Where is MH370 and how will it be found?
Richard Godfrey
10th July 2016
Introduction
Twenty-eight months after the disappearance of MH370, we still do not know where the aircraft crashed.
The ATSB has led an underwater search and is reaching the end of their allocated funds of $180M, used to search 120,000 square kilometres of ocean bottom.
The Government Ministers of Malaysia, China and Australia are meeting in Kuala Lumpur on 19th July 2016, and it is anticipated that they will announce the end of the underwater search for the wreckage of MH370.
Since 29th July 2015, at least fifteen internal and external aircraft parts have apparently been found, washed ashore in 11 locations on the coasts of Tanzania, Mozambique and South Africa and on the Indian Ocean islands of Rodrigues, Mauritius, Réunion and Madagascar. The majority have been confirmed as being from (or are regarded as highly likely to be from) MH370. Over 50 items of personal effects, suspected as being from the crash of MH370, have also been identified.
Background
Investigators have collected information from many sources: primary radar detections, satellite pings, aircraft performance data, standard flight routes and waypoints, autopilot modes, autothrottle modes, fuel range, fuel endurance, weather, winds, air temperatures, magnetic variation tables, debris finds, ocean drift analyses, satellite imagery, airborne reconnaissance, hydrophone acoustics, the underwater search, etcetera.
With all this information, why has MH370 not been found?
The debris finds have resulted in a number of drift analyses being published, but there are large differences in the results. Critics validly point out any drift analysis is subject to many uncertainties (see this paper and also preceding papers posted on this website, and indeed elsewhere).
There are even more satellite ping analyses that have been published, but there are also substantial differences between the results. Critics point out that although the BTO data has a ±10 km tolerance, the BFO data are proportionately worse, with a ±7 Hz tolerance.
Inmarsat engineers, in their paper dated 4th September 2014, explained that while the BTO figures render the aircraft’s instantaneous distance from the satellite, the BFO data can be deciphered so as to get the aircraft’s speed and track relative to the satellite, subject to various assumptions. Without the BFO data, one does not know which way MH370 was heading; the BFO information indicates a path southwards across the Indian Ocean.
The Inmarsat engineers pointed out that a ±7 Hz BFO tolerance corresponds to a +/- 9° latitude uncertainty or ±28° heading uncertainty. However, they appear to have ignored or neglected the fact that the BFO is not only related to an aircraft’s horizontal velocity but also to an aircraft’s vertical speed (or rate of climb, ROC). With three fundamental variables — ground speed, heading/track and ROC — rather than just two, fitting the BFO data to a flight path analysis is made more difficult, because you can easily adjust the ROC to fit against many different ground speeds or tracks.
If one sets aside, for the time being, the drift analyses and the satellite BFO data, what are you left with?
The major variable that determines the latitude of the end point is the ground speed. Not only the thrust setting and autothrottle mode are important in determining the ground speed, but also the weather data (including wind directions and speed); the air temperature will additionally impact both air and ground speeds.
Another key variable is the assumed altitude. The air speed, air temperature, radar information, fuel range and endurance and aircraft performance data all provide constraints on the range of possible altitudes.
A third key factor to consider is the autopilot and autothrottle mode. The air speed, radar data, fuel range and endurance, track/heading, weather data and aircraft performance data all provide clues as to the autopilot modes that were engaged.
A fourth key factor is the time and position adopted for the final major turn (FMT): was this immediately after the last reported primary radar position at 18:22:12 UTC, or was there an extended excursion northwest, over the Andaman Islands or elsewhere?
Finally there are uncertainties surrounding loiters, lateral path offsets, circling, aborted emergency landing(s), step climbs, and so on. Many previous posts on this website have involved discussions of such hypothetical manoeuvres.
In this paper I will try to determine the range of feasible MH370 end point latitudes along the 7th ping arc without using either (a) The oceanic drift modelling of floating debris; or (b) The BFO data. Herein I impose minimum and maximum speeds, altitudes, bearings, FMT position, loiters, etc., which constrain the derived end points for MH370. Obviously, if the drift analyses and the flight paths making use of the BFO data also indicate much-the-same latitude range, then a consistent picture is achieved and so one has added confidence that the derived latitude range is correct.
In this paper, then, I ask the following question (and also try to answer it): Can one find MH370 (i.e. indicate a latitude range near the 7th arc) without having to rely on uncertain drift analyses or imprecise BFO data?
Ground Speed versus Latitude
The Malaysian Preliminary Report (in April 2014) stated that “The tracking by the Military continued as the radar return was observed to be heading towards waypoint MEKAR, a waypoint on Airways N571 when it disappeared abruptly at 18:22:12 UTC [0222:12 MYT], 10 nautical miles (NM) after waypoint MEKAR.”
If the aircraft turned south immediately after it disappeared from the military radar, then at an average ground speed of 300 knots the end point on the 7th Arc would be around 23°S, and at an average ground speed of 500 knots, the end point would be around 43°S (see Table 1 below). The ground speed might have been faster than 500 knots or slower than 300 knots, but these two points are 3,452 km apart and already represent an extremely large search area (if one were searching say 30 NM each side of the 7th arc). If we could put a much tighter range on the ground speed from the available information, then the search area would be much reduced. Of course, we also have to know when and where the aircraft finally turned south (the FMT); this might not have been at the earliest possible moment but could have been much later.
Table 1: Range of latitudes reached on the 7th arc for different ground speeds based on a FMT just after the final radar detection.
Ground Speed from Radar Data
The Australian Defence Science and Technology Group (DSTG) report states that “The radar data contains regular estimates of latitude, longitude and altitude at 10 second intervals from 16:42:27 UTC to 18:01:49 UTC.” Unfortunately, this data set has not been publicly released, but the DSTG report includes a graph of ground speed derived from the primary radar data having applied a Kalman filter, which indicates a ground speed of 521 knots at 18:01:40 UTC, slowly tapering to 509 knots at 18:22:12 UTC (the final radar detection time), whilst over the Malacca Strait.
The Malaysian Preliminary Report gives a military radar return at 17:39:59 UTC, whilst still over Malaysia, which indicates a ground speed of 529 knots at an altitude of 32,800 feet. This is not inconsistent with the DSTG graph.
Bill Holland of the Independent Group (IG) analysed the radar trace shown by the Malaysian authorities to the MH370 Next-of-Kin (NoK) in Beijing in late March 2014. This trace shows MH370 flying via waypoints VAMPI and MEKAR. From his timeline analysis, Bill found the ground speed to vary between 495 knots to 515 knots and back down to 485 knots.
Figure 1: Bill Holland’s annotated trace of primary radar positions of MH370.
In summary, we can say that the range of ground speeds of MH370 when flying above the Malacca Strait, based on radar tracking data, was between 485 and 515 knots, as indicated in Table 2 below. 
Table 2 : Ground speeds and minimum altitudes of MH370, based on primary radar information.
Ground Speed in Mid-flight
Brian Anderson (IG) published a paper entitled “Deducing the Mid-Flight Speed of MH370”, dated 20th March 2015.
In this paper was presented a preliminary calculation of the average ground speed of 476 knots for the mid-flight phase between 19:41:03 and 20:41:05 UTC. Brian used planar geometry at the tangent point, as MH370 passed the closest point to the satellite.
Brian has later recalculated the average ground speed using spherical geometry, arriving at a figure of 494 knots.
Brian needed to make certain assumptions concerning the altitude of the aircraft and the ping ring distances.
Revisiting Brian’s planar and spherical calculations, employing a range of conceivable altitudes between 25,000 feet and 45,000 feet and using the best satellite data to calculate the ping ring locations, results in a range of ground speeds between 494 knots and 502 knots.
In summary, we can say that, subject to various necessary assumptions, the range of possible ground speeds in the mid-flight phase was from 494 knots to 502 knots.
Ground Speed between the 6th and 7th Arcs
Brian Anderson also published a paper entitled “The Last 15 Minutes of Flight of MH370”, dated 24th April 2015. This concerned the end-phase of the powered flight of MH370.
In this paper Brian analysed the available fuel, engine and simulator information, the timings of the right engine fuel exhaustion (first), followed by the left engine fuel exhaustion (second), and the resultant air speed and ground speed profiles.
Brian’s calculation indicate that following the first engine failure there was a reduction in air speed (an ongoing deceleration) by around 19 knots per minute.
At the time of writing the above paper, Brian concluded that only with ground speeds greater than about 440 knots at 00:11 UTC (i.e. the 6th ping arc) is it possible subsequently to reach the 7th arc, even if that arc were at sea level.
Brian analysed whether the aircraft continued to fly in a straight line or whether it banked left or right. He discussed various feasible scenarios, concluding that most likely a left turn developed following the second engine flame out (fuel exhaustion).
I have now revisited Brian’s calculations for positions defined by different latitudes along the 7th arc between 20°S and 40°S; different adopted ground speeds at 00:11 UTC (6th arc); different altitudes at that time; and for different tracks. The best-fit ground speed at the 6th arc was found to be 486 knots, from the perspective of requiring that the aircraft actually reached the 7th arc at 00:19:29 UTC (as is the case in reality).
In summary, we can say that the range of feasible ground speeds at the 6th Arc ranges from 392 to 486 knots.
Ground Speed from Fuel Data
Mike Exner (IG) analysed the information regarding fuel availability and concluded in his fuel burn analysis dated 25th April 2015 that the right engine flame-out occurred at 00:10:54 UTC, followed by the Left Engine flame-out at 00:15:49 UTC.
The ATSB interpretation initially aligned with Mike’s analysis but subsequently revised its evaluation of the likely left engine flame-out time to be near 00:17:30 UTC, with the right engine flame-out occurring up to 15 minutes beforehand (thus at some time after 00:02:30 UTC).
Barry Martin (IG) included in his flight path model version 7.9.4 (dated 3rd March 2015) a fuel consumption analysis including the Rolls Royce Trent 892 fuel model (at flight levels 350, 370, 390, and 410) for both constant Mach and also Long Range Cruise (LRC) modes: see http://www.aqqa.org
Considering the alternative fuel exhaustion times given above and based on a starting point at 18:22:12 UTC:
(1) Using Barry’s flight model in the LRC mode, a fuel exhaustion point would be reached at 00:15:45 UTC after travelling 2,897 NM (5,365 km), if an altitude of 39,000 feet is assumed.
(2) Using Barry’s flight model in the LRC mode, a fuel exhaustion point would be reached at 00:17:15 UTC after 2,885 NM (5,343 km), if an altitude of 41,000 feet is used.
For a turn south occurring at the final radar point at 18:22:12 UTC, the implied average ground speeds would be 491.6 and 487.5 knots respectively.
However, the LRC autothrottle mode includes a speed profile:
(1) At 39,000 feet, this LRC mode shows a decreasing speed profile from 479.0 knots to 438.4 knots.
(2) At 41,000 feet, this LRC mode shows an increasing speed profile from 478.7 knots to 494.1 knots.
In summary, we can say that the range of ground speeds fitting with fuel exhaustion at the perceived range of times lies from 438 knots to 494 knots.
Ground Speed Summary
In summary there is a range of Ground Speeds between 392 knots and 515 knots, starting faster and possibly ending a bit slower, which fit the available information (so long as we exclude all consideration of the BFO data and also the floating debris drift modelling). See Table 3 below.
The so called ‘low-and-slow’ scenario does not fit the available information, the best fit being from a ‘high-and-fast’ scenario.
The next key question that needs to be addressed, then, is this: Where did the FMT (final major turn southwards) take place? Was it immediately after the final primary radar detection point at 18:22:12 UTC, or did MH370 continue along standard flight route N571 for some considerable time before turning, or was some other route taken?
The Location of the Final Major Turn
The final radar detection at 18:22:12 UTC is near 6.5774°N 96.3407°E. This is 3,571 km from the sub-satellite location of 1.5317°N 64.5335°E.
The 2nd ping arc at 19:41:03 UTC indicates that at that time MH370 was 3,250.5 km from the sub-satellite location of 1.6400°N 64.5194°E.
Therefore, in this elapsed time of 78 minutes 51 seconds, MH370 moved 320.5 km (173.1 NM) closer to the sub-satellite point, indicating a speed component along the direction radial to that point of approximately 131.7 knots. Obviously, the path followed is not that simple; that is, the aircraft was not travelling radially towards the sub-satellite point, but rather at some oblique angle to that direction.
If MH370 had continued along flight route N571 at the minimum speed observed in the Malacca Strait (485 knots: see earlier) then the aircraft would have reached 11.2640°N 86.6963°E by 19:41:03 UTC , which is only 2,671 km from the sub-satellite position at that time (the 2nd ping); this is 579.5 km too close to the sub-satellite point, and so the aircraft must have turned before then.
From the primary radar trace, we know that MH370 appears to have overflown waypoints VAMPI and MEKAR on N571. If it continued on flight route N571 the next waypoint is IGOGU. At 485 knots (again, the minimum speed observed over the Malacca Strait), MH370 would reach waypoint IGOGU by 18:38:00, which is 3,376 km from the sub-satellite position of 1.5884°N 64.5293°E at that time. This is still 125.5 km short of the 19:41:03 ping ring, but with a little over an hour to go, this is not an issue.
If MH370 continued further on flight route N571, the next waypoint is LAGOG. At 485 knots MH370 would reach waypoint LAGOG by 18:57:31, which is 3,138 km from the sub-satellite position of 1.6175°N 64.5265°E. This is 112.5 km inside the 19:41:03 ping ring, but there is still 43.5 minutes to go and the aircraft could turn back and easily reach the 19:41:03 ping ring in time.
At a ground speed of 485 knots the latest turning point on flight route N571 is 96 km/52 NM beyond waypoint LAGOG, if the aircraft were to be able to turn back and reach the 19:41:03 ping ring on time. However, the next waypoint (BIKEN, 227 NM from LAGOG) is not feasible, at this assumed ground speed.
Autopilot Mode
According to the primary radar information (Figure 1 above), MH370 passed waypoints VAMPI and MEKAR and followed flight route N571 toward IGOGU and possibly LAGOG.
If we constrain the adopted flight path to waypoints, then the following question arises: Which waypoints fit the BTO data and the ping rings derived from the BTO data?
Victor Iannello (IG) recently published a paper entitled “Possible Flight Path for MH370 Ending North of the Current Search Zone” dated 25th June 2016.
Victor presented a hypothesis that MH370 continued on flight route N571 to waypoint LAGOG (as described above), and then turned back to waypoint BEDAX and finally turned south on a heading of 180°M (i.e. 180 degrees magnetic), with a slowly-reducing altitude.
An autopilot Lateral Navigation (LNAV) mode using waypoints followed by the ‘Heading Select’ function is easy for a pilot to implement, and fits the BTO data.
Assuming the flight path scenario via waypoint LAGOG, and given the fuel analysis discussed above, the range of latitudes reached at fuel exhaustion range from 31.7°S to 34.9°S.
Victor calculated the latitude reached at fuel exhaustion to be near 31.5°S, which aligns with that fuel analysis.
In summary, we can say that a flight path via waypoint LAGOG and BEDAX fits the primary radar information, the likely autopilot mode, the BTO data, and the fuel analysis; and also, it happens, the BFO data, which has heretofore been excluded in this paper.
Autothrottle Mode
Victor, in his paper, assumed a thrust mode as follows: speed Mach 0.84, followed by 310 KIAS (Knots Indicated Air Speed) after descending past the cross-over altitude of 31,560 feet.
The resulting ground speeds ranged from 504 knots at 20:41 UTC to 367 knots at 00:11 UTC. The upper limit fits with the discussion above, but the lower limit only fits when you take a descent to 11,824 feet into consideration; Victor required a gradually-descending path so as to fit the BFO data.
An alternative scenario is a constant ground speed of 486 knots from 18:22:12 to 00:11:00 UTC, which fits both the fuel range and fuel endurance analysis; the latitude reached in this case is 34.0°S.
In summary, we can say that a flight path via waypoint LAGOG and BEDAX fits the radar information, the likely autopilot mode, a likely autothrottle mode, the BTO data, and the fuel analysis (plus the BFO data).
Conclusion
Without using either the ocean drift analyses or the BFO data it is possible to describe a flight path that fits the radar, BTO, aircraft performance limits, flight routes, autopilot modes, autothrottle modes, fuel range, fuel endurance, weather, winds, air temperature and magnetic variation constraints.
The range of latitudes indicated to be reached at fuel exhaustion is from 31.5°S to 34.9°S.
An example flight path is shown in Table 4 below.
This flight path/end point also fits with the floating debris spotted in satellite imagery and in airborne reconnaissance photos, and the drift analysis of MH370 debris found in the western Indian Ocean region, although for the purpose of this paper such considerations were discarded.
Unfortunately, the current ATSB priority search area stretches from 35.5°S to 39.5°S along the 7th arc ±40 NM, so that the failure to find sunken wreckage from MH370 below its crash site is not surprising.
The underwater search has produced no results so far and the assumptions made in determining the ATSB priority search area should be re-examined. My view, based on the analysis summarized in this paper, plus preceding papers, is that the search area should be re-focused to cover 31.5°S to 35.0°S along the 7th arc ±10 NM.