Where is MH370 and how will it be found?

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.

RG_Table1

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.

RG_Fig1

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. 

RG_Table2Table 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.

In later discussions with Brian, the minimum ground speed at 00:11 UTC was revised to 392 knots, following the ATSB publishing updates regarding the events in the last 15 minutes of flight. 

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.

RG_Table3
Table 3: Summary of evaluations of possible ground speeds, and information sources. 

The so called ‘low-and-slow’ scenario does not fit the available information, the best fit being from a ‘high-and-fast’ scenario. 

Based on assuming an early FMT at 18:22:12 UTC, this result would favour latitudes ranging from 35°S to 43°S, rather than latitudes further north along the 7th arc.

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.
By using the maximum calculated ground speed over the Malacca Strait (515 knots) rather than the minimum (485 knots), slightly different figures are arrived at, but the same general picture arises: if MH370 were following waypoints, then LAGOG is the last feasible waypoint on flight route N571: the latest possible turning point on N571 is waypoint LAGOG, or shortly afterwards. 


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 
If the autopilot was engaged, was the autothrottle also engaged? 

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.
RG_Table4
Table 4: Example flight path fitting constraints as described in the text. 

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.

Possible Flight Path for MH370 Ending North of the Current Search Zone

Possible Flight Path for MH370 Ending North of the Current Search Zone

Victor Iannello, ScD,
June 25, 2016

 

(See also the addendum at the end of this post.)

Introduction

The underwater search for debris from MH370 has been unsuccessful so far. The current search zone in the Southern Indian Ocean (SIO) consists of a total of 120,000 square kilometers of seabed, of which 105,000 square kilometers (88%) have been searched to date. There have been no announcements from Malaysian, Australian, or Chinese officials indicating that the search will continue after the scanning of the current search area is completed.

The definition of the current search zone, shown in Figure 1, is based on reconstructed flight paths that are derived from available radar data combined with an analytical interpretation of satellite communications data. In December 2015, a comprehensive study of reconstructed flight paths was completed by Australia’s Defence Science and Technology Group (DSTG) [1]. The satellite data suggest that the aircraft continued to fly for nearly six hours after the last radar capture. As the satellite data are insufficient to determine the precise flight path of MH370, other constraints are imposed on possible flight paths that result in the definition of a more manageable search area. These constraints relate to performance of the B777-200ER aircraft as well as pilot inputs to flight controls. The ability to accurately define the search area is therefore limited by the accuracy of these constraints, and in particular, the accuracy of assumptions related to how the aircraft was flown by the pilots, including whether or not there were pilot inputs during the final hours of the flight.

In the past year, debris from MH370 that has drifted west across the Indian Ocean has been recovered from the shores of La Reunion, Mozambique, South Africa, Mauritius, and possibly Tanzania. Godfrey [2] and others have investigated the drift patterns of floating debris from various possible crash sites, and conclude that the crash site might have occurred outside and to the northeast of the current search zone shown in Figure 1. This could explain why no debris on the seabed has yet been found in the current search zone.

In this paper, we re-visit some of the assumptions that were used to define the current search zone and propose a possible flight path that ends northeast of the current search zone and is consistent with drift studies performed by Godfrey [2].

 

Definition of Current Search Zone 

After the last primary radar capture of MH370 at 18:22 UTC, the only data we have to reconstruct the flight path are the satellite data “pings”. The log-on sequences at 18:25 and 00:19 along with the handshakes at 19:41, 20:41, 21:41, 22:41, and 00:11 provide Burst Timing Offset (BTO) data and Burst Frequency Offset (BFO) data, while the failed telephone calls at 18:40 and 23:14 provide us with only BFO data.

We can use the BTO data to determine the distance between the aircraft and Inmarsat’s I3F1 satellite, which relayed two-way communications between the ground earth station (GES) in Perth, Australia, and the aircraft. This information can in turn be used to determine a “ping arc” of possible positions of the aircraft for each BTO data point. The BFO data, on the other hand, can be used to determine the approximate direction of the aircraft to discriminate, for example, between northerly and southerly trajectories. The details of these calculations have been presented elsewhere, such as Ashton et al. [3]. The last BTO value at 00:19 provides us with the best-estimate of possible locations for the crash, and this ping arc is known as the “7th arc” because it is the seventh BTO burst in the sequence of bursts starting at 18:25.

In addition to the speed and track, the value of the BFO is strongly influenced by the vertical speed of the aircraft, i.e., a climb and a northerly velocity for the aircraft both influence the BFO in a positive sense. If the vertical speed is not known, it becomes difficult to use the BFO to determine the direction of the aircraft. For instance, a particular value of BFO may indicate a trajectory to the south and level flight, or a trajectory to the north and descending flight. This ambiguity is removed if the flight is known to be level, for instance, at a particular time.

In an attempt to help define the search area, a detailed analysis of possible reconstructed flight paths was performed by the DSTG [1] using probabilistic methods. By assuming that random manoeuvers which change the speed and direction of the aircraft occur at randomly distributed intervals, and using previous commercial flight data to calibrate the stochastic model, a distribution of possible end points in the SIO was generated. Using the BFO data at 18:28 and 18:40, and assuming level flight, the DSTG analysis predicts that a turn to the south occurred at some time between 18:28 and 18:40. The probability distribution of the location of MH370 from this analysis is shown in Figure 1, which shows the highest probability at a position on the 7th arc near 38S latitude.

Vfig2

Figure 1. Probability distribution for location of MH370
from DSTG study [1].

Unfortunately, the search for debris on the seabed in the area defined by the DSTG analysis has been unsuccessful to date. Additionally, the timing and location of recovered debris from MH370 that has drifted across the Indian Ocean and landed in La Reunion, Mozambique, Mauritius, and South Africa suggest that MH370 might have crashed to the north of the current search area. For instance, Godfrey [2] performed drift studies of recently recovered debris which suggest a location along the 7th arc that is near 30S latitude. The failure to find the debris in the current search area combined with results from the drift studies provides a motivation to revisit the assumptions that were used in reconstructing possible flight paths.

Here, a possible flight path is proposed that terminates to the north of the current search area. The main differences in assumptions between the DSTG study and the present work are:

  1. In the DSTG study, the aircraft was assumed to be flying nearly level at 18:40 and on a southerly course. In the current study, the aircraft was assumed to be descending at 18:40 and following a northerly course until about 18:58. The later turn to the south produces an end point to the north of the current search area.
  2. At some time before 19:41, the aircraft began traveling along a path of constant magnetic heading and was slowly descending.
  3. There were no pilot inputs after 19:41, i.e., the aircraft was on a path of constant magnetic heading, scheduled speed, and constant (negative) vertical speed.

 

Methodology to Reconstruct Flight Paths

The methodology to reconstruct the flight paths is similar to what has been presented by others, including the published work of Ashton et al. [3]. A BTO value defines an arc on the surface of the earth, and paths can be reconstructed that cross these arcs at the appropriate time by matching the satellite-aircraft range. (The exact position of the arc depends on the altitude of the aircraft. At higher altitudes, the arc is located further from the subsatellite position.) The paths were reconstructed by forward integrating in time and matching within a tolerance of 10 km the satellite-aircraft range at handshake times as derived from the BTO values and the satellite position. The model includes an accurate parameterization of the satellite position and velocity, meteorological data, and the earth’s ellipsoid geometry. The satellite position and velocity vectors are estimated using the PAR5 parameterization of Rydberg [4], which agrees well with the position and velocity vectors presented by Ashton [3]. The earth is modeled as an oblate spheroid using WGS84.

Meteorological data were included in the analysis in order to properly model the effect of temperature and wind on speed and direction. The meteorological data for March 8, 2014 at 00:00 UTC were extracted from the GDAS database by Barry Martin [5], where data are available with an altitude pressure resolution of 50 hPa and a surface resolution of 1 deg in latitude and longitude.

After flight paths were reconstructed using the BTO data, the predicted values of BFO were compared to the measured values to ensure that match was within an acceptable tolerance of 20 Hz.

 

Vfig1

Figure 2. Flight path ending north of the current search zone.

 

Possible Flight Path Ending North of the Current Search Zone

The particular flight path of interest is the solid line shown in Figure 2. After the last radar capture at 18:22, we assume the aircraft continued to fly northwest, roughly following airway N571 to waypoint LAGOG, which it reached around 18:58. (The BTO and BFO data sequence between 18:25 and 18:28 suggest there might have been a small, lateral, side-step manoeuver to the right, but this does not change the end point location in a significant way and will therefore not be discussed here.) At waypoint LAGOG, the aircraft turned southeast towards waypoint BEDAX. Upon reaching BEDAX at around 19:25, the aircraft turned towards a heading of 180° magnetic, and continued on this heading for the remainder of the flight.

If the aircraft flew a track in which its path after BEDAX was always exactly in the direction of 180° magnetic, it would follow the path shown as a dotted line in Figure 2. The reason why this path deviates from the path of constant heading (solid line) is because of the prevailing wind pattern, which was blowing towards the west for positions to the north of about 22S latitude and blowing towards the east for positions to the south of 22S latitude.

As the dotted line in Figure 2 shows, the track of constant magnetic direction curves to the east at lower latitudes. This is due to the increasing deviation along the path between the magnetic north pole and the true north pole. This deviation is known as magnetic declination. The consequence of this curving is that constraining the aircraft to cross the ping arcs at the appropriate times requires that the ground speed of the aircraft reduces as the aircraft travels south.

The possibility that the aircraft’s speed continuously changed along the path was not considered in the DSTG study [1]. Here we consider the possibility that at a time near 19:41, the aircraft was at an altitude of around 38,800 ft and on autopilot with the following settings:

  • Roll mode: Heading Hold at 180° magnetic
  • Thrust mode: Speed at M0.84 followed by 310 KIAS after descending past the cross-over altitude of 31,560 ft
  • Pitch mode: Vertical Speed of -100 fpm (descending)

The descent rate of -100 fpm is the smallest rate of descent that is possible by setting a vertical speed. At this rate of descent, if fuel exhaustion had not occurred, the plane would have descended into the sea on March 8 at about 02:08 UTC, or a little under two hours after the estimated time of fuel exhaustion of 00:15. At 00:19, the aircraft is predicted to be in a steep descent of -4560 fpm.

Values for selected flight parameters is included in the following table:

Vtab1

Table 1. Flight parameters at selected points along path.

 

Conclusions

The present work revisits some of the assumptions used to reconstruct possible flight paths for MH370. In particular, by assuming the aircraft at 18:40 was traveling to the northwest and descending, a later turn to the south is predicted, resulting in an end point further to the northeast than the current search zone. By assuming the aircraft after 19:41 was on autopilot and in a constant state of slow descent, following a path of constant magnetic heading of 180°, a curved path was reconstructed that matches the satellite data and crosses the 7th arc near 31.5S latitude. This end point is consistent with drift studies that predict a possible crash point along the 7th arc at around 30S latitude, and should be considered for further investigation.

 

Acknowledgement

The author is grateful for comments and corrections provided by fellow Independent Group members: Brian Anderson, Duncan Steel, and Richard Godfrey.

 

References

[1] Davey, S., et al., “Bayesian Methods in the Search for MH370”, Defence Science and Technology Group, November 30, 2015, https://www.atsb.gov.au/media/5733804/Bayesian_Methods_MH370_Search_3Dec2015.pdf .

[2] Godfrey, R., “What the Nine Debris Finds May Tell Us about the MH370 End Point”, June 2, 2016, http://www.duncansteel.com/archives/2652 .

[3] Ashton, C., et al., “The Search for MH370”, Journal of Navigation, October 7, 2014, http://journals.cambridge.org/download.php?file=%2FNAV%2FNAV68_01%2FS037346331400068Xa.pdf&code=38b6842b760772f03a840b894cced959 .

[4] Rydberg, H., http://bitmath.org/mh370/satellite-par5-ecef.txt.gz

[5] Martin, B., http://www.aqqa.org/MH370/models/NCEP/GDAS_FNL/gdas2014030800f00.txt

 

Addendum regarding the large debris item found in Tanzania:
A discussion of the photographic evidence for this being a part of the right outboard flap from a B777 has been conducted by Mike Exner and Don Thompson; it is available here

 

What the nine debris finds may tell us about the MH370 end point

What the nine debris finds may tell us about the MH370 end point

Richard Godfrey
2016 June 2nd
Introduction
There have so far been  a total of nine finds of debris that are either suspected or confirmed to be from MH370. These are as tabulated below. 

The Rolls Royce name plate from an engine cowling was found twice, firstly by Schalk Lückhoff carrying many barnacles, and then three months later by Neels Kruger, denuded of barnacles.

This has led to the hypothesis that debris items clear of barnacles may have arrived several months earlier than the date of the find, the barnacles having been lost by the debris item after beaching through various mechanisms (physical abrasion; death of the barnacles; etc.).
Debris Finds
Method
In this analysis, I have assumed that all nine debris finds are from MH370. 

I used the Adrift model using the forward drift data starting at March 2014.

I found the probability for each point along the 7th Arc subject to two different assumptions:

(1) Assuming that we did not know the time of arrival; and

(2) Assuming that the time of arrival was the fastest possible given by the Adrift model.

For Method (1) I summed the probabilities for the timeframe between the fastest possible time point and the time point of the find to give a weighting.

For Method (2) I used the probability for the fastest time point only for each find and summed those values.

For both methods, it is possible that individual probabilities are zero.


Results
Using Method (1), the accumulated probabilities for all nine debris finds show a peak at 30S 98E on the 7th Arc as shown in the table and graph below.
Debris Finds vs Origins along 7th Arc - Data reduced
Debris Finds vs Origins along 7th Arc - Graph
Using Method (2), the single probability summed for each of the nine debris finds shows a peak at 29S 99E. The graph below shows another peak at 34S 94E, but this does not fit all debris finds (i.e. although the summed probabilities may render a large result, some end locations/find locations are found to have a zero probability in the Adrift model).
Debris Finds vs Origins along 7th Arc Earliest Month - Graph
 
Only two putative MH370 end points on the 7th Arc fit all the debris finds, as indicated in the table below: 29S 99E and 30S 98E.
Debris Finds vs Origins along 7th Arc Earliest Month - Data
Using Method (2), I checked whether there was a possibility that the MH370 end point was either inside or outside the 7th Arc.

There was a clear peak or hot spot at 30S 99E just outside the 7th Arc, almost twice any peak along the 7th Arc, as shown in the following table (red: geographical bins along the 7th Arc; green: the bin containing the peak probability).
Debris Finds vs Origins Earliest Zoom reduced
Discussion
The debris find at Mossel Bay, South Africa by Schalk Lückhoff and then 3 months later by Neels Kruger, as well as the find at Paindane Resort, Mozambique by Liam Lotter, fit only this hot spot and surrounding cells as a point of origin. 

The indicated average drift speed of the recovered debris is 0.37 knots, the maximum speed being 0.68 knots.

The map below shows the fastest drift from 30S 99E using the Adrift model. The yellow diamond shows the location of 30S 99E (i.e. the MH370 end point indicated above). The yellow squares give the mean locations of drifting debris after the stated number of months in each case. The green circles are the locations of the debris finds.
Indian Ocean Drift Map 30S 99E



On this basis it would seem likely that most of the drift items have reached the places where they were found several months before they were identified (i.e. they may have spent some considerable time on or near the coastlines/beaches).

For MH370 to have crashed at near 30S two possibilities immediately suggest themselves: either the flight south was “low and slow”, or the path of MH370 included a loiter around Sumatra and the Andaman Islands before heading south. The latter case would require that although the BFO data shows a southerly direction at 18:40, subsequently MH370 circled back before finally heading south.

Victor Iannello has suggested a third possibility: that the plane turned toward the south later than 18:40, and the BFO value at 18:40 is the result of a descent. This allows cruise speeds for the entire path and no loiter. It is interesting that the region around 29-30S was the hot spot suggested by the ATSB in their June 2014 report, in which the BFO at 18:40 was ignored for unknown reasons. Perhaps the ATSB was right after all, to initially ignore the BFO at 18:40.
Don Thompson has noted that a lower flight level may have been an intentional consideration: the cruise altitudes of flight routes from Australia to the Middle East would be in the path of an aircraft (i.e. MH370) heading south from its final major turn, and adopting a lower altitude would avoid the possibility of a collision.
Conclusion
The area around 30S 99E should be considered as a hotspot for underwater searching, as soon as all nine debris finds are confirmed as from MH370.
It is noted that drift modelling such as that employed here of necessity contains various vagaries and conditional outcomes. Alternative drift models should be used to check the above results, and it is urged that others should use such models so as to verify (or not) the results obtained here.
The possibility still remains that some contingent events (e.g. particular storms) may have made it feasible for the debris items that have been found in South Africa and Mozambique to have started out further south than 30S (e.g. the subsidiary peak near 34S mentioned above), but the discovery of the latest four items in Mauritius and Mozambique (yet to be confirmed to be from MH370) adds weight to the previously-stated result from drift modelling that MH370 appears unlikely to have crashed to the south of 36S. 


Acknowledgements
I am indebted to Dr Erik van Sebille of Imperial College, London, and the Adrift organisation.

I am also indebted to Henrik Rydberg, Mike Exner, Victor Iannello and Don Thompson of the Independent Group for their helpful suggestions in preparing this paper.

Space Scientist, Author & Broadcaster