Search Recommendation for MH370’s Debris Field

[This is the web version of a paper written by me, Bobby Ulich, Richard Godfrey, and Andrew Banks. The PDF version is available here.]

1 Introduction

Presently, there is no active search to find MH370’s debris field on the seabed of the Southern Indian Ocean (SIO). The last search was conducted by Ocean Infinity, who consulted with official and independent researchers, and subsequently scanned the seabed along the 7th arc as far north as S25° latitude. Since then, independent researchers have continued to analyze the available data to understand what areas of seabed are the most likely, and why previous search efforts have been unsuccessful. The objective is to define a manageable area for conducting a new search of the seabed.

In a previous post [1], we presented an overview of Bobby Ulich’s research [2], aimed at more precisely locating the point of impact (POI) using statistical criteria that requires that random variables (such as the reading errors of the satellite data) are not correlated, i.e., are truly random. A subsequent post [3] describes the work of Richard Godfrey et al. [4] to analytically evaluate a large number of candidate flight paths using these and other criteria. The results of that work suggest that the final hours of the flight were due south in the Indian Ocean along E93.7875° longitude, which matches a great circle between the waypoint BEDAX (about 100 NM west of Banda Aceh, Sumatra) and the South Pole. The POI was estimated to lie close to the 7th arc around S34.4° latitude.

Work continues to evaluate candidate paths using an accurate integrated model that includes satellite data, radar data, flight dynamics, automated navigation, meteorological conditions, fuel consumption, drift models, and aerial search results. That exhaustive work is nearing completion, and documentation of the methods and the results is ongoing. Like the previous work [4], the ongoing work suggests that the final trajectory of MH370 was most likely along a due south path along E93.7875° longitude.

In the interest of providing information in a timely manner, we have chosen to recommend a search area based on this most likely path. A comprehensive paper which expands upon the methods and results presented in previous work [2,4], and provides further justification for the selected path, will be available in the near future.

2 Best Estimate of Point of Impact

Using the results of the analysis presented above, the best estimate (BE) of the point of impact (POI) is based on a final trajectory of a constant longitude of E93.7875°, which is consistent with the aircraft traveling due south from waypoint BEDAX towards the South Pole. The BE of the POI is based on an impact exactly on the 7th arc, and the uncertainty associated with this BE is helps define the limits of the recommended search area.

When the SDU logs onto the Inmarsat network, the SDU begins the log-on sequence by first transmitting a log-on request, which is followed some seconds later by transmitting a log-on acknowledge. For MH370, those were the final two transmissions, transmitted at 00:19:29 (BTO = 23,000 μs) and 00:19:37 (BTO = 49,660 μs), respectively. From past work [6,7], we also know that the BTO values for the log-on request and log-on acknowledge are “anomalous” in that the raw values are outliers that require a correction. Fortunately, the required corrections are repeatable, and can be determined by analyzing prior flights.

Using the Inmarsat transaction logs for MH371 and MH370 [8], the BTO log-on statistics from March 7, 2014, 00:51:00, to March 8, 2014, 16:00:00, were analyzed to determine what offsets might be applied to log-on requests and log-on acknowledges. There were 29 cases in which there was an R-channel burst just after the initial (R600) log-on request and subsequent (R1200) log-on acknowledge. Of those 29 cases, the number of packets in the burst was 3 for 20 bursts, 2 for 6 bursts, and 1 for 3 bursts. The average of each burst was used as the reference for the log-in request and log-on acknowledge. In 4 of the 29 cases, the correction for the log-on request was near zero, i.e., the BTO values were not anomalous, so only 25 cases were included for log-on request statistics.

For the log-on requests, the mean offset from the R-channel burst is 4,578 μs with a standard deviation of 94 μs. The maximum offset was 4,800 μs (+222 μs from the mean) and the minimum was 4,380 μs (-198 μs from the mean).

For the log-on acknowledge, we considered a correction of the form (a + N × W), where a is a constant, N is an integer, and W represents the delay per slot. We found that the standard deviation of the correction error (using the average of the R1200 burst as the reference) to be minimized for W = 7812.0 μs. That’s very close to the 7812.5 μs value suggested by the 128 Hz internal clock of the SDU. By forcing W=7812.5 μs, the mean error to the correction is 23 μs, and the standard deviation is 30 μs. The observed standard deviation is very close to the 29 μs that DSTG recommends to use for “normal” R1200 values [7]. The consistency of the standard deviation of the corrected anomalous values with the standard deviation of the values not requiring a correction is reassuring. The total correction to the BTO for log-on acknowledges is therefore (23 + N × 7812.5) μs.

Using these log-on corrections produces corrected BTO values at 00:19 equal to:

00:19:29: 23000 – 4578 = 18422 μs
00:19:37: 49660 – 23 – 4 × 7812.5 = 18387 μs

We combine these values to determine the BE value of BTO by using the inverse of the variance as weighting, yielding a BE value of BTO = 18,390 μs (σ = 29 μs). Using this BE value of BTO with the longitude of E93.7875° and an assumed geometric altitude of 20,000 ft results in a position of S34.2342° E93.7875° at 00:19:29, which we assign as the BE of the POI.

3 Terrain Near the BE POI

Figure 1 shows the subsea terrain in the vicinity of the BE POI using data provided by Geosciences Australia [5]. Some of this area has already been searched by GO Phoenix (managed by the ATSB) using a towfish, and by Ocean Infinity (OI) using Seabed Constructor and its team of AUVs. However, as can be seen in Figure 1, some of the previously searched area has challenging terrain with steep slopes, and the debris field may have been either not detected due to terrain avoidance or shadows, or detected but not properly interpreted by reviewers. In particular, there is a steep slope that lies about 20 NM due south of the BE POI that was not scanned by the towfish and appears to have been only partially scanned by the AUVs.

Figure 1. Terrain in the vicinity of the BE POI

Figure 2 shows the ocean depth along a line of constant longitude in the vicinity of the BE POI. The previously identified steep slope to the south of the BE POI has a grade of about 30%. To the north, another slope has a grade of 44%. This slope was beyond the limits of the search boundaries of GO Phoenix, but was scanned by Seabed Constructor’s AUVs.

Figure 2. Ocean Depth at constant longitude and +/- 46 km (+/- 25 NM) from the BE POI

4 No Pilot Inputs after Fuel Exhaustion

In order to define the search area limits, we first consider no pilot inputs after fuel exhaustion. For this case, the search area limits are defined by the uncertainty of the BE POI and the uncertainty of the uncontrolled flight path before impacting the ocean.

4.1 Uncertainty Due to BTO Noise

The uncertainty in the BTO produces a corresponding uncertainty in the position of the 7th arc. The calculated sensitivity of the arc position to the BTO is 0.104 NM/µs, i.e., a 1-µs increase in BTO pushes the 7th arc outward (southeast) by 0.104 NM. The 1-σ uncertainty of the arc position due to BTO noise is therefore 0.104 NM/µs × 29 µs = 3.0 NM.

4.2 Uncertainty Due to Altitude at 00:19:29

The BE POI is based on an assumed altitude of 20,000 ft that is reached at 00:19:29, i.e., 1.5 to 2 minutes after fuel exhaustion. As the BTO represents the range between the aircraft and the satellite, the position of the 7th arc as projected on the surface of the earth depends on the altitude. As the aircraft would be between 0 and 40,000 ft at this time, we assign this altitude range as the 2-σ limits. The calculated sensitivity of the BTO to altitude is 12.8 µs/10,000 ft. The 1-σ uncertainty of the arc position due to altitude uncertainty is therefore 0.104 NM/µs × 12.8 µs = 1.33 NM.

4.3 Uncertainty of Turn Between Fuel Exhaustion and 00:19:29

Boeing conducted 10 simulations to determine the behavior of MH370 after fuel exhaustion with no pilot inputs [9] using a high-fidelity simulator for the 777-200ER aircraft. The trajectories for these simulations are shown in Figure 3. For each simulation, the autopilot was automatically disengaged after fuel exhaustion, and the aircraft turned slightly either to the right or to the left depending on a number of factors, including the electrical configuration, the initial conditions of the flight parameters, and the meteorological conditions. Within the 2-minute interval between fuel exhaustion and the log-on request at 00:19:29, the slight turn shifted the location that the aircraft crossed the 7th arc relative to where it would have crossed the 7th arc if the autopilot had remained engaged and the course was maintained. For the 10 cases, the lateral shift along the arc varied between 1.1 and 8.8 NM. As we don’t know how well the 10 cases represented the actual conditions, we conservatively assign a 1-σ uncertainty of 8.8 NM along the 7th arc due to the slight turn between fuel exhaustion and crossing the 7th arc.

4.4 Uncertainty of Trajectory Between 00:19:29 and the POI

In all 10 of the Boeing simulations, the aircraft banked after the autopilot was disengaged following fuel exhaustion. The magnitude and direction of the bank that develops is the net effect of a many factors, including thrust asymmetry, rudder inputs from the Thrust Asymmetry Compensation (TAC), rudder trim input, lateral weight imbalance, aerodynamic asymmetry, and turbulence, any of which increases the bank angle. On the other hand, the tendency to bank is opposed by the dihedral effect of the wings and the low center-of-mass. For all the simulations, the POI was within 32 NM from the 7th arc crossing at 00:19:29, as shown in Figure 3.

Figure 3. Calculated end-of-flight trajectories from the Boeing simulations [9]

In some of those simulations, the bank was shallow, and phugoids lasting many minutes developed. In only 5 of the simulations did the rate of descent exceed 15,000 fpm while also experiencing a downward acceleration exceeding 0.67 g, which are the values of descent rate and downward acceleration derived from the two final values of the BFO. For these cases, the POI occurred between 4.7 and 7.9 NM from the point where the descent rate first exceeded 15,000 fpm. Other simulations of a banked descent after fuel exhaustion [10] suggest that an uncontrolled Boeing 777 would travel an additional distance of about 5 NM after a downward acceleration of 0.67 g and a rate of descent of 15,000 fpm simultaneously occur.

None of the Boeing simulations predict that the aircraft was in a steep descent as the 7th arc was crossed, so there is an unexplained discrepancy between the Boeing simulations and the descent rates derived from the final BFO values. In light of this discrepancy, we choose to not limit the distance traveled after crossing the 7th arc by only considering the distance traveled after the steep descent. Instead, we assign a 2-σ value of 32 NM for the distance traveled after crossing the 7th arc, based on the farthest distance that was observed in all 10 simulations, irrespective of the magnitude and timing of the descent rates.

4.5 Uncertainty Due to Navigation Error

There are two autopilot modes that could result in a trajectory that nominally follows a great circle between BEDAX and the South Pole. After passing BEDAX, if the autopilot remained in LNAV and the active waypoint was the South Pole (entered as 99SP, S90EXXXXX, or S90WXXXXX), the aircraft would fly along the longitude E93.7875° within the accuracy of the GPS-derived navigation. In this case, the expected navigational error would be much smaller than other sources of error, and can be safely ignored.

The other possibility is that after passing BEDAX, the autopilot was configured to fly along a constant true track (CTT) of 180°. Selecting this mode would require manually changing the heading reference switch from NORM to TRUE, as directions on maps, procedures, and in ATC communications are normally referenced to magnetic north, except in polar regions.

Unlike LNAV mode in which the cross-track error of the target path is continuously calculated and minimized, errors in track (which may be positive or negative) in CTT mode produce error in the due south path that may accumulate without correction. We assume here that that course is nominally 180° True, with a 1-σ uncertainty of 0.1 deg (0.001745 rad). As the distance between BEDAX and the 7th arc along the line of constant longitude is around 2365 NM, the cross-track error has a mean value of zero and a 1-s uncertainty of 4.1 NM. However, since the path crosses the 7th arc at an angle of 46 deg, the 1-σ uncertainty in position along the 7th arc is increased to 5.9 NM.

4.6 Search Area Based on No Pilot Inputs

Assuming there were no pilot inputs after 19:41, the uncertainties in the POI are summarized in Table 1. The 1-σ uncertainty along the 7th arc is 19.2 NM, and 16.3 NM normal to the 7th arc.

Table 1. Summary of POI Uncertainties Assuming No Pilot Inputs

To achieve a confidence level of 98% requires searching an area defined by ±2.3-σ limits, with the BE at its center. Based on this, the recommended area is 91 NM × 74 NM, and the total area is 6,719 NM2, or 23,050 km2. This area is depicted as A1 in Figure 4.

Figure 4. Search recommendation, showing areas A1, A2, and A3

5 Controlled Glide Due South

We next consider the case in which there was a controlled glide after fuel exhaustion, which would extend the search area beyond the search area based on no pilot inputs. For a Boeing 777 gliding at an optimum speed, a glide ratio of about 20:1 can be achieved. This corresponds to a descent angle of 2.86°, and a continuous reduction in altitude of 1000 ft for every 3.29 NM traversed. Assuming an initial altitude of 42,400 ft (based on a standard altitude of 40,000 ft), the impact could be as far as 140 NM from the point of fuel exhaustion (ignoring the headwind at some altitudes, which would reduce the ground distance of the glide). If the glide started at a lower altitude, or if non-optimum airspeed was flown, the glide distance would be less. The uncertainty associated with the glide distance is much larger than other uncertainties, so we assume that with a glide, the POI might have been as far as 140 NM from the BE POI, and use that as the southern limit.

The width of the search area as defined by a controlled glide is more difficult to estimate. If an experienced pilot wished to continue the flight path on a due-south course, that could be accomplished quite precisely. For example, if the autopilot mode was CTT before the fuel exhaustion, then a constant (true) track of 180 deg could be maintained using the indicated track shown in the navigation display. On the other hand, if the autopilot mode was LNAV before fuel exhaustion, then the cross-track error could be minimized by following the “magenta” line defined by the BEDAX-South Pole leg. In either case, the search area width could be limited to less than 10 NM to either side of the projected flight path.

Because we cannot be sure that there was an attempt to precisely follow a due south path, we assign a generous width to this part of the search area, centered on the due south path. A width of +/- 33 NM results in an additional search area of 6,300 NM2 (22,000 km2), and produces an area in similar size to A1. It is depicted as A2 in Figure 4.

6 Controlled Glide in an Arbitrary Direction

If there was a controlled glide that did not continue along the path flown prior to fuel exhaustion, it is nearly impossible to predict the direction. For instance, a path to the west would shield the pilot’s eyes from the rising sun to the east. A path to the northeast would extend the glide due to the tailwind. A path to the west would create more distance to the Australian shoreline. A path towards the northwest would be towards Mecca. Any of these directions is less likely than a continuation of the due south path, but it becomes nearly impossible to prioritize among these or other directions. Instead, we define area A3 as the circle with a radius of 140 NM, excluding the areas already included in A1 and A2. The area is roughly 48,400 NM2 (166,000 km2), and is depicted as A3 in Figure 4.

7 Conclusions

Recent analyses suggest that MH370’s flight path in its final hours followed E93.7875° longitude, corresponding to a great circle path between waypoint BEDAX and the South Pole. Using this result, the best estimate (BE) for the point of impact (POI) is S34.2342° E93.7875°. Although some of the subsea was previously searched in this vicinity, the terrain is challenging, and the debris field might have been not detected, or detected and misinterpreted. There is also the possibility that there was a controlled glide after fuel exhaustion, and an impact well beyond what was previously searched.

To define the search area near the BE POI, three cases were considered, each with an associated search area. The highest priority search area of 6,719 NM2 (23,050 km2) assumes there were no pilot inputs after fuel exhaustion. The search area of next highest priority encompasses 6,300 NM2 (22,000 km2), and assumes there was a glide towards the south after fuel exhaustion. The lowest priority is the controlled glide in an arbitrary direction with an area of around 48,400 NM2 (166,000 km2).

8 References

[1] Iannello, “A New Methodology to Determine MH370’s Path”, May 31, 2019, https://mh370.radiantphysics.com/2019/05/31/a-new-methodology-to-determine-mh370s-path/

[2] Ulich, Technical Note presented in [1].

[3] Iannello, “A Comprehensive Survey of Possible MH370 Paths”, June 30, 2019, https://mh370.radiantphysics.com/2019/06/30/a-comprehensive-survey-of-possible-mh370-paths/, excerpted from [4].

[4] Godfrey, Ulich, Iannello, “Blowin’ In The Wind: Scanning the Southern Indian Ocean for MH370”, June 24, 2019, https://www.dropbox.com/s/9rpcnslz9g4izet/2019-06-30%20Blowing%20in%20the%20Wind%20-%20Scanning%20the%20Southern%20Indian%20Ocean%20for%20MH370.pdf

[5] “MH370 Data Release”, Geosciences Australia, https://www.ga.gov.au/about/projects/marine/mh370-data-release

[6] Ashton, Shuster-Bruce, College, Dickinson, “The Search for MH370”, The Journal of Navigation, Vol 68 (1), January 2015.

[7] Davey, Gordon, Holland, Rutten, Williams, “Bayesian Methods in the Search for MH370”, Defense, Science, and Technology Group, Australia, November 30, 2015.

[8] Iannello, “The Unredacted Satellite Data for MH370”, June 12, 2017, https://mh370.radiantphysics.com/2017/06/12/the-unredacted-inmarsat-satellite-data-for-mh370/

[9] Iannello, “End-of-Flight Simulations of MH370”, August 2018, https://mh370.radiantphysics.com/2018/08/19/end-of-flight-simulations-of-mh370/

[10] Iannello, “MH370 End-of-Flight with Banked Descent and No Pilot”, June 4, 2017, https://mh370.radiantphysics.com/2017/06/04/mh370-end-of-flight-with-banked-descent-and-no-pilot/

50 Responses to “Search Recommendation for MH370’s Debris Field”

  1. airlandseaman says:

    Thanks for the new post Victor. As discussed off line, I support all of the work you, Richard, Bobby and Andrew have documented in this new paper, except for the assumed max L/D. Regarding the three cases you describe:

    • No Pilot Inputs After Fuel Exhaustion
    • Controlled Glide Due South After Fuel Exhaustion
    • Controlled Glide in an Arbitrary Direction After Fuel Exhaustion

    …for the case of “No Pilot Inputs After Fuel Exhaustion”, the estimates are reasonable and well supported by the data and analysis (assuming the path was straight south). However, for the second and third cases (Controlled Glide), the assumed maximum gliding distance (140 nm) is based on the theoretical maximum “clear air” L/D ratio m (~20:1), while practical experience suggests a shorter maximum gliding distance.

    My analysis in support of a maximum glide distance of 97-110 nm can be downloaded here: http://bit.ly/2GMxzBo

  2. Richard says:

    @airlandseaman

    You question the range and L/D ratio regarding the piloted glide scenario.

    In our paper, the probability of this worst case estimate of 140 NM actually happening is described as the lowest priority. I agree with you that a glide to 140 NM is a “theoretical maximum”, however I never forget the case of the “Gimli Glider”, which you also mention in your paper. This accident was not theory but a real experience. The Gimli Glider was a B767, that lost pressure in both fuel pumps over Red Lake, Ontario (CYRL) and first diverted at 41,000 feet toward Winnipeg, Manitoba (CYWG), then 120 NM distant. The 39 NM distance from Gimli at the start of the emergency, you mention in your paper is factually incorrect.

    “The first signs of trouble appeared shortly after 8:00 p.m. Central Daylight Time when instruments in the cockpit warned of low fuel pressure in the left fuel pump. The Captain at once decided to divert the flight to Winnipeg, then 120 miles away, and commenced a descent from 41,000 feet. Within seconds, warning lights appeared indicating loss of pressure in the right main fuel tank. Within minutes, the left engine failed, followed by failure of the right engine. The aircraft was then at 35,000 feet, 65 miles from Winnipeg and 45 miles from Gimli.” Final Report of the Board of Inquiry into Air Canada Boeing 767 C-GAUN Accident Gimli Manitoba July 23, 1983.

    The pilots realised that they might not reach Winnipeg still 65 NM distant and decided to divert to Gimli, Manitoba (CYGM) then only 45NM distant. On approach to Gimli, the pilots realised that they still had too much speed and altitude and performed various glider manoeuvres to slow the aircraft and maintain the glide path including executing a slide-slip. The total distance flown from the start of the emergency over Red Lake to Gimli was over 100 NM and the pilots initially thought they could reach Winnipeg 120 NM away. 140 NM does not seem an unreasonable limit.

    We have presented our search recommendation with a clear differentiation between the highest priority areas and the lowest priority areas. I am confident that MH370 will be found in the higher priority areas, but if not, then we cannot exclude the lowest priority areas.

  3. airlandseaman says:

    Richard: I’m aware of all that.

    RE “The 39 NM distance from Gimli at the start of the emergency, you mention in your paper is factually incorrect.”

    I never stated anything about a 39 nm distance. I’m not sure where you read that, but it was not from me. What I wrote was:

    “In the case of C-GAUN (the “Gimli Glider”), the captain of the flight was an experienced glider pilot who was aware of the best speed to fly for maximum L/D (~220 kts). Flying at that speed, the FO estimated the glide performance over a 10 nm period during which the aircraft lost 5,000 feet for an effective L/D =12.1.”

    I agree the Gimli experience is based on real (767) data.

    Mike

  4. Andrew says:

    I sent the following to Mike in an offline discussion:

    “ I agree it’s important to not over estimate the potential gliding range. However, I think we all agree that it’s also important that we don’t cut things too fine and risk missing the debris field altogether, especially given the lack of data on the realistic gliding range of these aircraft and the actual atmospheric conditions at the time. In that light, I think the 140 NM that was proposed is a reasonable upper limit for what might theoretically be achieved under ideal conditions.

    I think we also agree that the probability the debris field will not be found within the primary or secondary search areas is somewhat remote. If the aircraft is not found within those areas, I would expect that any search of the tertiary area would start towards the centre (excluding the primary/secondary areas) and work outwards. Perhaps we should recommend that a search of the tertiary area should not proceed outside, say, 100 NM until the entire area inside that range has been searched.”

  5. airlandseaman says:

    Andrew: I agree with that characterization.

  6. Andrew says:

    @Richard
    @airlandseaman

    RE: “The 39 NM distance from Gimli at the start of the emergency, you mention in your paper is factually incorrect.”

    The Canadian accident report only mentions ‘miles’ and does not specify if the distances are statute miles or nautical miles. There is no mention of ‘NM’ anywhere in the report. A distance of 39 NM is the equivalent of 45 statute miles, so perhaps the 39 NM mentioned in the ATSB table that Mike included in his paper is simply a conversion of the ’45 miles’ in the accident report.

  7. Niels says:

    @VictorI et al.
    Thank you for the new article, which I appreciate for both the timing and the “operational” character of it. It can help the discussion forward.
    From a scientific point of view: the question how likely it is that BEDAX-SP (LRC) is the path that was followed, is still on the table. Nevertheless, also based on my own analysis, I feel reasonably comfortable with S34.3 at the 20000 feet 7th arc as a “centerpoint”.

    In the operational spirit of your article and taking into account:
    – What I know about your analysis of the satellite data
    – My own analysis of the satellite data
    – The recent article by sk999
    – The CSIRO debris drift analysis
    – Doubts about the reported “effectiveness” of the “GO Phoenix” / SAS search effort,

    I would tend to add an area (say A4) to the recommendation, stretching between S32.5 and S36.0 along the 20000 feet 7th arc, up to a width of about 25 nm at both sides of the arc.
    My current recommendation would then be to scan in the order A1, A2, A4, A3 or perhaps even A1, A4, A2, A3.

  8. David says:

    @Victor. I hope the reception of your collective work is commensurate with the effort put into it.
    Thank you for the clear presentation.

    Observations:
    • 4.3 “….the slight turn shifted the location that the aircraft crossed the 7th arc relative to where it would have crossed the 7th arc if the autopilot had remained engaged and the course was maintained.” I hope this is back-to-front since that would eliminate the “turn after fuel exhaustion” element in search planning.
    To me the final transmission is at the arc and that location shift should be applied backwards to the point of fuel exhaustion.
    • The first 4.4 Another good reason for not favouring the 4.7 to 7.9 NM is that doing so would imply the aircraft was in an abnormal configuration – and that would need justification.
    • Second 4.4. (Presume this should be 4.5, et seq?) Is the CTT route materially less probable? If so that could affect search priorities.

    About the effect of the APU on the farthest distance the aircraft could glide unpiloted, based on your home simulations and the manuals that could be expected to tighten left spirals, shortening the throw of those if anything. However for the right spirals, albeit both of the abnormal configuration, it is conceivable these could have been straightened. Still, I would have thought the probability of the spiral being one of those and, if straightened, that the flight would remain that way would be low.

    One other effect of APU operation, based on the greatly increased fuel consumption of its in-flight operation, is the appreciable effect its open intake can have on drag. However unpiloted I would expect that would reduce time in the air and so, all else being equal, distance.

    In a piloted glide over a distance it would be reasonable to assume that a lack of IFE connection was the result of the APU being unable to access all the residual fuel, the glide also being steepened a little from APU inlet drag. Alternatively it might have taken a while for the pilot to realise the APU had started and had shut it down at that point. (I will not go into what else he might have done.)

    • Now your 5. A 42,400ft starting altitude for a glide takes no account of the energy height lost in the descent needed for the final transmissions even though some could have been recovered. APU drag would cost more, that running for say 3½ mins (its inlet door will shut on APU failure).

    Regarding the glide search width for A2 you say, “Because we cannot be sure that there was an attempt to precisely follow a due south path, we assign a generous width to this part of the search area….”.
    I think it reasonable to suppose that his gliding would be with a distance purpose, that is he would glide in a straight line. In that case the glide area should be an rectangular still but could be of reduced width, that including just the ‘BTO Noise’, ‘Altitude’ and ‘Navigation Error’ from your Table 4.6, plus the 10NM either side that you mention.

    Search Priorities: For my part, the unsearched areas should be the priority. The first should be that unsearched part of the 30˚grade to the south, followed by the unsearched glide area, which would be from about 34.9˚S, width as above, to say 100NM from the POI; ie about 36˚S (as per the below to @Richard I agree with ALSM). The third should be your A3 unsearched areas followed by the remaining A3, noting that the simulations suggest little prospect directly under the POI (that’s why I have preferred to call it the Final Transmission Point!)
    Thence, review as to what next, depending on the time taken already etc and it may be an ask to seek a commitment to that now.
    There might be some search priority fine tuning based on the CTT route probability as above.

    @Richard. Re the 100 NM, from your quote the second of the Gimli glider’s engines failed at 35,000 ft, when the glide to Gimli was just 45 miles. The rest was powered: evidently to that point they had hoped the residual fuel on pump failure would last longer….
    They decided they may not make Winnipeg, 65 miles (presumably NM) away. Even so, that would have required just a 12:1 glide ratio assuming no headwind, that allowing a couple of thousand feet overhead there.
    So they thought they might not achieve even that glide ratio.
    To get to Gimli needed just 8:1.

    Subtracted from the best L/D clean there is also drag from the RAT to consider and in MH370’s case, the APU inlet drag for part of it.

  9. David says:

    @Victor. A logical refinement to my above is that assuming a straight glide, instead of the glide area being rectangular it is an isosceles trapezoid, tapering out reach the 10NM either side just at 100Nm from POI.

  10. Mick Gilbert says:

    @Victor Iannello
    @DrB
    @Richard
    @Andrew

    Gents, thank you and congratulations on this body work. I think we all understand how much time and effort has gone into it.

    From a purely pragmatic perspective, have you presented this work to anyone who can actually do something with it? If so, any initial reaction that you can discuss?

  11. Richard says:

    @airlandseaman

    You attached a paper that you wrote in your initial comment. In this paper you have a table that clearly states the maximum distance from the start of the emergency for the Gimli Glider was 39 NM.

    The emergency started at 41,000 feet over Red Lake and the captain immediately diverted to Winnipeg and started descending. Red Lake waypoint (CYRL) which was en-route between Montreal and Edmonton is 149 NM from Winnipeg Airport. The closest point of the actual lake called Red Lake is 140 NM or 161 statute miles from Winnipeg Airport.

    “the aircraft ran out of fuel over Red Lake, Ontario” Final Report of the Board of Inquiry into Air Canada Boeing 767 C-GAUN Accident dated July 23, 1983.

  12. David says:

    @TBill. Below are tank capacities. From the SIR fuel loads the figures are not much off yours, ullage being 3,112 US Queen Anne gallons (older than the Imperial!). However there is no space much when the main tanks are full (a little in vent channels) unless you count the surge tank (overflow) capacity. I have not found a figure for that. Normally no fuel in there.

    I have not yet had a look at your references thanks and how you come by 1700 gals of air dissolved in the fuel. That seems a lot in 16,008 gals of fuel; over 10%!!. More than Coke? Also, what is there takes a fair while to be drawn out by low atmospheric pressure.

    I think your scepticism of vapour lock in the gravity feed, “downhill” is justified, based on @Andrew’s advice as to NNC statements about that. As to the effect of a near empty tank I am unsure the NNC addresses that and presume there could be vortices that might cause air entrainment and leave residual fuel on flameout thereby. Then again the engines might just cough a bit, the combustion chambers flash igniting.

    Naturally none of that addresses APU “uphill” vulnerability.

    https://www.dropbox.com/s/cj81be99g2xfnro/777-200%20tank%20capacities.pdf?dl=0

  13. Richard says:

    @Mick Gilbert, @Niels,

    Mick asked “From a purely pragmatic perspective, have you presented this work to anyone who can actually do something with it?”

    Niels stated “From a scientific point of view: the question how likely it is that BEDAX-SP (LRC) is the path that was followed, is still on the table.”

    We received a request from Ocean Infinity to make a search recommendation, if possible by the end of January 2020, and we carved out that section of the upcoming paper and turned it into the self standing paper that Victor has published above. This paper was sent to Ocean Infinity in response to their request, just prior to its publication on this web site.

    We continue to finalise the full paper, which is meanwhile 50 pages long excluding appendices. As mentioned, a “comprehensive paper which expands upon the methods and results presented in previous work [2,4], and provides further justification for the selected path, will be available in the near future.” We fully appreciate in releasing the search recommendation without the full paper, that the full justification for our recommendation is missing. I can assure that the comprehensive paper will provide that full justification.

  14. Mick Gilbert says:

    @Richard

    Thanks Richard. I have no doubt that you fellows will have the BE POI nailed down six ways to sunset.

    I was curious as to whether anything is likely to come of it. And if OI were on the front foot asking for a recommendation then it sounds like there’s a live possibility that something might. That’s heartening.

  15. airlandseaman says:

    Richard: Sorry for any confusion about the Gimli Glider glide ratio. The Gimli 12.1:1 glide ratio was not derived from any information in the Table published by ATSB (39 nm distance). It was derived from information contained in the official Canadian Accident Report and other reports that described the procedure used by the crew to estimate the glide ratio in real time. They estimated the glide ratio by noting the altitude (read from the back up cockpit altimeter) at several points along the radar derived path. ATC gave the crew positions and distances. From those positions, they worked out the glide ratio. The numbers they used were: 5000 ft drop in altitude over a 10 nm path.

    Andrew and I discussed this off line. We agree that 12:1 is probably very conservative. The crew was under considerable pressure and needed a conservative estimate. The sample space was short (only 10 nm or 2-3 min). So it was probably on the conservative side.

    OTOH, in the case of C-GITS, the plane glided from 34,500 feet to 13,000 feet over a distance of 57 nm (effective L/D=16.1) before circling to land at Lajes Air Base in the Azores. This information can be found in the official accident investigation report. The average over a 57 nm stretch will be more accurate than the 10 nm sample in the case of the Gimli Glider.

    Thus, 16:1 is probably a very good estimate of the typical, achievable glide ratio, notwithstanding a somewhat higher theoretical L/D ratio.

  16. Richard says:

    @airlandseaman

    No worries!

    If 16:1 L/D ratio is a very good estimate of a typical achievable glide ratio, what is your best estimate of a worst case or conservative value, to be absolutely sure of the maximum range calculation.

  17. airlandseaman says:

    Richard: For the purposes of defining the area for a “controlled glide” scenario, either due south or random, I would limit the radius to 100 nm. That is consistent with 16:1 and 38000 feet starting altitude. Obviously, neither is an absolute certain number, but I believe 100 nm would surely cover 99+% of the possible glide scenarios.

    Note that people have flown gliders with a 20:1 L/D hundreds of miles, working areas of thermal, ridge or wave lift along the way. It really depends on the atmosphere you are flying through. But given the location and time of day, convection was probably not a significant factor, so realistically, 100 nm is a good number for budgetary purposes. If you don’t find it within 100 nm, go back and search further up and down the 7th arc. That would be a better bet than searching out to 140 nm.

  18. Niels says:

    For clarity, I made an illustration of the areas “A4” I wanted to introduce for the discussion

    https://www.dropbox.com/s/sfvkpyr9egpw3rn/A4_added_cropped.png?dl=0

  19. Victor Iannello says:

    @airlandseaman: As you said in a private email, in Appendix 1.6E, page 8 of the Final Report, Boeing advises:

    In general, the airplane could achieve an estimated driftdown range of 0.0034 nm per foot of altitude. Therefore, at FL350 the additional range after the dual engine flame-out would be approximately 120 nm and at FL400 it would be approximately 136 nm.

    Boeing’s descent angle corresponds to (L/D) = 20.7. We assumed a value of 20.0, based on lift and drag calculations using the “Obert curves” for the B777-200 at near optimum glide speed and a slightly higher (geometric) altitude. While our assumptions for glide distance may be optimistic and may not be achievable in practice, we also have to be careful about recommending a distance that might miss the debris field. In that regard, our glide calculation of 140 NM is consistent with Boeing’s advice.

  20. Victor Iannello says:

    @David: I agree that a case can be made to progressively increase the width of the search in the southern direction. However, compared to A2 that was proposed, I think we would narrow the width at the northern extreme rather than extend the width at the southern extreme. Considering that A1 is already wide at that latitude, I’m not sure there would be significant savings in search area.

  21. Victor Iannello says:

    @David said: Presume this should be 4.5, et seq?

    Another reader sent me a private email with this and one other correction. Those corrections should be already incorporated in both the web and PDF versions.

  22. Victor Iannello says:

    @Niels said: From a scientific point of view: the question how likely it is that BEDAX-SP (LRC) is the path that was followed, is still on the table.

    In some ways, we have put the apple cart before the horse in recommending a search area without full justification for the priority placed on the BEDAX-SouthPole path. However, the full paper has taken much longer to complete than anticipated, and there was a request to see our results. Hopefully, the full paper will be completed and released in the coming weeks, and the justification for the BEDAX-SouthPole path can be more fully debated.

    I should add that while the same four authors are writing the full paper as the search recommendation, the first two authors will be Bobby Ulich and Richard Godfrey. The search recommendation summarized in this blog post will be a part of the full paper.

  23. Victor Iannello says:

    In the article above, there is mention of the subsea terrain, and the difficulty in obtaining sonar data due to terrain avoidance and shadowing, especially for the towfish.

    Don Thompson has been analyzing the quality of the data collected by GO Phoenix, and has some interesting results. Perhaps he can comment on what he is finding.

  24. TBill says:

    @Victor and the Team
    Thank you so much for the new post!

    What was new for me was the visual detail of the cliff-obstructed search area, which seems to be both the Go Pheonix and OI areas. Trying to see how far off Arc7 that is. I seem to recall OI lost an AUV around there and had to go back for it. A nominal 180 South path was a earlier favorite of mine too, so sounds like at least filling those data gaps is readily agreed, and perhaps OI saw that and perhaps already knows that is an outstanding action item, perhaps bolstered after the experience from ARA San Juan. That specific detail would be a limited search objective though.

    @David
    Thank you for taking a look at the fuel model and also the design tank capacities and at least they give us a presumed fuel density close to my guess. Now if we only knew the actual KLIA MH370 fuel density.

    My understanding is the amount of oxygen (and nitrogen) dissolved is not totally understood…one reference says the data sources of O2 solubility ranges from about 40-80 ppm. Looks like the simple “DIY fuel tank model” is a little on the high side but for our purposes probably fine. The pro versions of the flash models give users a lot of choices of thermo systems conceivably we could find a best fit. I like the way the model shows how O2 dissolves more than N2 and such. If you want to calc the solubility, plug in the numbers and just do the flash at 14.7 psia and eg; 70F. You can use the UNIT button choose your favorite units of measure.

  25. Victor Iannello says:

    @TBill said: I seem to recall OI lost an AUV around there and had to go back for it.

    You have a good memory. Seabed Constructor made a 5-km circle centered on (-34.9564, 93.7768), which would be about 44 NM south of the BE POI, and only about 6 NM to the west of its longitude. That point falls within area A1.

  26. Niels says:

    @VictorI, Richard
    I understand the reason to do it like this, and appreciate you shared the recommendation soon, which is before the full paper could be finalized and shared. It makes the discussion a bit complicated though. I tend to agree with your A1, but for the discussion about what would be the next priority (A2, A4(A), A4(B), other?) it would indeed be important to have the info as complete as possible: preferably including your full paper. Also in this respect, it would be really nice to have some more info from Don regarding his sonar scan (meta)data re-analysis. I’ll be patient. I don’t want to push or criticize anyone in this regard: an enormous voluntary effort has been put in to come to the point where we are now.

  27. Victor Iannello says:

    Some of you might wish to independently explore the subsea data, which is available from Geoscience Australia’s Web Map Service (WMS). Using the WMS, data can be loaded dynamically into Google Earth (GE). The resolution of the sonar data seems to be less than what is stored on the Geoscience data warehouse, but the convenience of using GE is very attractive.

    Here’s how to create the dynamically-loaded overlay in GE:

    Go to Add/Image Overlay/Refresh/WMS Parameters/
    Add the following WMS: http://marine.ga.gov.au/geoserver/marine/wms
    Select which layers you’d like to add and “OK”
    Name the layer

    That’s it!

  28. David says:

    @ALSM. Re @Richard’s request for your “best estimate of a worst case or conservative value, to be absolutely sure of the maximum range calculation”, I note that at the ATSB’s Definition of Underwater Searches 3 Dec 2015, p18 they describe a simulation (presumably RAT deployed and by Boeing) where the glide was 125 miles from 33,000 ft, ie L/D of 23. Looks high but there it is.

    Another factor: unless the glide also allows a ditching some height will be lost in a final dive.

  29. Pax Lambda says:

    Some probable rantings…

    What to look for? And how?

    The past searches on the ocean floor seems to have focalized on debris around a cubic meter in size. The search was “systematic”, like grass mowing and the work has been “gigantic”. Nothing related to MH-370 have been found on the ocean floor: Or the wreckage is outside the search zone, or the debris field was missed. There is no other solution. But is there another way to find MH-370?

    Twenty something parts have been found: two very big (the flapperon and the outboard flap) and small ones. Many small parts were found by Blaine Gibson: How does he proceeded? Just looking on the beaches were currents from SIO could have brought them. There are kilometers and kilometers of coast line were debris could have landed: From Tanzania to South Africa, there are thousand of kilometers and even if BG has searched many, he could have only looked at a very few of the possible landing places. Some others have also found some parts, just by chance.

    The meaning of that is there are many debris which beached, the vast majority not reported: Too small, not recognizable and mostly not seen. I think that imply the plane has shattered on impact. How much debris? Thousands? Millions? And why there are also quite intact parts like the flapperon and the outboard flap? Could those two have detached in air before high speed impact of the main frame? Perhaps we can’t know before the wreck is found, but the high number of small parts is certain: if not, Blaine could not have found so much debris. And if there were tens of thousands floating parts, there has to be also many which have sunk.

    If tens of thousands parts have sunk, the debris field have to be large: the depth is in the order of kilometers and with currents, difference of “sunkability”, difference of shapes, a debris field in the order of one kilometer seems realistic. Ten thousand parts in one square kilometer (that is 1 million square meters) give around one debris for 100m², that is a 10 x 10 meters square. But the debris “concentration” could be lower at distance of the impact point. Supposing those guessed figures: say there are at least one 5cm² debris for 20 x 20 meters at 500 meters of the impact point. If we take a picture of this 400m² surface, to “see” a 5cm² part, 400m²/5cm² that is “only” 0.8 million pixels that is required. Take 10 times more “to be sure”: a 8 millions pixels picture of 20 x 20 meters of seabed every kilometer is enough.
    Are the guessed figures above realistic enough? Is this kind of search possible?
    It seems to me that “eye search” on pictures (or live cam) could be more efficient that automatic “radar” ones: the human “eye” (the brain, in fact) is very sensible to geometric “anomalies” and shattered parts on the seabed will be such anomalies as long as the “marine snow” have not concealed them: The time is against this search possibility. Is it too late?

    Sorry for my English… and for the length of the post…

  30. DennisW says:

    @Victor,

    I will simply say your last summary was not what I expected. You say

    That exhaustive work is nearing completion, and documentation of the methods and the results is ongoing. Like the previous work [4], the ongoing work suggests that the final trajectory of MH370 was most likely along a due south path along E93.7875° longitude.

    There is nothing in your narrative to support your assertion that a path due South along E93.7875 is most likely.

  31. Victor Iannello says:

    @DennisW: That wasn’t the purpose of this article. That will be explained in the paper that has not yet been released.

  32. paul smithson says:

    @Victor et al. Thanks for the new post. This does a great job of explaining the basis for the search area magnitude and priorities having assumed that a specific path was flown. I am still looking forward to the principal document that demonstrates the uniqueness of the “due south from Bedax” solution.

    I also look forward to hearing more about the “effective coverage” of the Go Phoenix and OI searches in this area. The magnitude of your top priority area corresponds to the whole of A1. Are you recommending that the parts of A1 that have already been searched be searched again? Or only those parts with data holidays?

  33. Victor Iannello says:

    @Paul Smithson asked: Are you recommending that the parts of A1 that have already been searched be searched again?

    That’s a good question. It would depend on the quality of the data. I don’t think we’re ready to make that determination. The investigators identified “data holidays” for offtrack, terrain avoidance, equipment failure, low probability of detection, and shadows. Even the “good” data might have some issues if the towfish’s height above the surface was not properly maintained. Don tells me the SAS technology requires accurate positioning to get good results.

    I’m expecting Don to chime in today. He can tell us more.

  34. paul smithson says:

    @Victor. Thanks, I look forward to Don’s inputs.

    In the same vein, your Fig 4 indicates in yellow the limits of the ATSB search. To put your A1 recommendation in context, it would be useful to show OI-searched areas on there as well. Eyeballing Fig 1, it looks like ATSB+OI is about 36NM wide? Implying that (excluding data holidays) nearly 50% of A1 has been searched. Does that sound about right?

  35. Richard says:

    @DennisW

    You stated “ There is nothing in your narrative to support your assertion that a path due South along E93.7875 is most likely.”

    Niels previously stated “From a scientific point of view: the question how likely it is that BEDAX-SP (LRC) is the path that was followed, is still on the table.”

    I previously explained: “We received a request from Ocean Infinity to make a search recommendation, if possible by the end of January 2020, and we carved out that section of the upcoming paper and turned it into the self standing paper that Victor has published above. This paper was sent to Ocean Infinity in response to their request, just prior to its publication on this web site.”

    “We continue to finalise the full paper, which is meanwhile 50 pages long, excluding appendices. As mentioned, a ‘comprehensive paper which expands upon the methods and results presented in previous work [2,4], and provides further justification for the selected path, will be available in the near future.’ We fully appreciate in releasing the search recommendation without the full paper, that the full justification for our recommendation is missing. I can assure (you) that the comprehensive paper will provide that full justification.”

    Why not read the previous comments first, before shooting from the hip?

    Victor even used the analogy of the cart before the horse. Even you must understand that picture.

  36. DennisW says:

    @Richard

    <i.Victor even used the analogy of the cart before the horse. Even you must understand that picture.

    Yes, I saw that analogy, and I don’t mean to shoot from the hip. I am just very dissappointed that the crux of analysis remains missing. The latest post is just a piece of fluff, IMO. Hard to imagine anyone putting any serious weight on it.

  37. Sid Bennett says:

    @Richrd

    While I can claim expertise in navigational instruments, the accuracy of inertial navigation is something I only know by rule of thumb. The cross track error, statistically, grows as the sqrt(t) since the initiation of the flight.

    It would be a great help to those of us who are still concerned with the totality of the path prior to the 7th arc if you would at least publish the track parameters (albeit as preliminary results).

  38. TBill says:

    @David
    Many thanks for the jet fuel theory info.

  39. Victor Iannello says:

    @Sid Bennett: The cumulative navigation error does not grow with time for modern navigation systems that incorporate GPS.

  40. Joe says:

    Wow. Thank you for all of your efforts. I hope a future search benefits from this.

    Do you think the debris drift analysis can help? It would seem like the northern half of your search area would have a higher probability.

    If the plane came in hot, which it seems like it did, then wouldn’t you also expect it to be in the northern half?

    Why so much focus on the far south / extended flight path?

  41. Richard says:

    @Sid Bennett

    We have decided not to release the track parameters or flight path charts separately from the paper, as without the explanation contained in the paper, this would lead to much unnecessary discussion. We prefer to focus on finalising and publishing the paper.

    We only wanted to release the search recommendation, that we had made to Ocean Infinity, out of consideration of transparency to this forum.

    You have already seen the criticism from DennisW: “The latest post is just a piece of fluff, IMO. Hard to imagine anyone putting any serious weight on it.”

    I disagree with DennisW, but he is of course entitled to his view. I respect his right to disagree.

  42. George G says:

    Comment on
    Release of Recommendation
    Prior to release of Finalised Report of Analysis :

    Victor,
    Dr B,
    Richard,
    Andrew,

    and all

    We all recognise the extent to which you must have gone to derive any conclusion, and the time you must have spent on the task.

    You have chosen to define your “Best Estimate of Point of Impact” by a point in space at the nominal time of the last satellite contact.

    Then you have considered uncertainties, including the uncertainty concerned with likely deviation from a previous flight path after the time of Main Engine Fuel Extinction and the time when the aircraft “crossed the 7th Arc”.

    You have given us explanations for how you have made estimates of those uncertainties.
    Areas A1, A2 and A3 on the surface of the ocean, may I note not on the sub-sea floor, are results of all the above.

    This release gives potential sea floor searchers an area or areas on which to concentrate review of existing data.

    Methinks this is not such a bad thing if they wish it.

    I checked and note that your refinement of your estimate has not varied significantly over months.

    For example:

    Richard, on October 8, 2019 at 7:29 am, you definitively said: “… flight path to 34.4°S is confirmed.”

    Later, Victor, on December 11, 2019 at 9:37 am, said: “… crossing the 7th arc near 34.3S latitude.”
    This was then queried by Paul Smithson;
    And on December 11, 2019 at 12:50 pm, Richard said: “Correct! 34.3°S”.

    You seem to be convinced of your data.
    Now, that you have been pressured into releasing your BE of POI,
    You are now under pressure to release the Finalised Report of Analysis.

    Would be unfortunate to let the meal go cold.

    _________________________________________________

    On a slightly (kinder) note:
    It has been some decent time since the last search was ceased.

    I wonder just how many changes and improvements and advances in searching for such as engines or undercarriage there might have been in the meantime.

    I wonder, if for example it would be advantageous to have two UAVs operating together at close quarters transmitting on slightly different frequencies.
    __________________________________________________

    Finally,
    Wonder how critical will be the uncertainty on the time of Main Engine Fuel Extinction.

  43. David says:

    @Richard. “We only wanted to release the search recommendation, that we had made to Ocean Infinity, out of consideration of transparency to this forum.”

    That seems to have caused some problems but thanks for the courtesy.

  44. CanisMagnusRufus says:

    …fleet is currently under construction and is expected to be deployable by the end of 2020.

    Each unmanned surface robot will serve a wide range of industries by being fully equipped to perform a multiplicity of offshore data acquisition and intervention operations down to a depth of 6,000 meters. These robot ships will be capable of remotely deploying a wide range of the latest sensors as well as AUVs and remotely operated underwater vehicles (ROV) for visual and acoustic data acquisition.

    Armada’s fleet requires neither people on board nor a host vessel nearby. Instead they will be controlled and operated by experienced mariners via satellite communications
    https://www.oedigital.com/news/475288-ocean-infinity-launches-armada

  45. DennisW says:

    @CMR

    Damn, and Iowa could not even count votes with a smart phone app.

    The issue remains A1,A2,A3 (above) could be in a lot of places without a lot more support for the 34.4S assertion.

  46. Ventus45 says:

    Ocean Infinity – Armada – is in the process of building 15 low emission robotic ships, a combination of 21 and 37 metre vessels.
    Some of the smaller ships will be available in the fourth quarter of 2020, the rest will be ready in 2021.
    The smaller vessels can be delivered to locations by air, while the larger ones will need to be moved by ship.
    The robotic ships will be deployed worldwide and can operate individually or as a fleet, from shallow to the deepest waters.
    The unmanned vessels will be able to launch ROVs and carry out surveys, on pipeline routes, or the acquisition of seismic data.

    (from) https://www.energyvoice.com/oilandgas/221895/armadas-robotic-fleet-to-shoulder-survey-work/

  47. Richard says:

    @David

    You stated: “ That seems to have caused some problems but thanks for the courtesy.”

    You cannot please all the people all the time (Abraham Lincoln).

    You can never please DennisW, any of the time (Richard Godfrey).

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