*The community of independent researchers is divided about where a new underwater search should be conducted. In this light, Bobby Ulich, PhD, has been quietly developing new statistical criteria that supplement the criteria that many of us have used in the past. The objective of this research is to define a new search area that is of manageable size and has a reasonable chance of success. Bobby has been working closely with Richard Godfrey to identify candidate paths, and with me to a lesser extent. At this point, the most promising candidate is a path of constant longitude, i.e., following a constant track of due south, aligned with waypoint BEDAX, and crossing the 7th arc near 34.3S latitude. This path, which was **identified** as a candidate path some years ago, could have been easily programmed into the flight computers with the waypoints BEDAX and the South Pole (e.g., by entering the waypoint S90E000). Work continues to evaluate this and other paths.*

*The note below from Bobby gives an overview of the new methodology, and is provided here to elicit comments from contributors of the blog.*

**Note from Bobby Ulich, PhD**

There are two pieces of available MH370 information that have not yet been fully utilized in predicting the southern route and the most likely impact latitude near the 7th Arc. Neither one was included in the DSTG Bayesian analysis.

The first item is the inclusion of a detailed and accurate fuel flow model. All DSTG analyses effectively ignored fuel consumption as a route discriminator by assuming “infinite fuel”. I and several others subsequently developed fuel flow models and compared them with Boeing tables, prior 9M-MRO flights, and the MH370 flight plan in order to validate the predictions. My model fuel flows are consistent with these comparisons, nearly always within +/- 1 %. As I understand it, Boeing did some range and endurance calculations and found that it was possible, at some combination of altitude and speed, for 9M-MRO to have reached a wide stretch of the 7th Arc, totally excluding only the region beyond circa 39S. However, the DSTG analyses did not factor in fuel consumption for each route they examined, so it is unknown whether or not that route was actually flyable with the available fuel. This is an important consideration, especially considering the fact that over a large portion of the SIO region of interest, the high-altitude air temperatures on the night in question varied by as much as 12 C with respect to ISA over an altitude range of only about 5,000 feet. Thus, small altitude changes had major effects on TAS and on fuel flow.

In my route fitter, one can either predict the main engines fuel exhaustion (MEFE) time using the known average cruise PDA for the engines, or hold the MEFE time at 00:17:30 (per ATSB) by adjusting the assumed PDA. I generally do the latter because that gives the correct weight as a function of time, which affects the commanded airspeed. It is also important to allow for the possibility that bleed air was turned off after diversion, reducing fuel flow by several percent. So, in fact the effective PDA which would give the correct endurance is potentially a range of values between 1.5% (the known value with bleed air on) and about -0.8% (the equivalent of bleed air off for the entire flight after diversion). Best-fit PDAs higher than +1.5% and lower than -0.8% are increasingly less likely.

Inmarsat and DSTG have provided some analyses of the BTO and BFO reading errors based on prior flights. Generally speaking, up to now, the statistics associated with those reading errors are the mean and the standard deviation. In many cases the RMS statistic has also been used as a convenience when performing route model fits to the satellite data, but the fundamental statistics are the mean and standard deviation of the BTO/BFO reading errors. In the case of the BFOs, we cannot know that the mean reading error (effectively the BFO bias term) did not change as a result of the in-flight power cycle ending circa 18:24. Therefore, we really only have three of these four statistics available for route fitting – the BTO residual mean, the BTO residual standard deviation, and the BFO residual standard deviation.

Regarding the standard deviation of the BFO reading errors, there has been much discussion in the past regarding the seemingly inconsistent criteria used by Inmarsat and by DSTG. I have been modeling the BFO reading errors comprising (1) random electronic noise, (2) non-ergodic and non-stationary OCXO drift, (3) trigonometric quantization errors in the AES Doppler compensation code that give the appearance of being quasi-random for readings widely spaced in time, and (4) vertical speed errors of roughly 40 fpm or higher from the nominal vertical speed profile (caused primarily by turbulence). I have developed a simple statistical model for the BFO reading noise, and this model gives results which are consistent with both sets of criteria. This new BFO reading noise model is what I use in my current route fitter.

The second item of previously unused information is also significant in discriminating against incorrect routes. That item is the fact that the BTO and BFO reading errors are *uncorrelated* with themselves and with each other, and, in effect, with most route-fitting parameters (with possibly one exception). Note that it is the *reading errors* which are uncorrelated, not the actual expected values for BTO/BFO. The degree of correlation of pairs of parameters is quantified using the Pearson correlation coefficient, and these values may be used as additional statistical metrics of the goodness of fit for the True Route. The one exception that could have occurred is for the BFO reading errors, which could change linearly with time due to OCXO drift. So, we must use that one correlation case (BFO residuals with respect to time) cautiously, knowing that it is possible such a drift might have occurred, although we do not see obvious cases of *large* linear drifts in previous flights. It seems possible that a very cold cycling of the OCXO might produce a shift in the bias frequency, but it is not apparent that such a cycling would be more likely to produce greater linear drift of the bias frequency well after warm-up. Small drifts of several Hz during a single flight are seen on prior flights, and it would not be surprising if they occurred in MH370 after 19:41.

We can substantially increase the number of statistical metrics that must be satisfied by a fit using the True Route by adding numerous correlation coefficients to the previously used means and standard deviations of the BTO and BFO residuals. Using more metrics (~10-12 total) provides greater selectivity in route fitting and better discrimination against incorrect routes.

A requirement for effectively utilizing these additional correlation metrics is the development of a method which allows us to obtain best-fit BTO/BFO residuals which behave statistically the same as the BTO/BFO reading errors. Those two parameters, the best-fit residuals and the reading errors, are generally not the same quantity. They are the same only when the model used to predict the aircraft location in 4-D (with 7 assumed route parameters) is perfect. No 4-D aircraft prediction model is perfect, especially in light of the expected errors in the GDAS temperature and wind data (which must be interpolated in 4-D for calculations along the route). At best, there will be small (a few NM) systematic errors in the model predicted position at the handshake times. The along-track and cross-track components of the position errors are systematic and must be allowed for in order to compare the expected BTO/BFO reading errors with the best-fit BTO/BFO residuals. If this is not done, then accurate correspondence with statistical metrics is impossible. In other words, just getting a fit consistent with the expected mean and standard deviation is not very discriminating because it ignores the even larger number of statistical metrics which the True Route must also satisfy. The question is, how can we remove the systematic errors in the handshake location predictions of the flight model (using GDAS data) so that the best-fit residuals are essentially just the reading errors?

I have found that this is indeed possible if the systematic prediction errors are small. Basically, the procedure is to fit lat/lon positions at the handshake times. I use only the five handshake points from 19:41-00:11. These data can be well-fitted with a single set of seven route parameters with no maneuvers, and this eliminates the need to make any assumptions about the FMT except that it occurred prior to 19:41. The MH370 data recorded by Inmarsat between 19:41 and 00:11 UTC on 7-8 March 2014 is entirely consistent with a path during that period, while southbound and heading into the Southern Indian Ocean, without major maneuvers such as turns or holds or major speed changes. With the assumption of a preset route during this period using the auto-pilot, solutions may be found consistent with the BTO and BFO data, comprising 5 sets of BTOs and BFOs at 5 known handshake times. The 23:14 phone call BFOs are not used because there is no independent determination of that channel’s frequency bias (offset).

Once I have the five fitted locations, I compare them to the model-predicted locations to generate a set of five along-track position errors and five cross-track position errors. Then I find the ground speed errors for each route leg that produce the along-track position errors. I also find the lateral navigation errors that would produce the cross-track position errors. Note that the cross-track position errors do not occur for LNAV (great circle) routes, but only for constant track and constant heading routes. The ground speed errors are caused by airspeed errors and by GDAS along-track wind errors. The airspeed errors are small (probably 1 kt or less) and are caused primarily by errors in the GDAS temperature data. The along-track wind error is probably at least several kts at any given location and time. However, we only need the average wind error for each ~1-hour long leg along the route, and these leg average errors will generally be smaller. I estimate that the overall along-track ground speed error using my model is about 1-2 kts. That means that we must constrain the fit so that the difference between the model-predicted location and the best-fit location (in the along-track direction) is equivalent to a maximum ground speed error less than about 1-2 kts. I also expect the ground speed errors to vary smoothly with time and location. So, I put constraints on the GSEs in terms of peak value and smoothness during the route fitting process.

For the constant track and constant heading navigation modes, the cross-track position errors are caused by a combination of cross-track GDAS wind errors and FMC lateral navigation bearing errors. The lateral navigation errors are largely undocumented publicly, but I expect them to be a small fraction of a degree for the constant track modes. The lateral navigation errors in the constant heading modes are caused primarily by errors in the predicted cross-track winds, and they will be larger than the lateral navigation errors in the constant track modes. In LNAV there are no cross-track position errors.

One benefit of this route fitting method is that it requires a very good, but not a perfect model. It must predict the locations, based on the 7 route parameters and the GDAS 4-D wind and temperature data, with an accuracy of about 5-10 NM. This is a significantly larger region than the location uncertainty (in one dimension) due to BTO reading noise. Still, one can estimate the true locations with the full precision of the satellite data following the route fitting method described above, using the statistical metrics to separate the truly random portion of the residuals from the systematic, non-random model/GDAS errors. When the synthesized locations are the True Route, the best-fit residuals will behave statistically identically with the BTO/BFO reading errors.

It is also possible to compute a single figure of merit for a given fit based on the 10-12 metrics described above. I use Fisher’s chi-squared combination calculation that finds a single percentile value that is most consistent with the percentile values for each of the independent statistics being combined. The percentile values represent the percentage of random trials which are no better than this fit result, assuming the null hypothesis. In the MH370 case the null hypothesis is the same for each statistic – that the fitted route is the True Route. The alternative hypothesis is that the route is not True for at least one of the statistics. The expected value of all individual and combined percentiles is 50%; that is, half of the random trials will fit better, and half will fit worse. We can use no other assumption than the route is True, because we have no idea what the values of the metrics should be when the route is not True. We only know their expected values (and their standard deviations) for the case when the route is True. Thus, we expect the True Route will have an expected Fisher combined percentile value of 50% (with a standard deviation of 29%). Non-True (i.e., incorrect) routes will have Fisher percentile values significantly less than 50%. This is how incorrect routes are discriminated. The route fitter objective function maximizes the Fisher percentile, so each trial is trying to match the expected values of the statistics for the True Route.

Two related activities have been carried out to validate the percentile calculations. First, a simulated processor was coded which generated random BTO and BFO reading errors. Then all the individual statistics and their percentile values were computed. Finally, the combined Fisher percentile was computed. Using 100,000 trials, the actual percentile values were found to be within 1% of their nominal values for all the individual and combined statistics. In order to achieve this result, the statistics were segregated into four classes, each with is own Z statistic and probability density function. The second validation experiment involved injecting random BTO and BFO reading errors into the route fitter program itself and verifying the correct combined percentiles were obtained.

It will be appreciated that this statistical fitting method, with a dozen or so metrics and with synthesized handshake locations, involves considerable computational time, so it is not ideal for identifying Regions of Interest (ROI). The previous generation of route fitters using just BTO/BFO metrics is much more efficient for evaluating the very large number of combinations of route parameters in order to identify all ROI, which may then be refined and evaluated using the statistical fitting method for assessment and comparison.

So far, after a lengthy systematic search, we have identified quite a few ROI, and these are being evaluated with the new statistical method. I have already demonstrated that one route in particular (LNAV at 180 degrees true bearing through BEDAX at LRC and at FL390, ending near 34.3S) is fully consistent with the True Route using the statistical method. At the present time, numerous other ROI are being evaluated and compared. Preliminary results to date show them to be inferior fits, but this work is not yet completed.

The goal of this work was to develop a means to better discriminate among routes by using additional metrics, including PDA and numerous correlation coefficients, and to compensate for systematic errors in model-predicted locations so that the best-fit residuals may be directly compared with the known BTO/BFO reading errors. Our initial results are promising. It may actually be possible to demonstrate that there is only one route solution which is fully consistent with the satellite data. More complete and detailed information will be provided once our assessments are finished.

@DrB

The one exception that could have occurred is for the BFO reading errors, which could change linearly with time due to OCXO drift. So, we must use that one correlation case (BFO residuals with respect to time) cautiously, knowing that it is possible such a drift might have occurred, although we do not see obvious cases of large linear drifts in previous flights.Please see figure 5.4 of the DSTG book. BFO is not a candidate for normal statistics. Dr. Allan realized this when he developed the Allan Variance, which has become an industry standard. No one, including manufacturers, uses mean and standard deviation to characterize oscillator behavior.

@DennisW,

Thank you for suggesting using the the Allan variance for the BFO reading errors. If that more extensive information is available for the same or a similar OCXO, I will see how well it can match the DSTG probability density function (PDF) by making some assumptions about the typical time interval between BFO recordings. I created my own function to match the DSTG PDF and it does not use a simple standard deviation. Neither does the expected value of the correlation coefficient depend on any other statistical descriptor such as standard deviation or even Allan variance. So, the (de)correlation analyses are not significantly affected by the exact nature and amplitudes of the variable variances. Unfortunately we don’t have that DSTG PDF data segregated by flight and time, so we can’t extract the Allan variance curve from the BFO reading errors during prior flights. In addition, the BFOs are not highly discriminating among southern routes, so the bottom line is the same, even if one ignores the BFOs altogether except to pick Southern Hemisphere arc crossings.

@DrB @Richard

I applaud the work, and happy to hear you are working so hard behind the scenes. It certainly does seem like new methodologies could help better determine the flight path.

One concern about fuel exhaustion modeling, is that the aircraft may have been flown in an unorthodox manner. For example at IGARI, I am thinking perhaps most electrical systems are off, perhaps with APU on, possibly allowing manual flight with DFDR depowered, and possible depressurization.

Also I like to consider active pilot. I also have a proposed 180S flight path but I like to consider desents and heading changes as daylight approaches aprox. 23:00 is going to be twilight and high winds below 22 South. In general I feel like 180 deg due south path with a later heading change to the southeast fits the data very well.

@TBill

The BTO and BFO data would pick up a major change in track or altitude.

The PDA and GSE will change as well.

I will try out track changes to the South East at ca. 23:00 UTC, as you suggest.

I will run a comparison using the new methodology against a standard LNAV180 LRC FL385 (without any track change) and let you know the results.

“As I understand it, Boeing did some range and endurance calculations and found that it was possible, at some combination of altitude and speed, for 9M-MRO to have reached a wide stretch of the 7th Arc, totally excluding only the region beyond circa 39S.”

Is there any more information on this? It is only possible to define a maximum southern fuel terminus probabilistically and by exploring all realistic combinations of altitudes, step climbs, etc. that provide an acceptable fit to satellite data. Thus, it would require a full-blown Monte Carlo with probabilistic inputs, similar to what DSTG did, but with careful attention to fuel, including realistic probability densities on fuel weight, plane weight, fuel burn IGARI to MEKAR, etc. That’s quite a chunk of analysis if they actually did it.

@DrB. Can I check my understanding what of you have said above?

1) Are you saying that a “true” route must not only be viable within allowable error bounds of BTO and fuel, but that the residual error pattern must be “well-behaved”? And that the routine that you have described above somehow enables us to discriminate a well-behaved from a badly-behaved pattern of residual errors?

2) If that’s the case, can you confirm that the solutions that your are subjecting to this filter are automated flight with constant altitude from 1941 to 0011?

3) Does the above therefore exclude paths where first engine has flamed out earlier than 0011? Or at least those that result in a significant slow-down pre-0011?

@TBill. About piloted, there could have been a powered glide at the end to a dive from low level, exchanging some height for extra range to the final transmissions.

@DennisW,

I looked again at the Allan Deviation to see if there are some representative data available and if they might prove useful in predicting MH370 BFO reading errors. Mike gave me his files on the SDU OCXO and similar units. There are some graphs which show the Allan 2-Sample Deviation at about 10^-11 for pairs of 1 second averages that are contiguous. The BFOs of interest here involve less than 1 second of frequency measurement spaced in time by 1-1.5 hours. There are no Allan variance data which directly address this case. The Allan Deviation is designed to specify short-term noise, and I don’t see how to derive anything useful from it that is applicable to the sparsely sampled MH370 case. If you have a method for doing this, please share it here.

I will also point out that the short term average frequency deviations of 10^-11 are several orders of magnitude too small to be detectable in BFO readings, so I don’t think the short-term noise in the OCXO readings contributes in a measurable way to short-term BFO reading noise (unless the duration of the frequency measurement at the GES is a VERY small fraction of a second, which could be the case. However, that still does not allow us to predict the frequency drift over several hours when sampled for < 1 second. The best basis for this is the Inmarsat BFO data for prior 9M-MRO flights. These are grouped in DSTG's Figure 5.5, which is what I have used, assuming that figure represents the PDF of a single reading, and each reading is independent. An unusual case is shown in Figure 5.4, and DSTG could not identify of the cause of the 10 Hz deviation that appeared and mostly disappeared in < 1-hour near 22h. That might be OCXO drift, or it might be due to a problem with the model equations. I wonder if it could be due to an eclipse of the satellite? The time scale and amplitude are about right. Has anyone looked at this possibility?

@Paul Smithson,

You asked: “1) Are you saying that a “true” route must not only be viable within allowable error bounds of BTO and fuel, but that the residual error pattern must be “well-behaved”? And that the routine that you have described above somehow enables us to discriminate a well-behaved from a badly-behaved pattern of residual errors?”

Yes, that is what I am saying (and not just the BTO residuals, but all the metrics). The BTO residuals, when accurately fitted to the True Route, MUST display the expected statistical behavior (mean, standard deviation) CONSISTENT WITH the prior flights. The overall figure of merit is a compound percentile value, which is the percentage of random trials that would be worse than the current fit, assuming the route is True. The expected value of this percentile is 50%. That means half the time the noise in the satellite data would produce better fits, and half the time the fits would be worse. So the True Route won’t be exactly 50%. It could be more, or it could be less, but is is less and less likely as the percentile drops below 50% towards zero. I have demonstrated that my statistical calculations produce the correct percentages of random trials for each statistic percentile and for the compound percentile. I have validated my route fitter code in the same way. I have a software switch that injects random BTO and BFO residuals, and I also do many trials of this to confirm the accuracy of the percentile calculations.

In this case I would use the term “statistical consistency at a reasonable probability” rather than “well behaved.”

You also asked: “2) If that’s the case, can you confirm that the solutions that your are subjecting to this filter are automated flight with constant altitude from 1941 to 0011?”

Yes, that is our working assumption. You don’t need changes of altitude or turns to identify quite a few Regions of Interest which have potentially acceptable BTO and BFO residuals. However, when you apply the remainder of the available statistics, all the ROIs have very low compound percentiles except for one route.

You also asked: “3) Does the above therefore exclude paths where first engine has flamed out earlier than 0011? Or at least those that result in a significant slow-down pre-0011?”

I found it is generally the case that the right engine flames out shortly before 00:11 and the aircraft is slowing by 00:11 and slowing and descending not long after 00:11. I would guess the altitude by 00:19 to be in the vicinity of FL200. My fuel model contains an end-of-flight model which figures the deceleration and descent based on the simulator results from Mike and incorporates suggestions from Andrew and Victor and others. The average leg speed from 22:41 to 00:11 is slightly reduced by the right engine flame-out circa 00:06. This slight slow-down adds to the inherent LRC slow-down as the aircraft gets lighter.

@Richard

Two 180 South cases I like are:

(1) 180S most of the way to Arc6 then 135 deg Southeast heading (which ends at Arc7 and Broken Ridge)

(2) 180S to around BEBIM and then approx. 167 deg heading (essentially picking up the simulator path at about BEBIM). @Nederland was the first one to notice this path, and the speed has to be lower (400-425 range) after BEBIM.

So the turn to southeast could be earlier than 23:00.

@globusmax,

You said: ” “As I understand it, Boeing did some range and endurance calculations and found that it was possible, at some combination of altitude and speed, for 9M-MRO to have reached a wide stretch of the 7th Arc, totally excluding only the region beyond circa 39S.” Is there any more information on this? It is only possible to define a maximum southern fuel terminus probabilistically and by exploring all realistic combinations of altitudes, step climbs, etc. that provide an acceptable fit to satellite data. Thus, it would require a full-blown Monte Carlo with probabilistic inputs, similar to what DSTG did, but with careful attention to fuel, including realistic probability densities on fuel weight, plane weight, fuel burn IGARI to MEKAR, etc. That’s quite a chunk of analysis if they actually did it.”

DSTG did not do that. They did get range and endurance calculations from Boeing that they used to limit the range of air speeds and altitudes they used in their statistical modeling. The section “Aircraft Performance Analysis” on page 16 in the ATSB Report from 3 December 2015 describes this in some detail. However, after describing how the southern range limit was calculated, they failed to say what that limit was.

As you point out, there are very many possible routes with maneuvers between 19:41 and 00:11 that can be matched to the satellite data. One of those could be the True Route, but there is no means for us to discriminate among the many possible “perfect matches” if additional maneuvers are added.

On the other hand, there is one, and so far only one, route which is completely consistent with the satellite data and which has no maneuvers between 19:41 and 00:11. I will also point out that this route is the best PDA match among all the Regions of Interest we have examined so far. In addition, it is the only ROI/route which is aligned (very accurately, by the way) with a nearby waypoint (BEDAX). Other positive indicators may be that is exactly due south toward the South Pole, and the high altitude and long-range cruise speed setting combine to provide a very long range.

@DrB

I am indisposed at the moment, but will try to answer your query in a day or two.

It is worth noting again that Inmarsat’s 2014 JON Paper predicted 34.7°S, 93·0°E, very close to Bobby’s “due south” intersection with the 7th arc at 34.3°. These two predictions are only 41 nm apart, and close to the area CSIRO estimated. See: http://bit.ly/2IhJreX

Of all the possible routes that could have been deliberately chosen to make the plane disappear, due south from the final turn is singularly simple and thus more likely than others IMO.

@TBill

I have run the 2 cases you propose through my model:

1. LNAV180 towards the South Pole until 30°S at 23:44:52 UTC and then CTT135 on a south easterly track to Broken Ridge at 00:19:37 UTC at 32.1°S at a reduced Mach 0.475 and GS of 273.24 knots and cruise at FL385:

https://www.dropbox.com/s/vhqhp4f8a5lvtth/MH370%20Flight%20Path%20Model%20V19.2%20RG%20LNAV%20LRC%20FL385%20180.0%20Deviation%2030S%20135.0%20Report.png?dl=0

2. LNAV180 towards the South Pole until waypoint BEBIM at 21:19:50 UTC and then CTT167 on a south easterly track to 00:19:37 UTC at 29.7°S at a reduced Mach 0.6675 and GS of 385.29 knots and cruise at FL385:

https://www.dropbox.com/s/ae2trtbehhk8r4w/MH370%20Flight%20Path%20Model%20V19.2%20RG%20LNAV%20LRC%20FL385%20180.0%20Deviation%20BEBIM%20167.0%20Report.png?dl=0

Here is the standard LNAV180 flight path towards the South Pole from close to waypoint BEDAX without deviation as a basis for comparison. In the standard case, the speed mode is LRC with a Mach reducing from 0.8391 to 0.8283 and average GS of 482.68 knots and cruise at FL385:

https://www.dropbox.com/s/nsumz0no91e2riu/MH370%20Flight%20Path%20Model%20V19.2%20RG%20LNAV%20LRC%20FL385%20180.0%20Report.png?dl=0

In both the cases you propose the tailwinds pick up significantly following the turns in a south easterly direction. In order to reach the 7th Arc at 00:19:37 UTC, the Mach and therefore the TAS is also reduced significantly. This leads to a fuel saving, where the BEBIM option is no longer likely as the fuel remaining at 00:17:30 UTC is too high. The Broken Ridge option is still within the tolerance of the fuel model with 443 kg remaining at 00:17:30 UTC.

In addition the mean BTO residual for the Broken Ridge option is -14.8 µs, for the BEBIM option is +44.7µs, compared to +0.4 µs for the standard flight route. The STDEV BTOR for the BEBIM option is too high at 59.6 µs and the STDEV BFOR is too high at 5.2 Hz.

The Broken Ridge option is less likely than the standard route but within the tolerances of my MH370 flight model. I would discount the BEBIM option on the basis of the fuel calculation and the poor BTOR/BFOR fit.

Please ignore the RMS GSE of 8.08 knots for the Broken Ridge option. This is an artefact of the reporting system, due to the deviation mid leg. The correct RMS GSE is 1.01 knots.

The standard LNAV180 flight path shows a PDA of 1% (nominal PDA is 1.5%) and I speculate that the Bleed Air may have been shut off for between 30 minutes and 1 hour following the diversion at waypoint IGARI.

Bobby’s and Victor’s models will give detailed alternative analyses and may possibly give further criteria for including or excluding either option.

I’ve long been a proponent of the BEDAX-SouthPole route because of the simplicity of the path after 19:41 and the excellent match to the BTO and BFO data. However, it does have its problems:

1) It requires a “delay” before turning south to hit the 19:41 arc at the correct time, which means more maneuvers are required between 18:22 and 19:41 than other paths crossing the 7th arc further south.

2) The area close to 34.3S latitude was already searched first by GO Phoenix and then later by Ocean Infinity, which means either the plane glided a long distance away from the 7th arc, or the debris field was missed.

Nonetheless, a search in this area might the most promising place to conduct a new search.

Decompression/bleed air off for the whole flight is unlikely unless the PF decided to pull his pressure mask off after the FMT. If the PF was alive to 00:19, he surely would have restored pressure after he was sure everyone else was dead. Flying 7 hrs with pressure breathing very unlikely.

@Richard

Thank you very much for running those cases! It will take me a little while to interpret. Usually I am 6 months behind understanding the blog topics, I will see if I can step up my game.

Re: “…the BEBIM option is no longer likely as the fuel remaining at 00:17:30 UTC is too high.”

OK I agree, that’s what I am saying about BEBIM/simulator path, enough fuel to get to the target which I envison could be Dordretch Hole some 270-nm beyond Arc7. Also maybe some loiter somewhere (non-direct south path to BEBIM).

@DrB

Re: Active Pilot vs. Passive Pilot

So far we have not been able to prove data match to passive flight. My terminology is that the data (to date) is ambiguous. It can be argued the complex end-of-flight sequence does not match passive flight unless we are lenient and accept some aircraft-specific (electrical?) things may have happened that we do not fully understand (which is of course quite possible).

>>Anyways the point, I don’t think you can say: active is ruled out because by definition we could invent an infinite number of perfect paths. If you can invent one perfect active path that is better than your passive path, then that demenostrates there could be better paths.

Also many people have pointed out fuel-dumping as part of the active-flight plan, because ZS was vocal about fuel-dumping on YouTube as far as video quality of the MS flight sim versions.

>>I am just trying to say you should not be ruling out the active path options, unless you truly have found the answer, which I am yet to warm-up to.

180S was my favorite for a long time too…I have flown it many times. I would certainly say it is one the BASE CASE MH370 flight paths.

>>The more cautious you can be with your conclusions, the more widely respected the work will be. Unless you really have 100% nailed it, in that case you can afford to be more assertive.

Fuel dump in flight sim:

https://twitter.com/HDTBill/status/1070717041856913408

@ALSM

“Decompression/bleed air off for the whole flight is unlikely unless the PF decided to pull his pressure mask off after the FMT.”

True enough, but there could be variations on that theme. My personal thought is at IGARI, LEFT Gen=OFF, RIGHT Gen=OFF, BLEED air=reduced or OFF, DFDR=OFF. If Victor is correct about AutoPilot=ON at Penang, that might mean DFDR=now ON again. And the DFDR data would show a power interruption but no “apparent” loss in cabin pressure.

Meanwhile we are left to wonder how the pilot managed the electric and bleed configs for the rest of the flight. I do not think we have very deeply delved into the rogue possibilties. So I am just giving my view for consideration.

@TBill: You are obviously frustrated that scenarios with pilot inputs after 19:41 do not receive enough consideration because you beat that drum on a regular basis. The problem is that with the data we have in hand, it is

impossibleto allow multiple pilot inputs after 19:41 and constrain the area to a manageable size with a reasonable chance of success without introducing arbitrary assumptions, i.e., “hunches”, such as Ed Baker’s hunch about the captain wanting to recite Muslim prayers at sunrise, or Captio’s hunch about intending to “safely” reach Christmas Island, or your hunch about Dordrecht Hole. That does not mean the hunches are wrong. It simply means that it is difficult to objectively rank the hunches, nor can we be certain the list of hunches is complete. For those reasons, many of us have resisted making a search recommendation based on a hunch unless more information comes to light in support of a particular hunch.@Victor

MH370 data is frustrating by definition, because as the title of this blog article indicates, the data seems good enough that it seems like it could be possible to find the flight path answer. Maybe we are wrong about that, but that’s what’s so intruiging about it.

But yikes I am certainly saying find the technical correct answer, and let ease of search be secondary (for the moment).

You guys had the blog aticle, I am just saying my general input prior to having enough confidence myself to endorse the new idea.

I am actually in quite excellent agreement with your personal way of qualifying preliminary technial conclusions. The only departure I may be developing now is that I am less inlcined to give a rosy outlook for any search site, but of course I am open to a breakthrough on that front.

@DrB

Some comments.

https://docs.google.com/document/d/1yN3HlBfFU_ZDdy8N1uacSRujyaG07Ti3wBRofVjfsMQ/edit?usp=sharing

@TBill With regards to your apparent preference for a more eastern terminus – I assume you believe this would be selected to cause the main wreckage to sink into deep and difficult subsea terrain.

It seems to me that if the objective was to “make the plane disappear” (to use ALSM’s phrase) the primary goal would be to conceal a floating debris field. If this were located reasonably soon following the crash, the task of finding the sea bottom debris is significantly reduced. Perhaps the best was to conceal the floating debris is to go as remote as possible giving it maximum time to disperse and sink while also hampering the operational logistics of searching for it.

I do understand this is influenced by the presence of absence of active control at the end. For my part I find it difficult to reconcile active control with the apparent high descent rate at that time. From the debris located to date, it does seem that the aircraft came apart, so probably there was a floating debris field.

Perhaps I misinterpret your views.

@Shadynuk

In Peter Lee’s book (MH370 By Accident or Design), an American oceanographer from NOAA makes a comment with BR graphic to say he feels the aircraft may have headed for Broken Ridge. I adopted that hypothesis.

If we give merit to the BR hypothesis:

(1) agreed that possibly means the high descent rate BFO’s was not a crash, but a descent maneuver. But some of us feel the final BFO’s are (that word again) ambiguous whether it is controlled descent or uncontrolled dive.

(2) possibly means the flaperon leading edge damage is skipping over the water, perhaps a high speed (fatal) ditch.

(3) It means the crash locaton was not random uncontrolled lcocation

So those are all somewhat looking-thru-different-pair-of-glasses theories admittedly. But those ideas are not intended to be disruptive, it is just where you come out if you accept the “BR hypothesis” as the central point of the flight.

I do feel the pilot may have been trying to conceal crash location, but I presume there could be some luck involved that the splashdown/debris was not quickly found. I tend to feel the pilot, if alive, may have been spooked by the 23:14 sat call…he might have wondered if that would give location clues.

So he could have changed heading towards or away from BR at that point. It is also 23000-ft deep at 22 South and Arc6 about.

Dennis: Fig 5.4 is a useful reference, but I don’t agree that you can infer so much from that graph, or the typical Allan Variance observed in quartz oscillators.

For starters, that graph is a plot of expected vs. measured BFO values, not OCXO drift values. There is a big difference. I suspect that the sum of the numerous other BFO component model errors were at least as large as the isolated OCXO drift term. Second, we know that the OCXO on 9M-MRO rarely required more than a single LSB correction when it was re-calibrated every few days (LSB bit = 16 Hz). Moreover, Thales via ATSB, informed me that the corrections were typically back and forth over a few weeks, not increasing or decreasing. IOW, the average drift was << 16Hz over a few weeks. If the possible drift was as great as your graph suggests, the typical correction (period always longer than 26 hrs) would be 10X what was observed over many weeks prior to MH370.

Perhaps the best data we have to estimate the BFO error is in the MH371 data set.

@DennisW,

I hope you are feeling better now. Thanks for responding with your note on the BFO drift characteristics. I don’t think we have any disagreement except on the magnitude of the potential drift in bias frequency. You think it is so large as to prevent using the BFO residuals at all for route discrimination, except for indicating a southbound FMT. I (and others of more note) disagree for the reasons discussed below.

Regarding DSTG’s Figure 5.4, the flight from Mumbai to Kuala Lumpur, you say that figure demonstrates 20 Hz of frequency drift in 6 hours. I don’t see that. What I see is a very stable set of data for the first 3.5 hours. ALL the BFOs then are within +/- 6 Hz, and the slope is close to zero. The scatter in the BFOs over this first portion of the flight appears to be consistent with the reading error contributions from all known sources other than oscillator drift. I do not interpret any or all short-term BFO variation as being caused by oscillator drift or noise (because as I previously showed, using the Allan deviation the short-term frequency noise is several orders of magnitude too small to be detectable in the BFO readings). Then, circa 22:00 there is a linear drop of 10-12 Hz, followed by a linear rise back close to the to the previous mean for the first 3.5 hrs. The disturbance appears and disappears in about 45 minutes. The amplitude and time scale of this event reminds me very much of the satellite eclipse which was underway during MH370 at 19:41. I would judge the mean frequency for the first portion of the flight to be within several Hz of the mean frequency for the last 45 minutes of the flight (not 20 Hz different). Regarding this figure, which seems to be presented by DSTG as a worst-case scenario, I do not see 20 Hz of frequency drift, and you are only guessing that the brief 10-12 Hz disturbance near 22h was produced by oscillator drift. To estimate oscillator drift, I essentially draw a smooth and slowly varying line though the sequence of BFO errors, and then I see how much that smoothed curve changes with time. You simply cannot assign the full peak-to-peak variation in BFO error 100% to oscillator drift, which seems to be what you are doing. That incorrectly ignores the other contributors to BFO reading errors.

What would you say if it turns out that an eclipse occurred at 22:00 hours? I hope someone can check out the possibility this occurred, to lay this potential cause to rest, one way or the other. DSTG was unable to ascertain a cause, and they did not conclude it was produced by oscillator drift.

Next, let us consider your informative Figure 3, the 8 random walk cases. My first reaction is that, if this accurately represented the oscillator drift, there would be several more extreme examples in prior flights to contend with besides just the one DSTG showed in Figure 5.4. I think your Figure 3 may be correct in principle, but it overestimates the actual amplitude of the frequency drift by a significant factor.

You said: “The BFO error due to the random walk of the AES oscillator frequency could be any of the results shown in Figure 3. We simply have no way of quantifying it. Saying a flight path “fits” the Inmarsat BTO and BFO data is just plain silly.”

On that I disagree with you, and so do Inmarsat and DSTG. It is already quantified. I believe we can use the BFO data for route discrimination, within the limits shown by the analyses of BFO residuals for a fairly large number of prior flights (and shown in DSTG’s Figure 5.5). It is not highly discriminating because of the known and fairly large scatter in the BFO reading errors due to multiple causes, including oscillator drift, but I see no reason why one cannot use Figure 5.5 to evaluate and discriminate among proposed routes. BFO residuals which significantly exceed those shown on Figure 5.5 may be assigned lower probability than other routes which have BFO residuals consistent with Figure 5.5, and that is what I have done.

@TBill,

I believe I can prove an excellent match for one route to “passive flight” between 19:41 and 00:11. Victor, Richard, and I have done a very detailed comparison of our flight and GDAS models, and each indicates an excellent fit for this route. We’ll see if anyone else can poke a hole in it after we publish it.

I don’t see any mismatch between the satellite data and a passive end of flight, just the lack of finding submerged debris near the arc at 34.3S. That could be due to the debris field being missed/misclassified by Fugro or Ocean Infinity, as happened by Ocean Infinity in the search for ARA San Juan.

You said: “If you can invent one perfect active path that is better than your passive path, then that demonstrates there could be better paths.”

Actually, there are no solutions that are “perfect” or even significantly statistically “better” than the one in hand. They can be “similarly highly probable”, but not really “better”.

Previously I said: “As you point out, there are very many possible routes with maneuvers between 19:41 and 00:11 that can be matched to the satellite data. One of those could be the True Route, but there is no means for us to discriminate among the many possible “perfect matches” if additional maneuvers are added.” As Victor pointed out, this opens the door to too many possibilities to be searched, excepting some new and credible information indicating a particular destination.

@ALSM

For starters, that graph is a plot of expected vs. measured BFO values, not OCXO drift values. There is a big difference.I realize that, but I don’t agree that there is a big difference. The aircraft speed, track, and position were well-known in the generation of Figure 5.4. The satellite orbit and down converter are well characterized. The location of Perth is relatively static. A BFO error budget has yet to appear in the five year history of this investigation.

I have no idea what you think the other sources of error (“at least as large as the OCXO drift”) might be. Enlighten me.

@TBill

You stated “Re: ‘…the BEBIM option is no longer likely as the fuel remaining at 00:17:30 UTC is too high.’ OK I agree, that’s what I am saying about BEBIM/simulator path, enough fuel to get to the target which I envison could be Dordretch Hole some 270-nm beyond Arc7.”

I agree that a flight path from waypoint BEBIM to the Dordrecht Hole at 33.50°S 101.33°E on a track of 162.9521°T at Mach 0.813 fits the fuel range and endurance with a PDA of 0.9845%, but the BTOR at 00:19:37 UTC is 2,456.2 µs, which is off the scale:

https://www.dropbox.com/s/0n8bpvxqja0v857/MH370%20Flight%20Path%20Model%20V19.2%20RG%20LNAV%20LRC%20FL385%20180.0%20Deviation%20BEBIM%20162.9521%20DH.png?dl=0

I would discount the Dordrecht Hole as the MH370 end point on the grounds that it does not fit the BTO data.

@DrB said:

The amplitude and time scale of this event reminds me very much of the satellite eclipse which was underway during MH370 at 19:41.For MH370, the effect of satellite eclipse is included in the residual C-band Doppler shift that was recorded at the GES in Perth. If this same measurement was used for other test flights, there should be no eclipse effect in BFO error measurements.

At some point, I asked somebody at the DSTG to explain the “geographic” dependence of the BFO error that was claimed in the DSTG report. He said they observed a BFO shift as the plane traveled from departure to arrival point, and then saw the shift reverse for the reverse flight. There was obviously was some systematic error introduced in their measurements or models that remains unexplained.

Dennis: Once external potential source of error is turbulence. If the plane was flying though a period of turbulence, the vertical Doppler component may have caused some error. It is unclear how well the instantaneous vertical speed was modeled, if modeled at all. As Bobby noted, the eclipse is another potentiaql source of error (s/c LO temperature). I do not know the specify flight number for the flight plotted in Fig 5.4, but I could check the time relative to the eclipse if someone can come up with that info.

Victor: I agree that the eclipse temperature effect on the s/c LO should have been compensated by the pilot carrier, if the technique used for 370 was also used by in DSTG Fig 5.4. It would still be useful to check the time of the flight compared to the time of the eclipse (local midnight for 64.5E).

I think it can be assumed with high confidence there is no real geographic related BFO bias. That is pure nonsense. The fact that DSTG reported the apparent geographic dependency is hard evidence the model was not exact, which may be another source of the BFO values in 5.4.

@ALSM

DSTG in fig. 5.4 refers to the March 2nd 2014 flight Mumbai – KL

Comparing with the MAS flight schedule (November 2013) it should then be MH195 scheduled 00:05 – 07:40 (local times). This suggests that the time base in fig. 5.4 is UTC. Not sure if it then was March 1 or March 2 UTC, however for the eclipse calculation that should not matter much.

I remember checking the eclipse and concluding it should have occurred earlier in the flight. It would be good if you could check as well.

The eclipse for March 2 was from 19:34 to 20:15 UTC. The flight was from 18:35 to 23:40 UTC. So the eclipse did occur during the MH195 flight on March 2, 2014, but it was during the first half of the flight.

@DennisW,

@airlandseaman,

For a description and discussion of the dominant contributors to BFO reading errors on short time scales (a minute or less), see Section 2 of my paper here:

https://drive.google.com/file/d/1N3AKqkrh50c0-ovUOloBcSRUpjXwAAIR/view

On short time scales (minutes or less) the oscillator drift is unimportant. I believe it is now known for certain that the trig quantization errors do exist in the AES frequency compensation code.

@ TBill,

(2) possibly means the flaperon leading edge damage is skipping over the water, perhaps a high speed (fatal) ditch.

It seems to me that everyone who suggests that the flaperon LE damage, [actually all those who think the flaperon TE damage too . . ], ignores the fact that there are massive engines directly in front of the flaperons. The engines will surely hit the water before any other part of the wings.

In a controlled ditching, where the pilot is holding a moderate positive AOA, say 10-12 degrees, it is possible, but not guaranteed, that the engines may shear off the mounting bolts and fold up and over the LE of the wing. If, on the otherhand, the aircraft contacted the water in a nose down attitude then it is almost certain that the engines would fold back under the wings, causing massive damage to everything behind them.

The possibility that the flaperon departed the wing in flight still remains. The high speeds reached in the final descent could well have induced flutter, causing the TE damage and then tearing the flaperon from the wing within a few seconds.

I’m of the view that the flaperon damage cannot be conclusive evidence of an [attempted] controlled ditching.

@Brian

One would think that the French forensic experts would be able to opine on whether the flapron trailing edge damage was caused by flutter or contact with the water. Why this information is not in the public domain is not clear, but it is frustrating.

@Brian Anderson

I agree the flaperon evidence is yet another ambiguous data point. I do not favor a controlled ditching but I suppose that is possible. I do not know whether if it was nose down crash or 250 knots skimming type fatal glide.

@DrB @Richard

Thnak you, I just wanted to let you know my feelings in advance, I will try to undertsand your model and to see what I think. I know I will apprecicate the good work.

@Dennis: The French report on the flaperon was included in the SIR as Appendix 1.12A-2. Separation caused by contact with the water at the trailing edge was proposed as an unconfirmed hypothesis. Separation in-flight was dismissed because it was believed the leading edge would have impacted the water first, causing more damage at the leading edge than was observed. From the French report:

First of all, it appears possible to exclude in-flight loss of the flaperon since its weight is concentrated forwards, which would a priori lead to a fall with the leading edge forwards and the probable destruction of the latter. The damage to the trailing edge would also likely be different. A simulation of a flaperon fall with an initial speed corresponding to that of an aeroplane in flight would enable this to be definitively eliminated.Considering the shape and weight distribution of the flaperon, especially with a ragged trailing edge that might have occurred before separation, there is ample reason to question the conclusion that the flaperon would have fallen with its leading edge down and without tumbling.

@Victor @all

Over on Twitter @DrMRHazard asked me to provide reference to ZS’s comments about the fuel jettison graphics on the PSS777 model, which is attached below.

https://www.youtube.com/watch?v=bCL5gLw_2Nw

See comment section by Zaharie Shah and many RIP replies to what was said to be his last(really?) YouTube post, according to one commenter. Victor I am wondering if ZS ever tried PMDG777 ?

Copy and paste-

zaharie shah

5 years ago

being a fan of MFS since the first version and a boeing 777 pilot all at once, , I hv yet to see a good addon as the PSS boeing777 which was release many years ago. Unfortunately its for FS9. I m still holding on to it awaits the same author rebirth. VC is crap, serious enthusiast would go for multi screens , technology is cheaper now.Some of the coolest funtionality on PSS 777, fuel trail on fuel jettision ! Comprehensive support nav data base by third party.

@Victor

Thx. I do recall the French “report”. I have no background in material damage assessment, but I find it difficult to believe the flaperon trailing edge damage was due to water contact. I share your view of a tumbling or spinning fall.

China 006 damage (747).

https://photos.app.goo.gl/vL44UNgCNEFj4yi18

@TBill: ZS had the PMDG 777 model, along with FSX, installed on drive MK26. That was the installation that was giving him trouble with crashes, and if I recall correctly, he was not happy with the support he was getting from PMDG. That said, based on the logs, he conducted many flights using the PMDG 777 model.

@DrB

You said:

“DSTG did not do that. They did get range and endurance calculations from Boeing that they used to limit the range of air speeds and altitudes they used in their statistical modeling. The section “Aircraft Performance Analysis” on page 16 in the ATSB Report from 3 December 2015 describes this in some detail. However, after describing how the southern range limit was calculated, they failed to say what that limit was.”

In the main post, you are attributed as saying:

“The first item is the inclusion of a detailed and accurate fuel flow model. All DSTG analyses effectively ignored fuel consumption as a route discriminator by assuming “infinite fuel”. I and several others subsequently developed fuel flow models and compared them with Boeing tables, prior 9M-MRO flights, and the MH370 flight plan in order to validate the predictions. My model fuel flows are consistent with these comparisons, nearly always within +/- 1 %. As I understand it, Boeing did some range and endurance calculations and found that it was possible, at some combination of altitude and speed, for 9M-MRO to have reached a wide stretch of the 7th Arc, totally excluding only the region beyond circa 39S.”

I am confused as to where the 39S figure comes from, since you say it’s not in the report you cited.

Nevertheless, the final ATSB report (2017) shows the DSTG residual probability graph on p. 81, with probability extending to 40S. With OI search completed, the northern lobe of this probability is blanked, leaving only the 40S southern lobe remaining (plus a tiny sliver <~25NM of the 7th arc). They make no mention of excluding the southern lobe or areas south of 39S due to fuel that I have found.

This 40S southern lobe is the only remaining unsearched probability area that CSIRO / DSTG / ASTB apparently all agree on that remains. If Boeing "totally excluded" the area beyond 39S, the Australians apparently rejected that hypothesis.

My interpretation of what defines the southern limit of this probability lobe is a 0.84 upper Mach limit imposed by DSTG.

@GlobusMax,

My estimate of 39S for the southern range limit is from Figure 20 in ATSB’s report “MH370 – Definition of Underwater Search Areas” updated 18 August 2014. That figure shows a southern “performance limit” circa 38.5S. I believe this was calculated by Boeing using Maximum Range Cruise airspeed. My fuel model calculations yield a similar prediction. DSTG did their calculations assuming infinite fuel, so the fact that the tail of their probability density distribution extends south of ~38.5S does not imply there was enough fuel to reach it. Boeing says not enough fuel. I concur.

@DrB

Did your calculation rule out that area for the error probability tail? I found the same thing with your model, but your stated error allowed the area to be reached.

The figure you reference is crude, but it implies it isn’t taking into account the fact that fuel was exhausted inside the 7th arc, not at the arc. Nevertheless, they went ahead and searched to ~39.5, beyond the 38.5. There seems to be disagreement between ATSB and Boeing.

Have you looked at fuel savings possible with a step climb?

@GlobusMax,

I estimate my worst-case fuel flow mode4l error at 2%. The only way to get near 40S is for my model to over-predict the fuel flow by 2%, and the bleed air must be off the whole time after diversion, which saves another 2%. The Boeing MRC performance limits don’t quite get to 40S even with bleed air off.

I have not investigated the step climb fuel savings in detail. Looking at the LRC and MRC fuel flow tables, the fuel flow varies very little (usually < 1%) between FL350 and FL400 at ISA air temperatures. So, in general, the fuel savings with step climbs above FL350 is quite small. On this particular night over the SIO the SATs relative to ISA varied a lot above FL350, so there was a fuel consumption advantage being circa FL390 versus FL350. The 40S route cannot take advantage of that, however, since the high true air speed requires the warmer air of the lower stratosphere circa FL355 in order to be achieved.

@Brian Anderson

Re: ‘

In a controlled ditching, where the pilot is holding a moderate positive AOA, say 10-12 degrees, it is possible, but not guaranteed, that the engines may shear off the mounting bolts and fold up and over the LE of the wing.Brian, in order for the engine to depart forward and over the wing (as in the case of EK521) it needs to be producing a fair bit of thrust when the mounting bolts shear. In an unpowered ditching I think that the chances of the engines going up and over the LE would be extremely remote.

In a powered ditching, the initial contact of the nacelle with the water would have to be just so to facilitate that sort of outcome. I think that even a well executed nose-up powered ditching would see the engines separating and going under the wing, most likely causing some strike damage to the flaperon, particularly if it was deflected.

@DrB

Thanks.

I obtain slightly better results using your model at 40S, but perhaps that is because I included the stated error estimate on the fuel exhaustion time, so the two error tails overlap. It’s certainly low probability, but possible (with packs off), I figured.

I have been meaning to ask you if your error estimate for fuel flow included any errors such as empty plane weight (MH370 was overdue), passenger weight, fuel quantity, fuel use IGARI to MEKAR, etc. I assume you did not. None of these are particularly large, I suspect, but they would expand the net error band a bit.

Are you saying zero fuel savings from step climbs above FL350 for 40S or minimal fuel savings?

@DrB

Presumably the Alt elec config saves a few % fuel ? and perhaps more in the left tank if L Gen = OFF.

What is think is wrong.

It is a lack of world class leadership. When Richard Feynman was appointed to head the shuttle diasaster investigation, he got results and opened a big can of “ass kick” for anyone who got in his way.

http://www.feynman.com/science/the-challenger-disaster/

What we have in the case of MH370 is an endless succession of people sucking on a government teat. It shows. Angus Houston was a refreshing choice, but my sense is he pissed off a lot of people (as did Feynman) and Abott took the easy way out by not supporting him.

The result is a mess, and no one is responsible for cleaning it up.

An interesting article in the NY Times on the 737 Max.

https://www.nytimes.com/2019/06/01/business/boeing-737-max-crash.html

@Tbill. I had also noted previously that generator load off on left side potentially contributes significant fuel savings. Per Dr B’s fuel model retrieved online, sheet FM V5.3 row 50, “Non-thrust-producing fuel flow (i.e., ancillary/parasitic fuel flow, or fuel flow at zero thrust) in 1 new engine; supplies bleed air, drives integrated electrical generators, hydraulic pump and fuel pump, and includes parasitic engine losses; value is best fit to Boeing fuel flow tables for this aircraft and engine type; is a primary component of idle engine fuel flow; =200 kg/hr/engine with Air Conditioning Packs ON and ≈145 kg/hr/engine with Air Packs OFF; estimate of Air Packs is 2.5% of typical cruise fuel flow of 3500 kg/hr/engine = 88 kg/hr/engine”. Dr B hasn’t specifically mentioned the fuel flow attributable to generator, but I’d expect this to be a major component of non thrust-producing fuel flow. If that amounts to, say, additional 100kg per hour and the left generator was shut off at diversion you get additional ~700kg of fuel (left side only). At cruise, close to zero fuel weight and two engines turning I think this gives you about +14 mins flight. However, this scenario would extend time with one (L) engine operational, in which case it will default to either max cruise thrust or max climb thrust, dependent on company policy/setting – and I don’t know what the fuel flow rate would look like for either of these. In any case, left generator off would, I think, give you “another few minutes” beyond the base case fuel model. Perhaps others could help to put a more precise number on this.

@Paul Smithson: In your scenario, with the left IDG off, what powers the left bus and the SATCOM after 18:23? If the right IDG was powering both busses, there would be some electrical loads shed, which would reduce the fuel consumption a bit, depending on the total electrical load. If the APU was powering the left bus, the fuel consumption would likely be greater than if the left IDG was powering the left bus, as the thermodynamic efficiency of the left engine would likely be greater than the APU.

@All

Through the link below one can download my preliminary paper “MH370 path reconstruction based on polynomial interpolation of BTO and BFO derived data, v.0.16”

The approach and first results (indicating a near 180⁰ TT path for the final hours of the flight) were introduced here on the blog back in March 2019.

The present document is a first full write-up shared hoping to stimulate discussion, and that possible errors or inaccuracies in the underlying analysis can be reported by critical readers.

https://www.dropbox.com/s/aji9c4uug7m1jm1/MH370%20path%20reconstruction_polynomial_WGS84_LRC_TT_report_v0_16.pdf?dl=0

@DrB @Richard

Below is my prior essay “BFO straightness” of 180 vs. 187 South flight paths. Could be flaws in my work, but I seemed to observe that the 187 South path (orig IG path) was perfect BFO match to Arc5.

The 180 South path is missing the reported 204 BFO value. So I interpret this as either: (1) MH370 did in fact go 187 South until Arc5; or (2) MH370 went 180 South and made a turn to the southeast before Arc5, which allows match to 204 BFO, or (3) the raw data is imperfect.

If the raw data is imperfect, it is imperfect in a way that makes 187 South look like an exact fit to the data to Arc5. After Arc5 all bets are off. If we had exact BFO fit all the way to Arc7, we might have the answer.

“On The Straightness of BFO Essay”:

https://twitter.com/HDTBill/status/1038108692611260417

@Victor. I’m thinking along the following lines:

1) At diversion, left side electrics isolated and Left IDG off

2) At SDU power-on 1825, left side powered from right IDG.

I understand that APU wouldn’t start if you still have right side power. So in this scenario you would have a greater electrical load on the right, none on the left. Perhaps with left side power coming from the right the left IDG doesn’t even need to be shut down to make significant savings – the absence of load alone would do this?

You would expect a longer time interval between engine flameouts under this scenario, a greater distance/BTO loss due to slow-down, and earlier descent to best one-engine altitude.

So not only would endurance be increased a bit, you would also expect the 0011 BTO to come in “under expectation” (by up to about 70 microseconds, from my calculations) as compared to automated 2-engine flight all the way through to 0011. That’s one reason that I’m circumspect about the underlying assumptions of the methodology outlined in the article.

@Paul Smithson: I’m sorry, but I don’t follow your scenario. Perhaps it would be easier to understand if you state which events occurred automatically (as well as the cause of the events) and which events occurred by pilot input. For instance, when you say the “left side power coming from the right the left IDG doesn’t even need to be shut down to make significant savings”, how can the left IDG be operational and yet the right bus power the left bus?

@Niels

Many thanks for your paper dated 4th June 2019.

I would like to run the 2 cases you propose through the new model.

Case A: CTT177.3 LRC FL348.

Case B: CTT180.0 LRC FL341.

I will report back with my results in due course.

@TBill

Many thanks for your paper dated 6th June 2018. Sorry I missed it back then.

I would like to run the 2 further cases you propose through the new model.

I assume these are CTT and not LNAV and by Speed you mean Ground Speed (GS) and not not TAS.

Please correct me, if I am wrong.

Case 1: CTT180.0 Constant GS at 478.0 knots FL351 from 6.0°N 94.0°E.

Case B: CTT187.0 Constant GS at 495.0 knots FL351 from 4.125°N 94.5°E.

I will report back with my results in due course.

@Richard

Correct ground speed, no winds etc. This was paper study (not flight sim) so I just was doing ground speed on Google Earth grid assuming CTT true. Just looking at BFO not BTO match. But if you wanted to look at real flight path cases, there is the orig IG path on the BTO/BFO spreadsheet by FFYap for ~187 deg, and its somewhat close to Victor’s BEDAX 180 South for the 180 S case.

@TBill said:

This was paper study (not flight sim) so I just was doing ground speed on Google Earth grid assuming CTT true.If you were using GE, you might have been modeling great circles (geodesics) and not rhumb lines (loxodromes).

@Victor

Correct my approach did not account for that. But seemed to me similar result to the real paths I could study.

@All

Regarding the 6th ping – 00:11z

I think it is a mistake, to continue to assume, that the aircraft was still in cruise at 00:11z.

That is the implicit assumption for all non piloted end of flight scenarios.

If the flight was piloted, the pilot (any pilot) would quite obviously know that fuel was nearly exhausted well before 00:11z. Whatever that pilot intended as “his end of flight scenario”, he would have been preparing for it, well before then, at least before 00:00z, and if ditching (my preferred option) then by 23:40z, since that would be a sensible time for TOD for a ditch.

I therefore feel that search area prediction studies, should be “backed up” as it were on the cruise segment. That is, I suggest that the “cruise south path studies” should be ended at 23:40z, and then look at descent scenarios that can fit the 00:11z data, and thence the 00:19z data.

@DrB:

“At the present time, numerous other ROI are being evaluated and compared. Preliminary results to date show them to be inferior fits, but this work is not yet completed. […]It may actually be possible to demonstrate that there is only one route solution which is fully consistent with the satellite data.”

Does your last sentence mean, that these “inferior fits” not “fully consistent with the satellite data” ?

correction:

Does your last sentence mean, that these “inferior fits”

arenot “fully consistent with the satellite data” ?Further safety issue found in grounded Boeing 737 Max planes:

http://www.theguardian.com/business/2019/jun/03/new-safety-issue-boeing-737-max-planes

Regarding contrail studies in the SIO.

A while back, some people were attempting to marry up known flights to or from New Zealand or Australia to observed, or suspected, contrails in the satellite photos. I requested any ADSB data that 16Right.com might have for Sydney that may be of use.

I have now received a reply from 16Right.com regarding that request for ADSB data from the Sydney NSW Aus area – for the night of 7-8th /march 2014 – as follows:-

Apologies for not replying sooner.

Unfortunately we do not maintain any historical raw ADS-B Data on our Aircraft Tracking site adsb.16Right.com

We do however record all the Flights operating within 250nm of Sydney, and this data can be viewed by going to adsb.16right.com

You can then search for a particular day, and check the list for Qatar or Emirates flights etc. from Auckland. This may still be of some use to you.

Regards, Grahame.

Unfortunately, this only gives us some data on flights that operated to or from Sydney, or overflew Sydney, it does not include any flights to or from any other cities that did not pass within 250 nm of Sydney. I have not been able to find any other Australian site that may record ADSB data, so I suppose we have reached a dead end on that front.

However, something is better than nothing.

I have done as Grahame suggested, and have so far obtained their recorded data (in html) for the 24 hours of 07Mar2014 (local = utc+11).

There are only 1,111 total flights recorded for the 24 hour day.

It includes only:

REGO, START TIME (Local = utc+11), END TIME (Local = utc+11), FLIGHT #, AIRLINE LOGO, MODE-S, A/C TYPE, Flight PLAN ROUTE

I have just had a quick look at it, and there appears to be only a handful of “possibles” (at this stage).

Next step is to do the same for the 24 hours of 08Mar2014 (local = utc+11).

When I have both day data sets, I will massage it and make up a spreadsheet.

@ventus45

“Regarding the 6th ping – 00:11z

I think it is a mistake, to continue to assume, that the aircraft was still in cruise at 00:11z.”

To some extent, I agree the fundamental problem we might have is that the 23:14 satellite call reset the clock and caused the normal hourly BTO/BFO (expected at 23:41) to be delayed until 00:11 which is when the end of flight situation is in progress. So we have Arc5 as the last “normal” data point.

@Peter Norton,

You asked: “Does your last sentence mean, that these “inferior fits” are not “fully consistent with the satellite data” ?

Yes. All Regions of Interest identified to date have been assessed, and none of them, with the one exception of the LNAV 180 degree BEDAX route, have probabilities of being the True Route which are sufficiently high to warrant searching. They are ~6X or more less likely than the BEDAX/South Pole route.

@GlobusMax,

You said: “I have been meaning to ask you if your error estimate for fuel flow included any errors such as empty plane weight (MH370 was overdue), passenger weight, fuel quantity, fuel use IGARI to MEKAR, etc. I assume you did not. None of these are particularly large, I suspect, but they would expand the net error band a bit. Are you saying zero fuel savings from step climbs above FL350 for 40S or minimal fuel savings?”

The airlines pre-flight estimate of take-off weight is presumed to be accurate. The fuel consumption from IGARI until BEDAX is a bit uncertain because we don’t have accurate knowledge of speed settings and altitude. I would make an offhand guess that it would be in error equivalent to probably 1% or less of the fuel consumed from 17:07 to 00:17, but that is just a guess. You are correct in your assumption that those errors are not included in my fuel model error budget.

The fuel savings of step climbs depends on the starting altitude. This would be minimal if the altitude were already FL385 or higher at 19:41. The slight fuel flow reductions are partially offset by the extra fuel required to make the step climbs, so I would expect a net improvement of < 1%.

@TBill,

You said: “Presumably the Alt elec config saves a few % fuel ? and perhaps more in the left tank if L Gen = OFF.”

I don’t have precise values for the portion of the single-engine fuel flow due to electrical generation. It is certainly just a fraction of the 145 kg/hr of the fuel flow at zero thrust with bleed air off. I would guess roughly 60 kg/hr. If the L AC Bus were simply shifted over to be powered by the R IG, there wouldn’t be any savings in fuel. If the L Bus were shut down for an hour, that might save 60 kg of fuel in the L tank. We know that at 18:24 the SDU was re-powered, but we don’t know how many equipment items remained de-powered for the remainder of the flight. I can see maybe 40 kg/hr savings for the last 6 hours due to load shedding. That would be a grand total savings of 300 kg of fuel, or about 4 minutes of equivalent operating time for one engine. I would also point out that the range is probably maximized when the L and R tanks run dry at the same time. Any increase in the time between first and second engine flame-out is likely to reduce the achievable range. This would be the case if the R engine powered the L Bus after 18:24. The R tank had less fuel at 17:07, the R engine burned about 1% more fuel than the L engine in cruise, and moving electrical loads from the L IG to the R IG would also increase R engine fuel flow. In this scenario, the R engine would flame-out prior to 00:06 (and the L engine would flame out circa 00:17:30).

You also said: “The 180 South path is missing the reported 204 BFO value.”

The BEDAX to South Pole Route has a predicted BFO at 22:41 of 200 Hz, which is only 4 Hz off the 204 Hz data point, so it is compatible within the expected error.

The Excel file linked below, contains a list of the 1,989 flights recorded by 16Right.com within 250nm of Sydney, for the 48 hours of 07Mar2014 and 08Mar2014 in local time, which was utc+11 (instead of utc +10) due to Daylight Saving Time being in effect.

https://drive.google.com/open?id=1sn2zHlNdteWL3uzZoMSDG9FTAIly_CnW

or at

http://www.mediafire.com/file/w13ab1xo1on2bth/16Right_ADSB_-_Log_7_and_8_Mar2014.xlsx/file

@Richard

“I would like to run the 2 cases you propose through the new model”

Thank you, I’m curious for the result!

I’m currently working on a case C (which is a “mix” of cases A en B). It gives TT 177.4 at FL336 (ending S33.3), at a Do = -2 Hz.

Note that the paths I’ve found contain a maneuver in the first hour / hour and a half of the 19:41 – 00:19 interval (see figs. 3 and 4). I’m not sure if the new model / method can deal with that..

Hi Victor. I was thinking primarily about potential fuel savings and greater disparity in flame out times R and L arising from:

1. Left power off from diversion to 1825

2. Left bus power restored from right side at 1825

So L IDG isolated/no load for ~7 hours.

Dr B has already responded above, estimating with a “thumb in the air” estimate of 60kg per hour saving on the left side, but a net saving (both sides) of “maybe” 40kg since loads are being carried on the R IDG, albeit with some load-shedding. And he’s suggesting that could give you an extra 4 mins (powered) flight under one engine.

What I hadn’t done was to think through the associated end of flight scenario and how you get from early R flameout to an extended one-engine flight, or how you get the last logon at 0019. Perhaps there’s a way it could happen but its not obvious to me.

Bloomberg: Ralph Nader Says Boeing 737 Max Is Flawed and Should Never Fly Again

@Niels

To ensure I model the manoeuvres correctly, can you provide the Lat/Lon data for the path graphics in your Fig. 3 and Fig. 4 please.

@Richard

Please see the link:

https://www.dropbox.com/s/mngfeahwh7qrcdn/PathCoordinates_NT_050619.pdf?dl=0

Ping times are rounded to the nearest (10s) time-step. I could provide coordinates also for every half hour or so, just let me know.

Note also that coordinates / path / GS is calculated for 11km altitude. I use FL for comparison of GS+wind based TAS with expected TAS (based on weight). I do not convert back the FL to “true altitude” and re-correct the path/GS for that. (I may try it however I could introduce cyclic dependency in the calculations, so it would require some more thinking and work to implement). As the FLs I find so far are typically in the 335 – 355 range I expect the errors to be limited.

@DrB

“(TBill) also said: “The 180 South path is missing the reported 204 BFO value.”

The BEDAX to South Pole Route has a predicted BFO at 22:41 of 200 Hz, which is only 4 Hz off the 204 Hz data point, so it is compatible within the expected error.”

Yes that is exactly what I am saying, 180 South path misses the Arc5 BFO by a certain amount 200 vs. 204. 187 South does not miss, 187 South seems to be near exact BFO data fit.

The reason is, the BFO calc wants to see 24 South at Arc5, whereas the 180 South path is only getting down to 22 South. I noticed this is characteristic of 180 South paths, as much as I liked 180 South myself.

If you have a model that is finding unique passive flight solution, I have trouble understanding how 180 South is the winner, at least up to Arc5.

@TBill,

You said: “Yes that is exactly what I am saying, 180 South path misses the Arc5 BFO by a certain amount 200 vs. 204. 187 South does not miss, 187 South seems to be near exact BFO data fit.”

You see to believe that the BFO reading errors must be zero, because you believe that 0 Hz is the best fit but 4 Hz is unacceptable. As I explained in this article above, and in my previous response to @DennisW, the BFO reading errors are substantial, typically as large as 5-7 Hz for a sequence of a few hours. The best-fit residuals for the True Route will not be zero (exactly matching the Inmarsat data) because that data contains the expected BFO reading errors. Thus, any single reading within +/- 7 Hz or so is expected and acceptable.

DrB: “none of them, with the one exception of the LNAV 180 degree BEDAX route, have probabilities of being the True Route which are sufficiently high to warrant searching.”

Thank you.

DrB: “They are ~6X or more less likely than the BEDAX/South Pole route.”

6x … that seems impressive.

Can your methodology also determine absolute probabilities (of the BEDAX/South Pole route for instance), or only relative probabilities (6 times less likely) ?

This debris discussion above revolves solely around the flaperon, however the rest of the debris paints a much clearer picture. The Tanzania wing flap was examined by ATS, Boeing, Annex 13, and Malaysia, and determined to be retracted at the time of separation, not deployed, as it would be in a controlled ditching. The other 30 pieces of debris in the Annex 13 report were all small and shattered, including many from the main cabin, also supporting a high speed forceful impact. The 17 pieces of debris I have held in my hands were all shattered. A significant 18th piece is still in Madagascar pending the investigation into the assassination of the Honorary Malaysian Consul before he could collect and deliver it. This debris appears to be the base plate of the vortex generator, or “chine” from the right engine cowling. Close examination could tell us a lot about how the engine impacted the water. Aviation experts to whom I have shown photos have said that piece would normally remain in the engine cowling, and that they have never seen it shatter like that in a crash … more evidence of a very high speed impact. The debris evidence strongly supports a high speed dive and crash that shattered the plane, not a controlled ditching.

@Peter Norton,

You said: “Can your methodology also determine absolute probabilities (of the BEDAX/South Pole route for instance), or only relative probabilities (6 times less likely) ?”

The simple answer is yes, it finds the absolute probability of each route assessed. The more complete answer is that it determines the percentage of random trials which fit no better than the current fit, assuming the route is True. It takes a while to fully grasp this concept. One MUST assume the route is True (the so-called. null hypothesis) because that is the ONLY case where we know the statistics of the BTO and BFO residuals of the fit, because in that case the best-fit residuals are equal to the reading errors. For example, if the combined P-value, or percentile. is 60%, that means that 60 out of 100 random trials would be worse than the current fit, and only 40 would be a better fit. Said another way, 60 percentile means the current fit is better than 60 % of random trials. If the percentile were 10%, then only 10 out of 100 would be worse, and 90 would be better. One can also say that the 60 percentile route is 6 times more likely than the 10 percentile route to be the True Route. A ratio of percentiles equals the relative probabilities of two candidate routes being the True Route.

@BG370

I am not personally a (slow-speed) controlled ditching advocate, although I could accept high speed (flaps-up) ditch. But I wonder how those who are slow-speed ditch advocates (eg; Larry Vance et al) would account for the apparent wing flap position?

@DrB

“You seem to believe that the BFO reading errors must be zero, because you believe that 0 Hz is the best fit but 4 Hz is unacceptable.”

Yes I am data centric. I have done some modelling myself but often in my career I was the end-user of the models, and sometimes outspoken if the model missed the data. So this is just my normal self.

@Niels

I have run your Case A through my new model.

At 19:41:03 UTC the aircraft position was 3.828265°N 93.695810°E and the Track was 180.882°T as you specified. The speed mode is Long Range Cruise (LRC) and the navigation method is Constant True Track (CTT) at FL348 (Altitude 36,395 feet). I appreciate your calculations were based on 11,000 m or 36,089 feet, but this will not make much difference.

I subsequently modified the Track according to your table:

20:41:05 178.7713°T

21:41:27 176.5822°T

22:41:22 176.6087°T

00:11:00 177.9511°T

00:19:29 178.3475°T

I calculate the overall average Track is 177.7753°T, which is not far off from your result of 177.3°T.

The results are in the following link:

https://www.dropbox.com/s/orn7i7s514h3wwf/MH370%20Flight%20Path%20Model%20V19.3%20RG%20CTT%20LRC%20FL348%20180.882%20Niels%20Case%20A.png?dl=0

The Mean BTO Residual (BTOR) is -117.0 µs with a standard deviation of 69.1 µs, which is too high in my view.

The RMS BTOR is 132.3 µs, which is also too high and the individual BTORs are out of the expected limit.

The standard deviation BFO Residual (BFOR) is 2.41 Hz, which is fine.

The RMS GSE is 1.77 knots, which is also good.

The PDA is 1.35% for a MEFE at 00:17:30 UTC, which is good.

The correlation coefficient BTOR vs Time is -0.8284, which is high.

I would discount the flight path on the grounds that the BTO fit is out of range.

You state that there was a manoeuvre after 19:41 UTC, but your flight path table implies multiple smaller changes of track even later in the flight path. If there was just one manoeuvre, then the CTT Track would be constant thereafter.

You appear to have optimised the BFORs, at the expense of the BTORs.

@Richard

Thank you for these calculations. I think the main problem (and perhaps misunderstanding between us) is that the maneuvring in the first part of the path includes consequences for the speed. From the way I performed the calculations my results for case A suggest a CTT/LRC path from 21:11 onwards, for case B from 22:41, and for case C from 21:11 onwards. Case A performs worst in terms of CTT.

So I’m not surprised that starting with LRC at 19:41 at the specified position results in large BTO errors.

What would probably be most useful (also to see if my different sub-models are correct) is if you could check for case A and/or C: from specified 21:11 position and FL, at the average track for the 21:11 – 00:19 interval.

@DrB: Thank you. Then what is the probability of the BEDAX/S-pole route according to your methodology?

@Peter Norton,

Currently the BEDAX to South Pole percentile is roughly 75%. The expected value is 50 % with a standard deviation of 29%. Thus, the current result is within 1 sigma on the high side.

That brings up an interesting consideration in the objective function used in the route fitter. If you set the objective to match 50 percentile, you can achieve that value (but only when fitting this one route). If you set the objective function to try to match 100 percentile, the closest you can get is about 75%. For all other routes, it does not matter whether the objective is 50% or 100%, since the best fits all have much lower percentiles than 50%. At this point in time, I interpret the 75% result as having two probable causes. First, the Inmarsat data may have been better than average statistically. Second, the optimization done by the route fitter may have driven the residuals lower than their average scatter. If this is happening, I suspect the cause might be the ground speed corrections added to the model predictions. Those corrections are made for each leg along the route. They are constrained to be within +/- 1.5 knots and they are low-pass filtered (smoothed). The ground speed corrections along the track primarily modify the BTO residuals. I wouldn’t be surprised to learn that the actual flight path flown by 9M-MRO was better matched by the 50 percentile solution than by the 75 percentile solution. Both are statistically acceptable, and they are indistinguishable from a search strategy perspective.

@Richard

On your comment:

“You state that there was a manoeuvre after 19:41 UTC, but your flight path table implies multiple smaller changes of track even later in the flight path. If there was just one manoeuvre, then the CTT Track would be constant thereafter.

You appear to have optimised the BFORs, at the expense of the BTORs”

I would like to add a small explanation here: My tool is a path generator. Basically, I only change/choose the starting latitude, FFB and FL, and the tool generates the path based on the r(t) and D(t) functions. Afterwards, I again choose a FL for LRC check. So:

– The points I’ve supplied should reasonably match both BTO and BFO data. (If not then there could be something wrong with my BTO/BFO models or with my coordinate transformations).

– Using this procedure it is not really surprising that there are small variations in the track. In fact I find it a bit surprising that through this procedure I can find such straight path segments especially as in cases B and C.

@Niels

My apologies! I had understood from your paper that your flight paths were using the navigation method Constant True Track (CTT) and the speed mode Long Range Cruise (LRC) from 19:41:03 UTC but with manoeuvres (i.e. changes of Track) and not just CTT LRC from 21:11:00 UTC onwards.

I have re-run your Case A through my new model starting at 21:11:00 UTC as you requested:

https://www.dropbox.com/s/3fu0fblxnet3nu2/MH370%20Flight%20Path%20Model%20V19.3%20RG%20CTT%20LRC%20FL348%20211100%20UTC.png?dl=0

Whilst the BFO still fits and the BTO at 21:41:27 UTC fits perfectly, the subsequent BTOs at 22:41:22 UTC and 00:11:00 UTC are still out of range.

Thank you, Richard! I’m checking some details. The 21:11 position I have is -9.0208, 94.0679 so that seems fine. The M and TAS values I have are pretty close, so I don’t think the problem is there. The average track I have between 21:11 and 00:19 is 176.8933. Not sure what would come out if you would use that as a fixed value after 21:11, but at first sight it will not improve things much. The strange thing is that I do a BTO check myself (positions versus vs. the r(t) target function) and I don’t see large range errors.

Would you know how many km’s range error 100 microseconds would represent?

@Richard

Sorry for asking this trivial question, I had the answer approx. 10 sec after I hit the submit button 🙂

I’ll (re)check the r(t) function vs. the BTO data points

@Richard

– The r(t) fit function looks fine (range errors of 2 km or below)

– I found an important difference: the wind at 22:41 in your calculations is much stronger than what I’m using. Resulting in lower GS than I have.

Can you please explain how you obtain the 22:41 “Predicted GDAS Wind Speed”?

@Niels

My apologies! You are correct, there was an error in my previous report.

The wind at 22:41:22 UTC should be 20.999 knots and not 31.356 knots.

Here is a corrected report:

https://www.dropbox.com/s/uwk61bdc1llp4hz/MH370%20Flight%20Path%20Model%20V19.3%20RG%20CTT%20LRC%20FL348%20211100%20UTC%20Corrected.png?dl=0

Essentially I interpolate the GDAS data every minute for the precise Latitude, Longitude, Time and Air Pressure at the Flight Level. For example, in this case, for a position at 19.841253°S 94.788942°E, time of 22:41:22 UTC and Air Pressure of 240.696 hPa, I interpolate the GDAS data between 19°S 94°E, 19°S 95°E, 20°S 94°E, 21°S 95°E, 21:00 UTC, 24:00 UTC, 200 hPa and 250 hPa.

@Richard

Ok, thank you and no problem. Also on my side there seems to be a problem with the read-out of wind data table. It might have slight impact on track and/or FL for the reported cases; I’ll report further once I understand better / fixed it.

@Richard

Based on your value for “Predicted GDAS wind speed” @22:41 in the corrected calculations for my “Case A” (21 knots from 216 degrees), I would like to ask if we can cross check the raw wind data that we are using. From direct read out (File: MH370 Weather Data – DrBobbyUlich – 2017.02.07) I’m extracting the following values (in m/s):

00:00, lat -20, lon 95, 250 mbar

windu: 1.3

windv: 0.9

00:00, lat -20, lon 95, 200 mbar

windu: 6.8

windv: 3.2

21:00, lat -20, lon 95, 250 mbar

windu: 2.0

windv: 1.0

21:00, lat -20, lon 95, 200 mbar

windu: 5.8

windv: 2.1

@Niels

In producing a version of my model to fit your specification, I inadvertently moved the indexing of wind data by 1° of latitude. My apologies again! The corrected version is here:

https://www.dropbox.com/s/6i0yrdwk4ja7hls/MH370%20Flight%20Path%20Model%20V19.3%20RG%20CTT%20LRC%20FL348%20211100%20UTC%2008062019.png?dl=0

However, this correction does not change the outcome of a poor fit to the BTO after 21:41:27 UTC.

As you can see at 22:41:22 UTC you are just before the southern boundary of the anticyclone in the SIO on the evening of 7th March 2014, where the winds change and start picking up strongly from the west.

I do not doubt that Bobby correctly loaded the GDAS data into his spreadsheet. The data you show agrees with my data 3.1 knots 214.7°T, 14.7 knots 205.2°T, 4.3 knots 206.6°T and 12.0 knots 199.9°T respectively.

However, as I mention, you need to look at the data at -19,95 -20,94 and -20,95 as well and not just at -20,95.

What I still do not understand is why you start at 21:11 UTC? Why not at 19:41:03 UTC as we know that the aircraft was already heading south at that time.

I also doubt that for a long flight of over 4.5 hours into the SIO that a pilot would not choose the LNAV navigation method and one or more waypoints. Why do you believe the pilot was using the CTT navigation method without waypoints and performing one or more manoeuvres by slightly adjusting the selected track on the MCP?

Many thanks for the feedback, and no problem for the wind data issue; I’m happy that with the data you provide I can do some rudimentary checking of my implementations. So far so good it seems (although much more testing is needed to be sure). Indeed I can improve the way I import the wind data slightly: Currently I’m just rounding to the nearest integer position and I’m just using the 250 hPa data.

Regarding your questions; good points and thanks for asking. What I try to contribute is a data driven tool that could help to quickly identify a “parameter space” of interest which could then be evaluated using for example the new method / procedure that Bobby and you are developing and exploring. A similar “path generation” method could as well be developed for other navigational modes; I started with CTT as it is the easiest to implement, but you are right that there should not be a preference for CTT only. Similarly regarding the “starting time” for a constant navigational mode: With the current “zeroth order” model for possible oscillator drift it is possible, even likely, that I’m only accessing a “sub-space” of the allowed “path solution space” to the BTO/BFO data. With the current D(t) fit I’m not seeing any potential CTT/LRC paths going back to 19:41. It doesn’t mean they do not exist and it seems that with BEDAX – South pole a potential important candidate has already been identified. I might move back to a “first order” approximation to account for possible oscillator drift as a first extension, basically increasing the number of different D(t) functions to evaluate.

For the case A: I thought for a while the problem might be in the proper incorporation of wind, but (part of) the problem of relative large BTO errors might be simpler: the question is if the 21:11 starting point should be exactly located on the “virtual arc” that my model basically is providing. Shouldn’t it be slightly varied around this position as to minimize the mean BTO error? Also, I’ve added a criterion for the FL optimization which is mean(delta_TAS) = 0. It gives a slightly higher FL (349.4). For the track indication I now have 176.8933. For the indicative 21:11 position I have -8.0208, 94.06789. I understand if you might not have time to do the starting position optimization (reducing the mean BTO error); with the above explanation in mind, I hope though that you would be willing to give it a final try.

@Victor

Files created for future ‘use’ or files created to be ‘deleted’?

Scenario #1 – Files created for future use. Whether they were actually used is moot. When they were deleted there was no intent that they be recoverable.

My view is that the files could have been intended for a demonstration to a potential co-conspirator as part of an attempt to recruit partners. The ability to show that an airliner in a hold somewhere could easily return to a bunch of airports could possibly be persuasive to a naive audience.

Commentators have suggested that the flight sim would not be a useful ‘planning tool’ and I broadly agree however it might have utility as a rehearsal tool sitting alongside a co-conspirator in order to review key decision points.

One possibility is that a recruitment attempt resulted in failure (particularly if ZS loaded up the final two files in an attempt to demonstrate his ‘commitment to the cause’).

Perhaps ZS deleted the files and uninstalled the sim in order to demonstrate that he had abandoned his ‘bad’ idea.

Maybe fear of being reported led ZS to go-it-alone rather than attempt to recruit anyone else. His plan being re-focused on the disappearance of the airliner as a means of putting the regime under international scrutiny and pressure.

N.B. the file dates and the volume shadow date imply that the files existed in an undeleted state for a period of time. It may be possible to put constraints on a period of time when it would be possible to use the files for a demonstration.

Scenario #2 – Files created to be ‘deleted’ in a way that they could be partially recovered by a state-level computer forensics lab. The intent being to leave clues and/or disinformation.

My take is that this would represent a ‘simulation of a complot’ rather than a ‘simulation of a simulation’. The intent being to make it look as if ‘negotiations’ had failed and to pin the blame for the deaths on Razak.

The biggest difficulty I have with this scenario is that ZS would be deliberately, not inadvertantly, throwing a lot of people under the bus. He himself, his wife, his children, his wider family, any possible co-conspirator(s) and the wider opposition movement would all fall under suspicion or suffer reputational damage. All efforts to give plausible deniability would be wasted.

It is hard to comment on analytics we have not seen.

@DrB

Apologies if this question has been covered already, but your prior model of March_2018 (approx 30 South pin location) had a somewhat similar goal to find best fit within fuel limits. So what is key difference now? and why not 30 South this time? Of course I am thinking it may have glided/flown beyond Arc7, so I am looking athe Arc7 intersection.

I don’t always fully understand the maths but this particular blog post and the discussions on the modelling has been especially encouraging.

Selecting a destination of the South Pole has always seemed an attractive explanation to me, with perhaps an intentional slight deviation to further make any investigation more difficult.

I hope your efforts bear fruit soon.

@Tom: Welcome to the blog, Tom. At this point, the work undertaken by contributors here represents one of the few efforts to define an area for a new search.

@DrB: “The expected value is 50 % with a standard deviation of 29%.”

Thank you. The expected value (of one path) is 50%? Doesn’t the sum of all probabilities (of all paths) have to be 100%?

@DrB Could you please share the details of the BEDAX – South Pole, LRC FL390 path? I’m trying to corroborate such path with my tool (basically by looking at different D(t) input functions). It seems that one needs to accept a rather large 19:41 BFO error to reduce path curvature in the first 1.5 hour of the 19:41 – 00:19 interval and to allow for the LRC speed.

@TBill

I have finally run the first further case you proposed through my model. The other further case you proposed in your paper will follow soon.

My apologies for the delay, I have been busy with a test program we have running comparing the flight models from Bobby, Victor and myself.

You proposed a CTT180 flight path starting at 19:11:00 UTC, reaching 6.0°N 94.0°E at 19:41:03 UTC and continuing at an average Ground Speed of 478.0 knots until fuel exhaustion. I used a Constant Mach of 0.812771, which gave an average Ground Speed between 19:41:03 UTC and 00:11:00 UTC of 478.0012 knots. I simulated a flight level of FL350 rather than FL351, only because it required no extra modification to my model, but it will make little difference to the conclusion.

https://www.dropbox.com/s/aaloa4kguers36n/MH370%20Flight%20Path%20Model%20V19.4%20RG%20CTT%20CM%200.812771%20FL350%20180.0%20Case%201%20Full%20Report.png?dl=0

As you will see from the results, I calculate that the BTO Residuals are off the scale.

@TBill

Here is the other further case you proposed in your paper.

You proposed a CTT186.7 flight path starting at 19:11:00 UTC, reaching 0.0°N 94.0°E at 19:41:03 UTC and continuing at an average Ground Speed of 495.0 knots until fuel exhaustion. I used a Constant Mach of 0.8479598, which gave an average Ground Speed between 19:41:03 UTC and 00:11:00 UTC of 495.0016 knots. I simulated a flight level of FL350 rather than FL351, same as for the first case.

https://www.dropbox.com/s/yxrq0hacvpk74z4/MH370%20Flight%20Path%20Model%20V19.4%20RG%20CTT%20CM%200.8479598%20FL350%20186.7%20Case%202%20Full%20Report.png?dl=0

The BTO Residuals are high and the BFO Residual at 19:41:03 UTC is also high.

@Peter Norton,

You said: “Thank you. The expected value (of one path) is 50%? Doesn’t the sum of all probabilities (of all paths) have to be 100%?”

The expected value of the probability when the True Route is used is 50%. Half of the random trials (with random BTO and BFO reading errors) will have a probability > 50%, and half of the random trials will be < 50%. The standard deviation of a fit of the True Route is 29%, so one would expect that 21% of the trials would exceed 50% + 29% = 79%, and 21% of the trials would be less than 50% – 29% = 21% (obviously). That means there is a 79% – 21% = 58% probability the True Route will be between 21% and 79%. Note that the probability of being within one sigma is slightly different for this chi-squared distribution than it is for a normal random variable.

For MH370 we only have one set of data, so the chances of its probability being between 21% and 79% is 58%, which is probable but far from certain.

To answer your question, no, the sum of the probabilities of all paths is unknown, and it is not 100%. I could argue it is extremely large/infinite. Remember that we only know the residual statistics when fitting the True Route. When the route is not True, then the residuals will be larger and unknown, leading to small, but not zero, probabilities. The expected value for incorrect routes is unknown but far less than 50%.

@TBill,

You said: “Apologies if this question has been covered already, but your prior model of March_2018 (approx 30 South pin location) had a somewhat similar goal to find best fit within fuel limits. So what is key difference now? and why not 30 South this time? Of course I am thinking it may have glided/flown beyond Arc7, so I am looking at the Arc7 intersection.”

The goal of my March 2018 paper was the same as now – to identify the True Route. It was the first attempt at synthesizing locations that allowed for the inevitable errors in the flight path model and weather data. That was a necessary, but not sufficient, step toward a discriminating route fitter. The first missing step in that paper was the lack of conditions on the correlation of the best-fit ground speed errors with the BTO residuals. With no constraints, that route fitter simply added whatever ground speed corrections were needed at each arc to make the BTO residuals tolerably small. So, when I evaluate those previous results, I see a very high (and negative) correlation between the ground speed errors and the BTO residuals. After a lot of thought about the previous method, I realized those decorrelation conditions were required and would substantially improve the route discrimination. That was the genesis of my improved methodology, which now appears to be bearing fruit.

You may recall that my 2018 paper described a 181.2 degree constant magnetic track, ending near 31.6S. The first part of that route is at exactly 180 degrees true, so it matches my current result in location, time, and true bearing. Of course, the eastward curvature of the CMT route is not present in the current result for the LNAV 180 degree route (which ends circa 34.3S).

The second shortcoming in my 2018 paper is the failure to identify a region of interest at very high altitude with a due south track. The reason for that oversight is that I only explored routes at altitudes and speeds previously identified in my fuel studies which offered correct endurance when using the correct PDA. Those studies assumed the air temperature over the SIO was +10C relative to ISA, and this causes higher than normal fuel consumption. This assumption is quite valid up to about FL360. However, on this particular night, the air above FL360 was very much colder – by as much as 12C relative to ISA approaching FL400. That colder air between FL360 and FL400 has two major effects. First, it lowers the TAS for the same Mach, so the ground speed is reduced. Second, the fuel consumption is substantially reduced by several percent. That allows, for instance, M0.84 and LRC airspeeds at FL390 at the nominal PDA.

These and other factors led Victor, Richard, and I to do a new search for potential regions of interest. Richard has done a very thorough, systematic search, and this has led to the identification of other possibilities which we are evaluating. To date, none of these appear as promising as the BEDAX LNAV 180 route. Richard is concluding his important work, and hopefully he will be able report on it in the near future.

@Niels,

You said: “@DrB Could you please share the details of the BEDAX – South Pole, LRC FL390 path? I’m trying to corroborate such path with my tool (basically by looking at different D(t) input functions). It seems that one needs to accept a rather large 19:41 BFO error to reduce path curvature in the first 1.5 hour of the 19:41 – 00:19 interval and to allow for the LRC speed.

Although my best prediction for the MH370 path from 19:23-00:11 is not yet finalized, I can provide some information on current BTO and BFO residuals. For the 19:41, 20:41, 21:41, 22:41 and 00:11 handshakes, I get BTO residuals of 10, 41, 21, -53, and 31 microseconds and for BFO residuals I get -7, -2, -3, -4, and -1. Note that the BFO residuals are only 6 Hz peak-to-peak, and their mean is -3 Hz. I suspect that 3 Hz shift is a bias change caused by a combination of OCXO drift and (cold) thermal cycling of the SDU.

@All,

Extracting the True MH370 Route from the Inmarsat BTOs and BFOs is a vexing problem, but I believe that if one applies ALL the information at hand a single solution may be obtained (under the assumption of no maneuvers between 19:41 and 00:11).

First, let us review what we know. We have BTOs and BFOs at 5 handshake times from 19:41 to 00:11. That is a total of 15 knowns. However, only 7 route parameters are sufficient to define a route (start time, start latitude, start longitude, flight level, lateral navigation method, initial bearing, and speed schedule). Still, even over the 7th arc, there are roughly at least 10^7 possible combinations of the 7 route parameters. How can we possibly find the one correct route in 10^7 possibilities?

Well, to start with, we have SUFFICIENT DATA for a solution. Even if one discounts the BFOs from 5 of the knowns to the equivalent of one known (that the plane headed south, not north), we have at least 11 knowns to use in solving for the 7 route parameters. So, in fact we have 4 EXTRA degrees of freedom we can use to either improve the precision of the fitted route parameters or to solve for 4 additional unknowns. Somewhat surprisingly, doing the latter is very helpful in discriminating against incorrect routes, by finding 4 ground speed errors for the 4 legs from 19:41-00:11. In that case we have 11 knowns and 11 unknowns.

A route fitter works by predicting the latitude, longitude, geometric altitude, and velocity vector at the 5 known handshake times, and these are sufficient for predicting the BTOs and BFOs. The altitude is important for predicting the aircraft air speed and endurance (given the speed control mode), but the BTOs are only very weakly dependent on the altitude, depending primarily on the latitude and longitude. Thus, the 5 pairs of latitude and longitude basically determine the sequence of BTOs. That is, we must find 10 unknowns (5 pairs of unknown latitude/longitude at the 5 known handshake times) in order to match the 10 knowns (5 times and 5 BTOs). However, it is important to understand that these BTO strings are NOT INDEPENDENT. In fact, they are correlated, because one only needs 7 route parameters to determine the 10 times/BTOs. So, in fact we have more knowns (5 times + 5 BTOs + 1 BFO = 11) than unknowns (7) (ignoring the ground speed errors for the moment), and the problem may be solved iteratively using trial and error with a multi-parameter optimizer (i.e., a route fitter).

@DrB regarding your last posting:

Interesting to zoom out and look at the problem at hand as you do. It has been a while since I studied mathematics in detail, so I find it hard to comment on all aspects, however two thoughts / questions come up:

– Is it correct to treat the times as “knowns” here? Aren’t they needed to connect the “knowns” (mainly BTOs) to the “unknowns” (the flight path parameters)?

– Even if the number of “knowns” looks sufficient for the number of “unknowns”, does that guarantee a unique solution? Just think of c as known and x as unknown, connected through a function f. Does f(x) = c has a unique solution? I think it depends on f.

So, while I’m enthusiastic about the progress, I’m still a bit worried about the uniqueness of identified path(s).

@DrB: Thank you for your helpful explanation.

@DrB Thank you for the latest post to @All where you provide a general description of your current work. I had been trying to piece together just how you do this, without much success. This explanation helps. But I do have some questions if I may. (These will likely reveal how poorly I follow your explanation).

1. If you assume no maneuvers after 19.41, does that not pretty much imply a straight-line flight expect for cross wind variations? If YES, do you use that to constraint on your solution?

2. At the end you mention that you can use an iterative solution. Is that really the same as a ‘trial and error’ method or are you using the result of one ‘iteration’ as input to the next iteration and expecting the solution to converge?

@Shadynuk,

You asked: “1. If you assume no maneuvers after 19.41, does that not pretty much imply a straight-line flight expect for cross wind variations? If YES, do you use that to constraint on your solution?”

There are five methods of lateral navigation in a B777:

1. Great cicles (geodesics) between defined waypoints. This is the shortest path from A to B. The bearing varies along the track because the Earth is not a sphere. This is the method normally used for long-distance flight.

2. Constant true bearing.

3. Constant magnetic bearing. This is what is used by ATC for controlling arriving and departing air traffic. It has its historical basis in magnetic compasses prior to the advent of ADIRUs and GPS.

4. Constant true heading.

5. Constant magnetic heading.

None of these are actually “straight” paths, and they generally don’t even lie in a plane (except for true N/S/E/W tracks).

You also said: “2. At the end you mention that you can use an iterative solution. Is that really the same as a ‘trial and error’ method or are you using the result of one ‘iteration’ as input to the next iteration and expecting the solution to converge?”

The iterative solution is a trial and error method which uses an objective function to keep track of the improvements as the solution converges. If an improvement occurs during an iteration, it keeps those fitted values and uses them as the starting point of the next iteration. The software engine for doing this is usually a Runge-Kutta algorithm that minimizes a multi-variate function following the path of steepest descent. In EXCEL this engine is called “SOLVER”.

@Niels,

You said: “– Is it correct to treat the times as “knowns” here? Aren’t they needed to connect the “knowns” (mainly BTOs) to the “unknowns” (the flight path parameters)?”

I compare the measured BTOs/BFOs at the handshake times with the route fitter predictions at the same handshake times. So the time unknowns are simply set equal to the known handshake times.

You also said: “– Even if the number of “knowns” looks sufficient for the number of “unknowns”, does that guarantee a unique solution? Just think of c as known and x as unknown, connected through a function f. Does f(x) = c has a unique solution? I think it depends on f.

So, while I’m enthusiastic about the progress, I’m still a bit worried about the uniqueness of identified path(s).”

That’s a good question. Fortunately, in the case of MH370, we know a solution exists because a real aircraft flew a route and generated the signals which were recorded as BTOs/BFOs. So, we know for sure that a True Route exists, and therefore at least one solution also exists. I have found one, and so far only one, solution without maneuvers. That does not prove it is the correct one, but if it is not, then there must be at least two solutions (one without maneuvers and one with maneuvers). I am very doubtful there are two solutions. What are the chances that the True Route has maneuvers, but a second solution without maneuvers also exists? I think this is extremely unlikely.

@DrB

You said “I compare the measured BTOs/BFOs at the handshake times with the route fitter predictions at the same handshake times. So the time unknowns are simply set equal to the known handshake times”

Ok, but if we try so (and if we just consider the BTOs), the way I look at it:

In general we have:

f(lat_0, lon_0, t_0, speed, nav, FL, bearing, t) = BTO(t)

For the five handshakes we are considering:

f(lat_0, lon_0, t_0, speed, nav, FL, bearing, t = t_i) = BTO_i, i = 1..5

To me that looks more like five knowns and seven unknowns, so I’m not really reassured. Of course, we have some information from the BFOs too; it looks we really need it..

Regarding: “What are the chances that the True Route has maneuvers, but a second solution without maneuvers also exists?” I find it difficult to answer this question. But I can agree that if a route without maneuvres has been found it should get first attention, and the possible routes with maneuvres should for now be more considered as “back-up”. In addition: the routes (with slight maneuver in the first hour / hour and half after 19:41) that I’m finding with my path estimator are not too far off from the BEDAX-South Pole path, so we are looking at the same general area (roughly S33 – S36). This I feel is an encouraging sign as well.

@Niels

Here are the results from my model for your refinement of your Case A.

You proposed a CTT176.8933 flight path starting at 21:11:00 UTC, at a position 8.0208°S 94.06789°E in LRC speed mode at FL349.4.

https://www.dropbox.com/s/b33b0b8wmew86mp/MH370%20Flight%20Path%20Model%20V19.4%20RG%20CTT%20LRC%20FL349.4%20211100%20UTC%20Niles%20Case%20A%20Revised%2011062019%20Full%20Report.png?dl=0

This shows an improvement in the BTO Residuals at 22:41:22 UTC and 00:11:00 UTC, but they are still too high in view.

@Richard

“…Here is the other further case you proposed in your paper.

You proposed a CTT186.7 flight path starting at 19:11:00 UTC, reaching 0.0°N 94.0°E at 19:41:03 UTC and continuing at an average Ground Speed of 495.0 knots…The BTO Residuals are high and the BFO Residual at 19:41:03 UTC is also high.”

Thank you. Keep in mind, in my “BFO straightness” essay, I was only looking at BFO matching, with no attempt to match BTO. Which, although it will take me a while to understand the new apparoach, my initial thought is the new approach is giving more weight to BTO match, with BFO match secondary.

Anyways, to paraphrase something @Victor said privately to me some time ago, we have to admit that the original IG path to nominal 38-South had a lot of apparent merit (in terms of match to the BTO/BFO data). You can refresh my memory, but I believe there were several versions of the orig IG path. The version that I personally use the most is FFYap’s spreadsheet for calc of BTO/BFO, I think ends 37.5 South.

>>Therefore the first big test for the new model is probably to show why 180 South is a better fit than the best of the orig IG path estimates to 38 South.

For the purpose of this fit test comparison, I am less interested in fuel constraints, although that could be of interest later.

@TBill

You stated “the new approach is giving more weight to BTO match, with BFO match secondary.”

I am only calculating the BTO and BFO Residuals based on the Flight Path parameters you specified.

My report that I linked in the comment above included both BTO and BFO Residuals calculated without any weighting.

I only commented on the BTO values being high, because the BFO values were not.

Your supposition is unfounded, in my view.

@Richard

I agree my first impression of the model could be inaccurate, but I still think the original IG paths to about 38S were quite good fits to the data, so that remains a question why 180 South would look better (other than a possible fuel issue).

If I may add a question – where does the 180S path intersect the 7th arc? Is that the 34.3º latitude?

@TBill

You stated “You can refresh my memory, but I believe there were several versions of the orig IG path. The version that I personally use the most is FFYap’s spreadsheet for calc of BTO/BFO, I think ends 37.5 South.”

There were 4 publications by the IG between 6th June and 26th September 2014. The first publication stated MH370 reached 36.02°S on the 6th Arc at 00:11:00 UTC. The last publication stated MH370 reached 37.71°S at the 7th Arc at 00:19:37 UTC. This was based on the average results from flight models from 5 IG members including Victor and myself, but not Yap.

In June 2014, I used my flight model V5.0, which assumed an altitude of 35,000 feet, a TAS of 487 knots and only calculated the wind at the time of the satellite handshakes and concluded a MH370 end point at 35.41°S on the 7th Arc at 00:19:37 UTC. There is no comparison with my current model V19.4, which recalculates the flight path every minute based on the speed mode, navigation method, weather data, fuel data, Boeing 777-200ER performance data, Rolls Royce Trent 892 Engine data and Inmarsat satellite data.

In an upcoming paper to be published here in due course, Bobby, Victor and I examine systematically all possible MH370 flight paths into the SIO. We then in a further paper examine a number of regions of interest and show why many can be discounted. This includes the original IG paths and a number of other flight paths proposed since 2014.

@DrB Thank you for your extensive response. That does help. I am just trying maintain enough understanding so I can follow these discussions in general.

@Richard

Thank you for the new calculations on my case A. From the results it looks mean and RMS BTO errors can be further reduced by shifting the starting position slightly south along the track. However, as the main aim for now is to establish a good procedure to transfer results from my path estimator to a route fitter it is probably better for the moment we don’t go that way, without a solid understanding and justification. I have some first qualitative thoughts there; I think it is needed to invest some more time to fully identify, understand and (if possible) quantify the main sources of the BTO errors that we observe.

@all:

what’s the upshot of this?

search the BEDAX/S-pole path (beyond 50nm)?

Or the remaining northern part of arc7 first?

something else?

@ArthurC,

You asked: “If I may add a question – where does the 180S path intersect the 7th arc? Is that the 34.3º latitude?”

Yes. The BEDAX to South Pole route intersects the 7th Arc at 34.3S latitude.

@Peter Norton,

My thoughts:

1. Re-map the Fugro area close to the arc at 34.3S.

2. Re-map the OI area farther from the 7th arc at 34.3 S.

3. Extend the search width N and S of the arc at 34.3 S.

Alternatively, one might begin by revisiting and re-mapping those Fugro/OI areas that were of lesser quality. However, the targeted area is not too large, and I think the most certain approach is to re-map it from scratch. I do not believe looking farther north on the arc has any significant chance of success.

@Niels,

You said: “To me that looks more like five knowns and seven unknowns, so I’m not really reassured.”

That is incorrect when one assumes no maneuvers occurred between 19:41 and 00:11. In that case, the locations, tracks, and speeds are not independent variables at each handshake time. They are correlated by the autopilot control settings, so the number of independent variables is less than the number of unknowns, and a solution exists.

You are correct that you can’t uniquely solve the problem if you allow independent values of location, track, and speed at each handshake time.

@DrB: The area of interest along the longitude 93.78E near the latitude 34.3S was scanned by GO Phoenix using SAS sensors, not Fugro.

@Victor Iannello,

Thank you for making the correction on the name of the initial company that searched near 34.3S.

@DrB

Your search area thoughts are potentially controversial because a lot of folks have pins elsewhere. There is of course the 38-39 South contingent, there are the folks that have paths to 20-25 South, there are the active flight folks, and long glide past Arc7 folks. Not to mention Xmas Island.

If you have a bona fide technical solution to the problem, then that will sway people including me. However, I am currently having some deja vu.

@TBill: The success of this method will depend on two things:

1) The development of path discriminator criteria that are objective, i.e., there are no built-in biases or unjustifiable assumptions.

2) The identification of a route that uniquely satisfies the path discrimination criteria.

To my knowledge, Bobby is the first investigator that has tried to separate the BTO and BFO errors into random and non-random (systematic) components. If the BEDAX-SouthPole path uniquely satisfies this expanded criteria list, it would be quite significant. It would also be quite a coincidence if this path, which was derived without assuming a starting position or starting track angle at 19:41, is perfectly aligned with BEDAX along a due south path.

@DrB

Thank you for confirming.

As a thought – that falls right in the middle of the original search area, if I’m not mistaken, could it have been missed?

Or could it be outside of the search bands centered on the 7th arc?

Rhetorical questions, but it would be sad if we really were that close to the wreckage and missed it…

@ArthurC: Some of us are trying to determine if there is a reasonable chance the debris field in that area was missed. Without a doubt, there was some challenging terrain for the GO Phoenix towfish that resulted in data holidays. Some, but not all, of those areas missed by GO Phoenix were later filled in, first by the UAV, and later by Ocean Infinity’s Seabed Constructor.

@TBill

I think DRB’s approach has merit for the constraints he assumes. Poorly correlated arc intersections (not autopilot control) are analytically intractable.

@Victor

Thank you. I apologize if I appeared critical in any way – far from it.

This is a fascinating discussion and any clue that might help restart the search is of hight interest.

I certainly hope that the next search will happen soon and it will be successful!

@ArthurC,

You said: “As a thought – that falls right in the middle of the original search area, if I’m not mistaken, could it have been missed?

Or could it be outside of the search bands centered on the 7th arc?

Rhetorical questions, but it would be sad if we really were that close to the wreckage and missed it…”

Yes, 34.3S is in the area highlighted by DSTG’s analyses and close to Inmarsat’s prediction. Misses have happened before. Ocean Infinity originally misclassified the ARA San Juan submarine debris field as a geological outcropping. To Ocean Infinity’s credit, they revisited the area after they were supposed to leave, and they subsequently found it in difficult terrain. My current opinion is that MH370 is more likely to have been missed than for it to have glided outside the past search width.

@Peter Norton

You ask a very good question “@all: what’s the upshot of this?”

In my view, the BFO data at 00:19:37 UTC reveals a steep descent at around 15,000 fpm and therefore MH370 is likely to be found close to the 7th Arc around 34.3°S, in the area originally searched by Go Phoenix. Their contact report reveals 44 contacts. Go Phoenix searched the initial area – 10 NM / + 13NM from the 7th Arc.

Of course, it is possible that MH370 is outside the initial Go Phoenix area. Ocean Infinity extended the searched area to +/- 30 NM from the 7th Arc, although this is less likely in my view.

Finally, it is also possible that MH370 recovered from the steep descent and is beyond the +/- 30 NM from the 7th Arc, although this is significantly less likely in my view.

I am now convinced that MH370 is not to be found either north or south of the area that has already been searched.

@DrB

Regarding “uniqueness”: I’m happy to be corrected, however I’m not yet convinced it is such clear-cut case

You wrote:

“That is incorrect when one assumes no maneuvers occurred between 19:41 and 00:11. In that case, the locations, tracks, and speeds are not independent variables at each handshake time.”

When I wrote the five BTO equations I was not assuming independent tracks and speeds at each handshake time. For clarity I will rewrite “speed” to “spd_setting_0” and “bearing” to “direction_0”. The five equations again:

f(lat_0, lon_0, t_0, spd_setting_0, nav, FL, “direction_0”, t = t_i) = BTO_i, i = 1..5

We can consider if “nav” and “direction_0” should be separate unknowns or could be combined in one, reducing the number of “unknowns” to 6, however the message would be the same: more “unknowns” than “knowns”. Of course the BFO also contains information; it would be better if we would not depend too much on it.

I’m trying to reduce lat_0, lon_0, t_0 which can be done at the expense of for example the 19:41 BTO. We then have four BTO equations left with five unknowns:

f(lon_19:41, spd_setting_0, nav, FL, “direction_0”, t = t_i) = BTO_i, i= 2..5

And we really start exactly at the 19:41 arc, not sure if that is ok.

To have four “unknowns “ and four “knowns” we would indeed need to combine nav(mode) and “direction_0”. Isn’t that the same as saying that all possible navigational modes in combination with all possible initial directions have to be considered / evaluated?

@DrB wrote:

“That is incorrect when one assumes no maneuvers occurred between 19:41 and 00:11. In that case, the locations, tracks, and speeds are not independent variables at each handshake time.”

In this technique – what is the rule for 19:41? in other words, could there be a maneuver pre-1941 that is still resolving itself? Or are we saying level constant flight at 19:41?

@TBill,

The assumption is that the aircraft is in stable autopiloted flight at 19:41. That 19:41 location is not near any waypoint, so it is highly unlikely in my opinion that a maneuver would be in progress at 19:41. The BEDAX LNAV 180 route leaves BEDAX at 19:23:43. An open and interesting question is how the approach to BEDAX was made. A lot could have happened between 18:22 and 19:23. Perhaps a feint was made on a northern track before turning south. I am still puzzled by the apparent lateral offset at 18:24. You can’t just keep on that track and then turn south to BEDAX, unless the 18:40 BFOs were the result of a descent and the FMT was after the phone call. If no descent, then you need a track of 215 deg or 145 deg at 18:40. A turn to BEDAX from N571 can match the 18:40 BFOs, but then you arrive at BEDAX much too early.

@Niels,

There are seven unknowns that define a B777 route. The lateral navigation method and the initial bearing are two separate variables available to the pilot. They require two degrees of freedom in the solution.

We have 11 to 15 knowns. There are 5 handshake times, 5 BTOs and 5 BFOs, for a total of 15. Even if you only use the BFOs to choose the southern hemisphere, we still have 11 knowns.

We can solve for the 7 unknowns using the 11 knowns, and we have 4 extra degrees of freedom with which to improve the precision of the solution. This may be useful because we don’t know the correct BTOs at the handshake times. Inmarsat records noisy readings, and thus all of our knowns are noisy except for the handshake times, which are quite precise and quite accurate. Alternatively, one can solve for four addition variables, such as the average ground speed errors (GSEs) for each leg. This is what I do, because that allows you to separate the systematic BTO errors due to incorrect route parameters from the purely random BTO read noise. I actually don’t obtain 4 independent GSEs. I smooth (low-pass-filter) the 4 GSE’s so they only use 3 degrees of freedom. In other words, I don’t treat the GSEs as a random, independent variable, because these are the systematic model errors and GDAS data errors, and they will generally vary slowly with time and location. So, I can find the correlated GSEs and simultaneously get a bit of noise reduction.

Your mistake is not counting the five handshake times as knowns. In your equation, we know the 5 t_i values and the 5 BTO_i values plus one BFO value, for a total of 11. As I have said, there are 7 unknowns and at least 11 knowns. A solution exists.

And no, you cannot start exactly on the 19:41 Arc. The BTO reading error of 29 microseconds 1-sigma applies at all the handshakes, including the one at 19:41.

@All

The GE Chart linked below shows the LNAV180 LRC FL390 flight path from waypoint BEDAX in white, the Go Phoenix contacts are marked with a diamond and numbered as per their report, the Ocean Infinity track is shown in red and the 7th Arc at 20,000 feet. The bathymetry was kindly provided by Don Thompson.

https://www.dropbox.com/s/lpibkx6jgnqrs87/LNAV%20LRC%20FL390%20180.0%20Trial%20%23%20671%20GE.png?dl=0

@DrB

If have to see more details of the path evaluation procedures that you followed to understand if either:

f(lat_0, lon_0, spd_setting_0, nav, FL, “direction_0”, t = t_i) = BTO_i,

i = 1..5

or:

f(lat_0, spd_setting_0, nav+direction_0, FL, t = t_i) = BTO_i, i = 2..5

Would be a good summary of the “BTO-only” case in terms of knowns vs. unknowns. We seem to disagree on the role of t_i in these sets of equations.

I don’t think that t_0 is really an unknown: it is just the chosen time you start the numerical route formation.

I would like to understand better the total set of paths that has been evaluated to get a feel about “specialness” of the BEDAX – 180 degrees south route. Even if mathematical uniqueness cannot be proven formally, it could well be special enough to give it serious attention and possibly work towards a recommendation.

So, altogether I’m really looking forward to a paper describing the work in more detail.

@Niels

I have run over 1,000 flight paths in total and around 600 flight paths in the course of the current systematic study over the last 4 months.

This includes all initial bearings, all navigation methods, all speed modes and flight levels from FL290 to FL415.

Bobby and Victor have also run a large number of flight paths.

About 30 flight paths were considered in more detail and double and triple checked by Bobby and Victor.

In the end 7 flight paths remained, of which only one was matching all the criteria.

It is tough to match the BTO, BFO, Fuel, Aircraft Performance, Navigation Method, Speed Mode and Weather en-route.

@DrB

“I am still puzzled by the apparent lateral offset at 18:24. You can’t just keep on that track and then turn south to BEDAX, unless the 18:40 BFOs were the result of a descent and the FMT was after the phone call. If no descent, then you need a track of 215 deg or 145 deg at 18:40. A turn to BEDAX from N571 can match the 18:40 BFOs, but then you arrive at BEDAX much too early.”

Yes I know. The most simple case, MH370 does a descent 18:37 and at 18:40 does an FMT 180 South at 0894E. If you want you can also accept MH370-Captio’s initial path, which is slightly more complex. But then you have to ascend again into 19:41.

@Richard

Many thanks for this additional information; it gives some further impression of the procedures that were followed (I would very much like to know the parameter space studied in detail, as well as the optimization/evaluation results (perhaps of the 30 paths that were studied in detail?)). It definitely illustrates the impressive effort done over the past period. I understand it is a lot, and precise and challenging work.

@DrB @Richard

Are you saying CTT or LNAV to 180 South? Which by the way, would seem to be an intentional, passive flight path. Seems to me a fine line between intentional/passive and intentional/non-passive.

By the way, I see 180 South possibly being 180 deg CTH from about ISBIX. The easiest way to think of it, on Google earth you are looking for a vertical line where Arc3 to Arc4 is approx. equal to Arc4 to Arc5. With the winds aloft being initially east to west, I estimated with FS9 that happens for a flight path starting around ISBIX. After Arc5 I have to assume active pilot to hit Arc6, otherwise the stiff winds below 22 South mess up the Arc timings. But it is not illogical to envision the pilot is slowing down, descending, and/or changing heading as daylight and high winds aloft approach.

TBill’s prior Proposal for 180S CTH Path-

https://twitter.com/HDTBill/status/1038437134791790593

@Niels

Please bare with us, the first of two papers is in internal review at the moment.

We are still running a test programme comparing the flight models from Bobby, Victor and myself in detail.

The purpose of the present post is to introduce the new methodology.

As you say, it is a lot of work and we do not want to make mistakes.

I have personally invested over 8,000 hours in the last 5 year’s. I am sure many others have done like wise and more.

DrB said:

I am still puzzled by the apparent lateral offset at 18:24. You can’t just keep on that track and then turn south to BEDAX, unless the 18:40 BFOs were the result of a descent and the FMT was after the phone call. If no descent, then you need a track of 215 deg or 145 deg at 18:40. A turn to BEDAX from N571 can match the 18:40 BFOs, but then you arrive at BEDAX much too early.This is an important point that I have been struggling with since I started examining the BEDAX-SouthPole path back in July 2014, and what led me to consider at that time a possible landing at Banda Aceh (ICAO: WITT). Now, the prospect of a B777 landing at night without any witness reports in the past five years does not seem likely. That said, if the true route was BEDAX-SouthPole, there was a significant loiter near Banda Aceh, as Bobby stated above, whether there was a holding pattern, a “back and forth” excursion, or some other path.

I will say that I have not completely ruled out a skyjump near Banda Aceh, but this scenario does have its own complications. After depressurizing the plane below 10,000 ft, the bulk cargo door in the aft cargo bay can be opened, as many have discussed. Access to the aft cargo bay is achievable via the modular crew rest area that was installed in the aft cargo bay. However, according to the loading sheets, access to the bulk cargo door would have been blocked by the Unit Load Devices (ULDs) that were loaded in KLIA.

But can we be sure that the ULDs were actually loaded? If they were not, it would mean that the loading records presented in the Safety Investigation Report (SIR) are false. To date, I have not been able to find any reference to security video recordings of MH370 near the gate. Does anybody know of any?

Would there be other indications if the cargo was not loaded? The CG would be shifted forward, so that when the FO rotated to takeoff, he would have exerted more backward force (more nose up) on the control wheel because the stabilizer trim (which is set based on a value for CG that is input by the crew) would not be correct. That change in backward force might not have been noticeable, especially to a relatively inexperienced PF. The fuel burn would also have been a bit lower, but the difference in onboard fuel at the time of the last ACARS report at 17:07 would have been small.

Could the disappearance of MH370 have been related to a cargo heist at KLIA?

@TBill

Regarding how the controlled ditching theorists reconcile their theory with the retracted wing flap determination, you would have to ask them. I have found that anyone who adheres too strongly to any pet theory tends to exaggerate the evidence that supports it, and ignore or dismiss the evidence that contradicts or disproves it.

Victor and Bobby Ulich and all contributors

Excellent analysis ! A crash site on or near the 7th arc at 34.3 S is consistent with the drift analysis of both Chari Pattiaratchi and David Griffin. Both oceanographers and I believe that area contains some places that are difficult to search where the underwater debris field could have been missed, and is worth a second look. We also think it is worth searching wider at 34.3 S and other high priority latitudes.

@Victor

Aha you have fuel problem if you have a loiter?

@Niels

You asked “I would very much like to know the parameter space studied in detail”.

1,372 flight paths in total.

828 flight paths since the start of this systematic study on 17th February 2019.

Start latitudes from 16.0°N to 4.3°S.

Start longitudes were unconstrained.

The final major turn had to be completed before the 2nd Arc at 19:41:03 UTC was reached.

Start times from 18:41:00 UTC to 19:32:00 UTC.

Systematic initial bearings from 155°T to 195°T, plus some exotic cases.

Navigation methods: LNAV, CTT, CTH, CMT and CMH.

Speed modes: Constant Mach 0.80 to 0.85, LRC 0.7047 to 0.8408, MRC, ECON CI52.

Flight levels: from FL290 to FL430.

Fuel endurance was allowed to vary around 00:17:30 UTC and the resulting PDA was noted.

The PDA was allowed to vary from the nominal 1.5% and the possibility that the bleed air was shut off for part or all of the time was considered.

The drift analyses, which in my view imply an end point latitude of between 25°S and 35°S, were not considered, due to their inherent inaccuracies (please see separate study by Bobby dated 20th November 2018 published here: http://mh370.radiantphysics.com/2018/11/17/ocean-infinity-finds-argentine-submarine-after-not-finding-mh370/#comment-20181).

The resulting end points were between 17.6°S and 40.3°S on the 7th Arc.

In addition there were a number of custom cases considered such as Christmas Island, Cocos Island, Learmonth, Perth, Jakarta, ZS Simulator paths, flight paths with manoeuvres, etc.

@TBill: Not if the average fuel flowrate during the loiter is less than for cruise. Remember that the minimum flowrate occurs at holding speed and FL200.

@TBill,

You asked Victor about a “fuel problem” if there was a loiter between 18:23 and 19:23. Please excuse my weighing in, but that depends on what you call a loiter. A HOLD almost an hour long would save some fuel, so that would need to compensated by higher fuel consumption between 17:30 and 18:23. A 18:23-19:23 route between multiple waypoints at cruising altitude and speed would be a good fuel match. Victor has looked at the fuel for a ground stop at Banda Aceh, and he can answer that one.

@TBill,

You said: “Are you saying CTT or LNAV to 180 South?”

Either LNAV 180 or CTT 180 can fit the Inmarsat data. We choose to highlight LNAV because we believe a commercial pilot would choose LNAV. CTT is much less likely because it requires the pilot to change the NORM/TRUE switch to TRUE, and that is never done in normal commercial flights except in polar regions.

You also said: “By the way, I see 180 South possibly being 180 deg CTH from about ISBIX.”

Richard will report in more detail on this soon, but we are not finding any CTH routes which match the satellite data.

@Niels,

You said: “If have to see more details of the path evaluation procedures that you followed to understand if either:

f(lat_0, lon_0, spd_setting_0, nav, FL, “direction_0”, t = t_i) = BTO_i,

i = 1..5

or:

f(lat_0, spd_setting_0, nav+direction_0, FL, t = t_i) = BTO_i, i = 2..5

Would be a good summary of the “BTO-only” case in terms of knowns vs. unknowns. We seem to disagree on the role of t_i in these sets of equations.

I don’t think that t_0 is really an unknown: it is just the chosen time you start the numerical route formation.”

Your first equation is correct. For a route to be determined uniquely, seven parameters are required. One of these is the starting time. One can choose to use the handshake time at 19:41 to start the route (and then solve for the starting latitude and longitude). So, in this case the starting time is set equal to t_1. Alternatively, can can choose a different initial condition, such as a starting latitude or a starting longitude, and then solve for the other two unknowns. Assuming one of those three starting parameters as an initial condition assures stable and efficient optimization.

Your second equation is wrong on two counts: (1) it is missing longitude, and (2) the navigation method is a separate variable from the initial bearing.

@Victor

It does seem like descent and slow down makes sense. About how fast is holding speed at FL200?

@TBill: At 20,000 ft and 205 MT, the holding speed is about 219 KIAS. That corresponds to around 296 KTAS at standard conditions, and around 301 KTAS at ISA+10K.

@Victor

RE:

“Would there be other indications if the cargo was not loaded? The CG would be shifted forward, so that when the FO rotated to takeoff, he would have exerted more backward force (more nose up) on the control wheel because the stabilizer trim (which is set based on a value for CG that is input by the crew) would not be correct. That change in backward force might not have been noticeable, especially to a relatively inexperienced PF.”I can’t think of any indications other than those you mentioned. I don’t have a trim sheet for the -200ER, but the trim sheet for the -200 shows that the required stab trim setting would only change by about 1.4 units if ALL the cargo in compartments 3 & 4 (as shown on MH370’s load sheet) were removed. I doubt the -200ER would be much different. As you said, an inexperienced pilot might not notice the difference in the control column force required during rotation if the trim had been set as per the load sheet.

It’s also possible that only a few of the containers were removed. There were several spare positions in the rear cargo compartment. It might have been possible to offload as few as three containers and still leave enough space for someone to squeeze their way out of the LLAR. Highly speculative, of course!

@Andrew: Thank you, Andrew. I’ve also thought about whether ULDs were loaded that were empty and had curtain sides with tarps that could be removed or cut. As you say, highly speculative!

@DrB

“Richard will report in more detail on this soon, but we are not finding any CTH routes which match the satellite data.”

At some point I give up, but are you ruling out passive flight CTH routes? I agree it would probably have to be active pilot to match Arc6/7 in that CTH case. I personally gave up on 180 South altogther because I was not happy with BFO data fit, and thinking a heading change enroute might be the answer.

@TBill: The purpose of this effort is to be quantitative and objective, and it will either succeed or fail. As has been said many times, it is impossible to reconstruct a path with pilot inputs after 19:41 that does not include unjustified assumptions, i.e., hunches. How do you determine the relative merit of the hunches? As for “not being happy with the BFO fit”, @DrB has already explained that your rejection of the BFO match is unjustified based on the uncertainty we have in the BFO measurement.

@TBill

You stated “At some point I give up, but …”

Please do not give up! We admire your scientific tenacity.

I appreciate you are challenging the assumption of no active pilot after 19:41:03 UTC.

I appreciate you are putting forward the assumption that the active pilot wanted to conceal the crash location.

If I list your 13 proposals mentioned in your comments to this current post:

1. 180°T towards 6th Arc then 135°T to Broken Ridge (flight model provided in response and in my view flight path disqualified).

2. 180°T to waypoint BEBIM then 167°T (flight model provided in response and in my view flight path disqualified).

3. 180°T to waypoint BEBIM then 162.9521°T to Dordrecht Hole (flight model provided in response and in my view flight path disqualified).

4. CTT180 constant GS 478 knots (flight model provided in response and in my view flight path disqualified).

5. CTT186.7 constant GS 495 knots (flight model provided in response and in my view flight path disqualified).

6. Bobby’s CMT181.22 (flight path disqualified by Bobby).

7. Original IG flight path to 37.71°S (in my view flight path disqualified).

8. 38°S-39°S contingent (in my view flight path disqualified).

9. Long glide contingent (flight path still under consideration but only from 34.3°S).

10. Christmas Island contingent (in my view flight path disqualified).

11. Manoeuvres between 19:41:03 UTC and 00:11:00 UTC (impossible to consider all the options, those proposed have been disqualified).

12. Captio’s path (in my view flight path disqualified).

13. CTH180 from SAMAK to NISOK to ISBIX then 180°T (CTH flight paths in general disqualified, CTT180 paths from waypoint BEDAX 93.787575°E are good, CTT paths from waypoint ISBIX 93.675108°E do not fit).

You could have also mentioned:

1. LNAV192.3072 CM 0.838 FL355 (disqualified).

2. CTT 183.2026 ECON CI52 FL400 (disqualified).

3. LNAV178.0111 CM 0.836 FL 405 (disqualified).

4. CTT160.0 CM 0.84 FL403 (disqualified).

5. CTT158.0 CM 0.84 FL403 (disqualified).

6. LNAV170.0 LRC FL350 (disqualified).

Personally I believe, we are narrowing the large field of possibilities down to just one.

A LNAV180 LRC FL390 flight path.

@DrB

On June 10th you wrote:

“Although my best prediction for the MH370 path from 19:23-00:11 is not yet finalized, I can provide some information on current BTO and BFO residuals. For the 19:41, 20:41, 21:41, 22:41 and 00:11 handshakes, I get BTO residuals of 10, 41, 21, -53, and 31 microseconds and for BFO residuals I get -7, -2, -3, -4, and -1. Note that the BFO residuals are only 6 Hz peak-to-peak, and their mean is -3 Hz. I suspect that 3 Hz shift is a bias change caused by a combination of OCXO drift and (cold) thermal cycling of the SDU.”

For the BFO residuals: 6 Hz peak-to-peak, indeed that looks reasonable.

I’m still struggling a bit with the BTO residuals. Perhaps something like an Anderson-Darling test could be applied (?) I’m curious to hear how you and others look at those.

@Richard

Regarding the parameter space systematically studied (828 paths):

What has been the typical “step-size” in bearing and FL?

I’m for example curious if you tried “nearby” routes, like TT 179.5, 179.0 etc. with slightly different FLs and initial conditions as the BEDAX – 180 degrees route.

@Richard

Personally I believe, we are narrowing the large field of possibilities down to just one.A LNAV180 LRC FL390 flight path.That path “feels” good to me as well. Analytics aside. The fact that it ends in a searched area is a negative, but I am warming up to your opinion about terminal locations North and South of the searched area. I am not yet ready to entertain areas farther from the arc.

@Niels,

You said: “For the BFO residuals: 6 Hz peak-to-peak, indeed that looks reasonable.

I’m still struggling a bit with the BTO residuals. Perhaps something like an Anderson-Darling test could be applied (?) I’m curious to hear how you and others look at those.”

I do the equivalent of Anderson-Darling. From analyses of other flights, we know the BTO reading errors have an expected value of zero and a population standard deviation of 29 microseconds. In addition, we know their probability density function follows a normal distribution. With 5 samples, the expected value of the sample standard deviation is 25.9 microseconds (i.e., it is biased low), and the standard deviation of the sample standard deviation is 9.9 microseconds. The expected value of the sample mean is zero and the standard deviation of the sample mean is 12.97 microseconds. So, in the route fitter I compute the sample mean and the sample deviation, and then I compute their Z-statistics (called Y_i in the Anderson-Darling Test). From the Z statistics and using a normal distribution, I find the P-values for each statistic, which are the probability that a random trial will be a worse fit (i.e., have a larger magnitude of Z), assuming the route is True. Then I combine all the P-values using Fisher’s chi-squared method, which results in a combined P-value, which is now a single figure of merit for each route fitted. Higher combined P-value means higher probability the route is True.

I use 10 statistics for LNAV routes (BTOR = BTO residual, BFOR = BFO residual):

1. Mean BTOR

2. STDEV BTOR

3. STDEV BFOR

4. Pearson’s correlation coefficient r for Leg Start BTOR to Leg End BTOR

5. r for Leg Start BFOR to Leg End BFOR

6. r for BTOR to BFOR

7. r for BTOR to Time

8. r for BFOR to Time

9. r for BTOR to Along-Track Position Error

10. PDA

For non-LNAV routes (CTT, CMT, CTH, CMH) I add 2 statistics for a total of 12:

11. r for BTOR to Cross-Track Position Error

12. r for Along-Track Position Error to Cross-Track Position Error

For each statistic, I know the expected value and the standard deviation, so I then compute the 10/12 Z statistics. Then I find the P-values using the appropriate distributions. The normal distribution is used for a number of the statistics, but for the correlation coefficients I use Student’s t distribution.

To check the math, I have a separate random BTOR/BFOR data generator program that runs 100,000 trials and estimates the percentiles for each statistic. These percentiles match very closely with the expected values, confirming my distribution functions are accurate. In addition, I inject random BTOR/BFOR values into my route fitter code and run several hundred trials to confirm it behaves similarly. This gives me high confidence that my implementation is valid and the results are to be trusted.

@Niels

You asked “What has been the typical “step-size” in bearing and FL?”

The scans start with a step size of 1°T for the initial bearing, 3 flight level/speed mode combinations (CM 0.84 FL403, LRCFL350 and LRC FL290) and each navigation method (LNAV, CTT, CTH, CMT and CMH). Generally the initial bearings between 160°T and 190°T are covered, but as long as the BTOR and BFOR are not going off the scale, then initial bearings between 155°T and 195°T are covered and sometimes even further as long as the fuel range or endurance is not going off the scale.

When a region of interest is found, the step size of the initial bearing is reduced to 0.1°T and flight level to 1.

Some special cases have been tested, where the bearing is determined to 4 decimal places and the flight level to 1 decimal place, e.g. a track of 162.9521 for TBill from waypoint BEBIM to Dordrecht Hole (LNAV LRC FL385 180.0 Deviation BEBIM 162.9521 DH) or for you at FL349.4 (CTT LRC FL349.4 211100 UTC Niels Case A Revised 11062019).

@Richard

Thank you for the nice comment. As far as Dordrecht Hole I am not thinking direct from BEBIM, although that is a possible idea. I am thinking the aircraft follows approx. home simulator path and maybe turns left towards Dordrtech later upon reaching Broken Ridge. Pilot may not have known if he could reach it, so I see the urgency to get to Broken Ridge first.

@DrB: It might be helpful if you explain the expected value and standard deviation for each statistical parameter.

Bobby Ulich,

Have you calculated and/or do you account for the covariances amongst your various statistics?

@sk999,

Covariance is another name for correlation coefficient. So yes, I do find the covariance, but I do it one pair of variables at a time instead of in matrix form.

Two of the statistics are expected to have non-zero correlation coefficients – the Leg Start BTOR to Leg End BTOR and the same for BFOR. This occurs because 3 of the 5 BTORs/BFORs appear twice in the calculation. There are also indications in the data of a positive correlation of BFOR with Time (I.e., there is a small linear drift).

Here are the sample expected values (mu_s) and the sample standard deviations (sigma_s) for the 12 statistics I use to find the probability for a route fit being the True Route:

1. Mean BTOR (mu_s = 0, sigma_s = 12.97 microsec)

2. STDEV BTOR (mu_s = 25.94, sigma_s = 9.90 microsec)

3. STDEV BFOR (mu_s = 3.90, sigma_s = 1.73 Hz)

4. Pearson’s correlation coefficient r for Leg Start BTOR to Leg End BTOR (mu_s = -0.237, sigma_s = 0.45)

5. r for Leg Start BFOR to Leg End BFOR (mu_s = -0.237, sigma_s = 0.45)

6. r for BTOR to BFOR (mu_s = 0, sigma_s = 0.50)

7. r for BTOR to Time (mu_s = 0, sigma_s = 0.50)

8. r for BFOR to Time (mu_s = 0, sigma_s = 0.50)

9. r for BTOR to Along-Track Position Error (mu_s = 0, sigma_s = 0.50)

10. PDA (mu_s = +1.5% or -0.8%, whichever is closer, sigma_s = 0.67%)

11. r for BTOR to Cross-Track Position Error (mu_s = 0, sigma_s = 0.50)

12. r for Along-Track Position Error to Cross-Track Position Error (mu_s = 0, sigma_s = 0.50)

Note that the sample means and sample standard deviations are different in the first 3 cases than the population means and population standard deviations. This is because our limited number of samples (5 generally) introduces bias in the statistics.

@DrB: For the correlation coefficients (r) that are expected to be zero, are the expected standard deviations of the sample really 0.5? That seems quite high.

@DrB

Thank you for the further explanation on the statistics used. Most of it I can follow; I need some time to fully absorb though. One question that arises now:

“Then I combine all the P-values using Fisher’s chi-squared method, which results in a combined P-value,”; Could you please explain more in detail? Can / did you consider to apply any weight factors there?

@Richard

Thank you for further explaining the approach in chosing the parameters in the systematic route evaluation study. I understand pragmatic choices have to be made to limit the total number of routes, as with all the degrees of freedom the multipication would otherwise quickly result in even larger numbers.

One of the reasons I asked for “nearby” cases is that it could help to check if the number of “knowns” is indeed enough for the number of “unknowns” (if not there could be lines / planes in parameter space of “fitting” routes).

@Niels

My choice of step size was not pragmatic.

I did a pre-study and concluded that the step size was sufficient to pick up regions of interest.

I was prepared to scan as many cases as necessary.

@Niels,

You said: ““Then I combine all the P-values using Fisher’s chi-squared method, which results in a combined P-value,”; Could you please explain more in detail? Can / did you consider to apply any weight factors there?”

Weighting factors can be applied in principle. However, I don’t have any reason, at the present time, to choose them, other than the possibility of assigning a lower weight to the “r” for BFOR with respect to Time. If one did that, or even ignored that parameter altogether, the overall outcome would not change.

Fisher’s method of combining percentiles is first to find chi squared:

X^2 = -2*SUM[ ln(P_i) ]

The number of degrees of freedom which is compared to chi squared is twice the number of statistics (2N = 2*10 or 2*12 depending on the lateral navigation method). Finally, the combined percentile is found using the chi-squared cumulative distribution. In EXCEL:

P = 1 – CHISQ.DIST(X^2, 2N, 1)

Here P is the percentage of random trials, assuming the route is TRUE, that are no better than the current fit. The index of 1 at the end indicates that a cumulative distribution is returned. Note also that when chi squared = 2N, P = 50%. Values of chi squared greater than 2N result in percentiles 50%. That is, since chi squared is a variance measure, the smaller the chi squared is, the better is the fit and the higher is the percentile.

@Richard

Where I was a bit surprised is in the limited number of FL/speed mode combinations. Given the changes in wind and temperature with FL, would that be enough to pick up (all) ROIs? And what about CI and possibly different Mach settings?

@Niels

Again the pre-study helped reduce the possible speed mode/ flight level combinations to ensure that a ROI would be found.

The 3 options were essentially high and fast , medium speed and medium altitude, and low and slow.

The aircraft performance prohibits certain combinations of speed mode and flight level.

In the pre-study I started with Constant Mach at 0.85 and reducing in steps of 0.01, without detecting a significantly different outcome in the standard deviation of the BFOR from step to step.

Similarly with the LRC, I started off reducing the flight level in steps of 10 without detecting a significant difference in the standard deviation of the BTOR from step to step.

We did try MRC and ECON CI52 as well, but again they are all variations of a well known theme.

Try running 615 scans and you will see what I mean.

@DrB

Thank you for the explanation regarding Fisher’s chi-squared method; that’s helpful!

@Richard

Ok, Richard, thank you for clarifying regarding the FL/speed mode combinations. This looks like a sensible approach/choice.

As said: I’m curious to see more on the results side; I’ll be patient.

@Richard

I was studying the results for my “Case A”, as you posted:

https://www.dropbox.com/s/b33b0b8wmew86mp/MH370%20Flight%20Path%20Model%20V19.4%20RG%20CTT%20LRC%20FL349.4%20211100%20UTC%20Niles%20Case%20A%20Revised%2011062019%20Full%20Report.png?dl=0

Possible sources of BTO errors that I have identified so far:

1. A non-zero RMS(deltaTAS) for mean(deltaTAS) = 0

2. Variance in the track

3. Along track position errors due to “smoothening” of the GS curve (intrinsic for the BTO interpolation method I use).

Especially (3.) could be reason for slight variation of the initial position in order to minimize overall BTO errors, however I have not been able yet to quantify possible along track errors.

For Case A (2.) could remain an issue, even if other sources are minor/minimized, so I’m also looking at a “Case C” where the variance in the track is much less in the 21:11 – 00:19 interval.

A question regarding the results for Case A (11/6): did you apply the 176.8933 degrees track all the way from 21:11 to 00:19?

That was what I had in mind when I proposed it in combination with FL 349.4.

As said, there is quite some variation in the track for Case A as produced by my tool, the 176.8933 is based on averaging the track over the 21:11 – 00:19 interval, and therefore seems a reasonable choice for the whole interval.

I share @TBill view that an active pilot COULD have engaged in planned maneuvers (item 11). Richard on June 14 declared that proposed maneuvers were disqualified. I raised the issue below before, but nothing was done to prove it not to be feasible and I do not have my own BTO/BFO model to prove it feasible. I would have liked to have seen BSTG insert a few programmed 20 minute holds at 20:00, 21:00, and 22:00 into their particle filter model to see what comes out.

The time of and the location at fuel exhaustion are separate, but related, problems. It is generally assumed that fuel is exhausted at 00:19 UTC (Arc 7) and MH370 entered a spiral dive into the ocean. The other problem is to define a viable flight path from a presumed location at 19:41 UTC that would cross arc 7 at 00:19 and the path must meet the BTO and BFO constraints.

If you assume no pilot or preprogrammed maneuvers after 19:41 and evaluate single setpoint navigation modes, the fuel exhaustion would be below 25 S on arc 7. The DTSG model center point was at 38S. It seems more recent analyses by this group may have it at 34S?

I believe that an active pilot COULD have planned to intentionally mess with the ability to perform post flight simulations by engaging in one or more planned delay maneuvers – such as a 20-minute circle at cruise airspeed.

If you assume that MH370 crossed arc 7 at 25S with zero fuel and followed a straight course from a known location at 19:41, how many time delays (at cruise airspeed) would be required along the route and meet all the BFO and BTO constraints at arc crossing times?

@Niels,

I learn something new every day. I found out from my comment above at 2:27 p.m. that if you put the symbols for “less than” and “greater than” in the same sentence, all the text in between gets deleted. Here is the complete text:

“Here P is the percentage of random trials, assuming the route is TRUE, that are no better than the current fit. Note also that when chi squared = 2N, P = 50%. Values of chi squared greater than 2N result in percentiles less than 50%, and values of chi squared less than 2N result in percentiles greater than 50%. That is, since chi squared is a variance measure, the smaller the chi squared is, the better the fit and the higher the percentile is.”

Wouldn’t it be nice if WYSIWYG?

@Hank

You stated “Richard on June 14 declared that proposed maneuvers were disqualified.”

Your statement is not entirely correct and misleading.

I was referring to “those” 5 flight paths proposed by @TBill, that were in my view disqualified.

I did imply that all flight paths with manoeuvres were disqualified per se.

You stated “nothing was done to prove it not to be feasible”.

For each case proposed by @TBill, I provided a link to a detailed flight model showing where the satellite data was not matched.

So it is simply not true, that nothing was done. I actually did quite a lot of work with @TBill’s 5 cases.

I also did not imply that there was no active pilot until the end of the flight.

On the contrary, I stated in my comment to @Peter Norton on 12th June 2019 “it is also possible that MH370 recovered from the steep descent and is beyond the +/- 30 NM from the 7th Arc, although this is significantly less likely in my view.” A recovery from a steep descent and glide beyond 30 NM implies, that I considered the possibility of an active pilot until the end of flight.

There is a full-length cover story on MH370 in the July edition of

The Atlantic.good article. thanks for sharing.

@Paul Smithson: Despite some technical errors, it is arguably the best article on MH370 to appear in a periodical.

@VictorI

Are middle-aged Malaysian pilots not allowed to mourn the passing of their youthfulness like men everywhere and go through a mid-life crisis?

Once again, yet another article casts aspersions on the pilot.

An otherwise excellent and intriguing article.

@Victor @ALSM

The Atlantic article helps a lot, but I would say PM Razak announced (under international pressure) intentional diversion about 8-days after the loss. Also the book by the same name Goodnight Malaysian 370 by Ewan Wilson/Geoff Taylor pretty much had the whole scanrio in their Sept_2014 book.

I was surpised, but in agreement, with ALSM quote of intentional depressurization after IGARI at high altitude.

One thing the article said, about interceptor jets, if they been launched by Malaysia, would have been able to look inside the cockpit. So my theory is the pilot was planning for a possible cockpit-look-in attempt. Therefore maybe @Victor is correct that the pilot put MH370 on auto-pilot near Penang so he could be absent from the controls if necessary. I also feel the pilot could have been in the co-pilot seat to allow view of Butterworth airfield out the window, and leave “proof” that the co-pilot seat was flying the aircraft.

Correction:

“Also the book by the same name Goodnight Malaysian 370 by Ewan Wilson/Geoff Taylor pretty much had the whole *scenario* in their Sept_2014 book.”

@Richard,

Sorry. My intent was not to question your overall comment. I have raised the issue of intentional holding to decouple range and endurance and this concept has been mostly just ignored during prior posts. And I have not been equipped with a simulation to investigate the feasibility myself. I do not believe that anyone else has looked at the feasibility either. This was my point and I did not intend any criticism of you and your work.

As a pilot and aero engineer, a straight cruise at 180 to fuel exhaustion couples the range and endurance problems. It also takes the aircraft as far south as possible. Because of this, if my objective was to hide the aircraft I would not fly directly 180 and I would decouple the range and endurance problem. I want zero fuel to minimize any slick, but max range is not relevant. A few periodic holds can add an hour of range uncertainty. Because the pilot would not know about the SATCOM pings it would require a very lucky sequence to result in a feasible sequence through the arcs. Intuitively there is enough time between the one hour pings for a more SSE course to fit. But there are infinite random possibilities of holds and routes to achieve a feasible BTO/BFO solutions. The NE-SW arc orientation means that any holds moves feasible courses from S to SSE or SE to meet arc crossing times. Clearly a SE or SSE course is not viable with the arc arrangement and fuel to zero at arc 7 without burning fuel without range – holding.

Sorry Richard for unintended criticism. I never get much discussion of why it is impossible that intentional periodic holding along a more SSE course might have resulted in crossing arc 7 above 25S and met all of the arc crossing times and BTO/BFO constraints.

I would have never used a 180 course because it’s too obvious to achieve max distance toward South Pole. Expect a search at max range at fuel depletion. Better to burn the fuel and not be on a 180.

..pilot was planning for a possible cockpit-look-in attempt.

really? wouldn’t it just be easier just to draw the curtains?

Re The Atlantic article.

Disappointed; the article made no attempt to explore any possible mechanical failure scenario. In my opinion, a crew O2 bottle rupture still can explain most of what happened on MH370 that night.

@All

In 2014, the ideal solution for PM RAZAK would be to assign the entire responsibility for deliberate redirection and all effects to the ZS. Why did not he finally use it (though he tried)? Today, the ATLANTIC article could not deny this recognition.

@All

I agree with the conclusion of the ATLANTIC article that solutions of the MH370 puzzle should be sought in Malaysia.

@Hank

No worries! I just wanted to put the record straight.

Here is a link to a LNAV flight path on an initial bearing of 167°T at a constant mach 0.80 and FL350, which ends at 26°S and matches the BTO satellite data and the fuel range and endurance with a PDA of 1.3%. This flight path does not match the BFO satellite data, but let us ignore that for the moment.

https://www.dropbox.com/s/s4136r0tf9uso4t/MH370%20Flight%20Path%20Model%20V19.6%20RG%20LNAV%20CM%200.80%20FL350%20167.0%20Hank%20no%20holding%20Full%20Report.png?dl=0

Here is a link to a similar LNAV flight path on an initial bearing of 167°T at FL350 ending at 26°S, but with a 20 minute holding pattern at 20:00 UTC. You can readily see how the BTO satellite data no longer matches at all. The BFO match is also poorer. The overall speed needs to increase from Mach 0.80 to Mach 0.8664 to make up for the 20 minutes holding. The holding pattern saves fuel, but the increased speed burns fuel. Mach 0.8664 is beyond the performance of MH370.

https://www.dropbox.com/s/gu44bxha2ol4cag/MH370%20Flight%20Path%20Model%20V19.6%20RG%20LNAV%20CM%200.8664%20FL350%20167.0%20Hank%2020%20minute%20holding%20Full%20Report.png?dl=0

As you say, ZS likely had no knowledge of Inmarsat satellite ping ring handshakes. The tracking possibilities have mostly been developed since the disappearance of MH370. Inmarsat only started to archive BTO and BFO data after AF447. Even if ZS knew, it would be an impossible task in my view to keep changing speed to meet the satellite handshakes at the right time and still meet fuel exhaustion at 00:17:30 UTC. There would have to be only short holds between the ping rings coupled with changes of speed or track to match the next ping ring.

So your conclusion that no pilot would select LNAV180 if he was trying to hide the aircraft, is based on the assumption, there was an active pilot trying to mislead a subsequent investigation.

What if there was no active pilot after say 19:30 UTC and the aircraft was just set on autopilot LNAV180 LRC at FL390 until fuel exhaustion?

Reverting to ET302; the BBC has published a fairly comprehensive article covering the major aspects of the accident and the surrounding after effects.

https://www.bbc.co.uk/news/extra/sd9LGK2S9m/battle_over_blame

Probably best viewed on a large display device.

@Victor Iannello,

You said: “@DrB: For the correlation coefficients (r) that are expected to be zero, are the expected standard deviations of the sample really 0.5? That seems quite high.”

The statistics of correlation functions are fairly well studied, and they generally require transformations before standard probability distributions can be used.

The Pearson correlation coefficient r is given by:

r = S_xy / (S_x * S_y) = [SUM(xy)/N] / SQRT{ [SUM(x^2)/N]*[SUM(y^2)/N] }.

Thus, r is simply the covariance of (X,Y) divided by the product of the standard deviations of X (= S_x) and Y (= S_y). That is why I said previously that the correlation coefficient is based on covariance. The correlation coefficient is invariant with respect to scale factor and offset.

The relatively high noise of the sample correlation coefficients is cause by the fact that generally there are two noisy variables being multiplied together in the covariance term. In addition, there are only 4 or 5 pairs of variables used, and thus there is not much noise reduction due to averaging.

The standard deviation of 50% is expected both theoretically [sigma_s = 1/SQRT(N-1)] with N = 5, and experimentally (average value of 600,000 trials is sigma_s = 50.05%).

For the 12 statistics used in the MH370 case, there are multiple categories of statistical analyses which I shall describe in detail in a later comment.

@DrB: Yes, I understand now. Simply said, you need more data to ensure that random points don’t fall on a line.

@Victor Iannello,

Exactly.

@Richard

Thanks for your response.

The DSTG model is reasonable for a ghost flight scenario. Even the infinite fuel assumption with post correction is not bad with no pilot to mess with intentional holding. LNAV 180 may have been programmed. I also can accept a undersea search could have missed wreckage. I have no reason to challenge any of the inactive pilot work.

My only point is what could an active pilot do to mess with the post simulation with no knowledge of SATCOM pings. If a pilot engaged LNAV 180 but broke off every hour for a 20 minute circle at cruise the plane would crash 500 miles or so early. Of course this would fail to meet all of the arc crossings and BFO/BTO data. The only feasible routes to reach arc 7 with 500 or so less miles is a more SE route such as the 167T. I will look at the links when I am at my PC.

Because there are infinite ways to have flown with holds it is possible that some combination could exactly meet the metrics. I think if you picked a specific end point you could construct a maneuvering profile that would fit the model. That does not mean it was followed – just possible. The problem with active pilot is too many option for route and water entry.

I have no reason to assume that there was a live pilot after 19:41. But I can’t rule it out either – who knows?

Thanks for the discussion.

Hank

I recently received a response from the FBI for my FOIA request related to the simulator data. My request was denied because there is a “pending or prospective law enforcement proceeding relevant to the responsive records.”

I suspect that this is a standard response for any FOIA request related to MH370, and not just for information related to the simulator data. As the disappearance may be due to criminal activity, and as there are still many unknowns, it is not surprising that the FBI chose to protect all data related to MH370.

@Hank

I apologise, I am obviously not communicating what I want to say very well.

In order to fly a path between an Initial Bearing of 160T and 170T at a cruise altitude around FL350 and meet the ping rings, the average Ground Speed needs to be between 459 knots and 482 knots.

The distance between 19:41:03 UTC and 00:11:00 UTC for FL350 is 2115.6 NM, which implies an average GS of 470.2 knots.

If you lose 500 NM through circling, then the rest of the flight has to be at around 600 knots to meet the ping rings.

A Ground Speed of 600 knots is simply impossible for MH370.

@Victor

Thank you for attempting the FOIA request. 10-bonus points for you.

Sounds like both USA and France (and others) are withholding MH370 info due to potential criminal act. By itself that says something. Seems like we ought to be able to ask, if that is true, what is the suspected crime? And why is it valid for Countries to hold that information indefinitely as a state secret? I am aware there is a possible (supposedly June_2019?) MH370 court case in Malaysia.

@Richard

Nederland and I both feel there seems to be a possible nominal “low and slow” 400 knot path from Arc4 (near BEBIM) to NZPG. @Nederland has actually published two versions of this path, one to NZPG, and his second path goes to WYKS. To accomplish that, MH370 woould presumably need a slow down at approx. BEBIM.

Nederland saw it first and published before me, so he gets any credit. I later indepedently noticed that ASTB’s early “low and slow” red flight path is almost identical to the ending of the home simulator path, is how I found it. Admittedly I and Nederland would welcome further IG review of that proposal.

My write-up is here:

https://twitter.com/HDTBill/status/1043496105252655105

@Richard

I did not mean to suggest the impossible. The problem I am posing is how do you fly at cruise airspeed at FL 350 from the assumed position at 19:41 and exhaust fuel at arc 7 above 25 S and meet all of the SATCOM constraints. This assumes s-turns or circles. Out of the infinite random possibilities it would seem one wiggly path could be found that met constraints and splashed above 25 S. I am not suggesting complex planning – just a result of some random maneuvering to decouple duration and range.

If a pilot assumed searchers would eventually figure a cruise start position at 19:41, he would also know for any course that a range line could be drawn E to W with some uncertainty. Any delays by holding or S-turns would widen the E-W band.

I have no reason to question this being a ghost flight on LNAV. This was the basis for the DSTG particle filter model and more recent work. Because some people believe that drift models may suggest a more northern location I questioned whether it is feasible (not likely) for a maneuvering flight path that meets all SATCOM constraints to exist.

Maybe it is not possible and the aircraft absolutely is located below 30S. And I am OK with that.

@Hank: It’s possible to construct a path that ends north of 25S. I devoted an entire post to an automated path that ends near 22S latitude after aligning with the airport at Cocos Island. CAPTIO has done a lot of work on a path that ends near Christmas Island. However, the criteria that Bobby is using would not allow these paths, which is why his work interests many of us.

@TBill said:

Sounds like both USA and France (and others) are withholding MH370 info due to potential criminal act. By itself that says something.I wouldn’t put too much weight on the FBI’s reply to me. It could be that at this point they can’t prove it was NOT a criminal act, so the case remains open, and releasing information would only hamper ongoing and future efforts.

I’ll add that on a single day, I submitted two FOIA requests related to MH370. One was on the subject of the simulator data, and the other was related to another aspect of the disappearance. The FBI lumped the two requests into one and replied with the letter I shared with the subject “Malaysian Airlines Flight MH370”. I suspect that ANY FOIA request related to MH370 gets the same response.

@Hank

Theoretically MH370 could have ended anywhere near the 7th Arc between 17°S and 39°S.

I appreciate that some people believe that the drift models may suggest a more northern location. I was one of them:

http://mh370.radiantphysics.com/2018/07/20/godfrey-drift-model-says-mh370-might-have-crashed-further-north-on-arc/

Fortunately, Bobby came to our rescue and showed that there is a wide range of possible MH370 end points that fit the drift analyses between 20°S and 35°S, some more likely than others. I no longer believe that the drift models are able to pin down the MH370 end point.

http://mh370.radiantphysics.com/2018/11/17/ocean-infinity-finds-argentine-submarine-after-not-finding-mh370/#comment-20181

For any given flight path, there is also not that much wiggle room to separate fuel range and endurance with manoeuvres and match the satellite handshakes between 19:41:03 UTC and 00:11:00 UTC as well as fuel exhaustion at 00:17:30 UTC between the 6th and 7th Arc.

@Richard

I really appreciate the work Bobby, you, and Victor have done recently (and previously). I liked your drift analytics a lot, and used them to conclude 20S was the Northern likely limit of terminal latitude.

If one uses simple logic to assign an equal probabily to terminal locations between 20S and 39S you can infer (using a 10% probabilty that the wreckage was missed) that there is a 90% chance the aircraft is in the 20S to 25S latitude range. I still do not want to consider areas beyond the current search width.

We have all seen this movie (analytically biased searching) before. I would be hard for me to do addtional searching below 25S until the 25S to 20S region has been searched.

Thanks Richard and Victor,

I have no reason to question the good work done by you, DrB, and others regarding a passive pilot from 19:41. A

LNAV 180 to cross arc 7 at 34.3 S is similar to the independent DSTG model with center at 38 S. These are directly associated with searched areas but debris could have been missed. All good work for an inactive pilot and there are good reasons why this may be true. I don’t question this model.

“Not much wiggle room” is not zero. I am NOT promoting an active pilot. It just seemed to me by looking at the NE-SW arc orientation that ground speed could be slowed at cruise airspeed by maneuvers and by probable accident the arc crossings would be met. Just dumb luck on a SE course. You indicate arc 7 can be limited to 17S to 39S so I was just thinking about how you get to the northern sectors and fit the SAT data. The duration is also key because you can’t cross arc 7 with lots of fuel at the NE sections.

It seems the IG has simulated viable flights to the NE sectors, which I was not aware.

Here are some articles that have recently appeared that rebut the article by William Langewiesche in the

The Atlantic.In Clive Irving’s piece in The Daily Beast, he brushes off the theory that the captain was responsible for the diversion because official statements and other reports say otherwise.

In an article in the

Malay Mail, former Malaysian minister Hishammuddin Hussein says that Langewiesche’s allegations are false, and his allegations can be debunked by authorities.@All: In Langewiesche’s article, there is a statement attributed to me that is incorrect, and should have been corrected by the fact-checkers assigned to the article.

Here is what appeared in the article:

Of all the profiles extracted from the simulator, the one that matched MH370’s path was the only one that Zaharie did not run as a continuous flight…Here is a portion of an email exchange with a fact-checker, who asked me to comment on this statement:

Fact checker: Of all the profiles on the simulator, the profile that matched MH370’s path was the only one that was not run as a continuous flight. Instead he had advanced the flight manually in multiple stages, subtracting fuel as he proceeded until the fuel was gone.

My response: We only have access to the flight files that were recovered from the Volume Shadow of drive MK25, so we don’t know how other sessions were conducted. It is true that the user “advanced the flight manually in multiple stages, subtracting fuel as he proceeded until the fuel was gone.”

@victor A number of noteworthy observations on the Atlantic piece by Aaron Connelly here: https://twitter.com/ConnellyAL/status/1140655256553975808?fbclid=IwAR2jDkvEsvR-dJ1vf4KM1xFrz5nwbsh4me367MHWcaxYYVc7Gu0TxLTu0xs

@koebeen: From that thread:

“Langewiesche has forgotten more than I’ll ever know about airplanes. The article is a compelling, heartbreaking read, and I suspect he’s right about Zaharie. But his portrayal of an entire political system as incorrigibly dishonest does not serve the interests of good analysis.”

The Malaysians hid, misled, and misinformed throughout this investigation. Whether or not the new administration does better remains to be seen.

@Victor

Najib has been out of office for over a year now. The new administration has already not done better in my view. Frankly, I think we have gotten all we are going to get from Malaysia. Different players same results.

@DennisW: You are probably right.

When (mis)translations of the Atlantic article reached Chinese audiences, it really stirred up quite a buzz, as it quickly became a trending topic on Chinese social media. Unfortunately, it was treated as another unfounded accusation on the pilot, and few bothered to read the original lengthy article. Many indeed have heard about the pilot’s simulator data, but thought it either had nothing to do with the event, or was “planted” by the US. That’s right, while Jeff Wise blames Russia, some Chinese folks blame the US. 🙂

Most people focused on 1) what ALSM was quoted as saying he believed the plane climbed up to 40,000 feet to accelerate the effects of depressurizing; and 2) what the anonymous “lifelong friend” of Zaharie’s had to say about his personal life.

Now, I understand the methodology Mike and other IG members used to reach the 40,000~43,000-feet conclusion, but did he really tell Langewiesche he thought the purpose was to accelerate depressurizing? Or was it another misquotation?

@haxi

I noticed at the 5th anniversary, a TV interview with I think the only China NoK who attended, the NoK said he had learned it was impossible for the pilot to turn off the transponder, so that’s why he knows the pilot did not do it. That was when I realized there was a disconnect.

@TBill,

Ha? Can you please provide the link to the interview? Because I happen to know the Chinese NoK member who attended the 5th anniversary event in Kuala Lumpur, and I can’t believe he said that. What I know is that, he taught himself a lot technical details in order to gain an understanding of the event. Could it be wrong translations?

@haxi

I will see if I can find it…

@haxi

Here is what I saw:

https://www.youtube.com/watch?v=YhxJ4hLth64

At 4:45 minute mark (according to the translator) Jiang Hui says that he believes turning off the transponder, manually by the pilot, sends an OFF signal (presumably to ATC). The fact that this “Transponder OFF” signal was not received from MH370 suggests there was an apparent mechanical issue (which cut off the transponder).

That statement made an impression on me because, I personally wonder if something like “Transponder OFF” signal might be a good thing to have in the future.

Thanks TBill.

Due to the voice-over, I can’t hear Jiang’s original words (whether he said “transponder” or something else). I’ll let him know. Maybe he confused the transponder with SDU log-off records.

@DennisW:

If Malaysia is incapable of assigning blame for the downing of MH17 where there is abundant evidence, how can we expect it to make reasonable conclusions and take reasonable actions regarding MH370, where there is less evidence?

Now in the news:

Malaysian Prime Minister Mahathir Mohamad said there’s “no proof” Russia is to blame for the 2014 downing of Malaysia Airlines Flight 17 over eastern Ukraine.“We are very unhappy because from the very beginning it became a political issue on how to accuse Russia of the wrongdoing,” he added. “So far there is no proof. Only hearsay.”@haxi

“Maybe he confused the transponder with SDU log-off records.”

The translator actually said “communications” so we do not know if Jiang was talking about Transponder, SATCOM, or radios. But the important point is that it certainly was possible for the MH370 pilot to manually turn off all communications without any warning signals.

@Victor

I still think it is significant that the very early stages of the MH370 diversion were “managed” by high level government officials, and not the usual resources assigned for that purpose. Even ICAO commented negatively on that activity.

@DennisW

In my view, the more important question is, if Ocean Infinity decide to go back and search, will the Malaysian government support their move and recompense a successful mission?

@Richard

Don’t know the answer relative to OI compensation, but it seems unlikely that it will be pledged by Malaysia. LANGEWIESCHE makes the point several times in the Atlantic article that Malaysia simply wants the whole issue to go away.

@DrB – this model is what I was hoping to hit all the data with a year or so ago. I lack the aviation knowledge to do what you’ve done so I was after a flight simulator with a CLI. It seems that doesn’t exist and I hit a wall and reluctantly gave up. I would very much like to throw some computing power at your model and come up with a long list of possible flight paths that fit the criteria you specify, with any number of turns, altitude changes and velocity changes. I have plenty – really, really plenty – spare overnight and at weekends. Perhaps enough for an effective exhaustive search over a month or two. Is there any chance we could work together on this? Some estimate of the required FLOPS per path would be great; that would allow me to estimate the path variation resolution we could target.

For the record, I fully expect the long list to be whittled down to an incredibly short list. But I want the numbers – all of them – down to the inch, if possible.

@DrB

I sort of agree with Rob’s sentiment that the most valuable contribution could be a model itself that could be used to gauge possible paths. Of course, if you have a clear definitve flight path answer, go with it. But I am having trouble seeing how active flight paths might not be better fit.

Also I am perhaps guilty of under-estimating the importance of the Atlantic article, which I need more time to review (tied up at the moment). But I think he is agreeing with me on active flight with active descent at end, think he is saying howver, intentional dive to blast aircraft into tiny bits, which implies close to Arc7 maybe 20-25 South due to active pilot, or maybe we missed due to small size of debris.

@TBill

I am having trouble seeing how active flight paths might not be better fit.An active flight path can always be created that is a better fit. That is not the point of the exercise.

@Richard

I have optimized “case C”. It has a much straighter track after 21:11 (more than ten times smaller variance) compared to “case A”. This comes at the cost of a slightly worse fit to LRC speed mode. It is still based on an assumed constant shift in bias frequency (to 151.5 Hz)

Could you perhaps help to evaluate the proposed route (21:11:02 onwards)?

The key parameters:

LRC to fuel exhaustion

FL 335.3

21:11:02 position of -9.191, 93.692 (11 km)

Constant track after 21:11:02 of 178.098 degrees (based on the average track over the 21:11 – 00:19 interval)

@Niels,

Interesting that your case “C” LRC track above leads direct to waypoint EKUTA -39.843334° 95.000000°

@Ventus45

Interesting, I’ll check more in detail. I already noticed it passes quite close to waypoint BEBIM (which is at -10.645, 93.835).

@DrB VI et al

How is the coriolis pseudo force handled by the different navigation methods?

Compensatory trim would increase fuel usage. Is this incorporated into the fuel model?

@flat pack: It has negligible effect on fuel consumption compared to other effects like wind, which is incorporated into the model. With autopilot engaged, it has no effect on the trajectory.

@DrB. Do we know the accuracy boundaries for wind, temperature and density altitude data on the different routes, particularly in the remote regions?

@TBill

@DennisW

@Victor Ianello

@Richard

I have effectively limitless computing capacity at my disposure for about three months. I just want to throw this model at everything that, no matter how unlikely, could potentially have happened and rule out 99.99% of the ridiculous flight paths and EOF locations. Please, let’s just get it done?

@TBill, @Niels

@TBill stated “@Richard Nederland and I both feel there seems to be a possible nominal “low and slow” 400 knot path from Arc4 (near BEBIM) to NZPG.” and “Admittedly I and Nederland would welcome further IG review of that proposal.”

@Niels stated “@Richard I have optimized “case C”. It has a much straighter track after 21:11 (more than ten times smaller variance) compared to “case A” and “Could you perhaps help to evaluate the proposed route (21:11:02 onwards)?”

I have noted both requests and will get to running the flight paths suggested through my model in the coming week.

I am very busy at the moment, helping to prepare the next paper that Bobby, Victor and I will publish here soon, describing the wide area scan of the Southern Indian Ocean.

@Rob Moss

Thank you for your kind offer, but what you are suggesting has already been done. Bobby, Victor and I have performed a systematic study during the last 4 months of all possible flight paths and are soon to publish the results.

In total 1,372 flight paths have been analysed, of which 828 flight paths since the start of this systematic study on 17th February 2019. Start latitudes from 16.0°N to 4.3°S have been covered and the start longitudes were unconstrained. Start times from 18:41:00 UTC to 19:32:00 UTC, but the final major turn had to be completed before the 2nd Arc at 19:41:03 UTC was reached.

Systematic initial bearings from 155°T to 195°T in steps of 1°T were analysed, plus some exotic cases in steps of 0.1°T. All navigation methods were : LNAV, CTT, CTH, CMT and CMH, all speed modes: Constant Mach 0.80 to 0.85, LRC 0.7047 to 0.8408, MRC, ECON CI52 and all flight levels: from FL290 to FL430. The fuel endurance was allowed to vary around 00:17:30 UTC and the resulting PDA was noted. The PDA was allowed to vary from the nominal 1.5% and the possibility that the bleed air was shut off for part or all of the time was considered.

You may have seen in the comments above, that I have in addition run a number of candidate flight paths from @TBill, @Niels and @Hank.

@Richard,

I look forward to your (collective) forthcoming paper that describes your method for generating and evaluating each path versus the particle filter Monte Carlo approach taken by BSTG as described in their book.

It seems that you select an exact navigation model and setup with maybe random winds aloft and then evaluate that profile using the arc crossing data to assign a probability for that model.

I had issues with the dynamic model used by DSTG to generate the “infinite” flight paths. Although I assume their PDF for the “infinite” flight paths may bear some relationship to the more likely explicitly programmed paths in your set of cases.

@DennisW noted “An active flight path can always be created that is a better fit. That is not the point of the exercise.”

“I still wonder whether one simple profile could exist where an active pilot could have flown to fuel exhaustion north of 25 S on arc 7 and “perfectly” met the arc crossing data constraints. Maybe it is not remotely possible?

@Dennis @Don

Does the coriolis pseudo force get felt by say a micro mechanical accelerometer?

In the case of MH370 the GPS apparently corrects the IRU with notional accelerations.

However if the GPS were somehow disabled by the pilot and if the IRU actually did drift then the pre-comp calculation could be off.

@TBill, @Nederland,

@TBill stated “Nederland and I both feel there seems to be a possible nominal “low and slow” 400 knot path from Arc4 (near BEBIM) to NZPG.” and “Admittedly I and Nederland would welcome further IG review of that proposal.”

In your linked paper, you state “it appears that MH370 could have instead flown due south, perhaps from BEDAX to BEBIM, in effect taking a shortcut down to the flight sim pathway” and “working backwards from Arc7 suggests waypoint BEBIM might have been the focal point for the pilot to change heading to fly towards McMurdo Station (NZPG), assuming an approximate 400 knot ground speed.”

You describe the test flight conditions that you applied:

Atmosphere: Set to 80 deg F at Sea Level

Winds: 0

Altitude: FL250 = approx. 25,000-ft

Heading: 168 deg South (True)

Ground Speed: 400 knots

True Air Speed: 400 knots = Mach 0.65

Indicated Air Speed: 275 knots

Flight Path: ISBIX to BEBIM to 78S67 (NZPG)

(1) BEDAX is at longitude 93.787575°E, ISBIX is at longitude 93.675108°E and BEBIM is at longitude 93.835000°E, so this route is not quite due south. I took waypoint BEBIM for the turn to NZPG, which I estimate was reached at 21:26:45 UTC.

(2) NZPG is at -77.963333°S 166.524444°E, which is close to your 78S67 waypoint. The initial bearing from BEBIM to NZPG is 168.12019548°T (Vicenty).

(3) FL250 at your surface temperature of 80°F (26.7°C) and a surface pressure of 1012 mB gives an air pressure at FL250 of 376.0041 hPa and a geometric altitude of 25,986 feet.

(4) I applied your Mach 0.65, but included the effect of air temperature and winds at FL250. In order to reach your latitude of 28.911°S at 00:11:00 UTC precisely, I slightly reduced the Mach after waypoint BEBIM to 0.642856.

The BTO and BFO results are excellent. My only concern is the high PDA at 00:17:30 UTC of 3.861% (nominal 1.5%), which represents around 1,470 kg fuel remaining at MEFE.

Here is a link to a detailed flight path report:

https://www.dropbox.com/s/m49r59myjljdrg2/MH370%20Flight%20Path%20Model%20V19.7%20RG%20LNAV%20CM%200.65%20FL250%20180.0%20BEBIM%20Diversion%20Full%20Report.png?dl=0

@flatpack

Modern inertial reference systems are good for about 30nm of error over an 8 hours flight without GPS aiding. A 30nm position error would have a negligible effect on Doppler compensation.

@All,

There are four varieties of statistical analyses which I employ in my new method of MH370 route fitting.

To review, a list of the statistics I use is:

1. Mean BTOR (mu_s = 0, sigma_s = 12.97 microsec, 5 samples)

2. STDEV BTOR (mu_s = 27.30, sigma_s = 9.90 microsec, 5 samples)

3. STDEV BFOR (mu_s = 3.90, sigma_s = 1.73 Hz, 5 samples)

4. Pearson’s correlation coefficient r for Leg Start BTOR to Leg End BTOR (mu_s = -0.237, sigma_s = 0.447, 4 sample pairs)

5. r for Leg Start BFOR to Leg End BFOR (mu_s = -0.237, sigma_s = 0.447, 4 sample pairs)

6. r for BTOR to BFOR (mu_s = 0, sigma_s = 0.50, 5 sample pairs)

7. r for BTOR to Time (mu_s = 0, sigma_s = 0.50, 5 sample pairs)

8. r for BFOR to Time (mu_s = 0, sigma_s = 0.50, 5 sample pairs)

9. r for BTOR to Along-Track Position Error (mu_s = 0, sigma_s = 0.50, 5 sample pairs)

10. PDA (mu_s = +1.5% or -0.8%, whichever is closer, sigma_s = 0.67%, 1 sample)

11. r for BTOR to Cross-Track Position Error (mu_s = 0, sigma_s = 0.50, 5 sample pairs)

12. r for Along-Track Position Error to Cross-Track Position Error (mu_s = 0, sigma_s = 0.50, 5 sample pairs)

In this list, I use the subscript “s” to denote “sample” statistical values, as opposed to “population” values. The sample standard deviations are smaller than the population standard deviations. Generally speaking, there are 5 samples (and in two cases of autocorrelation there are 4 pairs of samples). I denote the expected values by “mu” and the standard deviations by “sigma”. BTOR is BTO residual. BFOR is BFO residual.

1. The first category of statistics used in my new MH370 route fitter is the simplest. It applies to normal random variables, such as the Mean BTOR (my statistic #1 in the list above) and STDEV BTOR (#2). In this case we know that for the True Route the mu_BTOR = 0 and the population sigma is 29 microseconds. The expected value of the calculated sample mean BTOR (with N = 5) is zero, and 100,000 random trial sets of BTORs gave a mean of -0.07 microseconds. The sample standard deviation of the mean BTOR with 5 samples is expected to be 29/SQRT(5) = 12.97 microseconds. The 100,000 trial sets gave an average (sample mean) standard deviation value of 12.98 microseconds. So, the trials match the expected statistical values very closely for the BTORs.

The sample BTOR standard deviation is less than the population standard deviation of 29 microseconds, because of the limited number of samples. 100.000 trial sets had an average value of 27.30 Hz. The observed standard deviation of the sample BTOR standard deviation was expected to be 29*SQRT(1-9*PI()/32) = 9.90 microseconds, and the 100,000 trials gave an average of 9.90 microseconds.

So, the mean and standard deviation BTOR statistics appear to behave as expected.

In this category we simply find the Z transformation statistic as:

Z = ( Value – average sample mean) / sample standard deviation

and we find the percentile P (in EXCEL) from:

P = 2*NORM.S.DIST(-ABS(Z),1)

where the factor of 2 is needed because of the cumulative single-tailed normal distribution function used in EXCEL. We must use the absolute value of Z because we don’t know its sign. Here P is the percentile of random trials which are worse than the current fit, assuming the route is True.

I also treat the Performance Degradation Allowance (PDA, #10 in the list above) as a normal random variable and use the same analysis method. Recall that the PDA is determined by adjusting it so that Main Engines Fuel Exhaustion is predicted to occur at 00:17:30 UTC. The PDA is not a random variable in the strictest sense, but it has the same characteristics of interest in this problem. The expected value of the PDA is nominally the MH370 Flight Plan value of 1.50% (average of both engines in cruise). However, because we cannot rule out the possibility that the air packs were turned off at Diversion, the effective value could be much less averaged over the remainder of the flight. The impact of the air packs being off is about 2.3% in fuel savings, or an equivalent PDA of -0.8%. So, to allow for this possibility, I allow the PDA expected value to be either +1.5% or -0.8%, whichever is closer to the best-fit value. The uncertainty in the PDA is caused by the errors in the fuel consumption model. Based on comparisons with previous flights and with Boeing fuel flow tables, I have previously estimated that uncertainty to be 2.0% at the 3-sigma level. Thus one sigma is 0.67% in PDA. Treating the PDA in this fashion allows me to estimate a probability that the route being fitted matches the expected PDA. It also allows me to incorporate PDA as one of numerous statistics being evaluated to produce a single overall figure of merit for the fitted route. The PDA percentile is calculated as described above for the BTOR statistics using the Z transformation and the normal distribution.

2. A second category of statistical analysis is the STDEV BFOR (#3 in my list above).

I use an empirical method to match the DSTG’s empirical density function of the BFO reading errors. This involves generating normal random values having a zero mean and a population standard deviation that itself is a uniform random variable from 1 to 7 Hz. The average value of 100,000 trial sets of 5 BFORs was 0.004 Hz and the average population standard deviation was 4.35 Hz. This is in agreement with the DSTG estimate for BFO reading errors with outliers excluded. To find the percentile value, I find the Z transformation as follows:

Z = (value – average sample BFOR standard deviation ) / standard deviation of sample BFOR standard deviation

The average value of the sample BFOR standard deviation was empirically found to be 3.90 Hz using 100,000 trial sets of BFORs. This is in agreement with the theoretical value of 4.35*SQRT[ (5-1) / 5 ] = 3.89 Hz. The second factor in this equation is the reduction in the population standard deviation to the sample standard deviation. When we have a limited number of samples, there is a bias to a lower expected value than the population sigma. The standard deviation of the sample BFOR standard deviation was found to be 1.73 Hz. Then, using the equation above, I find Z and then the percentile P.

Using this method, the RMS errors in the percentiles from 1%-99% is low, being only 0.7%. Thus, my statistical model for the BFO standard deviation is accurate over the range of percentile values of interest.

3. The next two classes of analyses deal with correlation coefficients – those with zero expected value and those with a non-zero expected value.

Recall that the Pearson correlation coefficient r is given by:

r = S_xy / (S_x * S_y) = [SUM(xy)/N] / SQRT{ [SUM(x^2)/N]*[SUM(y^2)/N] }.

When the expected value of r is zero, the correlation coefficients are analyzed statistically using Student’s distribution, employing the t transformation:

t = r*SQRT[(N-2)/(1-r^2)],

where N = 5 pairs. The number of degrees of freedom is thus N – 2 = 3. Now “t” is approximately normally distributed, and the percentiles are found using the two-tailed cumulative Student’s distribution with 3 degrees of freedom. In EXCEL, this is:

P = T.DIST.2T[ABS(t),3].

Note the absolute value of t is used, since we don’t know the expected sign of t, and we must allow for both the positive and negative tails.

Using 600,000 sets of 5 pairs of uncorrelated random values, I get an expected value of -0.0009 (i.e., zero) and a standard deviation of 0.5005 (i.e., 50%) for r. The standard deviation is high because both variables are random and the number of pairs is small. For 600,000 trials of t, I get an expected value of 0.004 and a standard deviation of 1.723. The observed percentiles match the expected fractional percentages within 0.15% RMS for percentiles from 1% to 99%, so the statistical model is actually quite accurate. This method of analysis applies to those correlation coefficients which have an expected value of zero, which are # 6-9, 11, & 12 from the list above.

4. For the two autocorrelation cases of BTOR w.r.t. BTOR and BFOR w.r.t. BFOR, N = 4 (pairs) and the expected value is not zero. This applies to the statistics #4 and 5 in my list above. Using 200,000 random trials for this case, the expected value of r was mu_r = -0.237 (i.e., -23.7%) and the standard deviation was sigma_r = 0.446 (i.e., 44.6%).

Fisher’s F transformation is used in this case to obtain an approximately symmetric normal distribution from the asymmetric r distribution:

F = (1/2)*ln[(1+r)/(1-r)] = arctanh(r).

Due to the nonlinear transformation, the mean of F is slightly different than the mean of r (mu_F = -0.311).

Next we find the normalized Z-score:

Z = [F – mu_F] / sigma_r.

Note that in the equation above for Z above I use sigma_r, not sigma_F, because I found this substantially improved the accuracy of the predicted percentiles. The percentile is then found from the Z statistic using the two-tailed cumulative Student’s distribution (the same as in the zero-mean case above):

P = T.DIST.2T[ABS(Z),3].

The number of degrees of freedom in this case is N – 1 = 3 with N = 4 pairs of variables. The observed percentiles using 200,000 trials matched the expected percentages within 0.7% RMS from 1%-99%. The predicted percentiles with non-zero mean r are not quite as accurate as the zero-mean r case because the r distribution is asymmetric. Two transformations (F and Z) are needed to obtain an approximately symmetric distribution with the correct shape to match a standard distribution (like normal, chi squared, or Student’s). Still, the accuracy is more than adequate for the problem at hand.

Combined Percentile

Once the P-values for all 12 statistics (10 in the case of LNAV) are calculated, the last step is to combine them into a single percentile estimate. Fisher’s method of combining percentiles first finds chi squared:

X^2 = -2*SUM[ ln(P_i) ]

The number of degrees of freedom which is compared to chi squared is twice the number of statistics (2N = 2*10 or 2*12 depending on the lateral navigation method). Finally, the combined percentile is found using the chi-squared distribution. In EXCEL:

P = 1 – CHISQ.DIST(X^2, 2N, 1).

Again, the (combined) P-value is the percentage of random trials, assuming the route is True, that would be expected to fit the data worse than the current route. One can think of the P-value as being the probability that the route is True, and ratios of P-value therefore represent relative probabilities that the route is True.. The combined percentile is used in my objective function and is maximized by my route fitter. The expected value for the combined percentile is 50% for the True route. Half the trials would fit worse, and half would fit better. A combined P-value above 50% can occur half the time. If a fit has a P-value well above 50%, that implies either that (a) an additional degree of freedom in the route model (beyond the seven minimally required) is being fitted (thereby artificially reducing the residuals), and/or (b) the MH370 Inmarsat data have somewhat smaller-than-average scatter. To test this situation, I have embedded a means to inject random BTO and BFO reading errors into my route fitting program. When I do that for a fairly large number of trials using the one best-fit route (LNAV 180 through BEDAX), the average combined P-value is close to 50%. From this result I conclude that the excess in best-fit combined P-value (it is close to 80%) for that one route using the actual MH370 data is more likely to be caused by the actual MH370 data set than by over-fitting the route.

@Rob Moss,

I echo Richard’s sentiments. Thank you for your offer, but I believe our combined ROI search efforts over the past several years are adequate.

@TBill,

@DennisW,

Regarding “But I am having trouble seeing how active flight paths might not be (a) better fit”, I will say that, from a statistical point of view, no active route can be SUPERIOR to the LNAV 180 route through BEDAX.

It’s easy to create maneuvers during “active” routes which result in smaller BTO and BFO residuals, but that does not mean they are more likely. In fact, the smaller the residuals are than their expected values, the LESS likely is the route.

The LNAV 180 BEDAX route appears to be the only passive route which is fully consistent with statistical expectations. One can create active routes which are EQUALLY likely, but not significantly MORE likely.

@David,

You asked: “Do we know the accuracy boundaries for wind, temperature and density altitude data on the different routes, particularly in the remote regions?”

The simple answer is, not as well as we would like to know them.

Richard has compared a limited set of temperature and wind measurements made by 9M-MRO during MH371 with GDAS data. This will be reported in our next paper. Roughly, the temperature differences were about 1-2 C and the wind differences were about a knot in speed and several degrees in direction. I note that this latter result is superior to the expected GDAS global wind errors. It indicates that with our 4-D GDAS route models, we can predict the ground speed with systematic errors in the range of 1 to several knots, and this is most useful in discriminating routes. It is an integral part of my new route fitting method, because synthesizing small ground speed errors for each leg (mostly caused by GDAS errors), is the only way to segregate the systematic route errors from the random BTO reading errors using the MH370 data set.

In an interview with CNN, Malaysian Prime Minister Mahathir suggests that MH370 was hacked and diverted remotely.

This comes on the heels of his claim that there is no proof that Russia downed MH17.

@Victor

Mahathir raised the possibility of a remote take over shortly after MH370 disappeared, when he also accused the CIA of withholding information:

CIA withholding information on flight MH370, says former Malaysian PM Mahathir Mohamad

Many years ago, the former Australian prime minister, Paul Keating, labeled Mahathir Mohamad as a ‘recalcitrant’ and he is well known for his antipathy towards Western countries. For example, it was reported in

The Australianthat Mahathir oncespeculated that the 9/11 events were staged by the US “as an excuse to mount attacks on the Muslim world”:CIA ‘role’ alleged in plane mystery

Further to my previous comment, any hopes that Mahathir’s return to power would see Malaysia open up on MH370 are highly misplaced, in my opinion.

On another matter entirely, the following article from

The Seattle Timesis a very good account of how the implementation of MCAS on the B737 MAX went so horribly wrong:The inside story of MCAS: How Boeing’s 737 MAX system gained power and lost safeguards

@Andrew,

Re:

The Seattle Timesarticle.The legal eagles at Boeing will be under a fair bit of pressure, and the lid hasn’t yet been put on the pot.

The rather duplicitous actions described in the article permeating throughout the design, engineering, testing, certification and managerial levels of the organization; seemingly at the behest of the executive, can only be described as “chilling”.

And the excuse; not to let Airbus gain the lead in the short / medium haul market.