
You state that radar avoidance is not presumed, but at 39,300 feet the FMT is in full view of the Thai Military radar at Phuket and the Indonesian Military radar at Lhokseumawe. How do you explain that radar operators in two countries failed to see MH370 turning south near IGOGU?
[In return I ask why the same radars did not detect the aircraft prior to 18:22 over the Strait of Molucca? There no doubt exists ELINT data that would reveal whether the radars were emitting, but we are unlikely to gain access to it. Even so, the radar display may not have been monitored etc.]
2. Incorrect Model Comparison Start Altitude
You start your model comparison of our 180°T route near waypoint BEDAX at 19:22:45 UTC (not 19:22:52 UTC) at an altitude of 39,000 feet.
In our paper, we state, that there was a traverse at FL100 and the climb begins at 19:23:50 UTC after waypoint BEDAX was passed. At 19:22:45 UTC MH370 was at FL100, not 39,000 feet.
[So as to provide an exact comparison I did the final leg weather comparison starting at your location at 19:41 and LRC and 41000ft. As you know I cannot interpolate between 39000ft and 41000 in the spreadsheet, but the wind and direction data seems reasonable. Note the change in direction of rotation. The temperature is lower than your model at 40000ft, but it is slightly higher at 39000 feet, bracketing the result.
https://www.dropbox.com/s/7fkv0y00hxjzsmu/wind%20temp%20speed%20at%2041kft%20starting%20at%201941.pdf?dl=0 ]
3. Incorrect Model Comparison Altitude from 19:41:21 UTC
Your model comparison of our 180°T route uses an altitude of 39,000 feet throughout.
In our paper, we state that the climb ends at 19:41:21 UTC at FL390 or a geometric altitude of 41,207 feet.
[That may be true, but since you can run your model at 39000ft, you can let us know if there is a significant difference.]
4. Incorrect Model Comparison Positions by 22:14 UTC
Your model comparison of our 180°T route states that MH370 position at 22:14 UTC is 17.8042°S 93.7600°E.
In our model, the MH370 position at 22:14 UTC is 17.5728°S 93.7876 °E.
Between 22:14 UTC and 22:24 UTC, your model shows the wind direction from changing from 83.8°T to 272.8°T and effectively reversing.
[You have previously mentioned that the wind direction was not very relevant at that time due to the low wind velocity.]
By 22:14 UTC you are already 0.24° of Latitude out, because you ignored the climb back up to FL390 and you use incorrect wind speed and wind direction calculations.
[You are correct, my vaunted staff have let me down. I used the spread sheet starting at 19:22 instead of the spread sheet starting at your stated 19:41 position. I will correct this in my next release.]
5. Incorrect Wind Speed and Wind Direction
Your model comparison of our 180°T route calculates the wind speed and direction for the position of MH370 at 22:14 UTC, but using the GDAS data at 00:00 UTC.
There is a significant difference between 22:14 UTC and 00:00 UTC.
There is a huge difference between the timespan from 16:41:43 UTC to 00:19:37 UTC and the timespan from 00:00 UTC to 00:00 UTC. In our model we interpolate the wind speed and direction for the position, altitude and time. You are ignoring the time dimension.
[I admire what you have done with the data, but when you compare the wind speed and direction between the two models, there is little difference, except for the transition, which I maintain extremely odd in your plot.]
Between 22:14 UTC and 22:24 UTC, your model is out by 1.8 knots of wind speed, out by 48.7°T of wind direction and out by 3.75 minutes in the time of the reverse of the wind direction, because you use GDAS data only at 00:00 UTC.]
[From the point of view of its effect on the along path wind component, which is what counts, it is minimal. Can you post your along-path winds from 19:41?]
In your view, what was the wind speed and direction at each minute between 22:17 UTC and 22:25 UTC for the LNAV 180 flight path from BEDAX between 18.0°S 93.787575°E and 19.0°S 93.787575°E?In your view, did MH370 pass through the eye of the anticyclone slightly to the west (wind from the north giving a tailwind) or slightly to the east (wind from the south giving a headwind) on this flight path?’
[See new comparison]
To say there is a match in your Figure 10 is nonsense. To say we have got the wind direction wrong, when you ignore the time dimension is hypocritical.
[See new comparison]
You show in your Figure 13 and 14 the Tailwinds from 18:00 UTC to 24:00 UTC for both paths, but these are based on the winds at 00:00 UTC only! Your model positions may be between 18:00 UTC and 24:00 UTC, but the wind is stuck at 00:00 UTC. These Figures are only correct at 00:00 UTC, a bit like an old broken pocket watch will show the correct time twice a day.
[The winds at a same UT are not the same from day-to-day.]
6. Incorrect Fuel Calculation
You claim that the fuel surplus is 119 kg as shown in MAIN S16 at 00:11:00 UTC.
In our model the fuel exhaustion is at 00:17:30 UTC (as I already pointed out to you) and not at 00:11:00 UTC.
00:11:00 UTC is the time at which MH370 passes the 6th Arc. This has nothing to do with fuel exhaustion, it is the time of a satellite ping.
Your model of our 180°T route does not account for the fuel required to climb back up to FL390.
[Does not need to if we start the last leg at 19:41. My chastised staff will rectify.]
In our model we account for the fuel required to climb back to FL390, which is 1,847 kg.
Once again you are trying to compare apples with oranges and flog a dead horse, but I enjoyed your mention of “satellite debris”.
[Glad to inject some humor at a time like this. The horse laughed too.]
@Sid Bennett: We are not getting anywhere in this last exchange.
We believe the 186°T path should be rejected because of fuel shortage and because debris would take too long to reach East Africa. Let’s concentrate on the fuel shortage.
Let’s analyze the leg that starts with the established track of 186°T. What is the time, position, flight level, speed mode, and fuel quantity at this time? And what is the average temperature and tailwind from that time until 00:19? From these quantities, we can begin to compare fuel models.
@VI: “We believe the 186°T path should be rejected because of fuel shortage and because debris would take too long to reach East Africa.”
And almost certainly debris would have been recovered on Australia shoreline.
@VictorI
I did not start this debate over nits. But for the readers of this blog, I cannot ignore the challenges to the conclusions in my paper. I do not wish to abandon the IG original position as to the 6th arc intersection.
I would prefer to address the fuel issue. It has the most definitive quantitative data of the two issues.
Let me collect the data for the path outlined in the paper. It should begin at IGOGU (within 5 nm or so).
@Sid Bennett
You are missing the point about radar capture at the FMT.
As we explained in our paper, radar capture was intended as a ploy, whilst MH370 was heading North-West.
Radar capture occurred over the Malacca Strait as intended.
The PIC wanted to hide the FMT and that is why there was a descent to 10,000 feet, out of radar range.
With your flight path, the FMT was in full view of the radar. So please answer my question, instead of trying to avoid it!
With our flight path the FMT was hidden from radar.
@Richard
If I accept your premise that the perp intentionally wanted to deceive so that the apparent path on N571 would be considered to have continued past IGOGU, then I might be bound to accept your conclusion. There is no evidence that the perp intended such a deception.
The plane remained in radar coverage of Malaysian radar till about 18:22, which is approximately the geometrical range of the radar. But, before 18:22 there was no reported detection of the plane by either Thai or Indonesian radar. Whatever the intent of the perp, there is no evidence after 18:22 either.
The only evidence we have is the Inmarsat data.
Let us consider the hypothesis that the plane continued at high altitude to IGOGU and made the turn South and was detected by radar. (The feasibility of the plane being intercepted was studied by others and discounted) It would remain in view for a short time. Let us further assume that the radar track was well established, despite being at maximum range and flying tangential to the radar coverage and that an estimate of the azimuth of the plane was obtained +/- some number of degrees. Let us further assume that it was 186T.
The perp was UNAWARE of the Inmarsat communications activities. He/she would believe that the duration of the flight after the turn would not be known to anyone.
Now plan the search. Starting with the possibility that the plane crashed shortly after leaving radar coverage and extending to the predicted range for some unknown fuel strategy, a steadily widening pie shaped search area would be needed.
My guess is that no one would have tried.
Then the wreckage washed up in the western SIO and numerous drift studies were conducted assuming starting points ALONG a 186T path to the South. Wow!!
@Sid Bennett
@Richard
@DrB
Sid, You said:
QUOTE: I didn’t “choose to draw the paths that way for the 186T solution. That is the computed path from 18:22. The same cannot be said for the 180T solution where a start time of 19:22 is presumed, or for 19:41 where the final leg is asserted to start. END Quote.
That is a perfect introduction to that which I had next intended to write and post as part of a multi step process.
The first step was the Piece of String Analogy, the next step is re-enforcement of the distinction between Stages 3 and 4 of the flight. This will be followed by acknowledgement that the Piece of String Analogy is a simplistic basis, but upon which refinements for the real life environment can be applied. If you wish, the radii of the circles, or more distinctly the differences between individual radii, can be visualised as in the time domain, as they are only defined by the time at which the circles were generated. The final step of the series will be return to the subject of fuel consumption and the consequent limits applicable to candidate paths for Stage 4.
The Stages:
On October 17, 2019 at 4:59 am (Comment-25629) I wrote:
“The last flight of 9M-MRO as MH370 may be broken down into stages:”
which included:
“Stage 3: Flight from the region of Penang in a generally west-north-west direction ‘up’ the Strait of Malacca until finally making a turn to a generally southward direction;”
and
“Stage 4: Southward flight until fuel extinction;”
Stage 4 is defined by the information available from satellite communication “metadata”. For the analysis here-in it is ALSO DEFINED by the indications that the flight path from “Pings” or “Arcs” 2 through 6 was a flight with no deliberate course changes or manoeuvres. [As for the Piece of String analogy, “we will remove one of those circles from our analysis” and “we” have chosen to remove “Arc 7”.]
Stage 4 stands alone.
Stage 4 can only be described by (analysed by) use of the satellite data and analysis of the effects of the ambient conditions of pressure, temperature and wind direction upon the progress of the flight along any particular candidate flight path. [Analysis of the satellite data is complex and includes allowances for known variations in satellite position.]
Discrimination between, and elimination of, candidate flight paths may be due to any range of reasons, especially fuel endurance.
This is the ONLY reason that I (me, GRG) can think of that of might be dependent upon what happened during Stage 3 of the flight.
Stage 4, to some extent defines the limits to possibilities for what happened during Stage 3 of the flight.
For example: All hypothetical considerations of the flight prior to Stage 4 which do not result in the aircraft arriving at some point “on Arc 2” at the time of “Arc 2” may be removed from the list of possibilities. Similarly, all hypothetical considerations which do not allow sufficient remaining fuel (FOB) at the start of Stage 4 for the aircraft to reach “Arc 6” may be removed from the list of possibilities. And this is an approach taken by the authors of “The Final Resting Place”.
Stage 3 of the flight DOES NOT define any details concerning Stage 4 other than placing some basic limits on the list of realistic possibilities for Stage 4, as indicated above concerning fuel endurance.
Stage 4 – Start Time:
19:41:03
– The recorded Log-On time in accordance with Inmarsat SATCOM recorded data. Reference: Appendix A of ATSB AE-2014-054_MH370-Definition of Underwater Search Areas_3Dec2015.
Review of “The Final Resting Place” indicates that it is clear that this time (19:41:03 UTC March 7th 2014) was used during the route fitting calculations. Figure 4 of that report is the first mention, and Section 5.1, “Method for the Flight Path Analysis between 19:41:03 and 00:11:00 UTC” makes it abundantly clear.
In the Tables of Appendix D of that report, concerning Fuel Probability, or the balance between fuel available at the end of Stage 3 and that required to complete Stage 4, the time of “19:41:21” has been used. This timing is explained in the following sentence part extracted from Section D.2 of the report: “Our FMT Route includes the following manoeuvres:” the eighth and last of which is: “a climb from FL100 to FL390, reaching the Top of Climb at 19:41:21.”
It would seem that this hypothetical Top-of-Climb has been used during fuel usage analysis to separate Stage 3 and Stage 4, and certainly has been for the example fuel calculations as tabled in Appendix C.
The effect of 18 seconds difference in timing equates to around 31 kg difference in fuel estimates, which, of course, is minor.
However, 19:41:03 should be declared as Stage 4 Start Time.
Re-enforcement of the distinction between Stages 3 and 4 of the flight:
As above: Stage 4 is defined from satellite data and consideration of there being no deliberate course change during Stage 4.
Stage 3 need not be rigorously defined, other than the flight at Stage 3 should end up at Arc 2 with sufficient fuel to complete any specific Stage 4 candidate.
And it is accepted that a minimum of three turns may be necessary, one to match, or explain, the 18:40 phone call BFOs and the others to align with the specific Stage 4 candidate under consideration.
Clarification, typo correction:
Fuel availability, affecting subsequent fuel endurance, is the ONLY reason that I can think of that might be dependent upon what happened during Stage 3 of the flight.
@Richard. You said, ‘Perhaps the “The soldier fought his battle silently” was the note, that was left.’
Your post is a powerful statement but I think Matt’s post needs verification all the same.
Under are some subsequent exchanges to his post. Apparently these quotes had not been heard of before, or, so far as I know, since.
He is quite forcefully convinced but did “@littlefoot”, Sabine Lechtenfeld, ever confirm the provenance of his attributions?
https://www.dropbox.com/s/d9wgj5fxq0xag8q/Zaharie%20posts.%20For%20Richard%20Godfrey..docx?dl=0
@Richard. …and did she establish their context do you know, including those than around the elections, eg that of the poem?
@Sid Bennett
You state “The only evidence we have is the Inmarsat data.”
That statement is not true and worse, it brings bad news.
The bad news is: You cannot find an unique flight path from the Inmarsat data alone.
The good news is: In addition to the Inmarsat data, we have a long list of evidence.
– Aircraft performance data from Boeing (how it was designed, tested and operated).
– 9M-MRO engineering data from ATSB (how the MH370 aircraft actually performed).
– Fuel data from ACARS and MAS records (fuel on board, PDA, individual engine fuel rates).
– Fuel exhaustion time from ATSB and Boeing Simulator (00:17:30 UTC ± 20 seconds).
– Weather data en-route from GDAS (SAT, TAT, Wind Speed and Direction).
– Floating debris items from Africa and nearby islands (28 items of aircraft debris).
– Physical evidence from debris analysis (confirmed MH370 serial numbers).
– No floating debris found in Australia (except one MAS towelette).
– Debris from aircraft interior (seat back mounting, floor panel, wall panel).
– No aerial search finds from AMSA (despite large floating debris field).
– Radar data from 5 different radar stations (range and bearing).
– Radar data from Beijing Lido presentation to NOK (unofficial but not disowned).
The Inmarsat data allows several other conclusions:
– The BTO noise is random and uncorrelated with all other parameters.
– The BTO and BFO reading errors are uncorrelated with themselves and with each other.
– The BTORs are uncorrelated with the Along-Track Position Errors.
– The BFORs are uncorrelated with the BTORs.
– The BTO and BFO after 19:41 UTC indicate an automated flight path.
You state “I do not wish to abandon the IG original position as to the 6th arc intersection.”
It appears that you are stuck in a rut, since 2014.
It is also a capital mistake to theorise before one has all the data. In 2014, we did not have all the data.
You state “Starting with the possibility that the plane crashed shortly after leaving radar coverage and extending to the predicted range for some unknown fuel strategy, a steadily widening pie shaped search area would be needed.”
There is evidence that the aircraft continued until at least 00:19:37 UTC and did not crash shortly after leaving radar coverage.
There is evidence that the fuel strategy was the long range cruise (LRC) mode, which is a standard option for the Boeing 777 and not some unknown fuel strategy.
You state “As for the fuel model, I contend that the difference between my calculation and one which DrB would have made for the same route is minimal.”
You further state “As for the fuel model, it gives similar results as UGIA for a base case.”
This is not true and we have shown your fuel estimate is unacceptable, both using your own model and ours.
In ignoring certain data like the fuel differences, you are twisting facts to suit your theory, instead of trying to twist your theory to suit facts.
@Richard said: we have shown [@Sid Bennett’s] fuel estimate is unacceptable, both using [Sid’s] own model and ours.
This is the fundamental issue I wish we would address.
If we have confidence in the accuracy of the fuel model, and Sid’s path results in a fuel shortage well outside of the expected error of the model, the other points are moot. We arrived at that conclusion many months ago, but somehow Sid believes otherwise. If the speed is LRC, there should not be a dispute about endurance, as the fuel flows are tabulated, and we have established correction factors for ISA temperature offsets and fuel flow factors.
@David
You ask whether Sabine verified the ZS Facebook posts?
Sabine confirmed the ZS Facebook posts at the time and I have confirmed them more recently.
I have archived the entire ZS Facebook public site, his private Facebook site is not available, of course.
The “Dante” and “Soldier” quote came from a friend Art Harun at “The Malaysian Insider”:
https://www.dropbox.com/s/iowrkfkhnahb7it/ZS%20Dante%20Quote.png?dl=0
Later ZS quoted it of himself.
The “Desmond Tutu” came from a Malaysian General Election 2013 campaign poster:
https://www.dropbox.com/s/l2t3xwakpdbnebt/ZS%20Desmond%20Tutu%20Quote.png?dl=0
The General Election 2013 quote came from ZS (the reference to Pru 13 is simply the Malaysian abbreviation for the General Elections 2013 – Pilihan Raya Umum 2013):
https://www.dropbox.com/s/zopubdycofhi2t9/ZS%20General%20Elections%202013%20Quote.png?dl=0
The “Rebel” quote was the same day as the previous quote:
https://www.dropbox.com/s/uedpk4q8a1g2pa6/ZS%20Rebel%20Quote.png?dl=0
The ZS Facebook pages are subject of 65 pages in the RMP report and you will find he looked 6 times at the “Book of Quotes” and also at another Facebook page offering quotes entitled “Inspiration at its finest”.
ZS often quoted “The Malaysian Insider”. On 25th February 2016, The Malaysian Insider was blocked by the country’s Internet regulatory body, Malaysian Communications and Multimedia Commission (MCMC) on the grounds of national security following continuous publication of defamatory content.
The RMP report on the various ZS Facebook accounts focuses on his 116 views of Jasmin Lan, a freelance model with the JRo Modelling Agency and plays down his political activity and fight against corruption in Malaysia, which dominates his posting.
Several other commenters apart from Matt and Sabine analysed the ZS Facebook accounts, including @sipadan at airliners.net on 2nd July 2014 20:38, @tailskid at airliners.net on 6th March 2015 and @spencer on JW on 6th March 2015.
Sabine firmly believes that ZS had demonstrated signs of a serious midlife crisis and unravelling for a while. Especially his infamous poem about the anonymous soldier, who dies with a smile on his face – knowing that the people will thank him for what he did, is a very red flag in her view.
Sabine believes that ZS was steering towards some kind of action, because he was so frustrated with the Malaysian regime back then. Many of his Facebook entries show that he was far from the social minded mature and psychologically well balanced family man for quite a while. The interesting thing is, that after a time of frequent raving and rambling on his Facebook page, he suddenly went totally quiet and had only a few bland entries. She takes it as a sign that he was planning something very specific and that therefore his urge to be active on social media had ceased. He was busy with something else. A forensic psychologist will always look for significant behavioural changes of a suspect.
For me, ZS’s daughter sums it up, when she says “He wasn’t the father I knew. He was lost and disturbed”.
@Victor,
You said:
“If we have confidence in the accuracy of the fuel model, and Sid’s path results in a fuel shortage well outside of the expected error of the model, the other points are moot. We arrived at that conclusion many months ago, but somehow Sid believes otherwise. If the speed is LRC, there should not be a dispute about endurance, as the fuel flows are tabulated, and we have established correction factors for ISA temperature offsets and fuel flow factors.”
I still struggle with the fuel model issue. Not because I have made an attempt to generate a model. I have not. The DSTG book shows several examples of Boeing input. Chief among them is the descent kernal shown in Figure 10.9 and the fuel range. None of the DSTG authors could have possibly generated the descent kernal or modeled the fuel range. The evidence of Boeing input is overwhelming IMO. The DSTG would not have published their book with a terminal location beyond the fuel range.
Boeing has a whole floor full of lawyers. While they effectively muzzled any employee feedback outside of formal channels, it is very hard to believe that Boeing would sit back and allow the ATSB to spend millions of dollars searching an area that was beyond the fuel range. It would be a horrendous corporate embarrassment. Simply said, Boeing has skin in the game, and they would not allow that to happen. The other possibility is that Boeing estimated the fuel range incorrectly. I don’t put a lot of weight in that conclusion.
@Richard
Thank you for the above.
However I am thinking (presumably due to family pressure) the daughter later said she was misquoted and denied she said that. Personally, I tend to believe her first version as you stated above.
@DennisW: I have no doubt that Boeing formally responded to specific questions in an accurate manner so that it would difficult to accuse it of not fully cooperating.
But that doesn’t mean Boeing was intimately involved in all aspects of the work that DSTG performed. For instance, it is not hard to prove that the “infinite fuel, bounded speed” model employed by the DSTG is not adequate for predicting fuel exhaustion.
And Boeing range calculations were performed using standard temperatures, which will definitely introduce fuel flow and TAS errors. Why winds were included but not temperature offsets is a mystery.
We are fortunate that the preferred reconstructed paths use LRC speed mode, as the fuel flows were tabulated for this speed mode by Boeing. What then remains is the fuel flow correction for PDA, which know is 1.5% average for both engines, and the correction for deviation from standard temperatures, which we also know by reference to a footnote from Boeing.
This means we should be able to predict the endurance for LRC speeds with a high degree of accuracy using data supplied by Boeing for this airframe.
@Victor, DennisW,
It is possible that Boeing’s input to DSTG models was less extensive, while their inputs to ATSB “in parallel” with DSTG models was fuller.
Definition of underwater search areas Dec.3 2015 pp16-17 provides some information on the inputs from Boeing and concludes by saying: “The performance calculations gave a maximum range that was consistent with the DST Group PDF. These two sets of results were obtained independently and it is significant that they were in general agreement.”
It is true that use of temperatures was not specifically mentioned in the bullet point list. But does that omission prove that Boeing’s modelling excluded temperatures but included wind? I don’t think it does, and it would be a pretty odd thing for them to do.
“Boeing provided a southerly range limit for the aircraft using the following assumptions:
• realistic speeds and altitudes were used throughout the radar section of the flight to give a
conservative fuel load at the final radar location at 18:22
• the turn south was modelled at 18:28 – this is the earliest that the turn could be achieved
based on the analysis of the satellite data and also provides the maximum southerly range
• constant altitude from 18:28 to the end of the flight
• arc crossing times and locations must be met
• historic engine efficiency values were used
• wind was modelled throughout the flight
• maximum range cruise (MRC) cost index (0) was used.
Speed/altitude considerations
Boeing analysed the aircraft performance for various scenarios ranging from MRC to maximum cruise thrust limit (MCRT). The starting time for the analysis was at 18:28 and the end time was the flame-out at 00:17 (i.e. 2 minutes prior to the 7th arc). This gave a time interval of 5.8 hours. The Boeing analysis gave a series of ranges and time intervals for different cruise altitudes. It was noted that a constant altitude of FL350 or higher gave sufficient range to reach the region on the arc corresponding to the DST Group analysis. Applying the assumption that a series of stepclimbs had been performed during cruise, produced a range greater than that required to reach the region of interest on the arc.”
@Victor
I am working at assembling the information that you requested, some of which I have posted as graphs recently. But I am a little confused as to the starting point for comparison. If I start at IGOGU at 186T (I will consider the exact time but nominally 18:49), is that the route you will compute?
So that I can follow along, from where do you apply the PDA=1.5? and what is the FOB?
@Richard
I am attending to Victor’s request (among other things)and would rather debate the weight of the various pieces of evidence later. I apologize for putting it off, but Victor’s issue is more determinative.
@Victor. I see that constant TAS (implying no ISA delta) was the assumption for the range of path reconstructions described in Flight Path Analysis Update 8 October 2014 p9/15. However, if they were constant TAS, they cannot have been MRC path models, can they? What I understand ATSB to be saying is:
1) We did our path modelling using constant TAS at different altitudes including wind vectors to obtain paths that intersected arcs at the relevant times.
2) Boeing gave us an MRC range extended from a) earliest turn soon after 1828 b) later turn after 1840. They don’t tell us in this 2014 doc in any further detail the assumptions or methods used by Boeing. But from the description, it could be as simple as range boundary from 1828 and another from 1840.
So perhaps Boeing provided a simplifed maximum boundary using MRC initially, and fuller inputs for the 2015 report a year later?
@paul smithson: The most detailed description of the Boeing fuel and range calculations was a report prepared by Boeing in March 2014 and presented in Appendix 1.6 of the SIR. If you haven’t read it, please do. The list of assumptions for the modeling includes Standard day atmosphere. So, the ATSB report you cite is indeed silent on temperature, but the Boeing report says standard temperatures were used.
@paul smithson: Looking at Figure 1.3 from Appendix 1.6, which of the four (orange) routes at FL400 do you believe demonstrates there was sufficient fuel to reach 38S latitude?
@Sid Bennett: Start anywhere and anytime you want. To keep things simple, I’d like to do an LRC fuel calculation with temperature and starting fuel as input. The PDA applies for the entire flight. I’m trying to understand the basis of your claim that there was enough fuel to reach 37.5S latitude by going back to the basics.
The definition of performance limits in June 2014 “Definition of Underwater Search Areas” Fig.20 p22 looks to be virtually identical to that in subsequent reports. In this case, the assumptions set out on the previous page (21) include “an immediate turn south after the last radar point at 1822…” which would, of course, define a more southerly range limit than a turn soon after 1828.
Considering that the “kinks” in the MRC performace boundary coincide with paths models in 5000ft altitude increments, I am increasingly persuaded that the path modelling was entirely divorced from the fuel range/endurance modelling and that the former was simply an MRC range maximum without regard to endurance for FL200, 300, 350, 400 measured from “soon after 1828″ [or perhaps even soon after 1822] and ~1840”.
We can’t even be sure whether these Boeing maximum ranges were provided before or after knowledge about higher speed during the PSR track even though that was known about very early on (p6): “On 27 March (D20), the JIT advised they now had more confidence in the increased speeds provided by primary radar near Malaysia. This increased the aircraft fuel burn and the most probable track moved north to the S3 area.”
@Victor ref “The most detailed description of the Boeing fuel and range calculations was a report prepared by Boeing in March 2014 and presented in Appendix 1.6 of the SIR.” Thanks. I shall go back and re-read that.
@all,
To summarize the previous discussions, it appears that the Boeing range limits:
1. used ISA temperatures, not actual air temperatures,
2. used MRC, rather than LRC,
3. used a straight path from a turn off N571, with no lateral offset or zig-zag, and
4. did not account for any air speed above M0.84 prior to 18:22 (which we now know happened over Malaysia).
All four of these effects tend to increase the Boeing-predicted maximum range compared to our predictions. I seriously doubt there is any inconsistency. Rather, it is comparing apples to oranges.
We have the advantage of a number of additional years’ work to determine the post-18:22 air temperatures, the speed settings that match the satellite data at all bearings, a path between 18:22 and 19:41 which matches the satellite data from 18:27 until 00:11, and the geometrical altitude and Mach over Malaysia which matches the primary radar data. None of this was used by Boeing in 2014 because almost all of it was unavailable then.
@Dr B. Regarding #4, the appendix that Victor has kindly drawn to my attention again provides specifics on what/how fuel usage between last ACARS and Ping 1 was calculated, see http://mh370.mot.gov.my/Appendix-1.6E-Aircraft-Performance-Analysis-MH370-(9M-MRO).pdf Table 3 page 5.
They noted higher groundspeed during “segment 3” and accordingly assumed FL300 M0.865 for TAS 510kts.
Given these assumptions up to Arc 1, the subsequent table 4 p6 shows predicted range and endurance for a range of altitude and speed combinations.
As the assumptions are so clearly stated, the figures provided in this appendix may provide an additional opportunity to compare your model predictions against Boeing’s estimates.
I agree with Victor, ref his earlier comment, that this analysis indicates that none of the high-speed options have sufficient endurance to reach 6th arc.
I think we are in a better position now to estimate more precisely the likely fuel usage from last ACARS to first Arc, and that this is likely somewhat (but not a lot) lower than estimated in this Boeing appendix.
@paul smithson: The speed and altitude analysis performed by Boeing for the flight over Malaysia is imprecise. They looked at average speeds over segments, and then selected an altitude that resulted in Mmo when the FL350 Mach number became high. My guess is they also neglected temperature offset from ISA. They also did not consider the speed profile over that segment, nor did they try to estimate the altitude by using the methods we used.
Frankly, I think we’ve done better. That said, the quality of Boeing’s work, considering that it was performed in March 2014, is impressive, notwithstanding the omission of temperature offset.
@Sid Bennett
Victor’s issue is also my issue, the discrepancy in your fuel model.
Don’t bother reading my last post, here is a summary: “We have shown your fuel estimate is unacceptable, both using your own model and ours.”
Victor correctly points out, if your fuel model is wrong, then everything else is a non issue.
@DrB said: To summarize the previous discussions, it appears that the Boeing range limits:…2. used MRC, rather than LRC
I’m not sure even that was properly done. It appears that the MRC Mach number was determined based on the calculated weight and the assumed flight level at 18:28. After that, it appears that TAS, i.e., Mach and (ISA) temperature, was held constant.
@victor, agreed.
@richard. “everything else is a non-issue”. yes, if your model relies on a plane still in powered cruise at 00:11 and beyond.
@DrB @Richard @Victor
I am not a regular participant but I do check in and comment from time to time. I found your 7 March 2020 paper to be excellent work. The discussion about the flight path from 18:20:00 UTC to 19:41:21 UTC was very interesting to me. I had not thought much about how the aircraft got from the last radar fix to the final turn to the SIO. While unlikely, one could accept that MH-370 followed a random route from the turn back to the straights, but no way could the FMT route be random – obviously highly planned. This was no ghost flight, at least though BEDAX.
This is a great improvement on the work done by DTSG that centered at 38S on arc 7. I did not agree with their infinite fuel assumption. By ignoring fuel they did not recognize that the endurance and route were two separate, but related, problems to solve. By considering fuel consumption your crossing at 34S greatly improved on the DSTG work.
Clearly your flight path is an optimal fit for all of the arc crossing satellite data for straight flights – pulling the crossing up from 38S to 34S.
I still think a devious pilot that would even think of the FMT route would avoid a direct polar route because of its obvious link of endurance and flight path. Endurance and range can be decoupled by engaging in s-turns or even 360 clearing turn on a different route. After the fact, whatever path was flown had to meet the data. But out of the infinite ways to fly the aircraft from BEDAX and exhaust fuel at arc 7 at 25S, maybe a few would fit all of the data.
I think what you found is the very best solution for a straight flight from BEDAX. This is a significant contribution. And clearly this area needs to be searched.
I just question whether Z continued to perform maneuvers as he did during the FMT path and deliberately avoided a direct flight south. I don’t have the tools to do it, but it would be interesting to see if even one reasonable maneuvering flight could be created that crossed at 25S meets all of the data. Unlike the FMT path which had logic for the route, this flight could not be planned by Z around the unknowable SatCom data. He would pick the route but decouple the endurance. After the fact the path he flew would have to perfectly meet the constraints. But I expect there are many feasible flight paths to cross north of 25S.
@Victor,
“Frankly, I think we’ve done better.”
Wow, tough decade for Boeing engineering! Their floor of lawyers will be busy. I wonder if Australia will try to recoup some of the cost associated with searching what amounts to an impossible area.
@DennisW: As I said, it was an impressive effort for March 2014. The analysis they produced clearly stated what assumptions were made to arrive at their results, and those results seem to imply that the speeds required to reach 38S would not have the required endurance. The Boeing lawyers won’t be busy on this one.
@DrB
On March 30th you wrote:
“The available fuel for the “no-descent” FMT Route is given in Table D-1. For example, the 19:41 available fuel for Case 5A is 26,397 kg. This assumes the bleed air was on through 19:41. Slightly more fuel is available if one assumes the bleed air was off prior to 19:41, as in Case 7A.”
Thank you for that information.
Out of curiosity I did a quick optimization for CTT186, LRC:
I find a reasonable BTO fit (47 microsec RMS BTOR) for FL370 (air packs off). With a 19:41 latitude of -0.735 deg (and a longitude of 93.476) it brings us close to S37.5 at 00:19. My model estimates 201.23 tonnes total weight (required at 19:41), which means such scenario would be 0.46 tonne short in fuel (based on your case 5A estimate). I’m curious what your model gives, especially regarding fuel required at 19:41 and how significant 0.46 tonne would be in your estimates.
Based on a 485 kts GS the no-descent scenario could possibly go south as far as S1.3 deg at 19:41 (based on early turn south), so the problem is not in the 19:41 latitude.
@Nils.
I have been in the process for the past twp days of assembling the data that Victor wanted to assess my spreadsheet results. In the process, I re-addressed in detail the turn at IGOGU and the return from the track offset to N571 before that.
The statistical errors are further reduced, with no other changes in parameters.
A few days ago, in response to a question from Paul Stephenson, I ran a TT model from ISBIX (LNAV track goes right to it), to account for a case where the navigation was IGOGU LNAV to ISBIX as the final waypoint. The results are very good, but I haven’t redone it with the exact results of my latest path detail upgrade. It moves to a slightly lower azimuth than the LNAV case.
I should be able to post the LNAV results tomorrow and will move on to preparing the TT data.
Much of the hoo ha depends on the value of PDA that is used. At Victor’s request I used PDA=1.5. I use LRC for the whole path from 18:22 without any step climb.
Dinner is served….
@Victor. “@DennisW: As I said, it was an impressive effort for March 2014.”
Even so Boeing was a member of the SSWG, well after that, not a consultant to it. So far as I can gather all SSWG stances were unanimous.
@Richard. Thank you indeed for that expansion and summary. I for one was unaware of the specifics, extent, nature and interpretation of some of those Facebook posts.
Given 2 plus 2 equals 4 what you say plus,
• your group’s paper,
• Dr B’s highlighting that fuel saving en-route was not a priority,
• his opinion as to why there would be no packs on in the final leg,
those to me add to about 3.8, raising the question as to whether more searching is warranted for flight safety reasons.
“@Victor. “@DennisW: As I said, it was an impressive effort for March 2014.”
Even so Boeing was a member of the SSWG, well after that, not a consultant to it. So far as I can gather all SSWG stances were unanimous.”
I would regard it as a resume stain for Boeing if a small cadre of outsiders can provide a much better estimate of fuel range than the aircraft manufacturer.
@Niels,
You said: “Based on a 485 kts GS the no-descent scenario could possibly go south as far as S1.3 deg at 19:41 (based on early turn south), so the problem is not in the 19:41 latitude.”
As I have said several times before, for the no-descent route to reach the 19:41 location on time is possible for all the bearings we analyzed. However, the problem is that a simple turn off N571 reaches the 19:41 location too soon, by several tens of minutes, unless a Hold or a zig-zag is flown between 18:22 and 19:41.
That is one of the disconnects between the Boeing fuel calculation assumptions and the route fits by DSTG. There is a time disconnect of several tens of minutes, during which time fuel is burned without making progress toward the SIO, thus shortening the achievable range at 00:17.
You also said: “Out of curiosity I did a quick optimization for CTT186, LRC:
I find a reasonable BTO fit (47 microsec RMS BTOR) for FL370 (air packs off). With a 19:41 latitude of -0.735 deg (and a longitude of 93.476) it brings us close to S37.5 at 00:19. My model estimates 201.23 tonnes total weight (required at 19:41), which means such scenario would be 0.46 tonne short in fuel (based on your case 5A estimate). I’m curious what your model gives, especially regarding fuel required at 19:41 and how significant 0.46 tonne would be in your estimates.”
You will probably find a better fit at M0.84 (rather than LRC) and FL370 for 186 degrees CTT, based on our Figure 23. I also think CTT is much less likely than LNAV, and we did find that LNAV has a higher Route Probability than CTT at 186 degrees. There is insufficient fuel to fly this route, as we have already addressed numerous times on this blog and in our paper.
The 1-sigma uncertainty in our predicted fuel shortfall/surplus is given in Table D-2 as 427 kg. The uncertainty in the available fuel at 19:41 is 342 kg, and the uncertainty in the required fuel at 19:41 is 256 kg.
@paul smithson,
You said: “I think we are in a better position now to estimate more precisely the likely fuel usage from last ACARS to first Arc, and that this is likely somewhat (but not a lot) lower than estimated in this Boeing appendix.”
Why do you think the actual fuel USAGE may be LOWER than Boeing estimated from last ACARS to the first Arc? The largest error in their calculations is not including the higher fuel flow correction due to higher-than-ISA temperatures, and this is roughly several percent. So, I would expect their calculations to underestimate the fuel consumed (used) in the the actual case. The smaller effect of the brief high-speed segment might counteract the temperature effect, but I expect Boeing’s prediction of available fuel at 19:41 to be on the high side overall. The actual elevated temperatures cause higher fuel consumption, and this results in less available fuel at 19:41 (and a reduced range at 00:17).
@Hank,
You said: “I just question whether Z continued to perform maneuvers as he did during the FMT path and deliberately avoided a direct flight south. I don’t have the tools to do it, but it would be interesting to see if even one reasonable maneuvering flight could be created that crossed at 25S meets all of the data. Unlike the FMT path which had logic for the route, this flight could not be planned by Z around the unknowable SatCom data. He would pick the route but decouple the endurance. After the fact the path he flew would have to perfectly meet the constraints. But I expect there are many feasible flight paths to cross north of 25S.”
The pilot was unaware of the possibility of any position-related information being stored by Inmarsat. That was not known to anyone at the airline. The fact that he did not de-power the SDU indicates he did not perceive any risk in being tracked as a result.
Please tell me why you think he would want to perform maneuvers after 19:41, assuming he were not incapacitated? If he was beyond radar range and could not be tracked by other means, what would be the point of altering course after 19:41?
@Victor.
I have looked in some detail now at Appendix 1.6E. Thank you for drawing my attention. It is now quite clear how the “MRC performance boundary” was derived and we can see in figure 3 “possible flight paths” which paths correspond with assumptions in Table 4.
Orange “475kt” presumed FL400/0.828. “469” corresponds with FL400/0.818 (“MRC”). “443” corresponds with FL350/0.769 (“MRC”). “416” corresponds with FL300/0.706 (“MRC”). “383” corresponds with FL250/0.642 (“MRC”). And those points appear to correspond with what was subsequently depicted by ATSB as the “MRC performance boundary” for different altitudes.
Thus I think that we can conclude that Boeing’s key assumptions were:
1. Starting fuel 17:06:43 per last ACARS
2. Fuel consumed 17:06:43 to 17:28:15 was 10,276kgs (96,563lbs minus 73,908lbs), and that provides the starting fuel load for their path models from Arc 1.
3. “Using …. the wind data to back out ground speed from true airspeed in the performance analysis in Table 4, flight profiles for each altitude/speed combination were created and depicted in Figure 3”.
That sounds like a fairly crude treatment of wind vectors.
As Dr B points out, once ISA delta are considered the consumption would go up/endurance down. But this is offset to some extent by the increased range (due to higher speed for given M) for those paths that have sufficient endurance.
I believe that there is no ISA delta to apply by the time we get to altitudes as high as FL400. Applying to these paths only a gross 1.5% endurance penalty due to PDA, it would imply that Boeing models FL400/M0.828, FL400/M0.818, FL400/M0.727 all have sufficient endurance. The FL350/M0.769 and FL350/M0.694 models also have sufficient endurance if the gross temperature penalty is 3%.
Why does everyone believe the aircraft run out of fuel before crashing into the ocean ?
Or flew in a straight line until the end ?
The pilot was on a mission , his last .
I am inclined to believe he had a destination , the Diamantina Trench .
Carefully planned , brilliantly executed .
After all the careful planning , he wouldn’t just fly till the fuel ran out . He flew south , then east , ditching just above the trench at it’s western end .
And , instead of being 4000 meters down , he is 8000 meters under the waves .
@paul smithson said: That sounds like a fairly crude treatment of wind vectors.
In addition, I see no evidence that wind data above 30,000 ft was used to estimate the wind along the paths:
Wind data during the time period and covering the region of the flight were obtained for two time periods during the flight (18:00 UTC and 00:00 UTC) and at 8 altitudes (400 feet, 2500 feet, 4800 feet, 9900 feet, 13,800 feet, 18,300 feet, 23,500 feet, and 30,000 feet). The data contained time, latitude, longitude, wind speed, wind direction, and altitude.
I really don’t think we can use the Boeing results in a meaningful, precise way. They provide only a very general sanity check, which was appropriate in March 2014, but insufficient at this point in time.
@Robert Flemming said:
Why does everyone believe the aircraft run out of fuel before crashing into the ocean ?
The satellite data set at 00:19 is consistent with a flameout, APU autostart, and SDU reboot.
Or flew in a straight line until the end ?
The BTO and BFO data match a straight line path after 19:41 to a high level of statistical significance. It would be quite a coincidence if a path with multiple turns had the signature of a straight path.
I am inclined to believe he had a destination , the Diamantina Trench .
That’s your hunch based on your intuition, one of the many proposed.
After all the careful planning , he wouldn’t just fly till the fuel ran out . He flew south , then east , ditching just above the trench at it’s western end .
Again, you are proposing a scenario based on your intuition. The evidence suggests the aircraft reached fuel exhaustion and the flaps were not extended when they separated from the aircraft.
@victor – yes, I noticed that as well, and that may impact to a greater or lesser extent on the range calculations. However, it should not affect the endurance. I’d still be interested to know whether their sans-wind, sans-ISA delta fuel endurance estimates at different Mach/FL set out in Table 4 align with your fuel models (even if you take Boeing’s assumption of fuel remaining at 1st Arc).
@Robert Flemming
Hello Robert.
My personal hypothesis is also that ZS was heading for Broken Ridge or other very deep spot. The home simulator case passes by Dordretch Hole and I would not totally rule that out, even though it is 300+ nm from Arc7. My latest essay on the subject is below. I am not actively arguing the case here right now.
https://twitter.com/HDTBill/status/1235628571126710273?s=20
https://www.dropbox.com/s/yblbwii59zytx4g/Notes%20for%20Spread%20Sheet%20.pdf?dl=0
@VictorI
Here is the link to the spread sheet, met data and notes. The separate spread sheet for the met data starts at about 19:22 since it was prepared for comparison with your Fig. 17. The actual data is in the main spread sheet but needed unwinding for plotting, conversion of units for speed and addition of the temperature correction for plotting.
Let me know if you have any questions.
@David
You ask “whether more searching is warranted for flight safety reasons?”
You may be 95% convinced of the cause of the MH370 crash, but others are not.
In the case of the Germanwings D-AIPX crash on 24th March 2015, the final crash report concluded:
“The collision with the ground was due to the deliberate and planned action of the co-pilot who decided to commit suicide while alone in the cockpit. The process for medical certification of pilots, in particular self-reporting in case of decrease in medical fitness between two periodic medical evaluations, did not succeed in preventing the co-pilot, who was experiencing mental disorder with psychotic symptoms, from exercising the privilege of his licence.”
In order to finally determine the cause of the MH370 accident, the search for the underwater wreckage must continue and the FDR/CVR recovered. Only then, can investigators write a final crash report, publish their conclusions and safety recommendations.
You could argue, if the safety recommendations in the BEA final crash report for Germanwings 4U 9525 published March 2016, were in place before 7th March 2014, then MH370 may have never happened.
@DrB
@Hank
@TBill
„… why …… he would want to perform maneuvers after 19:41, assuming he were not incapacitated?”
In my opinion, there were two significant events that could have prompted an active pilot to change flight parameters. I mean sunrise and the last satellite call. What could he think when dawn began and the telephone rang after a few hours of silence? He thought “they” knew that the MH370 still flying, and it may have been just traced (by satellite, aircraft, ship?). A natural reaction would be to return under the cover of darkness or hide in the clouds. Two different options, but in both cases heading, FL and speed would change.
If any maneuvers have been carried out, then relations between Arc 2-5 and Arc 6-7 must be considered completely differently. The 180T / LRC solution loses its uniqueness. Until the start of maneuvers, the MRC option with a heading less than 180 (maybe towards Broken Ridge) seems more natural (considering motivation).
@Greg: The strongest case for no maneuvers is the excellent match with the satellite data after 19:41. It would be quite a coincidence if multiple maneuvers produced the same match to the data as a straight, automated flight with no pilot inputs. Any other justification for maneuvers is just supposition, and we are back to reconstructing paths based on hunches.
@Greg,
You said: “If any maneuvers have been carried out, then relations between Arc 2-5 and Arc 6-7 must be considered completely differently. The 180T / LRC solution loses its uniqueness. ”
I defy anyone to demonstrate a curve like our Figure 19 for any other route, especially for a route with maneuvers between 19:41 and 00:11. In my opinion, it is unique.
@Sid Bennett
The latest spreadsheet you supplied is locked and read only.
It is not possible to see any formula or trace any calculations or data fields.
It is not even possible to move the graphs that are covering the spreadsheet out of the way to see the data in the cells which are being covered up.
How is anyone supposed to do a comparison between your model and their model?
You are not making this comparison exercise very easy!
@Victor
@DrB
This was only the answer to the question: ” why …… he would want to perform maneuvers after 19:41…?”
If the pilot was alive and aware, he should react. So he was most likely incapacitated. If so, what happened to him? If he was implementing a complicated, perfect and the most important plan in his life, why didn’t he assure control until the end? I don’t expect an answer.
@Sid Bennett
I have managed to unlock your spreadsheet!
@DrB
In your model Z carefully planned a 3 dimensional route to minimize radar tracking, as described in the FMT model, and placed the aircraft on meridian E93.79 at N05.95. In your final model he continued on this meridian until arc 7. When you earlier evaluated alternate LNAV routes I do not know where the “final” turn from E93.79 was assumed for each simulation. Possibly at 19:41 UTC or possibly further down near N02.93.
For any straight coarse to fuel exhaustion the range problem and endurance problem are exactly linked and Z would clearly know that. This is a huge simplification. For any straight course an investigator could simulate the earliest and latest point of fuel exhaustion – the range and endurance are linked. This creates a band across the SIO.
If Z wanted to further complicate finding the aircraft he would intentionally decouple the range-endurance solution. This is easily done by performing an occasional holding circuit or even engaging in S-turns. This is the same evasive thinking used for the radar avoidance.
If Z performed a 15 minute circuit he could not have done that following a 180 degree course. The 180 course uses all of the time at M0.84 to satisfy the data constraints. But if Z flew a course more to SSW this would only work if he consumed time with no range along the way. This is with no knowledge of SATCOM arcs. I believe that if you picked a direct course from BEDAX to arc 6 and S25 you could adjust the duration for each segment to fit the BTO and BFO data. The crossing angle for each arc could be during a timing maneuver so it is flexible to fit the data. Remember, Z knows nothing about the arcs so this is not planned. What is planned is not just flying at M0.84 at FL39 in a straight line. It is reasonable for Z to add an hour of uncertainty to the range-endurance models.
Z could have planned a 180 course and done curves – but we know that he did not because it clearly would not fit the data. But he could have selected a different route with some holding and it fit the data. But I suspect there are infinite possible reasonable maneuvering paths at FL39 and M0.84 that would perfectly fit the BFO BTO data. But any intentional delay tactics with this data set have to be north of S34.
It is inconvenient to consider that Z may have intentionally messed with range and endurance. But it is also a great simplification to expect that this devious pilot just flew to oblivion on a direct 180S.
@all Let me be more simple.
If Z actively evaded radar detection and then just wanted to go to sleep and have the aircraft just fly directly down the E97.79 meridian on autopilot until fuel exhausted. That solution is well documented. I have no issues with that assumption.
If Z was not concerned about maximizing range but wanted to decouple the range and endurance for any future searches he could have done one or more holding patterns along the way. There is a good reason why he might have done it. It messes every post flight simulation up badly. Going to max range is not a very smart thing to do, IMO. But any holding moves any feasible course up for arc 7 crossing.
T@Richard
All Victor asked for was specific starting point information and along-path weather. I provided much more than that, but since it was going to be publicly accessible it seemed correct to present a clear baseline. It would have been the same, but much less useful, to have provided a pdf copy instead.
This version has had no code changes from the ones I have been providing as unlocked copies previously.
@Sid Bennett
You say there are no code changes from the previous version, but your model is parameter driven and you have changed a large number of parameters.
Your note is full of the changes you have recently made in response to the various discussions on this blog (altitude, fuel management model, Constant Mach or LRC, FMT route details, GCP or Loxodrome, LNAV or CTT, cabin depressurisation).
You then put out a new version of the spreadsheet that is 17.2 Mb, when the last version on 30th March 2020 was 15.4 Mb.
Then you lock the new version, so others cannot see the changes you have made.
You are not being very transparent.
@Richard
The parameters in the data entry boxes have not changed from the last LRC 39000ft case I sent you recently. Perhaps I ought to have sent the information to Victor privately.
I called attention to the alteration of the pre-FMT path which occurs in Main col P.
Specifically,it is quite clear from col P (to which attention was directed in the MAIN parameter block) that I have returned the plane from the offset to N571 at a time sufficiently earlier than the FMT to introduce a smooth FMT at 1 deg/sec.
I was aware that there are occasional interactions with the parameter data in col L2:15 and I needed to avoid them. The data in col O indicates the resultant azimuth.
You are much more familiar with spread sheets than I am. I am loathe to make code changes and have depended on Barry when they were needed in the past.
I had not considered that changes in recent spreadsheets were necessary. However, your fuel comparisons are being done in sufficient detail that I needed to select the “best” example, taking account of the data entry limitations that exist. In particular PDA=1.5 is an arbitrary change to match your model. I have not carefully studied the underlying assumptions. The model does not compute FOB on a per engine basis, so the implicit assumption is that both engines run out of fuel at the same time. A hand calculation would be needed to adjust it for unequal fuel expenditure.
I would have assumed that the lat long data itself at 15 second intervals would give you sufficient data to run cases in your model starting at 18:22, 18:42, 19:41 and elsewhere whilst varying the height to get the best result with your weather model. If those results prove sufficient to compare with the same paths, then there is no issue. If there is a significant difference, then further investigation might be needed.
If you find any anomalies, they are entirely unintentional and I will make every effort to resolve them.
res ipsit
@Hank,
You said: “When you earlier evaluated alternate LNAV routes I do not know where the “final” turn from E93.79 was assumed for each simulation. Possibly at 19:41 UTC or possibly further down near N02.93.”
No final turn assumption or fit was needed or used to fit the SIO Routes, which used the 19:41 – 00:11 satellite data. We assumed no maneuvers occurred after 19:41.
You also said: ” For any straight course an investigator could simulate the earliest and latest point of fuel exhaustion – the range and endurance are linked.”
One is not precisely derivable from the other, because of the unknown portions of the route prior to 19:41.
You also said: “If Z wanted to further complicate finding the aircraft he would intentionally decouple the range-endurance solution. This is easily done by performing an occasional holding circuit or even engaging in S-turns. This is the same evasive thinking used for the radar avoidance.”
I doubt that was a primary motivation, but the zig-zag FMT Route did just that prior to 19:41.
You said: “But if Z flew a course more to SSW this would only work if he consumed time with no range along the way. ”
There’s not enough fuel even for a SSW straight path, much less one which burned fuel and made no progress along a SSW route.
You said: “Z could have planned a 180 course and done curves – but we know that he did not because it clearly would not fit the data. But he could have selected a different route with some holding and it fit the data.”
I am unaware of any proposed route with a Holding pattern after 19:41 which fits the satellite data acceptably well.
You also said: “It is inconvenient to consider that Z may have intentionally messed with range and endurance.”
It’s not a matter of inconvenience. Our proposed zig-zag FMT Route did just that, although I don’t think that was a primary motivation for his flying it.
@Greg
Since you specifically mentioned it, it just so happens @ArtoL8 and I on Twitter are currently discussing one alternative might be 180 South until the 2314 phone call, at which point optional heading change ENE to 20-22 South. But it is not currently the favorite case for either one of us. Essay on that option has been on my to-do list for while now.
@DrB
You say above: “There’s not enough fuel even for a SSW straight path, much less one which burned fuel and made no progress along a SSW route.”
I am trying to resolve such a decisive statement into either a more perhaps constrained or a more perhaps unrestrained consideration. Although any route 19:41 through to 00:11 and eventually onwards to 00:19:29 and 37 will have the following additional constraints (limitations) as the route takes a more westerly path, so far it seems to me that the fuel constraints actually do not limit range quite as concisely as you and your co-authors have presented in Figure D-3 (and have incorporated into Figures 5 and 15).
The (two) additional constraints referred above are:
1. As a route takes on a more westerly component then the strong winds at the southern later stages of the route 19:41 through to 00:11 become more and more a headwind; and
2. As a route takes on a more westerly component then the geometrical flight distance from Arc 2 through to Arc 6 will increase. This may be simply explained by considering that a piece of string around the earth in the North-South direction will be slightly shorter than a piece of string around the earth at the equator.
@Sid Bennett
@Richard
1. Your discussion on Spreadsheets: a. My simple little laptop does not have the power to handle too large an excel file. b. It was my practice (still is I guess) to place graphs into separate Worksheets for a variety of reasons, including the specific reason Richard highlighted.
2. Would one of you kindly provide a set of loci (preferably in terms of Latitude and Longitude directly beneath the satellite) at the times of the Handshakes (pings, whatever you wish to call them). Yes, Sid, I know the basic information is in your spreadsheet but also refer to 1.a., above. I would like to have a simple representation of how significantly the “Arcs” differ from truly concentric “circles”.
Woops !
2. Would one of you kindly provide a set of loci (preferably in terms of Latitude and Longitude directly beneath the satellite)
OF THE SATELLITE POSITION
at the times of the Handshakes.
@Sid Bennett
You state “The parameters in the data entry boxes have not changed from the last LRC 39000ft case I sent you recently.”
But you have changed a large number of parameters, other than in the main data entry boxes.
You state “Perhaps I ought to have sent the information to Victor privately.”
When I asked Victor, he told me to feel free to respond.
But if you want to have a private conversation with Victor, that is fine by me. I will but out of your conversation.
I was hoping to clarify the many mistakes, that you are making in your spreadsheet.
You claim “res ipset”, or is that “res upset”.
I point out:
(1) The incident was of a type that does not generally happen without negligence.
(2) You are the one making changes in your spreadsheet under your control.
(3) I have not made any changes to your spreadsheet.
Res Ipsa Loquitur
@Richard (responding to @David)….
“You ask ‘whether more searching is warranted for flight safety reasons?’
You may be 95% convinced of the cause of the MH370 crash, but others are not.”
“…In order to finally determine the cause of the MH370 accident, the search for the underwater wreckage must continue and the FDR/CVR recovered. Only then, can investigators write a final crash report, publish their conclusions and safety recommendations.
….if the safety recommendations in the BEA final crash report for Germanwings 4U 9525 published March 2016, were in place before 7th March 2014, then MH370 may have never happened.”
I imagine that everyone still reading about this 6 years on must think it is DESIRABLE to locate the crash. But “MUST continue [until] the FDR/CVR recovered”? That’s hard to argue, I think. Aside from sunk costs and OI’s own interest in perfecting their technology, I’d think that a disinterested party would see little merit in continuing the search, beyond perhaps one more try based on the present analysis. But if I were in the Malaysian govt, I’d have trouble recommending more funding, even without facing a nasty recession. Nice if they do, but…..
[Odd that you mention Germanwings, which happened a year later, as an antecedent, rather than other earlier evident suicides as the Egyptair and Silkair cases. Although neither of these was admitted as suicide by home countries, they were enough to initiate “don’t leave a pilot alone” rules in many carriers..]
@ikr
The “black boxes” themselves I think are unlikely to provide much additional information. Simply confirming that the place was flown to where it was found. I don’t think many people still embrace a mechanical fault scenario.
Let’s not forget the phone event by Zaharie in the cockpit minutes before the aircraft lifted off. It was traced to a phone using a prepaid sim card purchased under a false identity. That is very curious, and supports the notion of messaging to collaborators on the ground in KL. The is probably the main reason I do not endorse the popular murder-suicide theory and prefer cosideration of a diversion for a purpose. Going down that path is difficult to reconcile with a 180 degree track 34.3S terminus.
@DennisW: In the RMP report, there is a reference to WeChat activity from the captain’s cell phone while lined up on the runway before takeoff. What is the evidence of a call “using a prepaid sim card purchased under a false identity”, other than some rumors?
If I remember correctly, the WeChat call “was to” a cell phone using a prepaid sim card.
@Sid Bennett: What I was requesting was the starting time, position, flight level, Mach number, fuel quantity, and path-averaged parameters such as temperature offset and tailwind so that simple comparisons of fuel consumption could be made. You returned a complicated spreadsheet that you admit you don’t fully understand. I don’t have the time to extract and compare the results. Richard seems more willing to do so, so perhaps you can interact directly with him.
@ventus45: We can’t put much weight on your recollection of a rumor.
@DennisW: The only information I have about phone activity on a prepaid phone is what appeared in UK tabloids in March 2014. I have been the victim of UK tabloids distorting comments I’ve made about MH370, and I refuse to work with any of them. The Malaysian Inspector General at the time also denied the story, although he has proven to be as reliable as the UK tabloids.
My recollection it was Tim Pardi who called ZS with sim card phone.
We have no smoking gun re: conspiracy, we do have innuendo and rumor.
To me, Tony Abbott’s recent disclosure that Razak admin thought it was murder-suicide implies the negotiation with Razak was probably an untrue rumor. Also it seems very likely that there was intentional depressurization at IGARI. If there was a negotiation, it was over by IGARI it would certainly seem. Or maybe there was a pre-flight negotiation Razak was aware of. But Razak apparently did not think Xmas was the end-game of the flight.
According to @TimR the negotiation rumor was brought to the attention of the search quite early, resulting in a brief possible search of Xmas by China en route to the deeper south SIO.
@TBill: Please, no more recollections of rumors.
In The Australian, Amanda Hodge reported the following:
The pilot of missing Malaysia Airlines Flight MH370 had grown close to a married woman and her three children, one of whom has severe cerebral palsy, in the months before his disappearance and the two had messaged each other about a “personal matter” two days before the ill-fated flight on March 8, 2014.
The friendship, which quickly developed to a level where Captain Zaharie Ahmad Shah was playing an almost fatherly role to the children, had cooled in the weeks leading up to the accident at his instigation, the woman has told The Australian. But Fatima Pardi would not reveal the subject of their last WhatsApp discussion before the flight.
“That last conversation was just between me and him. I don’t want to talk about it,” she said.
So this exchange occurred two days before the flight on WhatsApp, and did not occur while lined up before the takeoff of MH370.
The article is behind a paywall, but the contents can be accessed in this Reddit post:
https://www.reddit.com/r/MH370/comments/51g2al/new_report_mh370_pilots_friendship_with_mystery/
@Victor
You are correct. The original reference was made in a UK tabloid. Other sources subsequently picked up the story.
https://www.dailymail.co.uk/news/article-2587064/Probe-mystery-call-captain-doomed-jet-Unknown-woman-used-fake-ID-buying-phone-bypass-security-checks.html
I don’t think the fact that the call was made is in doubt. Is is also a fact that the person on the call has never been identified.
@lkr
I did not state “But “MUST continue [until] the FDR/CVR recovered”” as you misquote.
I stated “the search for the underwater wreckage must continue” AND “the FDR/CVR recovered”.
The “and” is a conjunction in between to separate sub-clauses in the sentence.
The first clause is “the search for the underwater wreckage must continue”.
The second clause is “the FDR/CVR recovered”.
Have you ever seen a final report of an aircraft crash without reference to FDR and CVR?
@DennisW: I don’t think the fact that the call was made is in doubt.
How can you say that? I doubt the veracity because there is no evidence other than a UK tabloid story. The reporter could have easily confused the call with the WeChat activity.
@DennisW: The RMP report says this regarding a call two hours before the flight:
Records also revealed that the MH370 Pilot made only one phone call to his wife, Faizah Khanum Binti Mustafa, which is about two hours prior to the flight taking off. It is also noted that his wife is also in his WeChat friends list. However, since WeChat did not provide any information regarding communications done via WeChat, MCMC is unable to confirm whether any communication between the two persons took place or not on the WeChat.
@Victor,
How can you say that?
I got it from you. 🙂 🙂
“@DennisW: In the RMP report, there is a reference to WeChat activity from the captain’s cell phone while lined up on the runway before takeoff. What is the evidence of a call “using a prepaid sim card purchased under a false identity”, other than some rumors?”
@Victor
Perhaps our disconnect is my use of the term “call” and the “WeChat” activity synomously. Both a form of messaging in the current context.
@DennisW: Here is what you said:
Let’s not forget the phone event by Zaharie in the cockpit minutes before the aircraft lifted off. It was traced to a phone using a prepaid sim card purchased under a false identity. That is very curious, and supports the notion of messaging to collaborators on the ground in KL. The is probably the main reason I do not endorse the popular murder-suicide theory and prefer cosideration of a diversion for a purpose. Going down that path is difficult to reconcile with a 180 degree track 34.3S terminus.
I referred to evidence of three different communication exchanges, but I see no evidence of “a call using a prepaid sim card purchased under a false identity…in the cockpit minutes before the aircraft lifted off”, except what was reported in the UK tabloids. The three communication exchanges are:
1. The phone call to his wife 2 hours before the flight
2. The exchange with Fatima Pardi on WhatsUp two days before the flight
3. WeChat activity while lined up on the runway before takeoff
@DennisW
I agree with Victor above, no reference to sim card phone for #3.
However, it seems to show the US policy for sterile cockpit rule was apparently not a Malaysian safety practice at the time.
@DennisW
@Victor
P.S.-
Reminds me that I was hoping for the MH370 6th anniversary that we would learn the nature of the runway WeChat call. A few months ago (caution-if I recall) someone from China came on Twitter briefly telling Victor that he knew the nature of the WeChat call. The implication was the person from China felt that the WeChat call was exculpatory or unrelated to the disappearance.
@TBill
I am not disagreeing with Victor either. Good grief. I am simply saying there was communication from the cockpit very shortly before takeoff. What difference does it make whether it was a call, WeChat, text message, email…
I provided a reference to a sim card purchased under a false identity as being the other party on the WeChat call. Victor does not like that source.
@TBill,
Also, to my knowledge, the other party associated with the runway call has never been identified. That is consistent with the fake ID sim card purchase.
@George G
George G says:
April 2, 2020 at 10:17 pm
@Sid Bennett
@Richard
“1. Your discussion on Spreadsheets: a. My simple little laptop does not have the power to handle too large an excel file. b. It was my practice (still is I guess) to place graphs into separate Worksheets for a variety of reasons, including the specific reason Richard highlighted.”
**I understand. It would take me a little time to find it as it is not ever changed. However, you should find the data in Fig. 8 of the Inmarsat (Ashton) paper in the JON accurate for any preliminary study. It should be available on line with free access.**
@Richard
Richard says:
April 3, 2020 at 2:00 am
@Sid Bennett
You state “The parameters in the data entry boxes have not changed from the last LRC 39000ft case I sent you recently.
But you have changed a large number of parameters, other than in the main data entry boxes.”
** I believe that I identified all of the input data that I changed, and clearly stated where the new azimuth data was found in the spread sheet by statements in the Notes document that contained the links to the spreadsheet. Please let me know what others there are. If there are, I will respond.
Changes such as PDA and a more detailed FMT were made in response to criticisms of my recent paper.**
Victor Iannello says:
April 3, 2020 at 7:55 am
@Sid Bennett: “What I was requesting was the starting time, position, flight level, Mach number, fuel quantity, and path-averaged parameters such as temperature offset and tailwind so that simple comparisons of fuel consumption could be made. You returned a complicated spreadsheet that you admit you don’t fully understand.
**As you are aware, the differences in fuel consumption between UGIA and my simulation are going to be of the order of 100s of kg. In past critiques of Barry’s model strong statements were made about the detail to which the weather model was employed in the two models. There have been conclusorary statements regarding the fuel quantities displayed in the spreadsheet I previously sent.
As I am not the author of the spreadsheet, I should not represent myself as being expert in all of the details.
In the past, either you or Richard stated that there had been a time when you and Barry cross-validated the spread sheets. I have used parameters that you have provided in the past, and in UGIA, to compute, for example, the final leg from 19:41 (except for fuel) and find close agreement.
I shall provide you with average tailwind, temperature data at 39000ft starting at the FMT** —-after lunch
@Sid Bennett
You stated “As you are aware, the differences in fuel consumption between UGIA and my simulation are going to be of the order of 100s of kg.”
Our paper shows a fuel shortfall at 00:17:30 UTC for scenario 7B1 of 95 kg, with a ZFW of 174,369 kg.
Your current model shows a shortfall of 741 kg at 00:17:30 UTC, with a ZFW of 174,369 kg.
The 1-sigma uncertainty in our predicted fuel shortfall/surplus is given in Table D-2 as 427 kg. The uncertainty in the available fuel at 19:41 is 342 kg, and the uncertainty in the required fuel at 19:41 is 256 kg.
Your own value of a 741 kg shortfall is outside the limits.
Your own value of a 667 kg shortfall (with your setting of ZFW at 174,000 kg) is also outside the limits.
@Dennis:”The “black boxes” themselves I think are unlikely to provide much additional information”
Thanks, I agree. The CVR probably contains nothing. And finding the wreckage will probably mean we already know what the FDR will say. That it was functioning perfectly, going exactly where it was programmed to go.
Something weirdly different from the above — the plane will never be found.
@Richard: “…as you misquote…”
Whatever.
What annoyed me in your original posting was the “must”. I was asking why a rational actor would plow limitless resources into the search for the wreckage and [yes, AND] the recorders.
My belief is that if we [OI, actually] were to find the wreckage, they would already know what the recorders say. Likely nothing but overwrite for the CVR, and on the FDR perfectly functioning systems for a plane programmed to end just where it did, with all passengers [and likely the pilot] long dead.
Your “must” is couched in an argument for safety, but here it’s a very legalistic ideal of closure. Yes, we should not expect a final report without the wreckage being found. But we could be satisfied of safety for the future being addressed — at a point where 95% of the evidence points to pilot suicide, or even, to any theory of directed flight to the SIO.
The rational actor [or competent Transport Minister] must [my “must” here] weigh the decreasing marginal advantage of finding the recorders vs. the increasing marginal cost of finding the wreckage [eg, re-searching supposedly cleared terrain…] and say that there is no reason to continue.
@DrB
Thanks for your comments to my posts.
I appreciate that your and colleagues work has been outstanding and that the 180 track at Mach 0.84 and FL 390 to cross arc 7 at S34.3 is optimum for all “straight” routes. And it is completely reasonable to assume that the aircraft followed the 180 track.
But you can not prove that the aircraft followed a straight path and did not engage in maneuvers between 19:41 and 00:11. I don’t challenge that the fixed 180 track may be the most likely scenario.
But, without the fixed course constraint, there is logically an infinite number of possible maneuvering routes (at FL 390 and Mach 0.84) that could exactly fit the SATCOM data but not cross arc 7 at S34.3. Because of the SW-NE slope of the arcs any maneuvering path would have to cross arc 7 further north than S34.3. You could not plan based on unknown arcs, but all that matters is that the pilot maneuvering along a different course created the exact BTO/BFO data.
If we look only at the route from arc 2 at 19:41 to arc 3 at 20:41. Along a 180 track at a GS of 480 knots the aircraft travels 480 nm to cross arc 2. Because of the arc 3 orientation, if the aircraft flew 480 nm on a direct 190 course it would go beyond arc 3 at 20:41. But if the aircraft was engaged in s-turns or a hold between 19:41 and 20:41 it could have exactly crossed arc 3 along the 190 nominal course. And the aircraft crossing angle at that time could be perfect for the BFO data because it could have been aligned with 180 at that exact time.
So it is possible to follow a straight 180 course from 19:41 to 20:41 and fit the data or follow 190 course with some maneuvering and exactly fit the same data. This is not by design, it is only an outcome.
The 190 maneuvering course between 20:41 and 21:41 could also exactly fit the data. You could say this is not likely. But this is not about planning this. It is just asking if the pilot had engaged in intentionally delaying progress along a selected course, out of the infinite choice of en-route maneuvers, could the path that day have fit the data.
Any direct course west of 180 moves closer to the arcs and at Mach 0.84 would have excess fuel at arc 7. But a hold or s-turns consumes the fuel without gaining distance.
It would be impossible to plan around unknown arcs. But a nominal path at 185, 190, or 195 with s-turns to burn fuel without range could have created the same arcs as the steady 180.
Flying to decouple range and endurance for four hours takes a lot more effort than setting the autopilot and sleeping. So I don’t question just setting the autopilot to fly the 180.
@Dennis
I wrote “Something weirdly different from the above — the plane will never be found.”
Which probably reads as obscure gibberish. I meant that a non-simple solution, ranging from a baroque curly-q routes that happen to cross arcs in the right manner, to a Whack-O interceptions at Diego Garcia or diversion to Kazakstan, mean the plane will never be found..
@Ikr
I interpretted your meaning as you intended. I don’t have strong opinions relative to the plane being found or the search continuing. The information on the FDR falls in the category of “interest” relative to the events speculated on this thread. I doubt it will provide any information relative to diversion causality.
@VictorI
Computed by “hand” from the posted spread sheet:
Start time:18:39:30, TAS= 483.6kn
Lat/Long 7.4856, 94.3766
Average Tailwind: -3.02kn
Average Temp (K) :220.76
Altitude 39000ft
@Sid Bennett: What is the Mach number? The fuel at 18:39:30? Is the altitude a pressure altitude or geometric altitude?
@VictorI
@ 18:39:30 FOB is 33102kg and M=.840. The altitude is geometric.
@TBill
A very good reason for using WeChat for “clandestine” messaging security instead of text messaging or email.
WeChat securely encrypts your sent and received messages between our servers and your device ensuring that third parties cannot snoop on your messages as they are being delivered over the internet. We do not permanently retain the content of any messages on our servers whether they are text, audio or rich media files such as photos, Sights or documents. Once all intended recipients have received your message, WeChat deletes the content of the message on our servers and therefore third parties including WeChat itself are unable to view the content of your message.
@DrB
Sorry, I am getting my headings mixed up in my last post and earlier. I meant taking courses more toward Australia. So I should have been saying a 170 versus 180 and not 190. I am getting reversed in my thinking for southern hemisphere courses versus aircraft headings from the nose. Sorry. 10 degrees left of 180 is 170 and not 190!
@DennisW: WeChat’s security is only as strong as trust in the Chinese government. Draw your own conclusions.
@Sid Bennett: Are you sure the reference altitude is geometric?
@DennisW
Interesting sounds almost impossible to get that convo
@TBill
Well, the RMP did not get it, if you trust the RMP. Frankly, I am surprised the RMP revealed that the WeChat messaging took place.
Dennis. Question: without forensic access to the phone or cooperation from wechat, what evidence is there of any specific messaging activity? Presumably all the carrier could provide is IP and data volume exchanged. The phone might have been unattended in his bag.
@lkr
Why do you suggest “limitless resources”? I am suggesting limited resources.
The Malaysian Government specified a long list of items, that they wanted recovered by Ocean Infinity, if the wreckage was found, including the FDR and CVR.
The major cost is finding the aircraft, not recovering a list of items requested by investigators.
Whilst you are there, why not survey the wreckage, video and photograph items of interest and recover selected items. That is the normal process.
AF447 was an example of an underwater search and recovery operation. Take a look at the final report from BEA. BEA recovered the FDR, CVR, engines and avionics bay.
“On 1st May 2011, the investigation team located and identified the protected module of the flight data recorder (FDR). The latter was raised and lifted on board the Ile de Sein by the ROV REMORA 6000 the same day. The following day the CVR was located and identified. It was raised and lifted on board the Ile de Sein on 3 May 2011. The flight recorders were first transferred to the port of Cayenne (French Guyana) by the French navy patrol boat La Capricieuse, then transported to the BEA by air on 12 May 2011. The recovery of aeroplane parts continued during that period, with in particular the engines and the avionics bay containing onboard computers being raised.”
@sk999,
Here is a report on my effort to estimate the “selectivity” of the 9-parameter Objective Function, which I call the “Route Probability”.
1. The route fitting problem is made difficult by the multiple peaks in the objective function with similar amplitudes.
2. There appears to be only one “global maximum”, and it occurs at or very near 180.0 degrees true bearing, both for the satellite data and for random data sets.
3. Identifying the global maximum requires a systematic survey, for each data set (real or random), of all feasible bearings.
4. Setting an initial condition of the bearing being within the range of 180 +/- 0.5 degrees generally locks the fit to the main central peak (containing the global maximum).
5. No minimization program I know of can automatically identify the global maximum out of the full range of feasible bearings. There are too many deep minima to be crossed.
6. Perhaps you can predict if the least-squares method you are using can do this. Is it possible and practical to expand the least-squares method to include all 9 parameters I am using?
7. I have done fitting tests using five sets of randomized BTORs/BFORs.
8. I generate the random data by first finding the global best fit using the actual satellite data. Then I assume those predicted BTOs and BFOs represent the True Route (i.e., with zero residuals). That is, I assume the mean of each of the measured BTOs and BFOs for many satellite data sets would equal those “best-fit” values of predicted BTO and BFO. Next, I add random BTO and BFO noise with the appropriate statistics to those best-fit predicted BTO/BFO values. This gives me random sets of synthetic satellite data, which I can then fit, and determine the precision of the 7th Arc location (i.e., the LEP).
9. Note that this process does not determine the BTORs and the BFORs when using random data. These residuals will continue to vary according to the fitted route parameters. Instead this method determines alternate sets of equivalent “measured” BTOs/BFOs (found using the global maximum route and the satellite data). So, the BTORs/BFORs will vary during the new fit to the randomized “pseudo-satellite data”.
10. I made three figures to illustrate the results of this work. They are available HERE .
11. Figure 1 shows a map of the predicted positions on the 7th Arc (i.e., the LEPs). The small cells in this figure are 1 NM squares. The black X is the global best fit. Note that here I have only made one assumption, namely that the air speed setting is LRC.The green and blue points represent different trials with random data sets. The blue diamonds are the predicted poositions for random data sets #2 – #5. Note that all random trials are within +/- 5 NM of the global best-fit real-data location.
12. To a small extent, the final result depends on the initial guess for the 19:41 bearing. That is, the fitting process has some “stiction”. For instance, using a random data set #1, if I start with a guess of 180.5 degrees for the bearing, the final LEP is slightly to the SW of the LEP I get when using a 180 degree initial guess. Similarly, if I start at 179.5 degrees, the final LEP is slightly to the NE. The green unfilled circles in Figure 1 are the results using 180.5 and 179.5 degree initial guesses. With an additional small step in the bearing, the fit can be made to fully converge (to the filled green diamond location).
13. All 3 LEPs for random data set #1 are within 4 NM of each other along the 7th Arc. So, the “stiction” effect is not large, being roughly +/- 2 NM.
14. This result demonstrates that there are some limitations in fitting with EXCEL SOLVER when the bearing is a free variable. The first result may be in error by up to 2 NM. This “stiction” effect does not occur when the bearing is fixed during the fit, as was done previously and shown in our paper. Indeed, that is one of the reasons we stepped the bearing between fits rather than allowing it to be a free variable in each fit.
15. The “stiction” effect can be avoided by using a multi-step fitting process. First, one takes an initial guess for the bearing and does a fit with it as a free variable. Next, one fixes the bearing slightly beyond the previous fitted value, and fits all the other parameters. Then one does a third fit with all parameters, including the bearing, as free variables. This process is continued until no futher change in the LEP occurs.
16. Figure 2 shows the route probability versus bearing. The highest route probability occurs quite close to 180 degrees, and all 5 of the fully-converged random trials are within 180 +/- 0.05 degrees.
17. Figure 3 shows the route probability versus 7th Arc latitude. All 5 random data sets lie within +/- 0.06 degrees in latitude of the global best fit.
18. In conclusion, and subject to the limitations of having only 5 random trials, the selectivity of the route probability function appears to be quite high. Note that this high degree of selectivity accommodates the BTO and BFO noise, which appears to allow only +/- 5 NM along the 7th Arc from that cause.
19. A second conclusion is that the high route probability found using the actual BTO/BFO data is due to the satellite data set (as we have suggested previously), not to overfitting route parameters. Note the 5 route probabilities using the random data sets are both lower and higher than the actual data set. Three of the random trials are < 50% and two are higher than 50%. So, within the limitations of having only 5 random trials, the expected value is close to 50%, as predicted and expected.
@Paul
Certainly the IP address, time tag, data volume, and caller sim ID, would logged by the carrier and be known. Beyond that I am not sure. WeChat uses symmetric end to end encryption in a client to server and server to client architecture. Messages can still be obtained through a back door at the server before they are deleted. One would have to layer a public key cryptography method to guarantee security. In the context of the MH370 cockpit messaging, the messages would have long been deleted if they were accessed hours after the fact.
@Richard
I am responding promptly so as to keep the dialog going. I may refine this analysis later.
As I have mentioned several times, the fuel calculation is done using the same PDA for both engines. So, as shown, all fuel runs out in both tanks at about 00:10:45 or so. Its 71kg short at 00:11. The value at later times is clearly erroneous as the engines have shut down and no account of the savings for one engine operation has been taken. The spread sheet design did not anticipate that fuel consumption would be considered a significant discriminant.
In making this comparison I have accepted without challenge your value of PDA=1.5 and I do so here to keep the comparison simple. In previous papers I believed you allowed PDA to vary below 1.5 for path selection.
Assuming at total fuel at take-off of 43800kg, with an estimated 2sig of 622kg, the difference in fuel consumption between the two engines to the time of REFE is 1.5×43800/2=394kg. So, when the total remaining FOB is about 394kg, there is REFE. That occurs at 05:45. There is still 394kg of fuel for the left engine. Your estimate (probably an upper limit) for fuel consumption at maximum cruise power is 4400kg/h or 74kg/m.
The amount of time the left engine then continues to run is 394/74= 5.33 min. So the predicted time of fuel exhaustion MEFE is 00:11:05.
That’s not much different than the spread sheet, and seems to leave about 6.5 minutes to account for to get to 00:17:30 (estimated MEFE) . But the fuel consumption is not more than 74kg/min and in 6.5 minutes we are only short 481kg.
You give a 1 sigma error in fuel as 427kg.
A small error in PDA for example or the one engine fuel consumption, would effectively wipe that out.
More importantly, as you assert, the plane should be flying about 1000feet higher than our simulation, and more efficiently, so there would be a lesser shortfall.
The only way to do the comparison effectively is for you to run the 186T route from my starting point at 18:39:30 and we can then compare the relative fuel consumption. It is a very simple route.
I can estimate the effect by running the model at 41000 ft. The BFO/BTO match is not as good, but the path is the same and the fuel consumption at 00:11 can be compared. At 39,000ft it is -71kg; at 41000ft it is +88kg, for a total improvement of 159kg. Interpolating between the levels to get to 40000ft, the improvement in fuel consumption is 159/2= 80kg.
The best estimate then adds about 1 minute to the flight duration and reduces the fuel “deficit” to 427-80= 337kg.
@Hank,
You said: “But you can not prove that the aircraft followed a straight path and did not engage in maneuvers between 19:41 and 00:11. I don’t challenge that the fixed 180 track may be the most likely scenario.”
I do not believe that the feature displayed in Figure 19 can be created by any maneuver or sequence of maneuvers post 19:41. The only explanation I can envision is that it is caused by the True Route with no maneuvers.
You also said: “Flying to decouple range and endurance for four hours takes a lot more effort than setting the autopilot and sleeping. So I don’t question just setting the autopilot to fly the 180.”
Who suggested the captain was sleeping?
@Richard, Ikr. About the need to search again:
https://www.dropbox.com/s/e0ik0yheb99hjgt/About%20whether%20a%20new%20search%20is%20now%20warranted..docx?dl=0
Minor amendments made
Hank said:
April 3, 2020 at 4:54 pm
” @DrB
Sorry, I am getting my headings mixed up in my last post and earlier. I meant taking courses more toward Australia. So I should have been saying a 170 versus 180 and not 190. ”
Hank: You seem to be in a trap which is so easy to fall into.
If we were to only limit discussion to “straight line” flight paths then that would limit us to “straight line” flight paths which cross the “Arcs” at approximately the time of the generation of those arcs. Now, the time is defined as immutable for our purposes. The location of the arc at that time [at any particular altitude] is dependent upon the time and the position of the satellite relative to the earth at that time and the calculated distance between the aircraft and the satellite at that time. For the purposes of this discussion the arc location may also be defined as immutable.
Note that in the above paragraph the discussion concerns paths which cross the arcs at APPROXIMATELY the time of generation.
The only means we theoretically have to accommodate for any initially approximate timing of any particular path candidate is to consider variations of other parameters affecting the flight path. This is the method taken by DrB and co-authors in their analysis.
Now, Hank, to return to your trap:
Your post, Comment-27729 on April 3, 2020 at 3:30 pm, together with your later clarification, clearly considers that your [170 degree heading] course covers less straight line distance (thus allowing for intervening manoeuvres) than the “straight line” path you are comparing it to. This implies to me that for your shorter overall distance to apply you are likely using the SAME Arc 2 crossing point as for the “straight line” path to which you are comparing it. This is NOT the GENERAL case.
It is accepted that there a myriad number of such shorter overall distance paths where a meandering path passes through each arc at the time of the generation of the arc and even passes through at such a bearing which satisfies the short term BFO data applicable at each arc. And for any number of such proposed paths there will always be another which might be proposed. As you say an infinite number. But which of any of the postulated or proposed paths are likely ?
The general case for a straight line path through the arcs approximately satisfying the requirement to cross the arcs at their times of generation may be described in any one of many ways, but for this discussion it will be described by the set of solutions passing through Arc 2 at the time of Generation of Arc 2.
Now, this set of solutions has some limits. For any deduced point on any proposed Pre-Arc 2 flight path there is a physical limit on the range of points along Arc 2. We may consider one limit as being the distance possibly travelled by the aircraft at MMO from the deduced point on the proposed Pre-Arc 2 flight path to either possible reachable extreme point on Arc 2. This would provide North and South limits on Arc 2, or outer bounds for the set of solutions.
Naturally, other limitations on the range of points along Arc 2 may apply, but these do not form part of this discussion.
As “one” progresses from the northern limit of the points along Arc 2 towards the southern limit then the corresponding bearing of the straight line path through the arcs approximately satisfying the requirement to cross the arcs at their times of generation will progress from below 180 degrees through to above. For each member of the set of (infinite) solutions passing through the range of points along ARC 2 there will be ONE and ONLY ONE bearing.
The trap for anyone trying to fit a meandering path through the arcs which passes through each arc at the time of the generation of the arc and even satisfies BFO data is making the choice of a specific ARC 2 starting point. Making this choice may seem to limit the possibilities. It does not.
The point (pun intended) of the foregoing discussion is to highlight that if there is not evidence for a “straight line” path having been conducted though Arcs 2 through 6 then there is no hope of determining a potential future search region. (Reportedly, analysis confirms there is such evidence.)
DrB, I have DELIBERATELY considered the location of the arcs to be immutable in the above discussion. Any uncertainty in the BTO, for any given arc, which BTO actually defines the arc, may be accommodated by considering that uncertainty as just one of the “other parameters affecting the flight path”. And you have effectively done just this as I see it.
@David
Many thanks for your paper “About the need to search again”.
The International Civil Aviation Organisation (ICAO) has published its International Standards and Recommended Practices for Aircraft Accident and Incident Investigation in Annex 13 to the Convention on International Civil Aviation.
The definition of an “accident” includes when “the aircraft is missing”.
“The sole objective of the investigation of an accident or incident shall be the prevention of accidents and incidents. It is not the purpose of this activity to apportion blame or liability.”
Investigators have an obligation to publish a final report including in the factual information:
“1.11 Flight recorders. Location of the flight recorder installations in the aircraft, their condition on recovery and pertinent data available therefrom.
1.12 Wreckage and impact information. General information on the site of the accident and the distribution pattern of the wreckage; detected material failures or component malfunctions. Details concerning the location and state of the different pieces of the wreckage are not normally required unless it is necessary to indicate a break-up of the aircraft prior to impact. Diagrams, charts and photographs may be included in this section or attached in the Appendices.”
Some have said the FDR will only tell you what you already know, in other words where the plane is. That is not true, the FDR contains much more data than just position. Some have said the CVR will be overwritten with silence and therefore blank. That is an assumption, however if proven true, that is also evidence.
You argue whether the cost of a further search is warranted. How do you assess the cost of a similar “accident” happening again? What is the cost of prevention of a similar “accident”?
You argue that the measures implemented after 9/11 and Germanwings are questionable and partially proven ineffective or counterproductive. Maybe we should review those measures and implement new ones.
You argue that the NOK may have sensitivities to the MH370 crash site being disturbed. I had some contact with the NOK recently for the 6th Remembrance Event under the motto: “Search ON: It’s not over yet”. The NOK clearly want the search resumed and are actively canvassing the Malaysian Government to that end.
I admit my use of the word “must” was influenced emotionally (and not rationally, as @lkr has pointed out). I was quoting from the closing lines from my video for the 6th Remembrance Event:
“I invite the Malaysian Government to consider our published findings and in the interest of the future safety of the flying public, to continue the search for MH370, until the cause for the accident can be finally determined and the next of kin know what happened to their loved ones.”
and
“the motto of VOICE370 – The MH370 Family Support Group “The Search Must Go On”.
@Sid Bennett
You stated: “Assuming at total fuel at take-off of 43800kg”.
This is not correct. The total fuel at take off 16:41:43 UTC was 49,700 kg. The fuel at the top of the climb twenty five minutes later at 17:06:43 UTC was 43,800 kg (according to the ACARS report).
We both agree that your model shows a shortfall in fuel. You say your current model shows that “all fuel runs out in both tanks at about 00:10:45 or so”. Actually the fuel runs at at 00:09:30 UTC in your model, when you set the ZFW to 174,369 kg.
You argue that the fuel shortfall of 741 kg at 00:17:30 UTC in your model may be incorrect as your spreadsheet may not correctly track the fuel consumption after both tanks are empty at 00:10:45 UTC. I agree with your assessment, as I have noticed you allow the aircraft weight to go below the ZFW after the fuel runs out.
You then argue that, if the PDA is wrong, then it could wipe out any fuel shortfall in any case. You say you have accepted my value of the PDA as 1.5% without question. This is not my value, but the MAS Operations value for 9M-MRO. In the RMP Report Folder 5 Aircraft Records, you will find a copy of the Operational Flight Plan for MH370, which shows that the PDA or Fuel Factor used for the Fuel Calculations for the flight was “P1.5” (P = Percentage).
Apart from that we have the MHXX Engineering data from a recently previous flight of 9M-MRO as well as all the ACARS messages from MH371 with the Fuel Flow Rates for both engines throughout the climb, cruise and descent.
There is little question that the PDA is seriously wrong.
Even if you set the PDA to your preferred value of 1.0%, that 0.5% difference from 17:06:43 UTC is 43,800 kg x 0.5% = 219 kg.
The fuel rate you show at 00:09:30 UTC (PDA 1.5%, ZFW 174,369 kg) is 1.536 kg/s, so another 737 kg is required to reach 00:17:30 UTC. Subtracting 219 kg would give a fuel shortfall of 518kg.
The fuel rate you show at 00:11:30 UTC (PDA 1.0%, ZFW 174,369 kg) is 1.529 kg/s, so another 550 kg is required to reach 00:17:30 UTC. This value is slightly higher than the previous calculation.
Both the fuel based on a PDA of 1.5% and 1.0% show a fuel shortfall, whether by 741 kg, 737 kg, 518 kg or 550kg is irrelevant. All fuel shortfall values are more than 1 sigma error in fuel of 427 kg.
@David
I believe we should commit to finding aircraft and determine to the extent possible cause(s) and provide closure to the families. It could be a decades long search under some kind of joint industry funding formula or ticket fee.
Why do I feel that way morally? not sure exactly, but like the Moon landing there are side benefits of learning techniques and mapping sea floor etc. Even if the cause of the crash is nefarious, I am not sure why that negates the need to determine actions taken to engineer such a “mystery” and of course there is the outside chance there was other cause or more complex cause than we presume.
I am actually a little afraid to find MH370, because I think the perp might have taken steps to obscure what happened.
@Richard
you said:
“Some have said the FDR will only tell you what you already know, in other words where the plane is. That is not true, the FDR contains much more data than just position.”
I think most of us know that. The question is whether that additional info will lead to the determination of a cause of the diversion. My opinion is probably not.
I would like to know if the plane was depressurized, which the FDR would record. That piece of info would shed some light on the perps intent. It would be nice to know the details of the flight between IGARI and the FMT, but that would do little more than satisfy my curiousity. Give me an example of what piece of FDR data would be useful relative to finding the reason for an intentional diversion.
Regarding ICAO, and their policy of not assigning blame, I find paragraph 2.5 d) in the attached report interesting and unusual. It specicifically comments on the interfence of “political decision makers” in the early SAR activities.
IMO, these “political decision makers” were aware of what was going on.
https://www.icao.int/APAC/Meetings/2015%20APSARTF3/WP05%20ICAO%20Brief%20on%20the%20SAR%20Response%20to%20MH370.pdf
@DrB
Regarding the CTT 186 deg route, LRC FL370, with LEP around S37.5 deg, you wrote on April 1st, 11:02 pm:
“You will probably find a better fit at M0.84 (rather than LRC) and FL370 for 186 degrees CTT, based on our Figure 23. I also think CTT is much less likely than LNAV, and we did find that LNAV has a higher Route Probability than CTT at 186 degrees. There is insufficient fuel to fly this route, as we have already addressed numerous times on this blog and in our paper.”
Assuming that the criterion would be that we need to stay within the 1 sigma error range (0.43 tonne) for fuel shortage/surplus I arrived to CTT 183 deg at FL375 (LRC). This route has a 00:19 latitude close to S36.0 deg and has a fuel shortage of around 0.36 tonne according to my calculations (and scenario 5A).
Based on this and other path calculations, and assuming that the models and error estimates are really good, I can agree that S37 seems problematic in terms of fuel needed vs. most favorable scenario for fuel available. However, I don’t understand why your “fuel” probability function has such a sharp drop in the S34.0 – S35.0 range. It looks to me that you are effectively “cutting out” a series of fully feasible route candidates; feasible both in satcom data consistency as well as in fuel required vs. fuel available.
@Richard
I agree that the take-off fuel should have been 49,700kg, but I seem to have also made an error in the computation of the fuel imbalance. It should be 1.5×49700/2=372kg.
I provided a complete spread sheet for you to review to possibly identify any obvious errors the might be identified. However, you have made errors in criticizing my reasoning from the spread sheet data.
You state that: “You argue that the fuel shortfall of 741 kg at 00:17:30 UTC in your model may be incorrect as your spreadsheet may not correctly track the fuel consumption after both tanks are empty at 00:10:45 UTC. We both agree that your model shows a shortfall in fuel.”
I state (not argue) that the fuel consumption calculation is based on the contents of the two tanks, taking account of a composite PDA. At the time that the right tank becomes empty, the left tank has 372kg of fuel left. This time can be determined by inspecting the cells in MAIN col GJ and determining the time at which the total fuel left is equal to the unbalanced value. (for the 39000ft case, it is GJ1396, which is 00:06:15; for the 41000ft case it is GJ1402/3 which is about 00:08:07)
You state: “as I have noticed you allow the aircraft weight to go below the ZFW after the fuel runs out.”
I would like to point out that the spreadsheet does what it is programmed to do. It computes the fuel consumption assuming both engines are operating and continues to compute the fuel consumption even if the fuel is exhausted. When that happens, the FOB goes negative (red) and one could have inserted a test in the cells to suppress the data. But I have found it useful to allow it to proceed into vapor land.
So, let me restate the case: with a PDA=1.5:
At 39000ft, the REFE is 00:06:15. The residual fuel of 372kg is expended at a rate of 74kg/m, leading to a single-engine operating time of 5.02m. MEFE is then 00:11:16.
At 41000ft, the REFE is 00:08:07. The single engine operating time is 5.02m. MEFE is 00:13:08.
Since the operating altitude is 40000ft, let us linearly interpolate between the results and get a MEFE of 00:12:12UT.
I have, for a long time, taken the position that the cabin was depressurized during some or all of the period of one hour immediately preceding the log on at 18:25, and that the electrical load on at least the bus supplying the SDU was totally shed. Barry’s model does not take this into account.
At UGIA A.12 para 15, you estimate the fuel savings at FL390 at 1.56%. for air pacs off. During the one hour time period ending at 18:25 about 6300kg of fuel would have been consumed. Thus the fuel saving due to depressurization would be 1.56×6300=98kg.
The electrical busses were shut down during the one hour time period. I did not find an explicit value for the fuel savings associated with this case. But as a rough estimate, one could take the fuel consumption of the APU if it were operating (and it was not) as 60kg/h to represent the burden of the electrical load. We save another 60kg/h.
So, adding the 98kg and the 60kg, shutting down the electrical systems and depressurizing the plane for one hour saves 158kg of fuel with respect to the base case computed in the spread sheet. At the single engine maximum continuous thrust fuel consumption rate of 74kg/m, this results in an additional 2:08m of operating time prior to MEFE.
The result is 00:12:12 + 2:08= 00:14:20UT.
For comparison purposes, we accept the MEFE as 00:17:30UT, and find that we are apparently 3:10 short. At the single engine fuel consumption rate of 74kg/m, this means that our estimated fuel shortfall is 160kg.
I find it difficult to be doing such precise computations given the limitations on the accuracy of the underlying data, but it serves to show that with reasonable values adopted the fuel is adequate to reach the 7th arc on the 186T path.
@Sid Bennett
Yesterday you claim your software does not work after fuel exhaustion.
“The value at later times is clearly erroneous as the engines have shut down and no account of the savings for one engine operation has been taken. The spread sheet design did not anticipate that fuel consumption would be considered a significant discriminant.”
Today you claim your software does work after fuel exhaustion.
“I would like to point out that the spreadsheet does what it is programmed to do. It computes the fuel consumption assuming both engines are operating and continues to compute the fuel consumption even if the fuel is exhausted.”</i"
You cannot have it both ways, either your software works or it does not work.
If your software works, then the fuel on board at 00:17:30 UTC is -741 kg (PDA 1.5%, ZFW 174,369 kg).
If your software does not work, then continuing this discussion is futile.
@Richard
Please take this seriously.
The spreadsheet computes the expenditure of fuel every 15seconds using the parameters
@RICHARD
Please take this seriously.
The spreadsheet computes the expenditure of fuel every 15 seconds using the parameters corresponding the the lat/long. (you know, M, temp, winds etc.). The location at any given time is computed in a manner that you are well familiar with and accept. The path is the controlling function, the resultant FOB is what would obtain if the path was flown and the fuel consumption were computed on a 15 second increment. All a negative number means is that (for the condition that BOTH ENGINES ARE OPERATING NORMALLY and the M is in accordance with LRC etc.) the fuel does not last until 00:19, for example.
The exact quantity of fuel at any time before fuel exhaustion (e.g., 00:05:00)is found in Main col GJ.
I am describing in detail a hand calculation I make for the case of a fuel imbalance between the right and left fuel tanks. You understand this situation quite well.
If it befuddles you, I will address the question to Dr.B.
@DrB
I didn’t intend my remark about “setting the autopilot and sleeping” to be snarky, sorry. I know there is much debate about whether the aircraft just entered a classic spiral dive at the end or was actively controlled.
@George G
Thanks for your comments.
I accept that it is not possible for the pilot to know about the arcs and to plan a flight path on that basis. The arcs locations and arc crossing BTO/BFO data only became a reality as the actual flight unfolded. But is is reality.
The question I am asking is whether it is possible (not necessarily probable) that a pilot could have actively engage in a some holding or s-turns along a planned flight path. The pilot would know that if he sets a fixed course and flies to fuel exhaustion the duration and range problems become linked. If the pilot engages in a cumulative one hour of holding along the way that introduces 480 miles of uncertainty in trying to locate the aircraft. Maybe he did this. Most people believe the flight was passive.
If the pilot flew along a flight path, for example, with the objective of hitting zero fuel near the location where the future arc 7 intersects with say S25.0, the aircraft would have excess fuel at the point. There are good reasons not to dump fuel. So the pilot could just engage in a few holding patterns along the way. Is it possible that this exact flight generated the recorded BTO/BFO data? The forward probability of this would be zero, but is it even possible to find a viable fit after the fact. Reality may have a zero probability of occurring in advance as long as it is possible.
@Richard. Thank you.
@Niels,
You said: “Based on this and other path calculations, and assuming that the models and error estimates are really good, I can agree that S37 seems problematic in terms of fuel needed vs. most favorable scenario for fuel available. However, I don’t understand why your “fuel” probability function has such a sharp drop in the S34.0 – S35.0 range. It looks to me that you are effectively “cutting out” a series of fully feasible route candidates; feasible both in satcom data consistency as well as in fuel required vs. fuel available.”
The simple answer is that none of those routes are actually “feasible both in satcom data consistency as well as in fuel . . . .” when you use all the available statistical metrics, as we have done in the route probability.
The sharp cutoff in fuel probability is simply what you get when you optimize the route probability for each bearing value. As I have demonstrated, the route probability is a much more selective objective function for SIO Route fitting than just using BTORs and BFORs, by about an order of magnitude. It is also true that less-than optimum route fits can have somewhat higher fuel probabilities, but the route probability inevitably suffers when one picks a lower-than optimum speed for bearings greater than 180 degrees. This also occurs at 186 degrees when using LRC, which is too slow to achieve a good route probability. So, in the region greater than 180 degrees bearing, the only way to raise the fuel probability into the acceptable range is to fly too slowly, which degrades the route probability into the unacceptable range.
@TBill. “I believe we should commit to finding aircraft and determine to the extent possible cause(s) and provide closure to the families.”
Finding the wreckage might be all that families want. Many might not be keen on disturbing it, seeking evidence.
I have made some final small changes to improve what I wrote. A little late I know but I mention it in case someone might like to update any download.
@DrB
Your assertions about the 186T route are not consistent with my simulations.
Earlier, I had determined the needed TAS by varying M at a fixed height. In response to criticism of this approach, I adopted LRC at 39000ft and the most detailed results were posted several days ago. In my previous post, I estimated the fuel requirements at 40000ft and found that they were within you error bounds for a plausible pre 18:22 scenario.
I await a response other than simply saying that you disagree with me.
Niels says:
April 4, 2020 at 11:16 am
QUOTE: I don’t understand why your “fuel” probability function has such a sharp drop in the S34.0 – S35.0 range. END Quote.
Niels, this is why I am slowly (very slowly, in the last few days) and progressively developing an overview of fuel usage by developing an overall (simplistic, I hope) overview of the whole problem, as much as possible devoid of bias from past efforts, which latter is of course not really possible.
Naturally, the aircraft could not have proceeded past fuel exhaustion, excepting as concerns “End of Flight Scenarios” which I am considering to be a separate subject.
However, I do not see how the probability can have such a clean cut-off as indicated by Figure D-3 in the report. This is most noticeable in the range S34.0 to S34.5. I do not see (have not seen) a clear explanation for this in the report.
In fact I do not think it does have such a clean cut-off.
So, Dear Authors, you may need to argue why such a clean cut-off, and provide clear evidence for such. In the meantime I will proceed, annoyingly, to investigate whether or not it is really justified.
Niels: And you say: QUOTE: It looks to me that you are effectively “cutting out” a series of fully feasible route candidates; feasible both in satcom data consistency as well as in fuel required vs. fuel available. END Quote. May I re-phrase this : It seems to me (George) that there may be some inadvertent aspect of the analysis which truncates the fuel usage analysis so dramatically. We must remove any doubt, if that is possible.
@DrB
I refreshed before I sent off the comment above addressed to Niels.
I started that last night and completed this morning.
Your answer may provide some details not previously covered, but I have sent my prepared post anyway.
If after review of your answer I find other than declarations, then I will respond accordingly.
Regards,
For each Singular Ending Latitude
There is a singular likely Bearing
And a singular likely Arc 2 Crossing Point
(hence starting Latitude, Longitude)
For each of these (infinite number of) Singular Ending Latitudes there is an optimum set of flight considerations for an Optimum “Straight-Line” flight path.
Having obtained (statistically determined) this set of Optimum “Straight-Line” flight paths, for each and every one there is a resultant SINGULAR fuel usage (consumption from the time 19:41:03 through to extinction) for Each and EVERY member of the set of Optimum “Straight-Line” flight paths.
This set of Singular Fuel Usages was used as a reference in construction of Figure D-3.
Am I right ?
I have been reading ‘ALL’ these posts and Dr. Duncan Steel’s blog for years. I believe that ‘several folks’ on this blog are semi frustrated; Heck, for once, I even sided with DennisW 🙂 …
I believe ‘insults’ and derogatory comments towards ‘Richard’ only hurts the cause; Recently, I witnessed 9 or more FAA folks that ‘cared about this topic’ subsequently retire. Just ‘hurry up a bit’ before there is ‘no one left’ who cares that can ‘modify policy that can reduce or prevent’ this occurrence again…Signed by a ‘miner league’ ‘miner’…lol…CPS
AND using your Fuel Model developed in Appendix A, Validated per Appendix B and used to prepare Appendix D.
@Carter Swenson: Thank you for the comment. We’d love to have more FAA individuals contribute. We’d be very interested to hear your perspective of the article and report.
@Carter:
I’m not sure why you think Richard is getting beaten up here [Sid and his model may be, but that’s another matter and grounded on the facts of the matter]. Richard merely presented his opinion that finding the wreckage and the recorders is a matter of moral urgency and legal necessity, and I suggested that a rational actor might disagree, in other words, taking a utilitarian stance. A couple other posters responded somewhere in the middle. Was there a derogatory, or even snarky, stance here that I’m missing?
@DrB
You wrote:”So, in the region greater than 180 degrees bearing, the only way to raise the fuel probability into the acceptable range is to fly too slowly, which degrades the route probability into the unacceptable range.”
Refering to your table shared in comment:
https://mh370.radiantphysics.com/2020/03/09/new-report-released-for-mh370-search/#comment-27425
Take for example your trial 707, with route probability .908 and ending S35.54. It has an initial bearing of 182 deg and FL374.
What would be the required fuel at 19:41 according to your calculations?
A second point I would like to address / discuss, you wrote:
“The sharp cutoff in fuel probability is simply what you get when you optimize the route probability for each bearing value. As I have demonstrated, the route probability is a much more selective objective function for SIO Route fitting than just using BTORs and BFORs, by about an order of magnitude. It is also true that less-than optimum route fits can have somewhat higher fuel probabilities, but the route probability inevitably suffers when one picks a lower-than optimum speed for bearings greater than 180 degrees”
I’m trying to understand what that means for the independence of “fuel” probability function from the “route” probability function.
@Carter Swenson
You state “I believe ‘insults’ and derogatory comments towards ‘Richard’ only hurts the cause”
Thank you for the kind words and they are well meant, but …
I disagree!
Even if, Richard is not a “rational actor” (@lkr), refers to things that are “odd” (@lkr), is squandering “limitless resources” (@lkr), is proposing a new search to finally determine the cause of the accident where “it seems distinctly possible that finding the wreckage will not further that determination anyway” (@David), “when it is unlikely to add anything useful to aircraft safety” (@David), is riding roughshod over the sensitivities and “opinions of families and friends as to whether the gravesite should be disturbed and any remains or personal effects recovered” (@David), is not taking this “seriously” (@Sid) and is “befuddled” (@Sid), is irrelevant.
Insults and derogatory comments towards Richard have nothing to do with the fact that we need to ensure that such an event as MH370 does not happen again. This common blog practice of insults and derogatory comments is fallacious because the personal character of an individual is logically irrelevant to the truth or falseness of the argument itself. In my view, this so-called ‘argumentum ad hominem’ is the lowest form of discussion and debate.
@lkr: I fully accept that there is a balance between the “moral urgency”, “legal necessity” and “a utilitarian stance”.
@David: I fully accept that “it would be useful were eminent suicide-homicide mental experts asked to confirm or otherwise” whether the public statements by ZS are relevant evidence and that measures introduced after 9/11 and Germanwings were partly “ineffective” and counter productive and “if such a door had not been fitted to the Lubitz aircraft [or MH370] that accident may have been prevented”.
@Sid: I fully accept that the FMT route remains “the weakest aspect of [our] case”, that MH370 “would have been observed over the Straits of Molocca [sic] by Thai and Indonesian Military radar and that “No such observation was reported” other than by the Malaysian Military radar (and then only after the event) and that the eye witness sighting by Kate Tee is not evidence of the flight path of MH370.
The co-authors of the report, published in this article, have spent over a year analysing MH370 and preparing the paper for publication. We do so, in order to help solve the world’s greatest aviation mystery.
It is a self evident truth, that every effort must be made to ensure that such a tragedy does not occur again. On this point, I fully agree with Carter Swenson.
Carter Swenson’s concern is that there are fewer and fewer people left at the FAA and soon there will be “‘no one left’ who cares that can ‘modify policy that can reduce or prevent’ this occurrence again”.
lkr’s reference to a “rational actor” equates to an ad hominem attack on @richard as irrational? I didn’t think so, but now that @richard has drawn our attention to a list of insults and derogatory inputs apparently masquerading as neutral commentary, I have to agree with him that there must be a good reason for his paranoia.
@paul smithson
Many thanks! I add your comment to the list of examples of discussion and debate of the lowest form.
@Richard,
“Closure” means different things to different people. Finding the wreckage is a step in that direction (for me). From the beginning (Duncan days), the motivation for the diversion had been considered “out of bounds” for this group, and I think that is still the reality.
@all
I am an original member of the IG. We may have different motivations to contribute to this work and different views on what the recovery of the black boxes would accomplish.
But, if the purpose remains to provide reasoned public advice to the authorities/companies who have to make the decisions regarding further searches, we must maintain civility and scientific discourse.
@Richard
Thank you for your remarks. It should be clear that we all have made supportive and favorable remarks on the recent paper, and I give it full credit for what it has done for this community. The assemblage of analysis, details and analysis has significantly advanced out understanding of the problem.
Moreover, I do not think that there has been a challenge to your proposed route (including the low and slow portion) on technical grounds.
However, I believe that it is not harassment to make a case that there is another route that is consistent with the known technical data.
I still remember our dinner in a little town in Germany some years ago.
@lkr
Thank you for your comments. I have tried to be completely open about the model I use. The latest runs of the model have been published to this blog, and any recent changes I have made to the parameters (not the code)have been in response to the constructive criticism that has ensued. I have also made efforts to reduce the difference between the parameters I use and those Richard et al. use so as to improve the comparability.
That I cite to UGIA for specific data and analysis results is not criticism, but an acknowledgement of its usefulness in the discussions.
Let’s get back to the actual topic.
@Sid Bennett: However, I believe that it is not harassment to make a case that there is another route that is consistent with the known technical data.
We are not converging.
The uniqueness of the proposed route includes statistical metrics based on the randomness of the calculated errors, as well as an advanced fuel model. Bobby has explained that the additional statistical metrics greatly improve (by a factor of 10) the discrimination of acceptable and unacceptable routes, which combined with the fuel model (and the drift model), rejects the path that the IG proposed back in July 2014.
The purpose of this blog was never to reach a consensus of the contributors, which I think is impossible for a group of this type. Rather, it is to exchange ideas and to provide peer review of work.
Unlike how the IG operated, contributors are free to release their recommendations to whomever they desire, whether or not there is consensus. Bobby, Richard, Andrew, and I have already done that. Others may choose to do the same.
All,
I have written a report explaining as best I can why the LEP is not known with the level of precision claimed in the UGIB report, although at this point I doubt I will change anyone’s mind.
https://drive.google.com/open?id=1lQz9iFjBH3YASQ1wV35UvVI3d20AdZqC
I have been asked whether I considered the various statistics involving the correlation of the BTORs with other quantities. In fact, I looked at the correlation with UT nearly 4 years ago, found it no where near as useful as the BFO correlation with UT, and turned the calculation off. I have looked at it again, this time computing the Spearman, Pearson, and Kendall correlation coefficients, and still don’t find it particularly useful, at least for the purposes of the report.
@Niels,
You asked: “Take for example your trial 707, with route probability .908 and ending S35.54. It has an initial bearing of 182 deg and FL374. What would be the required fuel at 19:41 according to your calculations?”
At 19:41 the required fuel for Trial 707 is 27,659 kg. The fuel probability is 14%.
You also said: “I’m trying to understand what that means for the independence of “fuel” probability function from the “route” probability function.”
They are not independent. For instance, changing Mach affects both the route probability and the fuel probability. However, that dependence is quite complex. It depends on many of the flight parameters, including speed, bearing, SAT, etc.
@DrB
You wrote:”At 19:41 the required fuel for Trial 707 is 27,659 kg. The fuel probability is 14%.”
Isn’t this for air conditioning packs on (at least I’m getting a value very close under that assumption).
What would be the required fuel with air packs off, and what would then be the route and fuel probabilities?
@Sid Bennett
I have tried to show your proposed MH370 flight path at 186° is not possible, because there is insufficient fuel.
You maintain the fuel shortfall is small and is not significant.
I tried to show you the fuel shortfall using your own spreadsheet is larger than the predicted fuel error budget for the whole route, but you did not accept this.
The essential problem with your spreadsheet is that it was designed for a flight model that fits the satellite data but not a fuel model.
You stated “The spread sheet design did not anticipate that fuel consumption would be considered a significant discriminant.”
On top of this your spreadsheet does not account for the following:
(1) Fuel for climbs.
(2) Extra fuel for turns.
(3) Different flow flow rates for each engine and quantities in each fuel tank.
(4) The ∂SAT is out by up to 1.7°C.
(5) ∂TAT is not calculated.
(6) Radiosonde data is not used.
(9) The tailwinds are out by up to 3.5 knots.
As Victor has said, we are not converging and at this point I can help you no further.
@sk999
Thoughtful post, thank you. In addition to the dispersion of the LEP shown in your Figure 4, the entire region shown in your Figure 4 has been searched. That fact also makes it difficult to embrace another search.
“The Malaysian Government, rightly in our view, set a high bar before they will engage in that discussion.” – Oliver Plunkett, CEO Ocean Infinity, Feb 20, 2020.
Spending is a zero sum game. $100M dedicated to infrastructure improvements will benefit more Malaysians than finding the aircraft wreckage (assuming a no find / no fee arrangement as previously). It would be very difficult to fund a search on a pay as you go basis.
@Richard. You have explained that your use of the word “must” was influenced emotionally, being taken from your video.
Understandably this has been an emotional time for you.
Even so I feel bound to emphasise that the previous need for a further search, for flight safety reasons, has been affected just now by Sabine Lechtenfeld’s interpretation of the Zaharie posts. As it stands that has lifted the likelihood of him having been the instigator and, in my opinion, considerably. So as I see it what now is being sought in a new search is confirmation of that. While such confirmation might prompt new thinking on the subject, that would be in the context that already it has been examined comprehensively and in recent times.
The merits of a new search depend on the gain versus not just the effort and expense but, if the wreckage is located, risk that the recovery of the recorders and a few other items will be insufficient. That might then require a wreckage and human remains recovery as foreshadowed by the ATSB’s ‘Operational Search for MH370’ (despite the AF447 experience). There is always the risk too that the confidence the wreckage will be found proves to be misplaced. These are cautionary notes.
I hope you do not see my drawing together these points as having an ad-hominem character; but should you, let me know please and I will desist from raising this with you.
Finally, I point out that if your paper satisfies the formal ‘new evidence’ criterion needed to resume the search it should go ahead anyway.
DennisW,
You commented: “… the entire region shown in your Figure 4 has been searched. That fact also makes it difficult to embrace another search.”
Maybe. Maybe not. Here’s a curious story you may know about. A person by the name of Paul Miller disappeared almost 2 years ago in Joshua Tree National Park. Searchers started looking for him within hours of when he failed to return. You can find the story online, so I won’t repeat. His bones were found about 4 months ago, not far from the route of his planned hike. In retrospect, in spite of the fact that the area where he disappeared is open country, searchers passed within 60 feet of where he was located and failed to spot him. It took aerial photography from drones and crowd-sourced examination of those photos to finally locate him.
The fact that an area has been “searched” does not mean that the plane ain’t there.
@sk999
The fact that an area has been “searched” does not mean that the plane ain’t there.
Of course, and that is not what I said. A previous search simply lowers the likelihood of the wreckage being in the area searched in accordance with well-accepted Bayesian statistics.
@sk999
BTW, your hiker story implies you think I am an idiot. Thanks alot. 🙂
@David
I thanked you for your paper “About the need to search again” and I thank you now for your thoughtful comment.
To be completely transparent with you, I felt you were trying to portray me in a bad light in your paper by implying, that I was pushing for a renewed search, irrespective of whether or not:
(1) it would help determine the cause of the accident or add to aircraft safety.
(2) the NOK wanted the gravesite disturbed.
I have answered both points and made it clear that I had considered both the ICAO regulations and the feelings of the families.
Your view, which I respect, is that a renewed search is unlikely to add to aircraft safety and it is distinctly possible will not help determine the cause of the accident. I disagree.
Your view, which I respect, is that a renewed search brings the possibility that the families having been re-sensitised, will be disappointed and frustrated once more. I disagree.
We will have to agree to disagree on both points.
@Carter Swenson, who is a neutral observer, pointed out “I believe ‘insults’ and derogatory comments towards ‘Richard’ only hurts the cause”.
In my response to Carter I disagreed, saying that even if his observation is true, it is irrelevant to the fact, that every effort must be made to ensure, that such a tragedy does not happen again.
@lkr responded to @Carter Swenson “I’m not sure why you think Richard is getting beaten up”.
@paul smithson, who is a neutral observer, concludes that I am paranoid, having twisted the implication from @lkr that I was not a “rational actor”, into a statement from @lkr that I was “irrational”.
The bottom line is, that I am sure you agree with me, that such a tragedy should not happen again.
@Niels,
You asked in your previous comment:
“You wrote: ”At 19:41 the required fuel for Trial 707 is 27,659 kg. The fuel probability is 14%.”
Isn’t this for air conditioning packs on (at least I’m getting a value very close under that assumption).
What would be the required fuel with air packs off, and what would then be the route and fuel probabilities?”
Yes, that value of fuel required is assuming the air packs are on, and the cross-feed valves are closed. This is Option A in our Table D-4. It was used for the route bearing study as the baseline case.
That same table indicates that Option B1, which has the air packs off and the cross-feed valves closed, requires 452 kg less fuel than Option A.
Our method of estimating fuel probability employs the evaluation of four post-19:41 aircraft configurations (Options A, B1, B2, and C) as shown in Table D-4 in Appendix D. We estimate the fuel probability using the smallest fuel shortfall/excess among the four options (and compared with the nine “available fuel” cases). In this situation, the smallest fuel shortfall is for Option B1, which has the air packs off and the cross-feed valves open. This option has the highest fuel probability – which is the 14% previously quoted. The fuel probability won’t change if one computes and analyzes the case with the air packs off, since this possibility is already considered as one of the allowed configuration options when finding the maximum fuel probability.
So, the short answer is the fuel probability is the same 14%. It was too complicated to keep track of four fuel probabilities for each route, so we simply selected the highest one among the four post-19:41 configuration options.
I have not fit that particular route with the air packs off, but in other cases where I have done that comparison the change in (maximumized) route probability was quite small. I expect the same in this case. One can understand this, because the slight reduction in aircraft Mach due to a very slight reduction in weight can be compensated by a slight reduction in flight level to keep the KTAS constant (which then keeps the route probability the same).
So, the very short answer is that neither the route nor the fuel probabilities change materially.
You will understand that the route fitting method described in our paper first found the highest route probability (at a given bearing, for instance). Later, we selected the highest fuel probability for that same route among the four post-19:41 configuration options and the nine pre-19:41 cases of available fuel. Recently, I have been exploring what happens when one fits the route parameters to maximize the product of the route and fuel probabilities. This was not possible at the time we did the route fits (by maximizing route probability), because we did not have a validated fuel model nor a thorough understanding of the impacts of the post-19:41 configurations on the fuel consumption. Now we have both. My initial comparison of the two objective functions, namely route probability or the product of route and fuel probabilities, was done recently circa 180 degrees, within the main central peak of the route probability function. Those results indicated there was no material difference in overall probability between the two objective functions. Since then, I have been looking at bearings outside that main central peak. Preliminarily, I see indications that there exist “compromise routes” in which the the product of route and fuel probabilities actually has a discernible peak which is not the same as the peaks of either the route or the fuel probability. I don’t expect those compound probabilities found using this new method will be as large as the 180 degree bearing case, so I don’t think the answer will change. However, it is possible the steep slope of the current fuel probability curve will be lessened using this new method, and the fuel probability for bearings greater than 180 degrees may increase. That will be accompanied, of course, by reductions in the route probability at those bearings. For bearings less than 180 degrees, where the fuel probability is generally very high, the overall probabilities won’t change materially between the two objective functions.
@Report Authors
In appendix D on page 114 you noted “Based on the smooth variation in BTO and BFO from 19:41 to 00:11, it became apparent early on that the SIO Route could have been flown in auto-pilot with no significant manoeuvres. If that were not the case, then it would be impossible to determine the true SIO Route, because there would be a very large number of matches to the limited satellite data if manoeuvres were allowed at arbitrary times.”
This is the point I have been trying to make. I believe that the direct 180 route to cross at S34.3 is highly likely because of its simplicity. And your report clearly shows this as the optimal autopilot solution.
However, the existence of a viable autopilot solution does not eliminate the possibility that a maneuvering route could have happened, so the qualifier “if that were not the case” is not really relevant.
You have clearly presented the optimal autopilot solution and I am not suggesting trying to find a maneuvering example. But if the aircraft is found someday above the S34.3 intercept it would have required maneuvering or fuel dumping.
I will not bring up maneuvering again because you have clearly addressed it in the report.
@Hank
“…it would have required maneuvering or fuel dumping.”
There is also the addl possibility that Arc7 was not end of fuel supply, so the aircraft kept going. inclusive of some extmargin of error due to various assumptions, and long glide after fuel exhaustion. That’s where I am afraid MH370 is, somewhere in that larger envelope. In other words, we could use the fuel model to map out the largest possible (worst case scenario) search areara
@TBill
Your suggestion above is difficult to reconcile with end of flight BFO values, and failure of inflight entertainment system login.
The only scenario that fits the observables is a terminus close to the 7th arc.
@DrB
That’s a long answer to a rather short question; much appreciated!
The exact procedure you followed is now getting much clearer, and I’ll take some time before reacting more in depth on your approach.
Regarding the LRC FL374 example:
Meanwhile I improved my “air packs off” calculation accuracy (FF reduction is now a function of FL) and I get for FL374, LRC:
air packs on: 19:41 weight 201.89 tonne
air packs off: 19:41 weight 201.42 tonne
I think that is rather close to your options A resp. B1 configuration values for this FL.
The 201.42 tonne results in 13% fuel probability using your formula (you reported 14%), when combined with Case 5A.
The product of route probability and fuel probability is then indeed not very high. It could possibly be higher if you trade route probability vs. fuel probability (slightly higher FL?). Also, I think case 5A is not necessarily the most efficient scenario and doesn’t fit very well to routes ending between S35.0 and S36.0. The pre-19:41 scenario I’m now looking at is based on your proposed route, with a descent to about FL250 (to avoid other traffic) in stead of FL100, and a direct (“diagonal”) connection from NOPEK to BEDAX.
@Victor
I am making this post in response to Richard’s specific criticisms so as to complete the exchange. I would be happy to continue to discuss the differences, as we are narrowing the number of issues where there is an apparent disagreement, but that is entirely up to Richard.
In order to reduce the number of long posts to the blog, I am happy if you disclose my email address to any regular user of this blog.
@Richard
To reiterate, the spread sheet does not incorporate a separate fuel flow model for each engine. The only time that this is of consequence is at the time of fuel exhaustion where one tank still has fuel. Since this is a later arising issue I have dealt with it in my recent posts using a hand calculation. I will ask Barry if he has the time to insert the end game algorithm which I have developed.
Nevertheless, you continue to ignore this fact and merely recited the un-adjusted two-engine FOB output of the spread sheet.
My premise is that the path calculation using the satellite data governs the path to be flown, and the fuel consumption is computed along that specific path. So the fuel consumption is valid only along the most probable path, and only until fuel exhaustion in accordance with the specific algorithm of the model.
I recently re-did my study of azimuth versus cost function for LRC and, as expected, the function has a much narrower peak, with the 10% values of the distribution lying between 185.7 and 186.3. I will publish it later when I have revised my paper. The effect of varying the M so as to have the plane reach the 6th arc on time has been eliminated. Now, when the plane overflies the 6th arc prior to 00:11 or does not reach the 6th arc by 00:11, the effect is seen quantitatively in the BTO error value in the cost function.
Nothing in my remarks should in any way be interpreted as challenging the technical accuracy of your proposed 180T path including a low-level segment.
My only, albeit contentious, conclusion is that there is a wholly high-altitude route. I believe you would agree that there is not a convincing high-altitude route at 180T.
Your critiques of my posts continue to improve my understanding and to inform my recent work.
1. Extra fuel for climbs: There are no climbs or descents in the scenario path from 18:22 to 00:11, except for a minor descent possible of 500ft for traffic clearance. We therefore assume that such a minor descent did not happen. Nor is there a step climb profile that might have been used to reduce fuel consumption.
2. Extra fuel for turns: In UGIB A.2, the effect of turns on FF is dismissed as small, although you include it. The path I describe includes the offset turns and the FMT all made at a standard rate. Your table C-2 indicates that no correction is needed at altitude for the turns.
3. The difference in average fuel flow rates is embodied in the PDA where I have used 1.5. I believe that the initial fuel loadings were within 100kg, at least according to the data provided. That is nominally 1 minute flying time. I am revisiting my corrections for air pack off and electrical off to consider the effects on MEFE in more detail.
4. SAT out: Is this the mean data I sent to Victor or the peak error between the two models for which I provided graphs? Regardless, I was prompted to hand check the temperature against the computed TAS and determined that I had taken the T values from the wrong column. The ones I gave previously are 2 degK too high at 39000ft. For example the value at 18:39:30 is 218.7K, corresponding to 484.1kn TAS. Thanks for checking.
5. TAT not computed. If I understand your appendix A.1 UGIB) the total effect of using the TAT is to multiply the PDA of 1.5 by a factor of 1.016. This seems negligible in terms of the error budget.
6. Radiosonde data not used: All of the modeled flight path is above the tropopause and the data is not used.
7. -8. (omitted from your list.)
9. Tailwinds out: : Is this the mean data I sent to Victor or the peak error between the two models? If it is the peak error, what is the average error? I assume you are comparing your data at 40kft with my data at 39kft, but no matter. At a mean error of 3.5kts, and a flight time of 5.5h from the FMT, this results in a maximum error of 19.25 nm in range, which at 484kt represents a flying time of 2.4mins. This is the upper limit on the effect. If the average wind difference is used, it should be much smaller.
I do think we are converging.
@Richard. Thank you. For my part I will leave it there.
@Sid Bennett
Your assumption is incorrect.
I not only looked at your model, I also rebuilt your flight path using your Timings, Positions, Altitudes and Bearings in my model (even though my results were different to yours).
I effectively overwrote and disregarded my Navigation model, including a Vincenty model.
I noted differences in the start point on N571, 10 NM beyond waypoint MEKAR, at 18:22:12 UTC (or 18:22:15 UTC which you use), the lateral offset, the position and timing of the FMT near IGOGU, the turn bank angle at the FMT and the initial bearing toward way point ISBIX, all of which I ignored.
I kept my Weather model, Mach model, Fuel model and Satellite Model.
I noted differences in the SAT, TAT, Mach, TAS, Wind Speed, Wind Direction, GS, ∂SAT, ∂TAT, Aircraft Weight and Fuel used at each point along your route.
I also noted differences in the BTORs, BFORs, fuel used to climb from 39,000 feet to 39,300 feet, the fuel used during the FMT turn and the altitude, temperature and pressure at the base of the stratosphere from the radiosonde data.
@DrB
@Niels
I having been preparing in my mind, in scribbles, and in Excel, etc, a note on Trial 707 (perhaps as a test case or specific example) and your DrB LRC Table 2020.03.20, in order to ask questions which may assist in my understanding, and I will append that note here,
but (DrB) following on from your most recent Comment-27798 of April 6, 2020 at 11:16 am –
You have written (posted): “In this situation, the smallest fuel shortfall is for Option B1, which has the air packs off and the cross-feed valves open.” whereas methinks you meant to write “cross-feed valves closed”. For the record.
DrB, you write: “Recently, I have been exploring what happens when one fits the route parameters to maximize the product of the route and fuel probabilities.” and that this consideration is with hindsight given the extensive fuel analysis conducted since the initial route fit analysis.
Fuel availability is a maximum at what I choose to call Scenario 11B1, which simply assumes Bleed Air Off for all time after the initial deviation (climb) from FL350, assumed at 17:26:00 for consistency with your report. Hence Scenario 11B1 is nothing but a natural extension from consideration of Scenario 5B1 of your report through 7B1 to 11B1. The calculated fuel shortfall is 27 kg for the combination of the Pre-19:41 “no-descent” FMT Route, in the terms of the report, and the 180 degree BEDAX SIO Route.
The above scenario thus considers there to have been 2 ¼ hours between when the Bleed Air was first switched off and when Arc 2 was crossed. Nothing is offered here concerning how the some of time between 18:22:12 was consumed and how long before 19:41 the final heading was achieved.
As recently briefly discussed or suggested here, it may remain to estimate atypical reduced electrical loading, and its effect on estimation of fuel availability. Without another review I’m not sure whether this was covered in Appendix A, or whether it would have any significant effect on fuel availibility estimates. I, for one, will review this, soon.
And, now, please bear with me:
@DrB
@Niels
References: DrB LRC Table 2020.03.20 and “The Final Resting Place”
The table is of a set of Optimum “Straight-Line” flight paths.
Please correct me if my interpretation is wrong.
The table shows a tendency for the Optimum Flight Level to be dependent upon the Flight Bearing.
In particular, for the set of Optimums tabled, the Optimum Flight Level consistently reduces as the sampled Flight Bearing is increased. [With the exception that FL403 is optimum both for 178.0 and 178.25 Degrees Bearing.]
The link below is to a subset graph of the relationship between FL and Bearing.
This is no more than a re-plot of the data from your table for LRC, and is the same as that shown in Figure G-8, the Airspeed and Flight Level Sensitivity Study, and in Figure 23 of your report. It has been re-plotted simply to possibly assist in my understanding.
Q1: Why the dependency ?
Q2: Can it be explained in simple terms ?
Q3: Which parameters contribute most to this tendency ?
Q4: Are the strong winds evident towards the latter stages of the flight, and contributing to more headwind component as the bearing tends more and more westward, considered a major contribution to this tendency ?
Q5: Following on from Q5 if the winds are a large contributor, are the winds less strong at the lower altitudes (say FL374 compared to FL395) when the aircraft is more southward in the latter stages of the flight ?
Comment: Looking at the simple plot, it becomes fairly obvious why the required fuel will increase markedly as the Flight Bearing changes from below, through, and to above 180 degrees. Hence the Fuel Probability WILL drop dramatically over a small range of any Optimum “Straight-Line” Flight Path descriptor, such as Bearing.
Reason: As the Flight Bearing changes from below, through, and to above 180 degrees and the Optimum Flight Level reduces then the increase in air density at the lower altitude will require more engine thrust and thus fuel to punch the aircraft through the more dense air at Long Range Cruise speed, which itself will be relatively unaffected due to being in a region of relatively unaffected standard atmospheric temperature.
https://www.dropbox.com/s/coi416lom0xx51o/LRC%20FLvsBrg.xlsx?dl=0
@George G,
You said: “You have written (posted): “In this situation, the smallest fuel shortfall is for Option B1, which has the air packs off and the cross-feed valves open.” whereas methinks you meant to write “cross-feed valves closed”.”
Yes. Option B1 has the cross-feed valves closed.
You asked: “The table shows a tendency for the Optimum Flight Level to be dependent upon the Flight Bearing.
In particular, for the set of Optimums tabled, the Optimum Flight Level consistently reduces as the sampled Flight Bearing is increased. [With the exception that FL403 is optimum both for 178.0 and 178.25 Degrees Bearing.]
The link below is to a subset graph of the relationship between FL and Bearing.
This is no more than a re-plot of the data from your table for LRC, and is the same as that shown in Figure G-8, the Airspeed and Flight Level Sensitivity Study, and in Figure 23 of your report. It has been re-plotted simply to possibly assist in my understanding.
Q1: Why the dependency ?
Q2: Can it be explained in simple terms ?
Q3: Which parameters contribute most to this tendency ?
Q4: Are the strong winds evident towards the latter stages of the flight, and contributing to more headwind component as the bearing tends more and more westward, considered a major contribution to this tendency ?
Q5: Following on from Q5 if the winds are a large contributor, are the winds less strong at the lower altitudes (say FL374 compared to FL395) when the aircraft is more southward in the latter stages of the flight ?”
My responses below are numbered to match your questions.
1. An increasing TAS is needed for bearings greater than 180 degrees, in order to match the handshake arc locations. This effect would not exist if all the arcs were concentric, in which case the average KTAS would be constant. So, we are fortunate that the satellite was moving during the flight, because otherwise it would be very difficult to discriminate bearing. The only remaining asymnmetry would be the position-dependent weather conditions, and this is unlikely to provide effective route discrimination on its own.
2. See #1.
3. The non-concentricity of the arcs is dominant. A lesser effect is the increasing headwinds late in the flight for bearings greater than 180 degrees. That requires a higher KTAS to overcome. This is partially accomplished by using M0.84 rather than LRC. The two speed schedules are nearly identical, except when the fuel load is light, when LRC reduces the Mach below M0.84. Additional increases in KTAS are provided by reducing the altitude to warmer air, when the Local Sound Speed is higher. Both effects increase the average fuel flow.
4. See #3.
5. The variation in headwinds after the second phone call at 23:14 is negligible between FL374 and FL395 at 186 degrees bearing.
Richard said:
“I noted differences in the start point on N571, 10 NM beyond waypoint MEKAR, at 18:22:12 UTC (or 18:22:15 UTC which you use), the lateral offset, the position and timing of the FMT near IGOGU, the turn bank angle at the FMT and the initial bearing toward way point ISBIX, all of which I ignored.”
I say: I can’t tell what “all of which I ignore” refers to. I think you mean that where your path simulation, for example, differs from my simulation you ignore my results. I suggest that the 3 second discrepancy in the start time is merely an accommodation to the fact that my model has been used in 15 second increments.
Do you mean that you ignore the FMT turn at IGOGU to 186 at 18:39:30?
I have provided you with a complete operating spread sheet on numerous occasions so that you have access to all of my data, the entire path, and the algorithms used. I sincerely regret that you have not seen fit to trust me, even privately, with the same information from your model.
@sk999,
In a recent comment you said: “I have been asked whether I considered the various statistics involving the correlation of the BTORs with other quantities. In fact, I looked at the correlation with UT nearly 4 years ago, found it no where near as useful as the BFO correlation with UT, and turned the calculation off. I have looked at it again, this time computing the Spearman, Pearson, and Kendall correlation coefficients, and still don’t find it particularly useful, at least for the purposes of the report.”
On page 153 in our paper we said: “Because the OCXO frequency drift might have a linear component with time during the SIO Route, we exercise caution in interpreting the correlation coefficients of the BFORs with themselves and with time.”
The BTORs (not the BTOs) should be decorrelated with time, and this is an effective route discriminator.
In fact, with the one exception we noted, the decorrelation of the BTORs and BFORs is a very effective route discriminator, subject to only the random noise of the satellite data.
Think of it this way: what can cause correlation among these parameters? We believe there are only four possible causes:
1. Noise in the measured BTOs and BFOs,
2. Errors in the flight model, and
3. Errors in interpolated GDAS data, and
4. Errors in the fitted flight parameters.
Our method allows for Cause #1. We are only concerned with correlation coefficients which are beyond that expected by the BTO and BFO noise.
We have eliminated Cause #2 to the greatest extent possible by intercomparisons in great detail of our three independently produced flight models, demonstrating a very high degree of consistency (generally to better than 0.1 PPM in latitude, longitude, and bearing).
Our method also allows for Cause #3. We have demonstrated that the errors in the interpolated GDAS data are small. Furthermore, we allow non-zero GSEs, which, in effect, allows for small errors in the GDAS data and in our interpolations of it. Thus, our method ensures GDAS errors do not introduce correlations.
Cause #4 is what is left (errors in fitted route parameters). If you do not eliminate correlations in the route fitting process, you allow route fitting errors to exist in the result. The result is bias and reduced route parameter discrimination.
In your recent paper you said: “The choice of “start time” is arbitrary; while UGIB chose 19:41, one can equally well chose the
time of crossing the 7th arc (00:19:37 or thereabouts.)”
The satellite data indicate a flight without major maneuvers between 19:41 and 00:11. That is the range we used to fit SIO Routes. Your statement about this being “arbitrary” is nonsensical.
@Sid Bennett
You are unbelievable!
“all of which I ignored” at the end of the sentence, refers to “I noted differences” at the start of the sentence.
I am not ignoring your results, as you claim with your obtuse question.
I am actually trying to analyse your results, why do you think I would ignore them?
I state: “I rebuilt your flight path using your Timings, Positions, Altitudes and Bearings in my model”
Which means, that I am ignoring the differences I found in Timings, Positions, Altitudes and Bearings.
To be even more clear, I state “I effectively overwrote and disregarded my Navigation model”.
Which again means, that I am ignoring the differences I found in Timings, Positions, Altitudes and Bearings.
@DrB
Thank you very much for your answers.
Your answers to 3,4 and 5 are very clear.
Similarly, most of your answer to 1 (and 2) is very clear and informative, but your reference to increasing TAS “needed for bearings greater than 180 degrees” followed in the next sentence by “in which case the average KTAS would be constant” has confused me.
I’m not sure when you are referring to “increasing TAS” whether you are actually referring to increasing TAS over a flight, or to a tendency for the values for Average KTAS to progressively change when considering a set of candidate flights in order. In context I suspect the latter (?).
Were you referring to the wide range analysis as plotted in Figure G-8 (and Figure 23) of your joint report, where there is a general tendency for the Average KTAS to be higher at 187 degrees compared to 172 degrees with several variations in between (?).
In the narrow range represented by your “LRC Table 2020.03.20” the tendency above 181 degrees is opposite; see linked graph.
https://www.dropbox.com/s/fs950qocg4l0p0h/KTASavg%20-%20Narrow%20Range.xlsx?dl=0
@DrB
I am focus on BFO section. Page 140/141 it is mentioned that we do not know when the previous 16 Hz BFO bias adjustments were made for 9M-MRO, that apparently would have been part of the oft quoted DSTG Figure 5.4. How hard would it be to get that? If DSTG or ATSB or Inmarsat already has that data handy?
@TBill,
I have requested the additional BFO data from ATSB, but my requests were never fulfilled. I believe DSTG has the data, but are either unwilling or unable to release it, possibly due to non-disclosure agreements among the various parties.
@George G,
You said: “I’m not sure when you are referring to “increasing TAS” whether you are actually referring to increasing TAS over a flight, or to a tendency for the values for Average KTAS to progressively change when considering a set of candidate flights in order. In context I suspect the latter (?).”
I was referring to the general tendency toward higher average TAS at bearings greater than 172 degrees, as shown by the black dotted line in our Figure 23. It also shows a few wiggles up and down along the way.
@DrB
Of course, DSTG has the data. I can think of no reason why that data is not in the public domain.
@DrB
Ta.
@Dr B and @Andrew
In your report appendix FUEL MODEL A.1O APU Fuel Flow you state “The APU will be ON during all main-engine INOP periods, assuming fuel is available from
the left tank and/or the APU fuel line.” It was my understanding from the ATSB’s end of flight descriptions that the APU would not auto-start unless and until the second engine had flamed out, so would not have started during the period between L and R engine going down. Can you confirm either way?
If there was an active pilot at end of flight, then it sounds as if normal procedure would be to start the APU when first engine goes down. If that is the case, and the APU feed is situated lower in the well than the L engine fuel uptake, it implies that APU would be running – and keep running – at the time that L engine flamed out. That in turn would permit controlled (straight) flight under Autopilot after second flame-out until the APU ran out of fuel.
The consensus 7th arc logon mechanism would then need to be adapted. Could the AP autostart again after fuel starvation if aircraft attitude once again allowed the AP fuel line to fill?
@paul smithson
RE: “It was my understanding from the ATSB’s end of flight descriptions that the APU would not auto-start unless and until the second engine had flamed out, so would not have started during the period between L and R engine going down. Can you confirm either way?”
Your understanding is correct. The event that triggers the APU auto-start is the loss of AC power to both transfer buses. That would occur after the second engine flame-out, assuming the electrical system was in the normal configuration.
“Could the AP autostart again after fuel starvation if aircraft attitude once again allowed the AP fuel line to fill?”
No. The auto-start is initiated by the Electrical Load Management System (ELMS) when power is removed from both transfer buses, at which point ELMS sends a start signal to the APU controller. The start signal is a discrete input and is not repeated.
The 7th arc logon suggests that electrical power to the SDU was interrupted when the second engine flamed out and restored when the APU auto-started. That scenario implies the pilot did not manually start the APU after the first flameout. It’s likely the pilot was incapacitated by that time if the cabin had been depressurised for several hours.
Hi @Authors,
I shall try to be careful 😉 it’s clear you’ve done an amazing amount of work on your paper, unpaid, and for that: thank you.
There should also be some limitations placed upon it : not least the likelihood of the wreckage lying in a data gap, but also (as @Victor) and others have said before : only unpiloted paths can be realistically considered. Piloted paths… they just cover too much space.
So can I ask – *if* the region you suggest were to be searched (in parts searched again), with no positive result…. would you continue with your work? or conclude the flight was probably piloted and hence almost irresolvable,? or a third option?
as I say, I’m stunned and thankful for the work you have all put into this. I just worry the horse you’re flogging is long gone
thanks.
@vodkaferret: I’ll only speak for myself. If the recommended area is searched with a null result, unless new data or insights surface, I have no further recommendations. If it does occur, this is likely to be the final search for a long time.
@Victor
thank you, We obviously all hope that is not the case.
Steve
@Steve (aka @vodkaferret),
I concur with Victor, there will only be one more search and it had better be in the right location.
The new Armada technology from Ocean Infinity allows efficient searching of a much larger area than before, but if MH370 is not found in our recommended search areas A1, A2 and A3, then I will hang up my laptop and apologise profusely for wasting everybody’s time and money.
@Victor. Area 1.
I refer to the paper’s 8.4. Uncertainties of the LEP along the arc add up to its extremities. At the extremities the uncertainty of the trajectory after LEP will be expressed as circular, i.e. on a radius from those extremities. Uncertainties normal to the arc would of course need to be added.
Thus I see Area 1 as a sausage shape, not rectangular.
If so its area would be reduced by about 74^2 less pi*74^2/4, i.e. 1175 sq nm
On a minor point I suggest 8.4.3, “Uncertainty of Turn Between Fuel Exhaustion and 00:19:29”, be renamed, “………Between Disengagement of Autopilot and…”, since the turns included some in the alternative configuration before MEFE .
Clarification please. The last line should have “commencing” before “before”.
@Richard
thank you for your reply. let’s hope it doesn’t come to that!!
@David: Yes, I took some liberties in representing the circular trajectory as uncertainty along and parallel to the arc.
It took a while to catch up with the conversation after only a brief interruption, but some comments here stand out as completely dismissing new acoustic evidence for a very specific FEP:
@DrB “Please tell me why you think he would want to perform maneuvers after 19:41, assuming he were not incapacitated? If he was beyond radar range and could not be tracked by other means, what would be the point of altering course after 19:41?”
@VictorI “It would be quite a coincidence if multiple maneuvers produced the same match to the data as a straight, automated flight with no pilot inputs. Any other justification for maneuvers is just supposition, and we are back to reconstructing paths based on hunches.”
@DrB “I defy anyone to demonstrate a curve like our Figure 19 for any other route, especially for a route with maneuvers between 19:41 and 00:11. In my opinion, it is unique.”
@VictorI “If the recommended area is searched with a null result, unless new data or insights surface, I have no further recommendations.”
@Richard “I concur with Victor, there will only be one more search and it had better be in the right location.”
I still cannot understand why such a specific endpoint is not on anyone’s mind. I do realize how a maneuvered scenario like CAPTIO may seem to be one of an infinite number of paths that fit the satellite data, making it incalculable compared to an unpiloted straight path.
Conversely, the 370Location.org reports describe a very specific endpoint on the 7th Arc. An infinite number of ways to fly there that fit the data would seem to be a strong point in favor of that destination.
If one were to construct a cumulative probability graph of BFOR, BTOR, Fuel Endurance, and unsearched areas for my endpoint, it would be a prominent peak on a flat 3D landscape relative to neighboring latitudes AND longitudes.
I estimated BFOR using Richard’s spreadsheet. I’m sure the simple path I laid could be optimized to match BFO, but I did not “contrive” to do that.
Previous studies of barnacle temps were not considered useful because they did not match with an SIO endpoint.
A tropical site is instead consistent with temperature, growth, and species of the barnacles and molluscs found.
There are a variety of drift studies, but most did not even look at the 7th Arc at latitudes near Java. The final reports state clearly that CSIRO was asked to compile drift studies *based on new data* which was the PDF of the SIO. CSIRO privately conceded that a location near Java could drift to the locations where debris was found, with the notable problem being that the debris arrives too early, months before it was found. That seems quite possible.
Fuel endurance for my published path at FL150 is within 50 km of the 333 kt MRC exhaustion documented by Boeing in SIR Appendix 1.6E.
Taking a path to a specific flyover detection time at Cocos Island that is compatible with the FMT and 2nd Arc location is not complex. There are few waypoints in that area. A direct flight is of course possible, but the plane had been flying waypoints up to the FMT. The reasoning for maneuvers beyond 19:41 in this scenario is that there is evidence of acoustic detections that appear to match up with MH370 arc timing and endpoint location.
The connecting airway between Cocos and a tentative detection at Christmas Island is rather obvious, still on a waypoint path.
Assuming a standard departure heading for Jakarta from Christmas Island and continuing to fly waypoints may be the weakest part of my proposed path. The timing might be better matched by a long climb followed by a short fast descent toward the 7th Arc. Perhaps an expert in BFO would be willing to check for compatibility.
I haven’t modeled the GDAS for fit, because modeling to that accuracy for fuel endurance is not necessary for the already located endpoint. What matters is whether the plane could have flown any plausible path to the endpoint.
That the endpoint acoustic event is 55 minutes after 7th arc timing is not unlikely. An implosion was suggested by the CTBTO when calling for researchers to investigate in the first days after the plane was lost. It was mentioned in the final reports. It was encouraged by the ATSB. Experts have advised that even a weak implosion of some component as the plane sank should be heard long distance, vs the difficulty of detecting a surface impact.
As to whether the search should be conducted, the threshold has long been for “new credible evidence”.
I’ve said that I do not see this as a zero sum game where only one search can be conducted. I support the authors and everyone here in their efforts to find the truth. I don’t think that should include ruling out any viable candidate, either statistical or acoustic.
A good reason to search the specific site of an anomalous acoustic event is that the search area is relatively small. Expert seismologists could certainly improve the accuracy with better tools and crustal data. The site might even be narrowed to the point that an entrepreneurial ROV excursion could suffice vs an extensive OI grid search.
I know that you will continue on with seeking consensus on your current conclusions specific to a straight path, and I agree that they are very compelling. In your negotiations for a future search, I ask you to please keep in mind the possibility of exploring more than one area.
In your logical arguments, please don’t rule out piloted maneuvers that would get to a known endpoint.
Thanks for all your hard work!
— Ed Anderson
@370Location (Ed):
I appreciate your support of the work of many contributors to this site, and I also have an appreciation of your scientifically-based methods to localize the debris field.
I estimated BFOR using Richard’s spreadsheet. I’m sure the simple path I laid could be optimized to match BFO, but I did not “contrive” to do that.
But that’s exactly what you’ve done with the BTOs.
Your endpoint succeeds or fails based on whether the acoustic event was from MH370. You seem certain it was, with a delay due to a component that sank and imploded. There have been a number of people (including David Mearns) that believe this is a very long stretch.
Frankly, I don’t understand what single component of a B777 would implode with enough energy to cause an acoustic event that is detected thousands of kilometers away. Contrast this to the hull of a submarine. At the same time, I profess no expertise in this area, which is why I neither support or dismiss your work.
I hope that others that have the time, expertise, and willingness to do a deeper dive into your work will confirm or refute your findings, regarding both the location and the possibility that the acoustic event was from MH370.
@370Location
Those of us favoring active pilot hypothesis could have similar list of comments. Below I attempt list to summarize MH370 SIO hypotheses:
MH370 Crash Location Hypotheses Groups (SIO):
(1) Active Pilot flew Straight No-Maneuvers to 38 South (many proponents)
(2) Passive Pilot flew Straight No-Maneuvers to 38 South (many proponents)
(3) Passive Pilot flew Straight No-Maneuvers to 32-35 South (many proponents)
(4) Passive Pilot flew Straight No-Maneuvers to 26-30 South (formerly in favor)
(5) Active Pilot conducted Maneuvers to Various Locations 10-32S (many proponents)
Philosophically I would say Search-1 (Fugro et al) addressed Group-1 and Group-2. The second search (OI) addressed Groups-3,4,and some of Group-5.
We are hoping for a Search-3 and IG is proposing that at least part of that search be centered at the current proposal (34S). I have long wondered if OI will search other areas, since we know several universities have been invited to develop models.
Those of us in Group-5 can only hope that either (1) additional regions are also searched, closer to our respective hypotheses, or (2) there is a future Search-4, which Victor discounts somewhat, or (3) our hypotheses are wrong and IG is correct about 34S region.
@TBill
As Victor has pointed out, the current paper UGIB) is not an IG position at this time.
How do you reconcile case (1) with the lack of a search strategy to deal with a glide? The UGIB paper presents a reasoned approach to revisiting the area at 34S but recognizing that the glide was not searched there either.
That searching the glide area substantially expands the search area is the worst reason to avoid doing it once a search effort is mobilized.
@Sid
Logic dictates I missed a lesser-favored Group-3a (analogous to Group-1):
(3)(a)
Active Pilot flew Straight No-Maneuvers to 32-35 South (less current support)
As far as Group-1, my understanding is Search-1 was much wider than +-25nm, so that hypothesis already benefited from an extra wide search, although I realize not the “full Monte” super-wide search that advocates feel is needed. I sympathize since I also feel long glide is possibly indicated by the data.
I personally feel, the current searches need to assume minimal glide. Assume Arc7 is the key place, but with margin of error, so perhaps 30-40 nm limit.
Tony Abbott basically said we should allow for active pilot possibility, which I agree with. But to me, that does not mean Group-1 is assumed to be the correct place for +-125 nm search. I believe we need some kind of future mathematical analysis or other lead for active pilot cases, and possibly a multi decade search.
PS Sid- I did take a look at your recent paper, but I did not immediately see your hypothesis. Do you feel active pilot? and if, so what was the intent or strategy? Most of the Group-1 feels it was a dash to sunlight terminator, which I guess had to be calculated pre-flight to hit that zone without maneuvers.
@Sid Bennett
The IG used to have 18 active members.
There are now only 7 currently active on this forum.
Out of these 7, 6 have expressed their support for our findings in the recent paper.
I know of only one vocal dissenter from the IG on this forum.
@TBill
In my recent paper I intentionally avoided taking a position as to whether there was an active pilot after 18:40 or so. My focus was on defending the original IG proposition of a 186T path at high altitude.
Now that I have understood the objections to my study at a constant altitude at variable M, and have determined that LRC at 39000ft gives an equivalent result, I redid the case at 18:40 and got a very tight fit . I am also going to re-do the turn time analysis using the LRC approach.
The evidence for an active pilot might be stated as follows:
At 18:22 (the 18:25log-in), someone (a human) had to have re-enabled the power to the SDU. I believe the offset route from N571 was manually initiated. Once that is done, I suppose that the human could have programmed the rest of a high altitude, including the turn at IGOGU to a ISBIX waypoint (with a continuation on 186T rhumb line) to the 7th arc. So, a human input cannot be definitively shown after 18:22.
But, if the human intended to end the involvement at 18:22 or so, why bother to re-energize the SDU? Why bother to re-pressurize (if indeed that was done?)
So far, I can find no evidence for or against the human being in position to maneuver the plane at the time of fuel exhaustion.
@Richard,
I miss Henrik.
@Sid Bennett said: Once that is done, I suppose that the human could have programmed the rest of a high altitude, including the turn at IGOGU to a ISBIX waypoint (with a continuation on 186T rhumb line) to the 7th arc.
After reaching an end-of-route in LNAV mode, the plane would follow a constant heading, not a constant track. Whether the heading is magnetic or true depends on whether the position of the HDG switch is NORM or TRU. Unless the plane is operating in polar regions, standard procedures would be to select NORM.
@DennisW
You stated “I miss Henrik”.
I included Henrik in the count of 7 IG members currently active in this forum, together with Victor, Mike, Don, Brian, Sid and myself.
@Richard: Barry Carlson also contributes here.
My apologies @Barry Carlson for leaving you off the list.
@Richard,
I’ve monitored carefully all the posts in this forum. Not having any compelling comments to make either in favour or against the UGIB proposal, I have refrained from muddying the waters.
Notwithstanding, I applaud the dedicated work all of you have made in presenting the paper.
@Ed Anderson,
You asked “@DrB “Please tell me why you think he would want to perform maneuvers after 19:41, assuming he were not incapacitated? If he was beyond radar range and could not be tracked by other means, what would be the point of altering course after 19:41?””
I don’t see any benefit of changing course after 19:41. I have wondered about step climbs, but that possibility would only be driven by maximizing range. Since he did not fly at MRC, fuel conservation does not appear to be a priority, so step climbs are unlikely.
You also said: “That the endpoint acoustic event is 55 minutes after 7th arc timing is not unlikely.”
I disagree. A well-known oceanographer does, too. There is far too little energy in anything that could implode, and the long delay is problematic, because the implosion would have to be located in the SOFAR channel to be heard at any significant distance.
Victor Iannello said:
April 10, 2020 at 7:58 am
@David: Yes, I took some liberties in representing the circular trajectory as uncertainty along and parallel to the arc.
Smile. (of recognition of some need for simplicity)
@George G. Increase of Area 1 by about 1175 sq nm from the 5,544 sq nm it otherwise would be, around 21%, is a large approximation, unparalleled in error estimates.
@David
Agreed, “21%, is a large approximation”.
I had left discussion of the End Point for some time. The rectangle is very rudimentary, and I presumed deliberately so. I had not yet reconciled the “uncorrelations” implied by Table 1 in Section 8.4.6. Although I felt “comfortable” that it would be reconcilable. These are used in definition of A1. In absence of that reconciliation, my making any other comment on the 74 by 91 representation would be inappropriate.
I had also interrupted discussion with Ventus 45 concerning End of Flight scenarios and BFO implied descent rates.
However, since that time, other reviews have led me to believe the most likely, and highly likely, situation is that the flight southwards was made with an incapacitated or deceased pilot.
Concerning the potential use of the 74 by 91 rectangle, I presumed that anyone seriously considering a re-search would be making their own analysis of where and most importantly in what order they would conduct a search.
(Presumably straight line boundaries will be used in any case)
Recently, or for some time, I have been more concerned with an overview of the data and analysis used by the report authors to narrow down the location of the LEP. That overview has been become somewhat prolonged.
As part of the overview I have become more acceptable of a sharp cut-off in fuel availability, as represented by Figure D-3, than I was previously.
@VictorI
“There have been a number of people (including David Mearns) that believe this is a very long stretch. Frankly, I don’t understand what single component of a B777 would implode with enough energy to cause an acoustic event that is detected thousands of kilometers away. Contrast this to the hull of a submarine.”
@DrB (Re: That the endpoint acoustic event [] 55 minutes after 7th arc timing is not unlikely.)
“I disagree. A well-known oceanographer does, too. There is far too little energy in anything that could implode, and the long delay is problematic, because the implosion would have to be located in the SOFAR channel to be heard at any significant distance.”
The tweets from David Mearns regarding implosion were his knee jerk reaction to the idea of an implosion. He called it a “red herring”, as if it were an intentional diversion away from the true path (which would of course be a reference your collective work). My work is not mutually exclusive of yours.
He assumed the discussion was of the plane ditching intact so the entire fuselage could implode. His experience is with ships, and perhaps he was also thinking of the implosion of submarine ARA San Juan. If he were familiar with SOFAR acoustics or had seen recent tweets, he would know that the discussion was of smaller components. Asked if he had examined any of the reports or background, he said he’d “already seen enough” [to judge, from tweets].
BTW, the San Juan was not in the SOFAR channel, but much shallower water.
Oceanographers calibrate distant hydrophones by small explosive charges, or triggered cracking of glass spheres at SOFAR depth. Tests with 10 inch (8.7 liter flask) and 22 liter glass spheres find that their implosion at 650m is about equivalent to 1-2 lb of TNT. (They were felt in the ship above, and deeper implosions should be stronger.) That equates to about a 200db sound level, expected to be heard across the globe at a distance of 8000km. From the Java Anomaly to the Diego Garcia hydrophone is less than half that distance. In contrast, a lightning strike may reach 270db, yet even nearby surface strikes that day were undetectable. There is a big difference between a surface event, and one that propagates into the SOFAR channel.
I can’t really know what made that sound. Anything from an O2 or CO2 cylinder to even a large thermos. Perhaps it was buckling or collision of larger sinking parts. Something made a very loud noise, right on the 7th Arc.
Rigorously challenging with dismissive language any evidence that doesn’t meet one’s own hypothesis or intuition seems to be the way of public debate. I appreciate your mention that I have taken a science-based approach. To me, that means being cognizant of our own biases and attempting to correct for them. It also means exploring credible leads, which doesn’t always lead to a single solution.
I suspect this is why my work got no mention at the MH370 research conference or in the ATSB report. ATSB even said that the plane could not be in multiple places at once. Presenting multiple search candidates, left them with much less confidence in any of them because they had to ultimately be mutually exclusive.
That is not the way I think, and certainly not my intent here. My path is premised on your good work, with additional evidence.
Thanks for allowing my comments here, and also for inviting others to assist with validation of my candidate. I am open to any collaboration.
@TBill
Thanks for breaking down the different proposed endpoint theories into subgroups. It does make it clear that getting a consensus as was the IG premise would be difficult. I also didn’t realize how broad the views were.
I also saw your condensed version as a tweet. A minor point is that you might list destinations beyond 10S to 8S, as that is the limit at the Java coast. (My anomaly event being at 8.36S.)
I realize why my candidate is lumped in with other maneuvered paths, but I think my approach stands alone as working backward from new evidence for a very specific location.
Your groupings do give me better perspective.
@370Location said: Rigorously challenging with dismissive language any evidence that doesn’t meet one’s own hypothesis or intuition seems to be the way of public debate.
I have never dismissed your work. I am neutral towards it. For me to warm up to it to the point where I would recommend it as a candidate search area, I would have to dive in to better understand and evaluate it, or trust the opinions of experts.
It would be an interesting experiment to drop fire suppression spheres or whatever you think might have caused the acoustic event at your location of interest to see if it matches the acoustic signature of the event you identified.
@370Location
I stand corrected, 8 South to 32 South for the range of more easterly active pilot path proposals.
Per your above post, when/what was the MH370 research conference?
@ VictorI
I was griping in general to uninformed but dismissive language by Mearns and many others. It was not meant personally. I realize I’m your guest on this forum, and grant you the full respect you are due.
Experiments dropping components were proposed and pursued by Don. I don’t know why it was rejected. It may take nearly resources to do that test as to search the sea floor at the candidate site.
@TBill
Thanks for the revision.
Griping again, I was referring to the conference referenced in the ATSB final report:
“In November 2016 experts from various organisations and agencies who had been closely
involved in defining the MH370 search area met for a first principles review. (the ATSB’s report of
the meeting can be found here: First Principles Review).”
https://www.atsb.gov.au/media/5772107/ae2014054_final-first-principles-report.pdf
“The meeting was to reassess and validate existing evidence and analysis and to identify any new analysis that may assist in identifying the location of the missing aircraft.”
The FPR notes:
” A presentation on the hydro-acoustic data at the time of the accident allowed meeting participants to determine that hydro-acoustic analysis did not contribute any useful new information to the search.”
That’s what I saw as the result of submitting too many candidates. I still think the work was well done, and the Gulden Draak acoustic candidate was prominent and specific, but it wasn’t where they wanted to look.
(Ref: the joke about looking for a lost watch under the streetlamp because the light is better. 😉
@370Location
I am quite interested in Gulden Draak event right now, because I believe you predict several candidate locations of the event.
The Java event you have well-documented and is of interest if Xmas region gets higher search priority in the future. The fact that Tony Abbott indicates Malaysian leaders thought it was pilot suicide, and presumably not the rumored negotiation scenario with Xmas/Java diversion plan, tends to further support the straight or semi-straight flight path to SIO 20-38 South.
@TBill
“The fact that Tony Abbott indicates Malaysian leaders thought it was pilot suicide, and presumably not the rumored negotiation scenario with Xmas/Java diversion plan, tends to further support the straight or semi-straight flight path to SIO 20-38 South.”
I certainly would not expect Malaysian leaders to support a negotiation scenario.
I can’t muster up anything convincing to support pilot suicide as the initial motivation for the diversion. Crashing became the only option after a negotiation failed. Hence, my preference for a Cocos or Xmas Island flight path.
@George G, Victor. George G’s, “.. I presumed that anyone seriously considering a re-search would be making their own analysis of where and most importantly in what order they would conduct a search.”
Yes, could be left to them.
There would be another couple of possible ingredients:
First, reducing a revised Area 1 end semi-circles to 32 nm radius (the allowance for the distance travelled after the LEP transmissions) from 74/2 = 37 nm, the further area excised would be 542 sq nm.
Second, should the 8.8 nm allowance either way along the arc for a turn after fuel exhaustion be that much? I suspect that extreme stems from Boeing simulations of descents in the alternative electrical configuration, i.e. the autopilot being disengaged at right engine fuel exhaustion.
Since the LEP transmissions would be 2 mins later, that would be 4½ mins before MEFE otherwise.
That would be beyond the fuel budget of the paper’s Fig 31.
As with it being necessary that the packs were off in the SIO leg to meet that budget, that same argument should exclude the alternative configuration simulations from consideration.
That done the 8.8 nm would drop to about 3.4 by my ruler, reducing Area 1 by two 5.4 nm (approx.) wide strips, 77 nm wide, an area of roughly another 832 sq nm.
The total Area 1 reduction from the current 6719 sq nm then would be, 1175(from earlier)+542+832 or 2549 sq nm, 61% of the new reduced area.
This would be immaterial of course were the search intention at the outset to include Areas 2 & 3; except for prioritising. However having to disregard fuel sufficiency to justify searching these, as distinct from saving the expense (cost vs the residual success likelihood) or searching other alternatives, might limit the search to just Area 1.
Days after the flight a retired Malaysian businessman discussed with me the political situation in Malaysia, explaining that Captain Zaharie had been caught up in it and that he was aware of a meeting Captain Zaharie had in the days before the flight.
I have known the gentleman for years and have no doubt of his integrity.
He did not know what actually happened to MH370 but he did know what was planned to happen.
He was quite categorical that Captain Zaharie had no intention of committing suicide.
Captain Zaharie’s intention was to ensure the plane landed safely and released the passengers.
Details of the plan and implications as I see them were outlined in a score or so of postings on this blog.
@370Location’s findings and final location are not inconsistent with the location that was suggested early on by my friend.
My above, correction. “That would be beyond the TIME budget of the paper’s Fig 31.”
@Sid Bennett,
To further investigate the 186 degree LNAV route, I did a number of case studies. A summary of those results is available HERE .
Table 1 in that document compares critical parameters for various cases of route fitting with different optimization functions and conditions. All route fits in this case study assume the air packs are always ON and the cross-feed valves are always CLOSED.
Case 1 is the route you proposed with a 186 degree true initial bearing at 18:39:30. It is flown in LNAV with LRC speed at FL390. I have left the results in the table blank for your fit, but maybe you can fill in some of them from your calculations. For my purposes, I only need the seven route parameters, which I have taken from the worksheet you provided to Richard.
Cases 2 through 5 are some of my new results.
In Case 2, I used your seven route parameters, and I defined the handshake locations by forcing the Ground Speed Errors (GSEs) to zero. These handshake positions, then, are simply what my flight model calculates along the great circle route, taking into account the GDAS local temperature and wind. In Case 2, the fuel probability is high (79%) as a result of assuming LRC at FL390. We already know that is the case, because this is the same speed setting and flight level we determined to be the global best fit at 180 degrees. At 186 degrees bearing, the primary weather change is greater headwinds late in the flight. We don’t expect a particularly high route probability with no allowance for GSEs, and this is indeed the case. The route probability is only 11%, and the compound (route X fuel) probability is 8%.
In Case 3, I allowed the GSEs to be non-zero and also to be consistent with the conditions laid out in our paper regarding magnitude, slope magnitude, and smoothness. This allows the handshake locations to move along the great circle path to maximize, in this case, the product of the route and fuel probabilities. The fuel probability does not change materially, but the route probability increases to 31%.
In Case 4, the GSE conditions are as given in our paper, but now the starting location (latitude and longitude), speed, and flight level are free variables which are adjusted to maximize the route probability. This is the same general method as used in our paper for the bearing study. So, in Case 4, the only assumed parameters are the 186 degrees in LNAV starting at 18:39:30. Everything else is adjusted to maximize the route probability. Just to be clear, I am following your bearing assumption of 186 degrees at 18:39:30, not at 19:41 (which was the convention we used in our paper). This leads to a bearing at 19:41 of about 185.95 degrees true.
The Case 4 results show a substantial increase in route probability, due to a significant change in starting latitude, a small change in starting longitude, and a substantial change in altitude (2,000 feet higher). Case 4 is optimized by maximizing the route probability. Here the route probability is up to 54%.
Case 5 uses the compound probability as the objective function to be maximized, but the results are not discernibly different from Case 4. So, again, as at 180 degrees, I see that the route fits don’t vary noticeably whether route probability or the product of route probability times fuel probability is maximized by the fitting process in a single fit at a given altitude. The altitude sensitivity is low enough that SOLVER won’t find the peak in probability with the flight level as an additional free variable (and neither will it find the best bearing that way). Instead, I have to step the altitude along manually to optimize it.
So, the bottom line in this case study is that there are two solutions, and one is better than the other other. You found one at FL390 that is better than the one we showed in our paper, but it is on the side of a second, larger peak at FL410.
The second item in the attachment is a plot of various probabilities versus flight level for this 186 degree route. This illustrates the difficulty in route fitting at 186 degrees caused by having two “local” peaks in the objective function. It’s hard to determine they exist, without a systematic altitude survey at a fixed bearing, much less to determine which one is the “global maximum”.
The red curve in Figure 1 is the route probability. The green curve is the fuel probability. The black curve is the product of the route and fuel probabilities.
You can see that, as it turns out, that there are two peaks in route probability for the 186 degree route. Our initial search in 2019 identified the one at FL370. You have found the side of another one at FL410. It has both a higher route probability and a higher fuel probability.
These studies indicate, as before, that fitting either the route probability or the product of the route probability times the fuel probability does not materially change the result when using SOLVER, although in principle a better optimizer might at least allow one to find one of the bearing/altitude parameters while holding the other one fixed. In this study, I found the fuel probability is essentially 100% at FL410, so one should not expect the two objective functions to produce different results.
What does change the result are the initial guesses for FL, latitude, and longitude. One guess lands the fit on one of the probability peaks. A different starting position and altitude can land the fit on a different probability peak.
This second peak shown in Cases 4 and 5 is better than our (and your) original solution, although it is still significantly lower in overall probability, compared to the 180 degree route (which seems to have only one peak in probability). Thus, 186 degrees has a route probability not all that different from many other nearby bearings (see the top panel in our Figure 15). The plot of probabilities for 186 degrees (Figure 1 in the attachment) demonstrates that a complete altitude survey at each bearing is necessary to identify the presence of multiple peaks and to discern the highest peak. Without that altitude survey, or a more effective optimizer, those bearings which have multiple peaks can lock onto a peak which is not the optimum for that bearing, depending on the initial guess for altitude.
My case study demonstrates that, at least at one bearing > 180 degrees, a high fuel probability is possible, and one might expect nearby bearings to behave similarly. When I have the opportunity, I will have a look at intermediate and larger bearings to see if they have more than one route probability peak, and I will update the route and fuel probability graphs in our paper accordingly.
@George G, Victor. I see from D1, page 115 that the abnormal configuration is not included anyway, suggesting to me that the 8.8 nm either way along the arc for a turn after fuel exhaustion could be reduced as outlined above.
@David,
Your potential refinements noted.
As stated previously, I have not yet reconciled the full implications of Table 1 in Section 8.4.6 and in absence of that would prefer to defer any specific comments re A1.
As I think the most likely, and highly likely, situation is that the flight southwards was made with an incapacitated or deceased pilot, then A3, even A2, become/s (in my opinion) irrelevant.
A final qualifier is, of course, is that all the above is in consideration of a “straight-line” path southwards, Post 19:41.
With respect to anyone seriously re-considering a re-search, it might be expected that anyone would be reviewing all previous search data very strenuously prior to any such consideration. Then they might be ensuring that they have proven methods to investigate very challenging bathymetry. The initial order of search might be based on the results of both the two previous, i.e. the data review and development of proven methods for searching very challenging bathymetry, and not necessarily upon wider considerations. (Just to explain my previous comment.)
@Sid Bennett,
Bobby requested “I have left the results in the table blank for your fit, but maybe you can fill in some of them from your calculations. For my purposes, I only need the seven route parameters, which I have taken from the worksheet you provided to Richard.”
I would much appreciate, if in addition you could clearly specify, whether in your view, there was an active flight plan, an active route, whether the waypoints IGOGU and ISBIX were used and when an active pilot ceased to control the aircraft.
In your paper dated 28th March 2020, you state:
(1) MH370 “continues on the N571 azimuth until at least waypoint IGOGU“.
(2) “The navigation mode is LNAV (at least until ISBIX, and possibly True Track thereafter)“.
(3) “the path overflies the ISBIX waypoint and we consider that this is the last waypoint used. Alternatively, the path coincidently passed very close to the ISBIX waypoint.“.
(4) “The aircraft is being flown using the automatic flight controls by manually entering commands and data in an alphanumeric display“.
If I understand you correctly, MH370 was in LNAV mode and the waypoint IGOGU was definitely used and the waypoint ISBIX may have been used. In any case, there were no waypoints used after ISBIX, so there was a route discontinuity.
If waypoint ISBIX was the last waypoint (which was reached at 19:32:41 UTC according to your spreadsheet), then as Victor has already pointed out, that following this last waypoint in LNAV mode, the aircraft would revert to a Constant Magnetic Heading (CMH) unless there was an active pilot who had previously changed the Heading Reference Switch from NORM (Magnetic) to TRUE and then the aircraft would revert to a Constant True Heading (CTH). Neither of these navigation modes reach anywhere near your end point of 37.3913 °S at 00:17:30 UTC.
Another possibility is, that you are saying that an active pilot at ISBIX selected the HDG/TRK switch on the MCP to TRK, entered a track of 186 (only 3 digits allowed) and pressed select. In this case, the aircraft would change to the Constant True Track (CTT) navigation mode and as you say this is a good approximation and reaches an end point of 37.4294 °S at 00:17:30 UTC.
Another possibility is, that you are saying that an active pilot at IGOGU selected the HDG/TRK switch on the MCP to TRK, entered a track of 186 and pressed select. In this case, the aircraft would change to the Constant True Track (CTT) navigation mode and as you say this is a good approximation and reaches an end point of 37.4286 °S at 00:17:30 UTC.
Please clarify, which navigation mode was used and when.
@TimR
@DennisW
Re: Xmas/Java Routes
Thank you.
Additionally there were social media accounts in the days after the crash, suggesting that at least one elected official was expecting MH370 to show up at a diversion airport.
So the “rumor” is semi-well supported. I just feel at this point, it seems like any such negotiation was over by IGARI. Or the plan was changed.
The rumor as we understand it, was an extortion plot. If ZS demands were met, MH370 would safely divert to Xmas/Java. We are told by TimR that ZS was also planning to safely divert to Xmas/Java if his demands were not met (apparent bluff). DennisW envisions, if demands were not met, the ultimatum was to crash, which is what we witnessed.
@Richard,
@Sid Bennett,
If the MCP were used to set a constant track angle, such as 186 degrees, that would only be a Constant True Track if the NORM/TRUE switch had also been set to TRUE. Otherwise the result would be a Constant Magnetic Track.
@DrB
I agree.
My point to @Sid Bennett was, that either a heading based or a magnetic based navigation mode (CTH, CMH or CMT) track ends up far away from @Sid Bennett’s end point, with no match to the satellite data.
Only a CTT loxodrome comes close to a LNAV geodesic.
That requires an active pilot to switch the heading reference from NORM to TRUE.
@DrB
@Richard
Thank you for further considering the 186T option. You have done so much work that I need to try and assimilate it before making any comments.
I had been working on a revision of my paper, but will put it aside for now and address your posts.
The only impediment is that my wife is trying to get me accustomed to playing on-line bridge :-). It is one of our many adaptions to the current situation.
As a brief comment on some of my recent studies, I redid the study that I did with Geoff Hyman in 2015 to determine the time of the FMT and the resultant azimuth (now using LRC at 39000ft). The time window for FMT has narrowed as has the distribution of possible azimuths. I will
@Richard
I prefer to take no a priori position on the route except that it starts at 18:22 on N571. The rest follows from the data. That the FMT seems to be at IGOGU and that the route seems to overfly ISBIX is highly suggestive of a LNAV route via known waypoints. However, that is an observation rather than a conclusion. If a end point is to be fine tuned, one of the approaches should be a IGOGU to to ISBIX route followed by a path that might depend on whether there was pilot intervention. But, first things first. (I tend to use IGOGU and ISBIX as a shorthand notation for their approximate location so as to help me visualize the scenario.)
You have mentioned a number of possible relatively minor path changes if indeed ISBIX is used as a waypoint and, again, I am not sure I have thought them through enough to firmly choose one. Considering the search area size, they are probably equivalent, but they all ought to be computed to see if any further insight can be gained.
https://www.dropbox.com/s/b9pstmt1crrp1a1/Preliminary%20Research%20Note%20041120.docx?dl=0
Just to update our previous study.
@DrB
You wrote:
“My case study demonstrates that, at least at one bearing > 180 degrees, a high fuel probability is possible, and one might expect nearby bearings to behave similarly. When I have the opportunity, I will have a look at intermediate and larger bearings to see if they have more than one route probability peak, and I will update the route and fuel probability graphs in our paper accordingly.”
To what extent have you studied LRC, CTT in the 180 – 186 degrees range for different FLs / are you intending to extend for CTT in similar fashion?
@Niels,
You asked: “To what extent have you studied LRC, CTT in the 180 – 186 degrees range for different FLs / are you intending to extend for CTT in similar fashion?”
I did look seriously at CTT some time ago, and near 180 degrees there may be reasonably good CTT fits. Doing that again in the future depends on how long it takes me to update the LNAV routes between 180 and circa 186 degrees for potentially better FLs. I will also see if there is a better speed mode, which is possibly M0.84 as an alternative to LRC (although this did not improve the 186 degree route at FL410).
In my opinion, CTT is much less likely than LNAV, because it requires setting the MCP track angle and changing the NORM/TRUE switch. Why would anyone change the switch, and why would anyone pick 186 degrees CTT?
@All,
Fuel modelling for MH370 was hampered in the past because we did not know the Performance Degradation Allowance or the Fuel Performance Factor for 9M-MRO. Finally the Operational Flight Plan for MH370 was leaked in the RMP report showing a fuel performance factor of 1.5%. We were also told in the Malaysian SIR that the right engine consumes on average 1.5% more fuel per/hour compared to left engine. I decided to use the ACARS data from MH371 to verify the Fuel Performance Factor and the Right/Left Engine Fuel Flow Rate Ratio
I used the Fuel Flow sensor calibrations scaling factors from the MHXX FOQA data as discussed in section B.2.2 of our paper. I used two methods to calculate the Fuel Performance Factor: (1) the fuel used method and (2) the specific range method.
Using the calibrated Fuel Flow sensors gives a fuel performance factor on average of 1.41% overall (for both methods) and a fuel flow rate R/L difference for the sensors of 1.53%.
Using the uncalibrated Fuel Flow sensors gives a fuel performance factor on average of 2.01% overall (for both methods) and a R/L difference for the sensors of 3.35%.
MAS Operations were regularly using data from ACARS downloads and quite likely were using the Boeing software tools to track the fuel performance factor of each aircraft in their fleet. MAS Operations were using the retained value method to update the fuel performance factor in steps of 0.5%. The 9M-MRO fuel performance factor was set at 1.5% and had not yet reached a sustained level above 2.0%, where MAS would increase the value to the next step.
If MAS Operations did not correct the raw Fuel Flow sensor readings, then they wouldn’t get an average fuel performance factor of 1.5%, nor a 1.5% fuel flow rate right/left engine difference. Using the fuel flow sensor calibration factors from the MHXX FOQA data and applying them to the MH371 fuel performance factor data collection, the average fuel performance factor and the fuel flow rate ratio between right and left engines, match the MAS values.
The detailed analysis can be found in the attached paper:
https://www.dropbox.com/s/0ef39vifgh09dnh/Performance%20Degradation%20Allowance%20and%20the%20Fuel%20Performance%20Factor.pdf?dl=0
@Sid Bennett
You stated: “You have mentioned a number of possible relatively minor path changes if indeed ISBIX is used as a waypoint and, again, I am not sure I have thought them through enough to firmly choose one. Considering the search area size, they are probably equivalent, but they all ought to be computed to see if any further insight can be gained.
A CTT path has a fuel exhaustion point 27 km from a LNAV path. This is within the A1 search area size.
A CTH path has a fuel exhaustion point 176 km from a LNAV path. This is not within the A1 search area size.
A CMH path has a fuel exhaustion point 684 km from a LNAV path. This is not within the A1, A2 or A3 search area size. It is a similar case for a CMT path.
@DrB
https://www.dropbox.com/s/hipueflj6bc9rjs/DrB%2BSid_041220.JPG?dl=0
I annotated your spread sheet with excerpts or computations from a spread sheet that I used for my recent paper.
As you would expect, the results match to within the range of values associated with slightly different met models and goodness of fit criteria.
The case I present is where there is an offset from N571 that is not cancelled prior to the turn. I believe that your cases 4 and 5 would be likely if the offset were cancelled before the turn and the turn was made from the center-line of N571. My modeled turn is a bit too sharp for an exact comparison.
Also I believe that the evidence supports a case of air packs off and a reduction in electrical load for the hour prior to 18:22.
When I was trying to compare met models with Richard, I believe I observed that the result likely lay slightly above 39000ft. The adjustment of altitude using the LRC model is analogous to adjusting M when using a constant altitude.
I have looked at this problem as one of step-wise refinement of the math model. However in the case of the fuel consumption, I wonder if we can consider the result “good enough”? If not, how can we proceed?
Based on this result, I think one can argue that there is only one high altitude path.
I look forward to your further comments.
@Richard,
I was considering the rhumb line selection by a pilot who didn’t want to bother entering a further waypoint.
In the case of a 180T path wouldn’t the rhumb line coincide with the GCP?
@Sid Bennett,
You asked: “In the case of a 180T path wouldn’t the rhumb line coincide with the GCP?”
My apologies to Richard for interjecting a nuanced exception. With no disturbances, the CTT path at 180 degrees true would match the LNAV (geodesic) path. However, with any variation in cross-track wind, CTT and LNAV are not the same. That’s because LNAV is following a prescribed path, whereas CTT is trying to maintain a constant direction of travel. The disturbances off the geodesic path will be completely corrected with LNAV navigation, but not completely by CTT navigation, which restores the direction of travel but not the lateral offset of the new path. So, CTT can slowly “drift” off the geodesic due to numerous small lateral displacements. I have estimated that this CTT error off the initial geodesic could amount to as much as 0.1 degrees of average bearing error.
@Sid Bennett,
You said: “I have looked at this problem as one of step-wise refinement of the math model. However in the case of the fuel consumption, I wonder if we can consider the result “good enough”? If not, how can we proceed?
Based on this result, I think one can argue that there is only one high altitude path.”
As I have demonstrated, at 186 degrees there are two candidate routes, with the higher one having a higher probability. It has a high fuel probability, so it is certainly feasible from a fuel perspective.
We can proceed by figuring the fuel probability using the method described in our paper. That puts the higher altitude 186 degree route into a similar position of importance as many of the bearings between 172 and 186 degrees. It has a fairly good overall probability, but it is still significantly lower than the 180 degree route, which has the highest overall probability and a unique “feature” in Figure 19 which has not been found at other bearings.
@Sid Bennett
You stated: “I was considering the rhumb line selection by a pilot who didn’t want to bother entering a further waypoint.
Do you mean, that the pilot on reaching waypoint ISBIX, selects Heading Reference Switch from NORM (Magnetic) to TRUE, selects HDG/TRK on the MCP to TRK and then presses HOLD, to initiate a CTT on the current track?
@Richard,
Something like that….
@Sid Bennett
The HDG REF switch is intended for use in polar regions, and only where the pilot needs to engage a HDG or TRK mode (ie HDG SEL, HDG HOLD, TRK SEL, TRK HOLD). In all other cases, the HDG REF switch is selected to NORM. The FCOM states:
“Use TRUE when operating in regions where true referencing is needed. Use NORM in all other regions.”
It is certainly possible to change the heading reference outside the polar regions, but as DrB asked above: “Why would anyone change the switch, and why would anyone pick 186 degrees CTT?” The likelihood of such a scenario is very low, in my opinion.
@Andrew
It matters little to me that SOP is to use NORM. The switch has a position and can be selected.
More importantly, the 186 path depends on nothing but the Inmarsat data.
To look at it another way, the pilot could have cranked in a 186T or whatever rhumb line azimuth would be the best approximation heading to the 186T path at about the location of IGOGU and called it a day. (Of course that is not how it happened.)
I’m not sure we could tell the difference. It needs to be computed.
Once we get away from the 180T hypothesis as the only solution, many options are open to testing.
(BTW, if there was something distinctive about the selection of CTT at ISBIX, it might help us understand the time when un-piloted flight began.)
For argument’s sake, let’s say the 180T and 186T paths have equal probability with respect to the satellite data, fuel, etc. Which path would you say is more likely – the one that requires unusual switching and an ‘odd’ choice of track (why 186°?), or the one that doesn’t?
My previous post should have been addressed to @Sid Bennett.
“Why would anyone change the switch, and why would anyone pick 186 degrees CTT?”
If you were going to “check out” at either IGOGU or ISBIX, I certainly would select true.
Why Switch ?: Two reasons.
(1) No one in the professional aviation world would think you would do so, so, confuse them (us) a bit more.
(2) Most important though, just look at the isogonic lines on any marine or air navigation chart of the IO.
Why 186 ?: Two reasons.
(1) He didn’t want to go anywhere near Australia and/or JORN (which he knew about).
(2) Without using an unreachable LNAV endpoint, prevailing westerly winds, particularly the “possibility” of encountering and crossing jet streams, would push it to the east. A 4 degree right offset would be a reasonable selection as an “averaging” countermeasure, indeed, it could have been 5 degrees, or more, and although the resultant straight path we think we see is 4 degrees, it may not actually be strait, it may have some minor “wiggles” in it, as it proceeds south through the variable ind fields, making it even harder for us to nut it out.
@DrB
Thank you for your reply yesterday 3:12 pm. I was not specifically aiming at CTT 186 deg. Personally I feel such path might end a bit far south in the light of indications from drift analysis.
For example I find really good BTO fits for CTT 183 deg for FL 374 and above.
Regarding control mode / navigation (why CTT): same can be asked for flying straight south by waypoint. Imo impossible to answer without knowing the exact intent of person in control.
With the great analytic tools that have been developed it is possible to leave it open, which I think is better (at the cost though of the incredible amount of time and effort you and others are spending on doing such complete analysis).
@Richard (cc DrB)
Thank you for your posting regarding fuel performance factor and flow sensor calibration. In the past days I have been reading more in detail about the fuel model error analysis and one of the main questions I have is what the impact would be if the estimated error probabilities for available and required fuel at 19:41 (which are assumed Gaussian distributed with zero mean if I understand correctly) would have a non-zero mean, for example due to a calibration error in the fuel flow sensors. It looks to me in that case the variance formula for error propagation would perhaps not be sufficient.
So I’ll read with great interest.
“Why would anyone change the switch, and why would anyone pick 186 degrees CTT?”
I am NOT a supporter of 38 South, but if I was, I would say perhaps the pilot had calculated the sunlight terminator and possibly had factors in his head for how many degrees track he needed depending on his arrival time at IGOGU.
@TBill
The terminator has been mentioned at times. How do you think it fits in the scenario?
@Andrew
Of course, all of our work has previously been done on a LNAV path. Once that path is considered probable, it is worthwhile to discuss any possible variations. So, whether the CCT is likely or not, changes the actual intersection with the 6th arc little from the point of view of the search.
@Andrew
You said:
“For argument’s sake, let’s say the 180T and 186T paths have equal probability with respect to the satellite data, fuel, etc. Which path would you say is more likely – the one that requires unusual switching and an ‘odd’ choice of track (why 186°?), or the one that doesn’t?”
The CCT is at the moment just a comment. The analysis, based on a start point at 18:22 on N571, revealed that, if a turn to the SIO at any azimuth was made and a LNAV mode was used, the turn needed to be made at about 18:40. The analysis further revealed that a turn at 18:40 had a best fit at 186T. (see my recent post on the subject where the data is linked)
Subsequently we realized that the turn occurred at IGOGU and passed over ISBIX. This could be a coincidence; but, it can be interpreted as continuing to fly on a standard waypoint path in LNAV. That is an interpretation, not a requirement.
Choosing 180T may be considered odd and arbitrary as well. It presumes a destination waypoint that, while not implausible, is not obvious.
@Andrew
I am lazy. Thanks for pushing me.
CCT LRC at 186T at 39000ft works just fine from IGOGU.
-37.67846 88.95534 at the 7th arc.
This is a preliminary result as I have not checked everything in the spread sheet but it looks good.
“CCT”=CTT
@Andrew
Let me withdraw the last post. I see some “minor” problems.
I don’t know whether I can get back to it today as I am expected to be an on-line bridge partner….
@Sid Bennett said: Choosing 180T may be considered odd and arbitrary as well. It presumes a destination waypoint that, while not implausible, is not obvious.
To say that the SouthPole is not an obvious waypoint is bizarre. It is easily entered and is consistent with creating a path that will end as far south as possible upon fuel exhaustion. In fact, I can’t think of a more obvious waypoint.
I seriously doubt that the pilot selected a navigation mode in which the plane flew in CTT mode over a distance of thousands of kilometers. That said, a custom waypoint could have easily been entered to fly a great circle path in LNAV mode until fuel exhaustion and achieved nearly the same path.
The advantage of either a great circle or rhumb line with a track of 186T near IGOGU is the simplicity over the BEDAX-SouthPole path–the entire path is flown at cruise speed and cruise altitude. The disadvantages are the lower route and lower drift probabilities (drift probability near zero, according to David Griffin’s model).
Bobby’s statement that there is sufficient fuel at FL410 to reach 37.5S latitude increases the probability of this path. The question is whether or not the probability increases to the point where it becomes a candidate search area. I have my opinion, but I’ll let Bobby and Richard weigh-in first, as they have studied this more than me.
@MH370Location
You stated “Fuel endurance for my published path at FL150 is within 50 km of the 333 kt MRC exhaustion documented by Boeing in SIR Appendix 1.6E“.
Be careful of using the Boeing Appendix 1.6E, because they got the winds the wrong way around.
The Boeing Segment 1 starts at 17:06:43 UTC and ends at 17:28:19 UTC and FL350 is maintained throughout.
At 17:06:43 UTC the ACARS data and the GDAS data show a wind speed of 17.13 knots and a wind direction from 070°T. The MH370 Heading was 26.70°T (according to the ACARS data) and there was a head wind of 12.75 knots.
By 17:21:12 UTC the GDAS data shows a wind speed of 14.48 knots and a wind direction from 92.4 °T. The Heading was then 32.62 °T and there was a head wind of 7.60 knots.
The ca. 180° turn back then follows, which ends at ca. 17:24:09 UTC. During these 3 minutes, the wind is fairly neutral, partly against you and partly with you.
4 minutes later, at the end of the segment at 17:28:19 UTC the GDAS data shows a wind speed of 15.05 knots and a wind direction from 90.3 °T. The Heading is now 226.03 °T and there was a tail wind of 10.54 knots.
Appendix 1.6E shows an average tailwind of 14.1 knots, whereas the flight path experienced an average headwind of 3.77 knots.
This of course, changes the fuel consumption.
Apart from the winds, Boeing list in their assumptions that they used the “standard day atmosphere“.
The ∂SAT averaged 10.1°C during Segment 1.
This of course, also changes the fuel consumption.
@Dr B. In the paper the fuel probability drops to zero around -37.3 judging from the figure. Now, if I’m reading correctly, it would appear that Sid’s 186 route ending -37.6 is judged feasible with high altitude route. With packs on. I don’t understand. What has changed?
@paul smithson,
You asked: “@Dr B. In the paper the fuel probability drops to zero around -37.3 judging from the figure. Now, if I’m reading correctly, it would appear that Sid’s 186 route ending -37.6 is judged feasible with high altitude route. With packs on. I don’t understand. What has changed?”
You must have missed reading my previous comment HERE .
The high fuel probability doesn’t actually occur for the 186 degree route at FL410 with packs on, but the same route flown with packs off has a high fuel probability.
@paul smithson,
If the link above doesn’t work for you, paste this in:
https://mh370.radiantphysics.com/2020/03/09/new-report-released-for-mh370-search/#comment-27866
For some reason the link is keeping a parenthesis at the end.
@paul smithson,
@DrB,
Confusion reigns.
Figure 37, Route Probability, in the joint report, or paper, and repeated in the top panel of Figures 5 and 15 was presumably prepared as part of the Route Analysis prior to the Fuel Analysis having been conducted. Derivation is part of Appendix G, but the overall Route Probability is not presented there, as it would appear that derivation of the Final Fitted SIO Route outweighed the overall probability in perceived importance.
Your confusion, Paul, was similar to my initial reaction.
But it soon became apparent that the route probabilities that DrB has recently tabled [such as 54.4 per cent for Trial#916 at FL410] were well below the highest route probabilities within Figure 37.
That there was a high fuel probability for a specific route example of relatively low route probability thus became less important.
But the question remains: What does the second-to-top panel of Figures and 15 represent ? This is Figure D-3 from Appendix D.
DrB: Please: Does this represent the fuel probability for the specific optimum routes whose probabilities are plotted in Figure 37 (and the top panels of 5 and 15). ?
If so, the second panel is dependent upon the first (where-as the third and fourth panels are completely independent).
@Dr B. I share @Paul Smithson’s confusion. Lines 6 and 38 say the packs are on and 38 the same. Your comment to Paul indicates that they were off. Maybe two earlier versions have been replaced by these?
I cannot find where in your comment 2786 this is clarified. In its para 2 it says they are on.
@Dr B. My problem is this. I had understood that you have maintained that a terminus south of ~37S is simply not fuel feasible. Specifically, Figure 15 p6/177 of the report showing “probability of the fuel model matching the known endurance” indicates probability <10% for everything south of 35.7S and zero for everything south of 37.3S.
I interpret your commentary on Sid's route (which ends around 37.6S) to be saying that it is fuel feasible at FL390, LRC and even more so at FL410, LRC – in both cases with packs on (albeit with start point shifted south ~0.3 degrees).
The "fuel required" (row 17) is 33,751kg for cases 2,3 and 33,599kg for cases 4,5. I am not sure what benchmark of "fuel available" you are comparing these to? In my estimation, fuel remaining at this point is 34,244kg – comfortably adequate with ~0.5T to spare.
In short, this commentary on the 186 degree route study appears to demonstrate that a final latitude of 37.6S is attainable. With packs off (about another 7 minutes?) and dipping into the 1 sigma error margin (about another 4 minutes) should get you down to ~39S.
My enquiry (and confusion) is not about the specifics of Sid's route, but whether you have revised your views on whether latitudes south of 37S are reachable. The issue is important because (as sk999 earlier noted) the fuel feasibility is the main factor that elevates the combined probability of your search zone compared to areas further south.
In addition to above questions:
For Cases 2 through 4, the value in Rows 17 and 22, The tabled Required Fuel on Board, is numerically equal to the (my) calculated Fuel Available on Board.
For example: Case 4: 201,205 – 174,369 = 26,836
I found this because I was interested if the fuel available produced a shortfall or excess.
For clarity,
That is, in addition to the above questions from Paul, David and George.
@Richard
Thank you for the GDAS wind computations vs Boeing approximations. They did say they only sampled winds twice at 1800 and 0000 and interpolated, so perhaps why their values are off.
They also fly at constant speed regardless of weight (and my path speeds may be worse).
Winds would not be favorable for the ENE segment of my path vs their SE heading, either.
Still, I take their fuel endurance as a ballpark figure. I think it would take a large FE estimate shortfall to rule out a specific location where a noise was heard. It would have to be enough to make the destination unflyable.
My path would be 68 km shorter if the plane flew direct from XMAS to the 7th arc.
Just curious, Appendix 1.6E notes that there’s an overspeed control law that automatically increases angle of attack, and it takes pushing forward on the column during an alarm to override it. Presumably that was taken into account for the end of flight scenarios. (Only works for level flight?)
While on the subject of latitude discriminators, allow me to comment on the drift study results described in Appendix H. The commentary on Figure H-1 states “Similarly, crash latitudes south of 37°S have very low probability (although the uncertainty is higher in this region because the number of drifts is low).
The Table H-1 describes the Girffin et al CSIRO 10 Nov 2018 as comprising “Crash latitude range 8 – 36S”. I can’t understand how the results can include latitude 36.0 – 37.0 if the source model was limited to 8S – 36S. I also don’t understand how “the number of drifts is low” south of 37S for the same reason.
If the drift model did not extend to crash latitudes south of 36 (or perhaps 37?) then the absence of results south of that is a limitation of the model parameters, not an “zero drift probability”. Since 36.0-37.0 is the mode in figure H-1, it would be very surprising if the actual probability distribution dropped abruptly to zero.
So what exactly is the evidentiary basis of the oft-repeated assertion that drift model results counter-indicate southerly termini?
@DrB. As now I understand it at the 18:39:30 start time at least 33,599 kg of fuel was required but that would need to be reduced by the packs-off 452 kg savings to get to -37.5+ S.
@Sid
Re: Sunlight on 38 South paths, the flight would be mostly in darkness but there would be sunrise just before the crash/landing. Some 38 South proponents cite that as the proposed strategy of the pilot. Presumably that assumes the pilot was active and attempting to execute a ditch-style landing, possibly with a glide.
@MH370Location
You stated regarding the Boeing Appendix 1.6E “They did say they only sampled winds twice at 1800 and 0000 and interpolated, so perhaps why their values are off“.
I agree, but my point about getting the winds the wrong way around was based on the ACARS data at the start of Segment 1 at 17:06:43 UTC. It appears that Boeing took the ACARS wind data from the aircraft showing a wind speed of 17.13 knots and a wind direction from 070.0°T and misinterpreted it as 17.13 knots to 070°T.
From the ACARS data, the resulting TAS is 484.4 knots and GS is 472.1 knots. Boeing state the average TAS was 478 knots and the average tailwind was 14 knots and you might falsely conclude that the average GS was 478 + 14 = 492 knots, when in fact Boeing probably meant 478 -14 = 464 knots.
I only pointed out that the ACARS matched the GDAS data, which shows for the ACARS position at 17:06:43 UTC of 5.299°N 102.183°E, altitude of 35,004 feet, a wind speed of 18.16 knots and wind direction from 76.1°T, to show the general alignment between the ACARS data and the GDAS data. I agree that the Boeing interpolation of the GDAS data may also have been in error.
In addition the official ADS-B data shows at 17:06:43 UTC a position of 5.289°N 102.803°E, heading of 25.4°T, altitude of 35,000 feet and GS of 469.3 knots.
Further the Kota Bharu TAR radar shows at 17:06:43 UTC a position of 5.285°N 102.801°E, track of 26.4 °T and GS of 475.3 knots (assuming an altitude of 35,000 feet).
Following the Boeing flight path through Segment 1 shows an average TAS of 484.0 knots (not 478 knots) and average GS of 479.9 knots (not 492 knots), based on Boeing’s assumptions.
The bottom line is you cannot rely on the fuel analysis from Boeing in Appendix 1.6E being accurate for our flight path modelling.
@370Location
You asked “Just curious, Appendix 1.6E notes that there’s an overspeed control law that automatically increases angle of attack, and it takes pushing forward on the column during an alarm to override it. Presumably that was taken into account for the end of flight scenarios. (Only works for level flight?)“.
Yes! This was taken into account for the end of flight scenarios.
The autopilot disconnects after dual engine flame out.
@Andrew has previously suggested, in order to explain the roll input necessary in order to achieve the downward acceleration in the required timeframe during the end of flight, there are only limited possibilities:
(a) An active pilot at the controls, helping the dive.
(b) The dead-weight of an incapacitated pilot, slumped over the controls after the autopilot disconnected.
(c) The asymmetric yaw from an unlikely momentary engine relight.
@370Location: To follow up on @Richard, the overspeed protection only occurs when the flight control mode is NORMAL. After the second flameout and power is lost for both transfer busses, the flight control mode transitions to SECONDARY. Even after the APU comes online and power is restored to the main and transfer busses, the flight control mode remains in SECONDARY, unless the Flight Control System (FCS) switch position is manually cycled, and then only until the APU shuts down.
@TBill
Yes, I have heard that explanation. I just wondered if there were any other factors to consider.
If that were the case, what sun angle to the flight path would be most advantageous during the descent?
@Richard
I didn’t grok on the first reading that Boeing actually flipped the wind direction 180. Thanks for making that clear.
Thanks also for the recap and details on the overspeed discussion. I was not around for that. Very Helpful.
@VictorI
So, no overspeed correction after second flameout without pilot intervention, if I understand right.
Thanks once again.
@paul smithson
You stated: “I can’t understand how the results can include latitude 36.0 – 37.0 if the source model was limited to 8S – 36S. I also don’t understand how “the number of drifts is low” south of 37S for the same reason“.
David Griffin’s and the CSIRO analyses covers from 7°S to 45°S.
In the CSIRO first report they concluded:
“There is a region within the 36-32°S segment of the arc, near 35°S that is most consistent with all of the following lines of evidence, taken together:
(1) absence of detections during the 2014 surface search .
(2) absence of findings on the WA coastline.
(3) July 2015 arrival time of the flaperon at La Reunion.
(4) December 2015 and onwards (only) arrival times of other debris in the western Indian Ocean.
We therefore conclude that while the whole 36°-32°S region is prospective, the subset region near 35°S appears to be the most likely location of the aircraft.
In the subsequent CSIRO reports, this conclusion was confirmed each time.
Therefore David Griffin suggested, that he only need give us the data from 7.5°S to 36.5°S for our analysis, as below 36.5°S was not possible in his view.
@Sid
The 38S sunlight theory I am not the expert, but I assume it presumes the pilot wanted to see the surface of the water for a ditch. So perhaps about sunrise +15-30min would give adequate surface visibility.
@Richard, thank you for this clarification. Then the “probability of the CSIRO Drift Model matching the 9M-MRO Debris Reports” was assessed as far as 36.5S and the region beyond that was “not assessed” in your reanalysis rather than being probability=0.
However, it is simply wrong to say that “below 36.5 S is not possible”. That is not what the data shows and it is not what the authors say in their interpretation and commentary.
The Part 1 report debris results basically concluded that debris items came from between 32S and 39S. “Are other regions also prospective? If the flaperon had remained the only piece of debris found we would have to say ‘perhaps’, but now many debris items have been found, we can conclude that regions north of 32°S and south of 39°S are both less likely. Drift modelling suggests that debris items originating north of 32°S would probably have been detected by the surface search, and that items would have probably arrived in Africa before December 2015. Regions south of 39°S are not prospective either, because debris from those regions would more likely have turned up on Australian coastlines than west Indian Ocean ones.” Discussing the effect of local NW/SE currents along the arc and its influence on subsequent trajectory, they also argued (p23) that “This absence of findings argues against three latitude bands as potential entry locations. These are near 33-35°S, 36-37°S and 39-42°S, leaving sites north of 32°S and bands around 35-36°S and 37-39°S as being more consistent with the absence of Western Australia (WA) debris findings.”
The Part II report updated these results with important insights gained from the drift characteristics of an actual flaperon – travelling faster than they had assumed in their original model, and to the left of wind direction by 10-20 degrees (their empirical mean 16 degrees). The updated conculsion on the origin of the flaperon? “The July 2015 arrival date of the flaperon at La Reunion island is consistent with impact occurring between latitudes 40°S and 30.5°S.” They also cited additional observations (width of undersea search to date, absence of debris in Australia and null result of the aerial search) to say that they favoured 35S as “the only one that is also consistent with other factors”. The Part III report also updated their drift simulation to inlude high windage debris items (figure 4.1)
Part IV report focuses more on the consistency of the Pleiades imagery with the purported 35.5S origin. However, at page 21 I noted that even from this preferred location “Panel 3 shows that there is only a very small chance that any of the low-windage debris would have washed up on the coast of Australia. Panel 4 shows that a few items of high-windage debris – if they were still afloat – are hindcast to have washed up at some remote locations on Australian shores.” So it appears that even the non-recovery of drifted items from Australia is also not quite the binary qualifier that it is sometimes depicted as.
I have responded at some length because I happen to have re-read these reports today and I think it is important not to misrepresent their findings and conclusions.
Still on drift… The executive summary of the report says:
The third panel in Figure 5 (the grey curve) is the probability that the CSIRO debris drift model predictions are consistent with both the locations and the reporting dates of MH370 debris. A novel method for combining time and location was applied to provide a single figure of merit (probability) for each crash latitude. Crash latitudes between 35 °S and 33 °S have the highest debris drift probability.”
The panel in question exhibits a maximum at 36.0-37.0 (right before it has been cut off). 35.0-36.0 has a high probability that is virtually indistinguishable from 33.0-34.0. That doesn’t quite align with the statement in the last sentence above.
Let me offer a status report, in the hope that comments from readers will assist in the analysis.
I have constructed a scenario comprising a start at IGOGU with ISBIX as a waypoint. Subsequent to ISBIX as a discontinuity, the path continues as a loxodrome at the entry azimuth to ISBIX. I fixed the altitude at 41000ft with LRC (constant M at about 0.84 is similar). I obtained quite good results and a reduction of about 70kg in fuel consumption. The end point moves slightly North along the 6th arc.
Exploring the effects of start time and start latitude on cost, it appears that changes of 15 secs (current step resolution) and 0.05 in latitude of the start are meaningful changes. This suggests an unique start point. However I expect that a GCP starting at a similar point would also be considered a fine fit.
Since some of the details of the path near IGOGU are really difficult to model in the type of spread sheet that I am using, I raise the question that I posed about 6 months ago as to whether one of the better flight simulators could help in refining the start conditions for the southern leg.
I particular, whether the turn was made from the N571 center-line or
a path offset to the North (and how far North). A program which obeyed the FMC rules would be the most straightforward approach. It is not a good use of my time to learn to run one of the simulators, but perhaps there is a reader who wishes to collaborate.
If this is not be best place to do that, can anyone recommend a suitable site to try?
@David, George G, paul smithson,
Let me address your questions in a general sense with a brief summary of how we calculate the route probability in our paper. There is a description of this in Appendix D, but it is unclear on one point (due to some inadvertently missing text), and this may be causing some confusion. I shall add that missing text to that section to make it very clear.
1. There are 9 Cases (numbered 1-9) of pre-19:41 routes which produce 9 estimates of available fuel at 19:41. These are intended to cover the range of possibilities.
2. There are four post-19:41 Options (A, B1, B2, and C) which address the four possible post-19:41 aircraft configurations.
3. Thus, there are 9 x 4 = 36 possible combinations, of which 9 are excluded due to incompatibility, leaving 27 viable combinations.
4. Each of those 27 viable combinations has a unique value of fuel shortfall/excess. The smaller the shortfall/excess, the higher is the probability.
5. To standardize the route fitting method, and to minimize the amount of work involved, we fit all routes with Option A, which is the air packs ON and the cross-feed valves CLOSED.
6. We generally show the required fuel available at 19:41, for a particular route, assuming Option A.
7. The required fuel at 19:41 may be calculated for the other three Options (B1, B2, and C) from the Case A value by scaling, as we showed using the percentages given at the top of Table D-3.
8. Thus, we only need to fit Case A, and then we can simply find the fuel shortfalls and probabilities for the other three options by scaling.
9. When we quote a “fuel probability” for a given route fit, we select the MAXIMUM probability among the 27 viable combinations. In most situations, this occurs for Case B1 (air packs OFF).
10. So, while we fit a route using Case A assumptions (air packs ON), the route probability we generally quote is for the highest probability, which in most cases is Option B1 (air packs OFF). This maximum fuel probability is what is plotted in Figure D-3 and the second panel in Figure 15, and it corresponds to the same SIO route fits whose route probability is shown in the top panel in Figure 15.
I think this last item is creating confusion. The method we chose is intended to separate, as much as possible, the route fitting process from the fuel probability determination. We can’t fit each SIO bearing for 27 combinations of pre-19:41 fuel availability and post-19:41 fuel requirement. So, we fit one post-19:41 route assuming Case A, and we can then compute the fuel probabilities for the other 26 viable combinations. Then, we find the highest fuel probability among the 27 values. The intended description of that last step, selecting the maximum value, got lost somehow in the paper preparation process, and I shall put it back.
To demonstrate this methodology further, I modified the table of 186-degree fits that I showed previously, to include the fuel probabilities for the four post-19:41 Options. That allows one to see what the fuel probability is with air packs ON and with air packs OFF (and with cross-feed valves CLOSED and OPEN).
The extended table is available HERE .
I also added a route fit using M0.84 at FL370, which is the original peak found in the route probability and used in our bearing study.
@paul smithson,
You asked: “So what exactly is the evidentiary basis of the oft-repeated assertion that drift model results counter-indicate southerly termini?”
It is primarily the lack of debris finds in Western Australia, which appear to increase rapidly to the SW along the 7th Arc.
David Griffin’s latest data set extends somewhat beyond 36S crash latitude, to about 36.5 S.
To illustrate the effect, I have made a new plot of the probability that a drift that beaches somewhere, actually lands in Western Australia. It is available HERE .
This plot shows that for all crash latitudes north of 31.5S, less than 3% of the beached debris should land in Western Australia and nearby islands. With about 28 debris, that corresponds to an expected value of less than one debris find. The plot shows how rapidly the probability grows with more southern latitude. In only 5 degrees farther south, at 36.5S, the probability is up to 12%, so one out of every eight beached debris land in Western Australia. With ~28 debris, that is 3-4 expected finds in WA. Clearly, this is unlikely to have actually occurred, because there were concerted efforts to find MH370 debris on WA beaches, and none were found. So, crash latitudes below 35S generally become more and more improbable. There are some narrow variations with latitude due to localized currents, but the general trend is quite clearly shown by the CSIRO predictions.
The black dashed trend line in the figure indicates that the probability of beachings in WA is expected to be even higher for crash latitudes south of 36.5S, and the discrepancy with actual debris finds grows even larger. This large discrepancy is what drove us to the conclusion that a far south crash is improbable, because the probability generally decreases rapidly the farther south you start the drifts.
The novel drift probability formulation we developed was, of course, not used by Griffin et al, although private communications indicated David thought our formulation was a useful single metric that combines all the available information (beaching location, drift days, flaperon, non-flaperon, etc.). It has a high peak with essentially constant probability between 33 and 37 degrees south latitude. We believe that beyond 37 S the drift probability declines fairly rapidly to negligible values. It would be nice to have more drift predictions in that latitude range, to better define the drop-off, but as far as I know there are no plans at CSIRO to do this.
@DrB
Thank you very much.
Please allow time for consumption. 😀
@paul smithson
(1) Misrepresenting the CSIRO findings as showing a MH370 end point at 39°S.
CSIRO Report – The search for MH370 and ocean surface drift – 8th December 2016
Conclusion: “We therefore conclude that while the whole 36°-32°S region is prospective, the subset region near 35°S appears to be the most likely location of the aircraft.”
“Latitudes south of 39°S are quite strongly contra-indicated by the arrival times of the flaperon and other debris reaching Africa, and the fact that those items were many while findings anywhere on the Australian coastline were nil”
CSIRO Report – The search for MH370 and ocean surface drift Part II – 13th April 2016
Conclusion: “In summary, our conclusions with respect to the location of the aircraft are unchanged.”
“Modelling the flaperon’s drift as being 20° left of the wind, and 10cm/s in excess of the Stokes Drift, is very consistent with the July 2015 arrival time of the flaperon at La Reunion. But this is true for all potential crash locations between 40°S and 30.5°S, showing that the arrival time at La Reunion of a single item is, unfortunately, not a precise guide to the location of the crash.
CSIRO Report – The search for MH370 and ocean surface drift Part III – 26th June 2017
Conclusion: “Assuming that some of the objects identified in the Pleiades images are indeed debris items from 9M-MRO, we have shown that there is an impact location that is consistent with those sightings, as well as all the other evidence reviewed by the First Principles Review. This location is 35.6°S, 92.8°E. Other nearby locations east of the 7th arc are also certainly possible, as are a range of locations on the western side of the 7th arc, near 34.7°S 92.6°E and 35.3°S 91.8°E.”
No mention of 39°S.
CSIRO Report – The search for MH370 and ocean surface drift Part IV – 3rd October 2017
Conclusion: “We stand by our earlier conclusion that the surface search had a fairly high chance of detecting a debris field if the impact had been near the segments of the 7th arc postulated at the time of those searches”
No mention of 39°S.
(2) Misrepresenting our findings as showing a MH370 end point from 36.5°S southwards is not assessed.
We have completed 46 MH370 drift analyses of MH370 floating debris from 10°N to 50°S, many of which have been published on this web site and presented to CSIRO, ATSB and Ocean Infinity.
We have reviewed in 17 MH370 drift analyses by renowned oceanographers.
We have participated in MH370 drift analyses by renowned oceanographers and our work on MH370 drift analyses has been cited by renowned oceanographers.
A summary of our assessment can be found at the following links:
https://www.dropbox.com/s/kvopmlhyxej0cbu/Drift%20Analysis%20of%20MH370%20Floating%20Debris.pdf?dl=0
https://www.dropbox.com/s/savkhqzrjxbz1qd/Bobby%20MH370%20Debris%20Drift%20Model%20Analyses%20%28published%29.pdf?dl=0
@DrB (cc Richard)
You wrote: “David Griffin’s latest data set extends somewhat beyond 36S crash latitude, to about 36.5 S”
Is there a difference to the data used for the second CSIRO report? There (figs. 3.2, 4.1) starting latitudes down to -42 degrees have been included.
@DrB. Thank you for your most helpful explanation and the expansion of your 186˚ LNAV Table 1.
Supposing I have it right, packs-off from 18:39:30 in Cases 4 & 5 would extend those fuel savings by (33,599 – 26,836)*0.017, another 115 kg.
@Richard.
“Misrepresenting the CSIRO findings as showing a MH370 end point at 39°S.” Who said that?
What I did say is that it is NOT correct to characterise the conclusions of CSIRO reports I-IV as declaring that south of 36.5 is impossible. I stand by that.
As you are well aware, the conclusions of the CSIRO reports drew upon the convergence of multiple criteria (such as the width of search along the arc to date, the coverage of the aerial search) in their assessment of “the most likely” locations along the arc. Their preferred/recommended locales between ~32S and ~40S draw upon those additional observations.
CSIRO’s quantitative DRIFT results for non-flaperon debris are shown in lower 3 panels of Figure 3.2.1, page 18 https://publications.csiro.au/rpr/ws/v1/download?pid=csiro:EP167888&dsid=DS1
CSIRO’s updated quantitative results for “genuine flaperon” inclusive windage and 2 variations (10 degree left, 20 degree left) leeway angle are shown in Figure 3.2, page 14. Quantitative results for high windage items are shown in Figure 4.1, page 15 of the same report.
https://publications.csiro.au/rpr/ws/v1/download?pid=csiro:EP172633&dsid=DS4
Rather than blustering and setting up a straw man, you might care to address the facts at hand.
@Dr B. Thank you for your comments on drift analysis.
1. I second Niels request for clarification on the dataset that you are referring to. How does this differ from that used for the CSIRO Part I and Part II report?
2. “We believe that beyond 37 S the drift probability declines fairly rapidly to negligible values. It would be nice to have more drift predictions in that latitude range, to better define the drop-off, but as far as I know there are no plans at CSIRO to do this.” Although the dataset you allude to doesn’t extend that far, the published results of CSIRO’s quantitative analysis do. And I believe that their results are somewhat more nuanced than a steep drop-off beyond 37S.
3. I acknowledge the general tendency for the beaching probability Western Australia:West SIO ratio has a *general* tendency to increase the further south along the arc you go. However, the overlay of the effect of local currents has a surprisingly large effect on W Australia beachings, to the extent that Part 1 report says: “This absence of findings argues against three latitude bands as potential entry locations. These are near 33-35°S, 36-37°S and 39-42°S, leaving sites north of 32°S and bands around 35-36°S and 37-39°S as being more consistent with the absence of Western Australia (WA) debris findings.” I also acknwoledge that this differention of specific latitudes that tend not to send debris to W. Australia is less pronounced (though still evident) in the case of high windage items.
4. The new plot that you provided on “the probability that a drift that beaches somewhere, actually lands in Western Australia” is elegant and informative. Is this low-windage items? Of course CSIRO didn’t depict their results in this ratio form. Nonetheless, your results appear quite different to those depicted in figure 3.2.1, at least as regards the 35S “lacuna” in W.Australia beachings. Would you care to comment?
@paul smithson
I addressed all the misrepresentation that you made.
@Sid Bennett
Victor stated “The question is whether or not the probability increases to the point where it becomes a candidate search area. I have my opinion, but I’ll let Bobby and Richard weigh-in first, as they have studied this more than me.”
I do not believe your MH370 end point is a candidate search area, for the following reasons:
(1) Compared to our baseline flight path which has a composite probability of 72.7%, your baseline flight path has a composite probability of 0%.
(2) Your flight path does not match the drift analyses, in particular the absence of findings on the Western Australian coastline as both Victor and Bobby have already pointed out.
(3) The combined route and fuel probability is at best 53.5% and then only changing the flight level to FL410, changing the start point to near waypoint ANOKO and using fuel option B1 (air-conditioning packs off, no rebalancing and cross feed valves closed). Our combined route and fuel probability is 86.0%.
(4) The random data trials performed by Bobby on a LRC path show a track of 180°T and an end point of 34.25°S with a route probability of 93.0%. Random LRC path data trials do not show a flight path near 186°T.
Here is a link to a comparison table in more detail:
https://www.dropbox.com/s/sh2muxavdr4doin/Flight%20Paths%20Comparison.png?dl=0
@Richard. “I addressed all the misrepresentation that you made.”
Oh dear. There goes another one.
@Richard. Re: your comments on “Sid’s route”.
Your composite is zero because it is scored “0” on drift probability. By your own description above, your drift model used here does not cover latitudes beyond 36.5S. Sid’s route terminus is indicated variously as 37.4S-37.6S.
The main paper Figure 5 panel 2 shows fuel probability of zero at 37.3 and beyond. Your table referred above now shows fuel probability for a route ending between 37.5 and 37.6 of >90%, even from the more northerly starting point at FL410 LRC. This is no longer consistent with Figure 5.
Thus of the two chief criteria previously cited to rule out flights ending in this zone, one is”not available/applicable” or “reconsidered/no longer applies”.
Since I don’t have a dog in this particular fight, I shall refrain from any further commentary on the merits or otherwise of Sid’s route. But it appears things are not quite as black and white as Fig 5 panels 2 and 3 might suggest.
@Sid
Trying to understand your case in pilot terms.
I think you are saying discontinuity at ISBIX. After that, is the aircraft flying south normally (magnetic heading)? Or did the pilot switch to True Track? Alternate case might be pilot never used waypoint but set to CTT at IGOGU and just happened to cut close to ISBIX, and perhaps used ISBIX as guidepoint vs. waypoint.
As far as flight sim, not sure what your question is, but it is somewhat complicated case coming off N571 Offset to an alternate heading with sharp turn >90 deg. That was one of the first things @Andrew did for us, he used a commercial flight sim to define how DrB’s earlier path would behave with FMT at IGOGU.
@paul smithson
I already explained our analysis covered 10°N to 50°S.
@richard. Nevermind, I see no point in continuing. My points have been made – and you have manifestly failed to address them.
@Paul Smithson
My position is much simpler than that. A waypoint route from IGOGU to ISBIX with no additional waypoints represents a discontinuity in the flight plan and the FMS handles the overflight of ISBIX by adopting the incoming azimuth to ISBIX as the true azimuth to fly subsequently. I have seen this described in a number of the 777 manuals.
As it turns out, the 186 route from IGOGU to ISBIX is essentially the same in loxodrome or GCP and probably cannot be distinguished except using other evidence or inference. The difference is in what the pilot did.
But, when a waypoint route is flown, after the discontinuity a loxodrome is flown, not a GCP. This slightly shortens the path.
Can you provide a reference for @Andrew’s work?
@DrB
As for your latest table:
In case 6 why did you start a full degree further North?
Also, since it is clear from previous discussions that the LRC and fuel model works better above 39000, why didn’t you run a case 2 at FL400 or FL410?
I have found that very small changes in the initial conditions of the route at IGOGU can optimize the path errors. But I would like to link this start point more clearly to a FMS-flown preceding route
Unfortunately, we only have a model and it is only an approximation to the conditions existing at the time. Except for a high altitude LRC, how would the pilot choose an altitude?
None of the fuel model cases address a situation where the air packs and most of the electrical load were off for the hour prior to 18:24. Also, one assumes that the electrical load subsequently was much lower than normal, and the fuel savings were not addressed. Since the amount of fuel needed to be considered between the various cases differs by only about 300kg, this is an important consideration.
To be clear, I am not proposing a specific route where the altitude, and starting position are exactly specified. I think it is close, but until this recent round of discussions, I have been content to describe the route as IGOGU-ISBIX +186T. A more precise definition is not needed to define a search area.
@Sid. Your first queries mis-addressed to me. Returning to sender 🙂
@Sid Bennett: But, when a waypoint route is flown, after the discontinuity a loxodrome is flown, not a GCP. This slightly shortens the path.
As a number of us have said, that’s false. That discussion occurred here years ago. After finding contradicting statements in manuals, Andrew resolved the issue by running experiments in a Level D simulator.
After a discontinuity in LNAV mode, the plane continues on a constant heading (while remaining in LNAV mode). Whether it is a true or magnetic heading depends on the position of the HDG REF TRUE/NORM switch.
@paul smithson
You appear to be rather obtuse. I included links to previous studies, which explain why we had discounted end points southwards of 36.5S, but it seems that you did not read them.
David Griffin also agrees that points southward of 36.5S do not match his drift analysis, but you choose to ignore this.
Meanwhile you harp on like a broken record and continue to cherry pick any statement, that you can twist into fitting your flight path model ending at 39.5S.
This area was not searched for a reason, because the fuel exhausts before you can reach it.
@Richard. Hell’s bells. I don’t know why I bother.
@Niels,
I have recently asked David Griffin about differences between the two prediction data sets, if any. I also requested the predictions down to 42°S. If that is forthcoming, I will extend the drift probability curve as far south as his data set goes.
@paul smithson,
You asked: “The new plot that you provided on “the probability that a drift that beaches somewhere, actually lands in Western Australia” is elegant and informative. Is this low-windage items? Of course CSIRO didn’t depict their results in this ratio form. Nonetheless, your results appear quite different to those depicted in figure 3.2.1, at least as regards the 35S “lacuna” in W.Australia beachings. Would you care to comment?”
On the first question, the answer is yes, that data set includes only the flaperon and low-windage non-flaperon debris.
Regarding the gap in Figure 3.2.1, it is evident in my Western Australia figure as the point at 2% and 35.5. I don’t see it as being “different” at all. There are two things which can affect such comparisons. One is that I used 1 degree wide bins for crash latitude. I needed that to get enough trials included to have reasonably good statistics. The other effect is that my drift probability is a compilation of 5 geographical zones, whereas the third column in Figure 3.2.1 is for Western Australia only. So, I would not expect my 5-zone drift metric to match the lower right panel in Figure 3.2.1, which is for a single zone.
@Sid Bennett,
You asked: “In case 6 why did you start a full degree further North?”
I didn’t pick a starting point. That’s what resulted from the route fitting process.
You also asked: “Also, since it is clear from previous discussions that the LRC and fuel model works better above 39000, why didn’t you run a case 2 at FL400 or FL410?”
Case 2 is not an acceptable fit, because it forces the GSEs to be zero. I included it as Case 2 as an academic exercise because I thought it might be useful to you to compare the ground speeds I got with your predictions for your best-fit route. I guess you didn’t do that.
You asked: “Unfortunately, we only have a model and it is only an approximation to the conditions existing at the time. Except for a high altitude LRC, how would the pilot choose an altitude?”
One way is to pick the optimum cruising altitude from the Boeing Flight Crew Operations Manual at the current aircraft weight.
You also said: “To be clear, I am not proposing a specific route where the altitude, and starting position are exactly specified. I think it is close, but until this recent round of discussions, I have been content to describe the route as IGOGU-ISBIX +186T. A more precise definition is not needed to define a search area.”
As you have been told several times, it is not possible for the aircraft to fly either a geodesic or a loxodrome after a route discontinuity, with an incapacitated pilot.
@TBill
Please see response above addressed incorrectly to Paul Smithson.
@Richard. One last attempt.
1. My interest in a terminus around 39.5 is no secret. This is certainly a motivation for my interest in southerly parts of the arc and a reason that I critically evaluate claims that it can be ruled out on the basis of evidence. I have not published my proposition, mainly because I have so far not found a scenario that reconciles it with available fuel.
2. If I have been “banging on about it” in my queries and critique over recent days, kindly point out the examples (pl.). Otherwise withdraw your mendacious statement.
3. Your personal belief that the weight of drift evidence completely rules out areas south of (roughly) 36.5S is plain and (you say, without citation) that Dr Griffin agrees with you. You further explained that this is why you didn’t bother including drift data further south than 36.5. Dr B offers a different explanation – that the new dataset did not extend further than that. Whichever the case, it is a matter of fact, not conjecture, that the drift model evidence employed for the purpose of compound probability of terminus does not extend beyond 36.5S. You may believe as righteously as you like your own interpretation of drift evidence. But please do not inflict your blinkered approach to evidence on the rest of us.
4. The CSIRO drift modeling, cited specifically in my previous posts, indicates that debris that reached Reunion and other western parts of the SIO could have originated pretty much anywhere between roughly 32S and 40S. Latitudes further north are counter-indicated by speed of drift – the debris should have shown up earlier. Latitudes further south are counter-indicated by the absence of debris finds in W. Australia and it is “generally” the case that the further south you go, the more likely debris recovery in W. Australia should be. This generality is overlaid with the peculiarity of initial current conditions along segments of the arc referred previously.
5. The CSIROs conclusions on most likely origins are clearly and explicitly based on multiple considerations. These considerations variously include: areas of the arc searched to date, width of that search, aerial search coverage and Pleiades imagery – as well as the timing and distribution of debris finds in Western SIO and the apparent absence of debris recovery on W. Australian coasts. They have been quite explicit about how they reached this recommendation: informed by the drift evidence plus additional considerations.
6. Nowhere in the CSIRO’s DRIFT evidence are locations south of 36.5S explicitly ruled out. On the contrary, with reference to the influence of local currents along the 7th arc, Part II p19 states: “It appears, from our modelling, that the initial direction of movement had a lasting impact on the long-term trajectories…The fact that no aircraft debris was ever found on Australian shores suggests that the aircraft is more likely to have entered the water in one of the latitude bands where the flow was westward.” Then on p23/38 “This absence of findings [in W. Australia] argues against three latitude bands as potential entry locations. These are near 33-35°S, 36-37°S and 39-42°S, leaving sites north of 32°S and bands around 35-36°S and 37-39°S as being more consistent with the absence of Western Australia (WA) debris findings. The point is that CSIRO (not I), state that various locations along the arc that were experiencing NW currents around and after 8 March are less likely to have beached in W Australia. The model of fine-scale local currents along the arc based on altimetry (and supported by SST observations and drifters) is shown in Part 1, Fig 3.3.1 on page 20 and the animated daily snapshots of fine-scale currents can be viewed here (go to date index for alternative dates)
http://www.marine.csiro.au/~griffin/MH370/br15_MH370_84102_1_tp3l1p2d_bh_arc7_4031/20140315.html
7. And by the way, since you mention it, I did read both reports that you cited in your earlier reply. Dr B’s report dated Nov. 2018 seems to be based on the same dataset employed in “The Final Resting Place of MH370” that does not extend beyond 36.5S. Your report dated July 2018 “used the GDP buoy data to build a model of the Indian Ocean from 20°E to 130°E and from 10°N”. This model provides a crude, low resolution, historic representation of ocean surface currents based mainly on drogued drifters. As such, it provides, at best, a qualitative impression of SIO circulation. Ironically, your discussion section includes the statement: “With the benefit of hindsight and the knowledge of the search results from Fugro between 39.5°S and 33.0°S as well as the search results from Ocean Infinity between 36.4°S and 25.0°S, we can rule out 34.5°S and 30.0°S as MH370 end points to a 97% level of certainty”.
@DrB said: One way is to pick the optimum cruising altitude from the Boeing Flight Crew Operations Manual at the current aircraft weight.
The optimum altitude for ECON and LRC is calculated by the FMC, is displayed, and can be selected.
Another strategy would be to choose the maximum altitude, recognizing that the optimum altitude will increase as fuel as burned.
@Sid
OK I see it now.
So you need either (1) an active pilot at ISBIX to reset the A/P controls to True Track at the time of the ISBIX discontinuity (approx 1941) or (2) the aircraft was already flying in True Track mode and it happened to pass by ISBIX.
Bumped into this classic earlier paper by Richard and DonT:
http://www.duncansteel.com/archives/2321
Talks about hybrid path reverting to magnetic course after discontinuity near 37S.
As far as Andrews earlier work, it goes back to early days of Victor’s blog here, but what is the question you have about it? Whatever Andrew discovered is embedded in DrB’s 2016/2017 path to approx. 35S. So you could adopt that path if you like it, or you could adopt the new path, which is slightly different. DrB has a fantastic list of links to all of his papers.
@VictorI, @DrB
I believe that the magnetic correction table is in the AIRDU. The display is on the dashboard.
If you turned the switch from TRUE to NORM, I would guess that the displayed azimuth would change from a heading shown with respect to true North to a heading with respect to magnetic North. The plane, of course would keep flying in the same direction. You could wait a while and switch it back, and it would come back to the original value. (I think.)
It seems to me that the function of the switch is so that instructions for headings given to pilots by ATC are given in degrees, where it is assumed that the instructions are in degrees magnetic. In polar latitudes
the magnetic tables change much more rapidly and using true tracks are more accurate.
Right now you wouldn’t want to believe that the actual magnetic heading in the France/UK area is numerically correct when obtained from the aircraft navigation system. The location of the North geomagnetic pole is changing rapidly and the tables are out of date. But they are out of date for everybody, so things stay organized.
Its sort of like a thermometer display. I can get it in C of F, but the temperature is the same.
@Dr B. Thank you for the clarification. Since timing and distribution of debris on the W side of SIO is a lamentably poor discriminator of starting location along the arc, the absence of debris recovery in Western Australia assumes particular importance. It is clear that from most locations along the arc – even the more southerly ones – debris is more likely to beach in Africa than Australia. The question is to what extent, and that is why I think your ratio approach of Aus vs Africa is an appealing and interesting one.
Given the CSIROs finding that local current conditions exercise a surprisingly large effect on probability of beaching in W.Australia, it is important for such an exercise to use suitably fine resolution boxes for model start segments. It would also be interesting to see the empirical results for arc segments south of 36.5.
For a more complete view, I think high windage items should also be included since a high proportion of recoverable debris – the shattered composite panel – should be of a highly buoyant, low-draught nature. In CSIROs modeling, they found that high windage items from every section of arc sometimes beached in W.Australia.
Whereas previous discussion of the absence of finds in W Aus was quite categorical about the high likelihood of debris identification and recovery there, this (Part III, p21) uses rather more value-laden language: “Panel 4 shows that a few items of high-windage debris – if they were still afloat – are hindcast to have washed up at some remote locations on Australian shores.”
The likelihood of items beaching being seen, identified/recovered and reported is largely the subject of speculation. I am personally of the view that it is not as likely as most folks seem to believe. According to Wikipedia, 92% of W.Australia’s rather small population lives in the SW corner. Judging by this depiction of population density I find it surprising that absence of debris finds there is considered to be remarkable.
The link for W Australia population density referred above was dropped from the post. That’s quite a lot of coastline and not a lot of people. See here:-https://en.wikipedia.org/wiki/Western_Australia#/media/File:WApopDist2006.png
@All
We have made some clarifications and additions in the paper in the download link above. Apologies for the confusion caused!
In Section D.4.2 immediately after the Table D-4 we have added a clarification as follows:
“If no particular post-1941 Option (A, B1, B2, or C) is identified, then generally we choose the maximum fuel probability among those four Options. This is the quantity that is plotted in Figures 5, 15, and D-3.”
In Section D.5, we have added a clarification as follows:
”Figure D-3 shows the maximum fuel probability (of the four post-19:41 Options) calculated using the method presented in this appendix.”
In Section 5.5, we have made a correction as follows:
“David Griffin kindly provided us with the data of the drifts modelled from start points along the 7th arc from 7.5 °S to 36.5 °S for both flaperon . . . .”
In section H.3 following Figure H-1, we have added a clarification:
“Figure H-1 shows that crash latitudes north of 27 °S have very inconsistent predicted and actual landfalls, and therefore they have low probability. Intermediate latitudes, from 27 °S to 37 °S have significant probability. The crash latitudes from 33 °S to 37 °S have the highest probability because they best match both the observed locations and the actual drift days. This includes the 34.2 °S latitude of our BEDAX SIO Route at the 7th Arc, shown by the dashed red line in Figure H-1, which has an estimated drift probability of 95%.
Crash latitudes south of 37 °S are expected to have low probability based on two factors: (1) the increasing inconsistency of predicted drift days due to the longer drift durations required to make landfall at the find locations (especially Africa), and (2) the lack of debris finds in Australia, which is inconsistent with the expected high percentages in that zone. Figure H-2 illustrates this second point.”
We have added a Figure H-2, MH370 Debris Drift to Western Australia, and the following text:
“In Figure H-2 we plotted the fraction of debris trial predicted to make landfall somewhere (within the allowed time window) which were predicted to make landfall in Western Australia. At crash latitudes north of 25 °S, only about 0.3% of the predicted landfalls would occur in Western Australia. That fraction increases very rapidly for more southerly crash latitudes. It rises to about 3% at 34 °S. With 27 debris, that corresponds to an expected value of less than one debris find. The black dashed trend line in the figure indicates that the fraction of beachings in Western Australia is expected to be even higher for crash latitudes south of 36.5 °S , and the discrepancy with actual debris finds grows even larger. At 36.5 °S the probability is up to 12%, so one out of every eight beached debris would land in Western Australia. With ~27 debris, that is 3-4 expected beachings. Clearly, this is unlikely to have actually occurred, because there were concerted efforts to find MH370 debris on WA beaches, and none were found. So, crash latitudes below 36 °S are expected to become more and more improbable, because the predicted drift days become too long to match the find dates and because there is an inconsistency between the predicted and actual number of debris finds in Western Australia. There are some variations with latitude due to localised currents in this area, but the general trend is clear.
Our drift probability curve in Figure H-1 is based on a large data set provided by David Griffin which only extends to 36.5 °S. However, the CSIRO drift studies were done down to 42 °S [Griffin, DA, Oke, PR and Jones, EM (2016). The search for MH370 and ocean surface drift. CSIRO Oceans and Atmosphere, Australia. Report number EP167888. 8 December 2016]. Their Figure 3.2.1 illustrates the decreasing probability, for flaperon and non-flaperon debris, of far south crash latitudes. This figure specifically illustrates the first point mentioned previously that the predicted arrival times are late, and especially so in Africa. In fact, the probability of timely arrival drops by a factor of about two at 37 °S and beyond for non-flaperon debris. This figure also displays the generally high probability of predicted debris arrival in Western Australia, with far south crash latitude, which did not occur.
To quote from CSIRO’s 2016 report: “Latitudes south of 39°S are quite strongly contra-indicated by the arrival times of the flaperon and other debris reaching Africa, and the fact that those items were many while findings anywhere on the Australian coastline were nil.” Crash latitudes between 37-39 °S are also contra-indicated, although not as strongly as south of 39 °S. Therefore, between 37 °S and 39 °S the drift probability declines from a very high value to a very low value. The exact shape of this decline is not known at the moment, but two conclusions are unchanged – at circa 36 °S the drift probability is very high, and at 39 °S the drift probability is very low.”
The following link (added for convenience) is the same as the link above:
https://www.dropbox.com/s/lszarw2w8qb2a3p/The%20Final%20Resting%20Place%20of%20MH370%20-%207th%20March%202020.pdf?dl=0
@Sid Bennett: We were discussing the behavior of the autopilot in LNAV mode after reaching a route discontinuity. You claimed (incorrectly) that track is held constant. We know that heading is held constant, and we believe that the reference is true or magnetic based on the position of the HDG REF switch.
You said that it does not matter if magnetic variation tables are outdated as long as everybody uses the same outdated tables. First, there is no guarantee that everybody uses the same outdated tables. But also, it is not uncommon for heading indication systems to use integrated magnetometers, which do not need tables to convert from true heading to magnetic heading.
@Richard and co authors. Thank you for those additions. That sounds reasonable.
@VictorI
I should have bookmarked the documents I scanned through, but didn’t.
Surely the 777 navigation system only uses the magnetic compass as a manual instrument of last resort. Can you find it referenced in any description?
@Sid Bennett: I never said the 777 navigation system uses a magnetic compass. It surely does not. However, other (much smaller) planes use magnetometers to indicate magnetic heading.
@DrB
Thank you! Yes it would be important, if possible, to extend the drift probability curve to the south.
@VictorI
But the subject under discussion is how the M370 nav system functioned, not others…
@Sid Bennett: We know how the autopilot of a B777-200ER behaves when it reaches a route discontinuity in LNAV mode: it maintains a constant heading. That was confirmed by a Boeing reference and also in a Level D simulator. This was discussed and resolved several years ago on this blog. End of story.
@Richard
In Section D.5, you have added a clarification as follows:
”Figure D-3 shows the maximum fuel probability (of the four post-19:41 Options) calculated using the method presented in this appendix.”
Please consider also adding the following sentence:
The maximum fuel probability plotted in Figure D-3 is that in the second panel of Figure 15. The fuel probability plotted is that for the SIO route fits with route probability shown in the top panel of Figure 15.
That additional sentence helps in understanding.
DrB has said:
“This maximum fuel probability is what is plotted in Figure D-3 and the second panel in Figure 15, and it corresponds to the same SIO route fits whose route probability is shown in the top panel in Figure 15.”
@ George G
You proposed adding in section D.5 “The maximum fuel probability plotted in Figure D-3 is that in the second panel of Figure 15. The fuel probability plotted is that for the SIO route fits with route probability shown in the top panel of Figure 15.”
In Section D.4.2 immediately after the Table D-4 we have already added a clarification as follows: “If no particular post-1941 Option (A, B1, B2, or C) is identified, then generally we choose the maximum fuel probability among those four Options. This is the quantity that is plotted in Figures 5, 15, and D-3.”
Are you proposing to repeat a similar clarification 3 pages later?
@ Richard
You said:
April 16, 2020 at 2:07 am
QUOTE:
@ George G
You proposed adding in section D.5 “The maximum fuel probability plotted in Figure D-3 is that in the second panel of Figure 15. The fuel probability plotted is that for the SIO route fits with route probability shown in the top panel of Figure 15.”
In Section D.4.2 immediately after the Table D-4 we have already added a clarification as follows: “If no particular post-1941 Option (A, B1, B2, or C) is identified, then generally we choose the maximum fuel probability among those four Options. This is the quantity that is plotted in Figures 5, 15, and D-3.”
Are you proposing to repeat a similar clarification 3 pages later?
END Quote.
Richard, Sorry for the confusion.
My proposal is to document/state/record that the fuel probability plotted is that for the SIO route fits with the route probabilities shown in the top panel.
Nowhere in the report have I yet found such a statement, but of course I may be mistaken.
It may be implied by the placement of the fuel probability plot directly beneath the route probability plot, but excepting by this inference, I can find no statement of the fact in the report.
I asked recently:
“DrB: Please: Does this represent the fuel probability for the specific optimum routes whose probabilities are plotted in Figure 37 (and the top panels of 5 and 15). ?”
And he replied, in part:
“This maximum fuel probability is what is plotted in Figure D-3 and the second panel in Figure 15, and it corresponds to the same SIO route fits whose route probability is shown in the top panel in Figure 15.”
The statement linking the fuel probability plotted to the specific optimum routes whose probabilities are plotted, is what I was requesting.
(by such as my suggested additional ” sentence”).
Reason:
To increase understanding that some non-optimum routes (routes with poor Route Fit and thus not plotted) may actually have a fuel requirement closely matching fuel availability even though they might otherwise be quite unrealistic.
@Victor
Your comment yesterday was quite interesting about magnetic heading possibly being generated by the aircraft itself. Until now we’ve been assuming 2005 magnetic tables used by the aircraft, which if I recall comes from ATSB to IG. The exact magnetic translation makes a big difference in path projections. In flight Sim I use 3 different tables pre-2000, 2005, and 2017 and for the MH370 flight path, it varies from substantial curve to much less curvature (recent years), presumably due to Earth’s magnetic south pole moving around a lot down there.
@Sid
I don’t know if you saw my comments above April 15, 2020 at 2:16 pm. You can still have the flight path you wanted, you just have to require that the pilot switched over to True Track before or after ISBIX. That’s why unintentional/accident flight theory does not work well, because to fit the data, we have to use True Track or LNAV which imply intentional flight.
@TBill: You are misunderstanding my statement. I was referring to other (mostly smaller) aircraft, not Boeing transports.
@All
We have made one more clarification in the paper in the download link in the article above.
Thank you @George G for pointing out the need for clarity.
In Section D.5, immediately below Figure D-3:
“The maximum fuel probability is what is plotted in Figure D-3 and in the second panel in Figure 15. It corresponds to the same SIO route fits whose route probability is shown in the top panel in Figure 15.”
The following link (added for convenience) is the same as the link in the article above:
https://www.dropbox.com/s/lszarw2w8qb2a3p/The%20Final%20Resting%20Place%20of%20MH370%20-%207th%20March%202020.pdf?dl=0
@TBill
Thank you for reminding me of your post. I agree that the pilot could have selected True Track at any point, or actually entered a DIRECT TO in the flight plan.
I haven’t thought about unintentional/accidental causes in years. The question for me is whether the pilot was in command at 00:11.
But the pilot could have done either of the actions mentioned above at any time after 18:22 when the power was apparently restored and the plane configured for automatic flight.
@All
The aerial search for MH370 in the Southern Indian Ocean began on 18th March 2014. AMSA published a chart of the planned search area, depicting two possible flight routes given to them by the NTSB, who in turn got the analysis from Boeing. The estimated MH370 end points were at 48.3°S 82.0°E and 46.2°S 86.5°E. These were both straight line paths at MMo based on fuel exhaustion at 00:19:37 UTC but without consideration for the required or available fuel.
Two days later, these estimates were revised to 46.0°S 82.0°E and 44.5°S 82.0°E. These were now LNAV paths on an initial bearing of 191.7°T and 188.3°T respectively. Both flight paths were at FL400 and used the constant mach speed mode. A week later a minor revision was made to one of the estimates.
On 28th March 2014, these two estimates were abandoned and three new estimates replaced them. This time the average TAS was specified as 475 knots, 469 knots and 400 knots respectively. The first two estimates were still at flight level FL400, but the third estimate was at FL350. Various speed modes were considered including MRC, CI=52 and LRC INOP.
The MH370 end points were given as 31.5°S 88.8°E, 34.0°S 88.8°E and 31.1°S 96.7°E based on initial bearings of 189.3°T, 188.6°T and 181.5°T. For the first time, the new estimate at 31.1°S 96.7°E showed an MH370 end point close to the 7th Arc at only 28.9 km east of the 7th Arc. All previous end points were between 247 km and 618 km east or west of the 7th Arc. The next day, only the new LRC INOP estimate was shown in the search plan and for the following 4 search days, only the area around this new estimate was searched.
0n 4th April 2014, ULB detections were made by Haixun 01 and Ocean Shield. The same day Curtin University announced that they had picked up an acoustic anomaly using the IMOS hydrophones HA01 at Cape Leeuwin. The aerial search moved from around 31.1°S 96.7 °E to around 20.0°S 104.5°E, a distance of ca. 1,460 km further north.
The details are in the attached presentation. It is interesting to note that the three routes, shown for the first time in the search plan on 28th March 2014, are included again in the Boeing analysis in the Malaysian SIR Appendix 1.6E. It is also interesting to note that Boeing were very close to the MH370 end point of 34.3°S defined in our current paper, based on a LNAV180 LRC flight path at FL390. Boeing were 6 years ahead of us, despite making a few mistakes in the urgent situation to define the aerial search area.
https://www.dropbox.com/s/ji539we0q3y943p/AMSA%20ATSB%20NTSB%20Boeing%20Flight%20Routes.pdf?dl=0
@Richard
Important background, thank you. I did not realize there were so many Boeing/NTSB paths. I had seen prior reference to 400 knot NTSB path.
Was it the acoustic anomaly or something else that inspired them to move so far north to search for the ULB detections?
Richard wrote “ the IMOS hydrophones HA01 at Cape Leeuwin“
I’m sure you meant to write [CTBTO] IMS HA01 hydrophone array. IMOS is the Australian Integrated Marine Observing System.
Dr Alec Duncan at Curtin did attempt to supplement the CTBTO data with the IMOS recorded data. As I recall, the IMOS hydrophones are only single source devices thus not providing any directional information. The IMOS hydrophones operate over a much wider bandwidth but only recorded on a 50% duty cycle. Being submerged and autonomous, the IMOS hydrophone recorder time of day clocks lacked UTC synchronisation & exhibited drift.
@Richard. That is a very interesting trip down memory lane. I’d be interested to know a bit more about the provenance of these various estimates. Way back I spoke to someone at NTSB (I can’t even remember who it was not) about these early, deep-south path estimates. I was told that they were well aware that these went well beyond the 7th arc. Since pings were hourly, the early interpretation was that it had gone down somewhere between Ping 7 and an anticipated Ping 8 that hadn’t happened, so maximum travel distance beyond Ping 7 was an hour. The person I spoke with didn’t sound as if they had first hand knowledge and may have been speculating rather than explaining actual rationale.
I also understand that these paths were an early arc-derived path. I’d have thought that Inmarsat might be the main analytical brains behind that, rather than Boeing.
I do recall having some difficulty scaling an accurate GE overlay to estimate the actual lat/long. In the end, I got a better overview of those paths and where they came (over the NW corner of Sumatra – consistent with Arc 1) from from some video footage around that time where the charts were on a big screen in the background.
If memory serves, the main prompt for the abrupt shift to much more northerly search area (28th) was the confirmation of high speeds in the flight over the peninsular and therefore more limited fuel range. None of the paths from 28 onwards were attributed to “NTSB”.
Could you comment on how/why you believe that Boeing was behind those “NTSB possible paths”? Boeing surely knew enough to tell that the plane could not have got that far.
@Don Thompson
Many thanks for spotting my mistake!
I had just re-read the Curtin report on the IMOS Scot Reef and IMOS Perth Canyon and obviously had too much IMOS on the brain. I meant to write, that I concluded that it was the CTBTO HA01 at Cape Leeuwin, that first reported a detection on 4th April 2014 and help caused the change of location by AMSA to 20°S near the 7th Arc. I think AMSA was more excited by the ULB detections from Haixun 01 and Ocean Shield, though all 3 detections coming at the same time, was not to be ignored.
I have updated the attached presentation:
https://www.dropbox.com/s/ji539we0q3y943p/AMSA%20ATSB%20NTSB%20Boeing%20Flight%20Routes.pdf?dl=0
@Richard and Authors
There appears to be a grammatical error in the sentence beginning with, “In Figure H-2 we plotted…”
I’d like to raise a point about the treatment of northern routes. I realize that they are not compatible at all with a straight path, but I would hope that the drift predictions in your report fully take them into account.
I’ve mentioned recently that I don’t think early arrival of debris should be a problem, because most of the later finds were when someone took the initiative to go looking. (Recall that Roy was first discarded because it was smelly).
You have added that David Griffin provided drift data from 7.5S (to 36.5S), but the first drift Figure H-1 cuts off at 20S, where probability appears to be increasing going north.
(The aerial search probability figures likewise cut off at around 20S but we know there were no 7th Arc searches beyond that).
Far northern drift probabilities may be artifically low due to a penalty applied if the debris arrived earlier than the modeled time minus 10% ,with 47 days (?) allowed for discovery. For the flaperon, that would be a penalty if there was more than 98 days between prediction and discovery, which presumably applies to my site near Java.
(I recall a report that the flaperon had been found previously and considered as a table for cutting fish, but can’t seem to find the article.)
Does this minimum time penalty affect only northern crash sites where drift is directly west?
A +30% maximum time penalty also may not reflect late debris discovery. Johnny Begue found a concave piece of debris in 2016, a year after he found the flaperon, that might correspond to grey and blue paint above the wing.
https://twitter.com/RideSoulSurf/status/706094798558490624
Even if it does not change your detailed report, I am very curious to see what Figure H-1 would look like without the time penalties, and extended to 8S. I’d truly appreciate the visual if it’s not too much effort.
@Richard
Interesting slides you shared; thanks!
The estimate 8 route (MRC) ending 34S with initial bearing 188.6 degrees, what navigation mode would that be?
@ paul smithson
You ask “Could you comment on how/why you believe that Boeing was behind those “NTSB possible paths”?”
You state “Boeing surely knew enough to tell that the plane could not have got that far.“.
Response to your question.
Boeing state in their Event Report in the Malaysian SIR Appendix 1.6E:
“This event is being investigated by the Malaysian Ministry of Transportation (MOT) with the assistance of accredited representatives from the United States National Transportation Safety Board (NTSB), the Australian Transportation Safety Board (ATSB), and the United Kingdom Air Accidents Investigation Branch (AAIB). Boeing is providing technical support to the US NTSB“.
The ATSB state in their Final Report:
“The work of many organisations and individuals from Australia and around the world was coordinated by the ATSB. Of particular note was the contribution of members of the search strategy working group (SSWG) including; Inmarsat, Thales, Boeing, the Air Accidents Investigation Branch (AAIB) of the United Kingdom, the National Transportation Safety Board (NTSB) of the United States, the Defence Science and Technology Group (DST Group) and the Department of Civil Aviation Malaysia. Other significant contributors were the Commonwealth Scientific and Industrial Research Organisation (CSIRO) and Geoscience Australia“.
Also ATSB state formally:
on page 159, that they sent a draft copy of their report to Boeing.
on page 160, that they received a submission from Boeing.
In Appendix B:
(1) “that no current investigations or assessments are currently being undertaken by Boeing into the identification of the most probable final location of flight MH370, but the appendix provides a copy of the analysis as provided post a Joint Investigation Team (JIT) briefing to AMSA on 2 April 2014“.
(2) The report includes the results of calculations made by Boeing: “The altitude was recorded as 35,000 feet and from the other recorded parameters Boeing calculated a ground speed of 473 kts“;
(3) “Boeing undertook a number of performance calculations varying the speed and altitude to determine the range of the aircraft“;
(4) “The first proposed search areas were established by using Boeing’s performance predictions and the criteria that for a track to be valid it must reach the 6th arc“;
(5) “Boeing’s analysis of the aircraft’s movement from the last ACARS reporting position and the end of the primary radar coverage showed that the aircraft had accelerated from 473 kts to 500 kts as it transited across the Malaysia Peninsular and along the Straits of Malacca. This was confirmed by the last two Royal Malaysian Air Force air defence radar returns“;
(6) “In this refinement Boeing used the performance based flight tracks, previously identified, and compared the Doppler that these tracks generated with the Doppler information obtained from the OBF“;
(7) “The final refinement to the underwater search area was obtained by overlaying the results of the refined Inmarsat Doppler analysis, Boeing refined Doppler and range analysis, and air route M641;
(8) “Boeing analysis using a combination of aircraft performance and Doppler data, obtained from the satellite, to generate a range of probable best fit tracks. This work was supported by a Root Mean Square analysis that took account of a number of variables;
(9) “Flight planning carried out by MAS independently showed that there was sufficient fuel onboard the aircraft to reach the positions determine by the Inmarsat and Boeing analysis“;
(10) “The length of the arc that defined the most probable area was obtained from the overlay of the results of the Inmarsat and Boeing approaches“.
Response to your statement.
MAS did the fuel analysis independently of the Boeing and Inmarsat approaches. I assume Boeing also did a fuel analysis, but their first estimates were clearly without regard for the required or available fuel. The MAS fuel analysis may have been at a later point in time. Even by the time the DSTG produced their analysis, there was no agreed fuel model, resulting in the DSTG assuming “infinite fuel“. I believe that our paper is the first flight route analysis based on a validated fuel model.
@Richard. The questions below intended in spirit of factual enquiry. I’d like to understand how much of the info that you have kindly shared in this doc is “as provided by third parties” and how much of it is your assumption/estimate/derivation.
1. Are you quite sure that the terminus of “NTSB possible paths” version 18th and 20th are different? Are the lat/long of your slide headers estimated by you or provided to you? The AMSA slides are not mercator and there is a shift in projection angle. By my eye, judging from alignment with seafloor features, they end at the same latitude as far as one can tell.
2. You have also attributed the yellow (eastern) path on slide 28th March and 29th March to “NTSB (Boeing)”. What is the basis for this attribution? I can see that the grey/orange paths on the slide from 28th correspond with the earlier NTSB possible routes but the yellow done doesn’t.
3. Your slide on p6/10 is headed “AMSA estimated MH370 end point – assumptions”. Whose assumptions are those – yours, AMSA’s, NTSB’s, Boeings? What is the basis for the estimated start time and location of the NTSB paths?
4. Your slide on p7/10 provides details for Estimates 1 through 10. Of the parameters that you have tablulated for these first six (the ones that went to 40+S), can you explain which of the parameters shown you have assumed/derived yourself (FL, TAS, Mach, Speed mode, duration, range, initial bearing, endurance, average groundspeed, etc) and which were provided by AMSA/NTSB/Boeing or other third parties?
Thanks in advance.
My second post crossed with your first response above.
I am familiar with the Appendix 1.6E and that work is clearly attributable to Boeing. However, I’m not aware of any reason to suppose that Boeing were involved with derivation of those “NTSB possible paths”.
@Richard
Thank you.
@paul smithson
You state “I’m not aware of any reason to suppose that Boeing were involved with derivation of those “NTSB possible paths”.
I already gave you most of the following 7 reasons. I don’t think I could be much clearer, but I will give it one more try:
(1) Boeing was providing technical support to the NTSB from the outset.
(2) Boeing were a member of the ATSB search strategy working group (SSWG) together with the NTSB.
(3) The ATSB Final Report Appendix B provides a copy of the analysis as provided post a Joint Investigation Team (JIT) briefing to AMSA on 2 April 2014 of which both Boeing and NTSB where active participants.
(4) Appendix B is the formal protocol of the “Identification of the most probable final location of flight MH370 (Issue 2)”. It specifically states “This document records the development of a process, up to 2 April 14, to determine the most probable final location of Flight MH 370“.
(5) The protocol states “Boeing undertook a number of performance calculations varying the speed and altitude to determine the range of the aircraft“.
(6) The protocol states “The first proposed search areas were established by using Boeing’s performance predictions“.
(7) Nowhere in the protocol does it mention a NTSB contribution, only Boeing is mentioned and then in 10 places in the protocol as the organisation providing position, speed, altitude, range and performance predictions.
I don’t dispute that a whole bunch of organisations were working together. Who exactly contributed what is another matter. AMSA slides clearly attribute those early “possible routes” to NTSB. I was interested to learn if you had an specific insights into their provenence and the assumptions underlying them. It is of no tremendous consequence so if you don’t have anything further to add then let me not labour the issue.
Could you offer clarification on the question about which columns in your tables are “data” and which are your estimates/derivations?
I dont understand, why all of you are not discussing Ed Andersons story which is supported with some evidence, and yet you have only statistics
Why is Ed Anderson so ignored here?
@Sultan. Ignored? Not too sure he has been. Even so, if his theory has not been given the attention it warrants, part of the reason I think is concentration on the current review of the BRVA paper proposing a new search. That proposal has been offered to OI for consideration. As such it is a clear and present candidate, warranting close and early examination.
Its data support is excellent and that has withstood an array of questions to date. I would have thought that amounted to “evidence”.
@Dr B et al. Putting all that to one side I take the opportunity here to continue with that review theme. To be balanced, apart from prompting questions and praise the review should identify weaknesses in the proposal also.
One is how the characteristics of the final transmissions resulted without an active pilot.
Banking of the aircraft by a relight would be unlikely, as per your paper.
The remaining possibility raised there, of a pilot being slumped over the controls, might explain it though that would suppose his body had not interfered earlier with autopilot operation.
There needs to be a reasonable likelihood too that the characteristics of the final transmissions would result, particularly their timing. Two minutes after MEFE suggests a slow induced downwards acceleration or bank. Yet some descent examples I have posted that illustrate pitch down as the descent’s cause suggest that would be initiated briefly before the transmissions, not two minutes, whatever prompted it.
About bank, with dihedral tending to stabilise the aircraft the initial bank rate would need to be enough to overcome that and yet take 2 mins for the bank to become steep. That might be hard to model.
Another reservation I have is that it quite possible that the APU auto-start explanation for the powering of those transmissions, if at high altitude, might be precluded by vapour lock in its fuel supply.
A solution that included an active pilot would not be bound in some of the above ways: not that that proves there was one!
Added to the above there is also of course the earlier unsuccessful search of much of the area close to the LEP. If added into the probabilities of the paper, that would reduce them.
Incidentally a passing observation. While packs off for the SIO leg would have led to an inactive pilot, I speculate that the converse might not be the case. Because there might have been depressurisation may not mean necessarily the packs were off, particularly after IGARI. Since the outflow valves normally are little open at altitude given the high differential pressure and lowered mass bleed rate, conceivably opening them wide manually would realise depressurisation, though slowed, the packs operative still. The aircraft would be warmer.
@Niels
You ask “The estimate 8 route (MRC) ending 34S with initial bearing 188.6 degrees, what navigation mode would that be?“.
An excellent question.
The ATSB Final Report Appendix B states on page 10 of the appendix “It was concluded that in order to be assured of flying a required track, the aircraft lateral navigation would probably have been selected to the ‘track’ mode. This would maintain the desired track with the increasing magnetic variation being compensated for“.
I calculated the Boeing assumed start point on Flight Route N571 at 18:28:27 UTC as 6.942°N 95.597°E. The MH370 end point, described as the investigation team’s 469 knots path (estimate 8 in my list), ends on my estimation from the AMSA chart dated 28th March 2014 at 34.0°S 88.8°E. A geodesic with an initial bearing of 188.578°T would be required to fit the calculated start point and estimated end point.
Since the magnetic declination at 34.0°S 88.8°E on 7th March 2014 was 23.16° West, the CMT navigation mode was not used by Boeing otherwise the depicted track would have a greater curvature.
The CTT navigation mode could have been used, but that would require an active pilot to switch the heading reference from NORMAL to TRUE. Boeing may have considered CTT as a possibility.
The LNAV navigation mode could have been used and an ultimate waypoint of 45S 86E fits the initial bearing exactly. Boeing may have considered LNAV as a possibility.
The LNAV navigation mode could have been used and an ultimate waypoint of 45S 86E fits the initial bearing exactly. Boeing may have considered LNAV as a possibility.
Interesting.
The 00:00 utc surface terminator for 08Mar14 at Lat 45.00°S was Lon 086.49°E.
(45S 86E was 00:02 utc)
Just saying.
@TBill
You asked “Was it the acoustic anomaly or something else that inspired them to move so far north to search for the ULB detections?“.
Excellent question.
In the ATSB Final Report Appendix B we are told that it was a combination of factors: “The final refinement to the underwater search area was obtained by overlaying the results of the refined Inmarsat Doppler analysis, Boeing refined Doppler and range analysis, and air route M641“.
Initial Inmarsat Doppler Analysis.
“Inmarsat analysis showed that the best fit for the Doppler frequency was at a ground speed of 400 kts, with slightly ‘less’ best fits at 375 and 425 kts. A Monte Carlo style analysis, using a number of different starting positions on the 2nd arc also gave a best fit at 400 kts. From this approach a most probable speed range of 375 to 425 kts was selected“. (note: This was before the eclipse effect on the BFOs was taken into account)
Initial Boeing Performance and Doppler Analysis.
In carrying out the Doppler and performance analysis, two scenarios, 1A and 1B, were developed. Scenario 1A required the aircraft to fly in a southern direction after it crossed the 1st arc. Scenario 1B required the aircraft to fly a northern route through waypoint IGREX and waypoint LAGOG, before flying south. The LAGOG waypoint was included as it was close to a supplied, high confidence position labelled ’19:12Z’.
The “NW Point” or “19:12Z” point was marked with a Yellow Pin in a folder entitled Report Maps in Annexe I of the Malaysian Preliminary Report dated 9th April 2014:
https://www.dropbox.com/s/gwafdzsi3o6o2y5/Yellow%20Pin.pdf?dl=0
Refined Inmarsat Doppler Analysis – End Point 23.4°S.
“Inmarsat reran their analysis using the 19:12Z position as a starting point”.
“Starting from position 19:12Z, the best fit is shown in Figure 9. It is within 1 Hz of the prediction for the final three data points, and results in a crossing of the 7th arc at Latitude 23.4°S, Longitude 102.8°E”.
Refined Boeing Performance and Doppler Analysis – End Point 20.3°S to 22.2°S.
“In this refinement Boeing used the performance based flight tracks, previously identified, and compared the Doppler that these tracks generated with the Doppler information obtained from the OBF. The difference between the Doppler values was then classified as red, yellow, green or blue, with red being the ‘best fit’°. (note: OBF is now called BFO)
The best fit red area defined by Boeing was between 20.3°S 104.3°E and 22.2°S 104.1°E.
Air Route M641 – End Point 20.7°S.
“The track following the initial left turn off the planned route was towards Penang, from there the aircraft appeared to follow air routes to the 19:12Z position. The use of stored waypoints in the aircraft Flight Management System (FMS) suggests that the navigation was carried out using the Automatic Flight Control System (AFCS) in the lateral navigation mode. When the aircraft departed LAGOG the next major waypoint to the south was COCOS, which could be linked to the M641 air route”.
The intersection of M641 and the 7th Arc at 20.7°S 104.2°E became the AMSA priority search area.
Underwater Locator Beacons (ULBs).
Both the FDR and the CVR have Dukane Underwater Locator Beacons. AMSA were concerned that the battery life would not last much longer. The minimum battery life is 30 days from impact with water and the 2nd April 2020 was already 25 days after the impact.
“Consideration was also taken regarding the area that the towed underwater detector could cover before the predicted life of the batteries in the Dukane beacon expired”.
AMSA decided to follow Inmarsat’s 23.4°S, Boeing’s 20.3°S to 22.2°S, the ATSB/AMSA’s own view of 20.7°S based on the M641/7th Arc intersection and on 4th April 2014 the search moved north. A possible ULB was detected by Haixun 01 on 4th April 2014 and by Ocean Shield on 5th April 2014. Curtin University also reported an underwater acoustic detection on 4th April 2014, that came from the direction of the search area.
Summary.
AMSA decided to move the search north to around 20°S, based on the presentations from Inmarsat and Boeing, their own scenario involving the flight route M641 and in consideration that the battery life of the ULBs would soon expire.
@paul smithson
You asked “Could you offer clarification on the question about which columns in your tables are “data” and which are your estimates/derivations?”
(1) The end point positions are taken from the AMSA charts as shown in the linked presentation.
(2) The average speed is taken from the AMSA chart dated 28th Arch in the linked presentation.
(3) The BTOR errors are calculated using my MH370 satellite model.
(4) The Boeing Assumed Start Time, Start Position, Start Fuel, Flight Level, Assumed TAS, Assumed Mach, Assumed Speed Mode, Assumed Time (Duration) and Assumed Range are taken from Boeing data in the ATSB Final Report Appendix B, the Malaysian SIR Appendix 1.6E and published Boeing data.
There is one exception: in Appendix B it stated “The length of these arcs was constrained by the maximum speed of the aircraft, which was initially set at a ground speed of 652 kt“. I considered 652 knots as a typo and was probably meant to read 562 knots.
(5) The Aircraft Start Weight is calculated from the Start Fuel and the ZFW of 173,469 kg.
(6) Initial Bearing, Range, Endurance, Average GS, Fuel Rate, Specific Air Range and Mileage are calculated using my flight model.
(7) The last column MRC mileage is taken from Boeing documentation.
@Richard. Thanks.
@Richard: The LAGOG waypoint was included as it was close to a supplied, high confidence position labelled ’19:12Z’.
It’s never been explained why the position at 19:12Z was initially considered to be “high confidence” and later completed ignored. That position was based on a mobile radar source belonging to Singapore. Details surrounding this source have never been disclosed. That’s unfortunate because whether or not MH370 targets were received, the radar data could be used to allow or dismiss certain paths.
@paul smithson
You asked “AMSA slides clearly attribute those early “possible routes” to NTSB. I was interested to learn if you had an specific insights into their provenence [sic]”
The ATSB Final Report Appendix B, Section “Initial Predictions of the Aircraft Flight Path”, Sub-Section “Development of Northern and Southern routes” states “Boeing undertook a number of performance calculations varying the speed and altitude to determine the range of the aircraft. The speed chosen affected where the aircraft crossed each of the arcs. This resulted in a family of solutions along the arc generated by the satellite data from the 6th handshake. These northern and southern solutions are shown in Figure 3 and are bounded by the low and high speed flight paths which terminate on the final position arcs (6th arc)“.
The southern high speed flight paths shown in Figure 3 appear rather similar to the two possible routes shown in the AMSA chart dated 18th March 2014 and attributed to the NTSB. NTSB were the accredited representative in terms of ICAO Annexe 13 and Boeing were asked by the NTSB for technical support, as they were the aircraft manufacturer.
@Victor
I agree! The lack of transparency is indeed unfortunate. The Malaysian military radar data has been given to the ATSB, DSTG and Boeing, but never published. The only statement about the NW Point at 19:12 UTC was in the ATSB Final Report page 44 and Table 19, where the ATSB state “1912 NW point (80 35.719’N, 92035.145’E) reassessed as invalid and no longer used by flight path reconstruction groups.
In my view, it is not credible to base a search costing A$198M on a “yellow pin” defined as a “supplied high confidence position” on 2nd April 2014, which is a short time later deemed as “invalid” on 14th June 2014.
@Sultan
“Why is Ed Anderson so ignored here?”
It is not ignored. Several months ago Victor introduced Ed’s work as serious scientific effort that is perhaps being under-valued. That was an important endorsement. Victor has also summed up the technical questions, and IG members suggested experiments that could help rule-in or rule-out the close-to-Java acoustic observations. Some of these discussions with Ed have been on Twitter.
There are many theories on MH370 end point. Various groups are making proposals to OI where to search (IG et al/Captio/etc).
@Richard. “The southern high speed flight paths shown in Figure 3 appear rather similar to the two possible routes shown in the AMSA chart dated 18th March 2014 and attributed to the NTSB.” I agree that they bear a passing resemblance. However, the text says and the figure shows that these end at the 6th arc; whereas the “NTSB possible routes” end a good deal further south (as you you have demonstrated). As I said, it’s only a matter of historic curiousity so please don’t devote any further time to it on my account.
@Richard
That was great explanation above! thank you. To summarize, there was early period when 20-22 South became temporarily favored, coinciding with the remaining battery life of the ULB’s.
I remain very interested in the 400 knot options, so I can perhaps understand why that looked promising. The early days of the search make much more sense with your explanation above.
@Victor
Nice add re: 1912
@TBill
Many thanks for the kind words!
@Richard
Regarding possible navigation mode assumed by Boeing/NTSB: First of all, I’m not really sure slides 4 and 9 match very well.
In slide 9 it looks like bearing is changing at arc crossings, perhaps as to make given GS / distance covered match to subsequent arc location?
Is there any indication how they incorporated effects of wind?
One of the issues that was raised regarding my recent proposal for a route combining a waypoint route including IGOGU and ISBIX and continuing on CTT at the discontinuity was that the selector switch had to be set to TT instead of Heading.
Well, take a look at this thread:
https://www.pprune.org/tech-log/355864-mnps-nats-crossing-techniques-fmc.html#
You will note that the date is well before the M370 incident and can therefore be considered an unbiased input.
So, what was the MY SOP and what was the practice of experienced pilots?
The resultant path intersects the 7th arc at-37.426 with LRC at 41000ft and consumes 160kg less fuel than the 186GCP.
The path was computed from 18:22 with the offset cancelled as part of the turn South to ISBIX.
I have no doubt that further refinement could be made, but since this is good enough, I prefer not to fine tune it.
@Sid Bennett: You are conflating sooo many topics…
Whether track or heading is displayed as “up” depends on the configuration preferred by the airline, and is independent of what is flown after a discontinuity.
Regardless of the display configuration, and independent of the position of the HDG/TRK switch, when in LNAV mode, at a route discontinuity, without further input, a B777 continues by maintaining a constant heading, either magnetic or true, depending on the position of the HDG REF switch.
That said, after a route discontinuity, a pilot can choose to fly a true track by leaving LNAV mode and selecting either HDG/TRK HOLD or HDG/TRK SEL (depending on whether a change in track is desired) and ensuring the HDG/TRK switch is in the TRK position and the HDG REF switch is in the TRU position.
@Niels
I agree that there is a poor match between slides 4 and 9.
As you point out, slide 9 from Boeing is simply made up of straight lines between the arcs.
In the ATSB Final Report Appendix B, there is no mention of winds or air temperature at altitude.
I find this strange, when Boeing make it very clear in the Malaysian SIR Appendix 1.6E, that winds and air temperatures were incorporated.
“Wind data during the time period and covering the region of the flight were obtained for two time periods during the flight (18:00 UTC and 00:00 UTC) and at 8 altitudes (400 feet, 2500 feet, 4800 feet, 9900 feet, 13,800 feet, 18,300 feet, 23,500 feet, and 30,000 feet). The data contained time, latitude, longitude, wind speed, wind direction, and altitude. These data were applied to the available radar data to calculate the true airspeed of the airplane that would be used in the fuel burn analysis. The wind data were also incorporated into the analysis to determine the possible paths of the airplane using the constraints of the satellite data. Linear interpolation of the wind data occurred at the location and time of the assumed flight path in cases where known wind data was not available“.
@VictorI
The blog addressed both issues. Did you read it? Sometimes I find manuals too cryptic.
The IGOGU+ISBIX+CTT path would appear to be executable, with one remaining question.
The path could have been entered in the FMC with the ISBIX discontinuity.
After the offset is selected, the pilot can climb to 41kft to avoid crossing traffic and then let the pane fly itself.
But, the offset is not automatically cancelled at IGOGU since the turn is not 135deg or greater. But I have assumed it is. Is the offset cancelled prior to ISBIX? All of these “minor” details would be important to understand if the hypothesis tended to support an un-piloted flight after about 18:30.
Sid Bennett,
Several years ago I also went down a hole trying to make an IGOGU-ISBIX-constant track route work, with the last stage being due to a route discontinuity such that it all could have been set up at 18:30. It doesn’t work. The reason has been beaten into you ad infinitum – the plane will follow a constant heading, not track, at a route discontinuity. The pprune link you posted above (which I also read several years ago) does not address the issue. Boeing aircraft (and I have checked the 737, 747, 757, 767, 777, and 787) all have the same behavior. There is a lot of misinformation posted on the pilot forums, and even in vendor and training documentation – be careful of what you read.
(I am actually unclear how a 737 behaves – LNAV is disconnected at a discontinuity.)
@sk999
I have a very thick skull.
I also have found that the criteria for cancellation is given as 90deg turn, but the Boeing documentation (somewhere) gives 135 degrees. Nothing is certain or simple.
Perhaps you could read that thread again and explain what happens when the pilot flies tru rather than mag? It appears that that is what the discussion was about.
@sk999
Since I retired from industry 20 years ago I have practiced patent law. I am quite comfortable asking inventors dumb questions 🙂
Hard habit to break now.
@Sid Bennett said: The blog addressed both issues. Did you read it?
The blog comments you cite are concerned with configurations and settings that affect the navigation display (ND), i.e., heading up versus track up, normal (magnetic) reference versus true reference, and track versus heading. In LNAV mode, these settings and selections have ZERO effect on the great circle path that is navigated, and have ZERO effect on whether a track or heading is flown after reaching a route discontinuity (other than we believe the HDG REF switch determines whether the constant heading is magnetic or true). The settings DO affect how a pilot might compare while in-flight the direction of the plane with the direction included in the log generated before the flight.
You are asking questions that were studied and addressed here three years ago. At this point, we have little question about how a B777 behaves in LNAV mode at a route discontinuity. Please move on.
@Victor/Richard/DrB/Andrew
Do you believe the diversion of MH370 was motivated by suicide. “Don’t know” is not an acceptable answer. No one knows. “Don’t care”, is equally not acceptable since it has such a large impact on the route selection.
Just tell us what you believe.
@DennisW: If you are asking whether I think there was a negotiation that occurred before the murder-suicide, I would say probably not, for a number of reasons, including:
1. Other than the story that @TimR has relayed, we have no evidence that a negotiation occurred. I think @TimR is an honest broker. However, I have less confidence in his source, or his source’s sources, nor do I think a negotiation could easily be kept secret.
2. I don’t think it’s possible that the captain could control the passengers and crew without incapacitating them by depressurization.
3. The civilian radar data suggests a climb after the turnback from IGARI. That is consistent with a depressurization.
@DennisW
You asked “Do you believe the diversion of MH370 was motivated by suicide. “Don’t know” is not an acceptable answer. No one knows. “Don’t care”, is equally not acceptable since it has such a large impact on the route selection.
Just tell us what you believe“.
In two comments above, I made my views about the psychological state of ZS very clear, having listened to a trained psychologist Sabine Lechtenfeld on the subject.
https://mh370.radiantphysics.com/2020/03/09/new-report-released-for-mh370-search/#comment-27621
https://mh370.radiantphysics.com/2020/03/09/new-report-released-for-mh370-search/#comment-27646
@Sid Bennett
RE: “Perhaps you could read that thread again and explain what happens when the pilot flies tru rather than mag? It appears that that is what the discussion was about.”
The PPRuNe discussion was about the use of a true north heading reference* and TRK SEL when operating in Minimum Navigation Performance Specification (MNPS) areas such as the North Atlantic and northern Canada. The discussion was not about the aircraft’s behaviour on reaching a discontinuity with LNAV engaged, and it is not relevant to MH370.
To give you some background, before entering MNPS airspace pilots are required to independently check the full lat/long coordinates of non-database waypoints entered in the FMC against the clearance provided by ATC. Some airlines also require that pilots check the initial true track and distance between those waypoints by comparing the OFP with the FMC data. The latter procedure requires pilots to temporarily select the heading reference to TRU so that the FMC displays the initial true track between waypoints. The heading reference would ordinarily be restored to NORM after completing the check, in accordance with Boeing’s procedures.
Regarding discontinuities, the manuals caused some confusion because the Honeywell B777 FMC manual states the aircraft maintains the current track on reaching a discontinuity, while Boeing’s 777 FCOM states the aircraft maintains the current heading. It was confirmed several years ago that Boeing is correct; with LNAV engaged and no other inputs, the aircraft maintains the current heading. If the HDG REF switch is selected to NORM, the heading will be magnetic unless the aircraft is within a polar region, in which case the heading will be true. If TRU is selected, the heading will be true regardless of the aircraft’s position.
It IS possible to program the FMC to fly a specified track after reaching the next waypoint, using the ‘intercept course from’ function. In your scenario, that could only be done if ISBIX were the active waypoint; the aircraft would need to have already passed IGOGU, or the pilot would need to have executed a ‘direct to’ ISBIX before he inserted the ‘intercept course from’. The aircraft would then reach ISBIX and turn to fly the specified track. Again, the heading reference for that track (ie magnetic or true) would depend on the position of the HDG REF switch, which would ordinarily be selected to NORM.
[*For interest, at ICAO’s 13th Air Navigation Conference held in 2018, Canada proposed moving from magnetic to a True North reference system. That proposal is currently the subject of a feasibility study.]
@DennisW
I suspect the diversion was motivated by ZS’s profound disillusionment with the political situation in Malaysia. It was intended to send a message, which necessitated his own suicide and the murder of 238 others.
@Ventus45
I recently commented to @Niels on the Boeing analysis”The LNAV navigation mode could have been used and an ultimate waypoint of 45S 86E fits the initial bearing exactly. Boeing may have considered LNAV as a possibility.”
You responded “Interesting. The 00:00 utc surface terminator for 08Mar14 at Lat 45.00°S was Lon 086.49°E. (45S 86E was 00:02 utc) Just saying.”
As you know, in our recent paper, we state the MH370 end point at 00:19:37 UTC as 34.2342°S 93.7875°E.
The NOAA Solar Calculator shows an apparent sunrise at this position on 8th March 2014 at 05:38 Local Time (7th March 23:38 UTC).
The muslim custom for dawn prayers is to face Mecca. I did consider whether at dawn MH370 was turned toward Mecca.
At 23:38 UTC, MH370 would be running low on fuel. I calculate the position of MH370 at 28.9514°S 93.7875°E. Mecca would be on a great circle path with an initial bearing of 307.7°T. At 480 knots and a bank angle of 25°, it would take about 2 minutes to turn the aircraft from a 180°T track to a 308°T track. In order to match the BTO at 00:11:00 UTC, 00:19:29 UTC and 00:19:37 UTC, we know that MH370 could not have remained on a track of 308°T.
I then considered whether it was possible, that MH370 turned toward Mecca for a short time (say 2 minutes) and then reverted to the original track. This whole hypothesised turn process might take 6 minutes from say 23:36 UTC to 23:42 UTC from 180°T to 308°T back to 180°T. These two turns through 128° plus a 2 minute straight flight at 480 knots toward Mecca, leaves MH370 about 41.7 NM west of the original flight path. We know this did not happen, as the BTOR errors from 00:11:00 UTC onwards are in excess of 240 µs (standard deviation 29 µs) for a longitude of 92.997°E.
This leaves only the possibility of a more complex set of turns from a 180°T to a 308°T for 2 minutes, then a 180° turn to a 128°T track for 2 minutes, then finally a 52° turn back to the original 180°T track. This whole manoeuvre would take about 10 minutes and leaves MH370 about 31.8 NM further south than the start point of the manoeuvre. If MH370 had carried straight on from the start point of the manoeuvre at 480 knots, the aircraft would be 48 NM further south after 10 minutes. This more complex manoeuvre costs 16.2 NM of progress in a southerly direction.
The average GS for the final leg is 470.2 knots, so 16.2 NM represents 124 seconds of flying time. The average fuel rate for this final leg is 5,607 kg/hr for air conditioning packs on and cross feed valves closed. 124 seconds represents 193 kg of fuel. In addition there would be ca. 50 kg of fuel required for the turns.
The fuel prediction error for the whole journey from 17:06:43 UTC to 00:17:30 UTC is 427 kg and the fuel exhaustion error is 255 seconds, so 243 kg of fuel or 124 seconds of time, although significant, fits within the fuel budget prediction error limits.
In summary, a 10 minute detour for a 2 minute prayer at dawn toward Mecca is complex, unlikely, but feasible, assuming there was an active pilot. “Just saying.
(note: By the terminator, we do not mean Arnold Schwarzenegger.)
@Andrew
If the diversion was meant to send a message, I find it odd that ZS did not make it more explicit. A suicide motive for personal reasons would be confusing competitor to a “message to the government” motive.
The following will not be well-received. I realize that, and I have been reluctant to air it. Please do not take it as anything resembling criticism of tedious and high quality work that has been going on.
Relative to the latest analytics – we have all seen this movie many times before. It has never had a happy ending. To expect one now seems a bit optimistic.
There is a consistent underlier for this result history. It is Maslow’s hammer – “if your only tool is a hammer every problem looks like a nail”. So it goes with the math and physics endeavors. (I have, of course, labored in that domain extensively as well).
What is currently being under-considered, IMO, is significant peripheral information.
> A ZS WeChat moments before takeoff with an unidentified recipient (false ID SIM purchase)
> Malaysian high level interference early in the S&R (uncharacteristically noted by ICAO)
> ZS suicidal ?? He was a Malaysian patriot (Sabine’s conclusion as well)
> ZS was active in Malaysian politics, and troubled by the rampant corruption
> A lack of transparency relative to data release (radar, prior flights,…)
The diversion seems unlikely to have been a suicide at inception. It might have become one after a different intended purpose failed.
The post FMT flight paths for aircraft recovery are toward the Cocos or Xmas Island. The “logical” post FMT flight paths for suicide are more Westerly. There is little reason to believe a 34.2S 93.8E terminus makes (human) sense for either scenario. Plus that, it has been searched.
@Richard
I came across this image today.
https://www.pprune.org/rumours-news/535538-malaysian-airlines-mh370-contact-lost-368.html#&gid=1&pid=1
It illustrates those “NTSB possible routes”, the related initial aerial search area and their relationship with the ping rings. The picture illustrates what I relayed previously from my exchange with NTSB: that the first search zone and the terminus of those possible routes was predicated on the notion that the flight must have ended between Arc 6 and one hour’s travel time beyond.
@Richard
It is interesting that you raise the subject of dawn prayers again.
This subject was raised long ago by Edward Baker on his blog.
http://mh370apilotperspective.blogspot.com/2015/12/my-hunch-about-mh370s-pathand-it.html#comment-form
At the time, I posited that it was most likel