Some Observations on the Radar Data for MH370

by Victor Iannello, ScD,
August 18, 2015

A PDF of this paper is available for download from here (720  kB).

Please note: The views expressed here belong solely to Victor Iannello and do not necessarily represent the collective view of the Independent Group (IG), or any other group or individual. 

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Summary

This work analyzes the position and time data derived from the publicly-available radar data for MH370. Some of the findings are:

• After the turn back towards the Malay Peninsula, the flight path recorded by civilian primary surveillance radar (PSR), civilian secondary surveillance radar (SSR), and military radar are consistent with a flight at a Mach number (M) equal to 0.84 at a cruising level of FL340.
• If the aircraft did fly at a steady M = 0.84, then the timestamps for some of the PSR contained in the Factual Information (FI) [1] are offset by about 35 s.
• After the left turn at around 17:23:38 UTC, the aircraft might have descended from FL350 to FL340 and accelerated from a ground speed of 473 kn to a ground speed of greater than 500 kn.
• In the FI [1], the PSR data between 17:47:02 and 17:52:35 UTC are attributed to the radar site at Kota Bharu, but more likely were collected by another radar site. The PSR data between 17:30:37 and 17:44:52 are correctly attributed to Kota Bharu.
• In the FI [1], it is stated that Indonesian military radar recorded MH370 as it traveled toward IGARI but not as it traveled back over Malaysia. One explanation is that Indonesian radar site was powered down after midnight, local time.
• The sharp turn to the left at around 17:23:38 UTC is unexplained, and could be due to either an inaccurate graphical portrayal of the radar track, or crossing radar tracks from two aircraft.
• The curve in the radar path close to Kota Bharu can be explained by “slant range” due to high altitudes and close distances.
• Fuel consumption models which assume that MH370 flew near Long Range Cruise (LRC) speeds and at cruising altitudes between 17:07 and 18:22 are likely accurate.

The estimated path for MH370 from takeoff to the last radar point is shown in Figure 1.

 

Introduction

After the SSR data were lost from MH370 at 17:21:13, the only quantitative data that have been publicly disclosed are the PSR data that were collected by the radar head at Kota Bharu Airport, selected military radar data from one or more undisclosed radar sites, and the signaling data from the Inmarsat satellite network. In this work, we take a closer look at the radar data by individually treating the following four segments of the path:

• The known path northwest over the Malay peninsula ending with the last SSR data point at 17:21:13 just after passing IGARI
• The change in direction that started at 17:21:13 and ended with the resumption of the PSR data at 17:30:37, as captured by military radar
• The southwest path over the South China Sea, over Kota Bharu, and ending just south of Penang Island, as attributed in the FI [1] to the PSR data from Kota Bharu
• The northwest path over the Malacca Strait, as captured by military data

Figure 1. Summary of Radar Data

Solution Procedure

After analyzing timestamps, positions, and speeds for individual segments of the flight path, it was decided that the imprecision of the measured data precludes accurately determining the speeds for the individual segments due to the short time intervals and uncertainty in position and time. Instead, we hypothesized that the Mach number and altitude were essentially constant from the time of the left turn until the last radar point in the Malacca Strait, and then we tested whether this hypothesis is consistent with the data that was measured between the first and last data points.

In order to simulate the path of MH370 over the entire interval, an Euler integrator was used. For the segments of the path where there were turns, a time step of 1 s was used, and a 1-min time step was used for straight parts of the flight. The track angle was allowed to vary from time step to time step by imposing turn rates, expressed in units of deg/s. In this way, realistic curvature of the path could be modeled. The speed was adjusted so that two points are pinned in time and space: the left turn at 17:23:38 UTC, and the last radar point at 18:22:12 UTC. By iteratively varying the speed and the turn rates, a match of the flight path was obtained.

In order to properly include the effects of temperature and wind on the calculation, meteorological data were included in the analysis. The meteorological data for March 8, 2014 at 00:00 UTC [2] for a pressure altitude of 34,000 ft (FL340) were extracted from the GDAS archive provided by Barry Martin. This tabulated data has a spatial resolution of 1 deg in latitude and longitude. The wind data were used without alteration, but the temperatures were adjusted by -1.98 K / 1000 ft for altitudes equal to and less than FL360. (The tropopause for the ISA is at FL361.)

It was found that a constant true air speed (TAS) of 498 kn satisfies the time and distance relationship after accounting for wind. At FL350 and the prevailing temperature, this corresponds to M = 0.844. This is a higher speed than recommended for the B700-200ER to achieve Long Range Cruise (LRC) fuel efficiency. On the other hand, TAS = 498 kn corresponds to M = 0.840 at FL340, which is a more typical speed for cruising with a B777-200ER [3]. Therefore, we assume that MH370 likely flew at FL340, which required a descent of about 1000 ft after its last recorded value of FL350. An even cruising level such as FL340 is generally required of westbound flights in Reduced Vertical Separation Minimum (RVSM) airspace, such as within the Kuala Lumpur FIR. At the prevailing conditions on that day, FL340 corresponds to a geometric altitude of about 36,000 ft.

As a rough check of the validity of the tabulated wind and speed data, we can compare it to the data that were measured by the aircraft and included in the ACARS report at 17:06:43 [1]. At FL350, the temperature was 229.4 K and the wind speed was 17 kn from a direction of 70 deg. For the position of the aircraft at this time, the meteorological data predicts a temperature of 229.1 K and a wind speed of 15 kn from a direction of 67 deg. Therefore, the measured and tabulated temperatures match well, and the wind data values are also close.

 

Northwest Path over Malay Peninsula

The path of MH370 out of Kuala Lumpur International Airport (KLIA) and over the Malay Peninsula was captured by PSR and SSR data from the civilian radar site at Kota Bharu, as well as by ACARS data transmitted over the Inmarsat satellite network at 16:41:43, 16:46:43, 16:51:43, 16:56:43, and 17:06:43 UTC. The FI [1] reports that radar data showed that the aircraft passed over IGARI at 17:20:31 UTC, and the last SSR data position was recorded at 17:21:13 UTC, at which time the ground speed was 473 kn.

In order to quantitatively analyze the PSR data from Kota Bharu, the image of the PSR from the FI was positioned and sized on Cartesian coordinates using the waypoints PHUKET, MEDAN, PENANG, IGARI, and MERSING as registration points, where the position of the waypoints could be discerned from the image by the intersection of airways. The result is shown in Figure 2.

As can be seen in Figure 2, the agreement between the PSR (underlying black), SSR (white line), and the ACARS (white circles) data is excellent.

The FI [1] states that the Indonesian ATC in Medan, Sumatra, did not record an SSR transponder signal from MH370. Indonesian military radar did record MH370 as it headed towards IGARI but recorded nothing after the turn back towards Malaysia. As the aircraft left KLIA at around 16:41 UTC and passed IGARI at around 17:21 UTC, it appears that Indonesian radar lost the signal in that time interval, corresponding to 23:41 to 00:21 local time in Sumatra. One possibility is that at midnight, the military radar sites in Sumatra were powered down.

Figure 2. Primary Surveillance Radar (PSR) Data

Southwest Path over Malay Peninsula

Also included in Figure 2 is the PSR data from the time it reappears at 17:30:37 UTC to the last point at 17:52:35, for a total time interval of 21 min 58 sec, or 21.9667 min. Over that duration, the PSR data consist of four segments separated by three gaps in the data. From the FI [1], the time at the start and end of each segment is known, and is shown in Figure 2.

Figure 2 shows the calculated path (yellow) for the time interval. The meteorological data indicates that over the interval of the southwest path, there was an average tailwind of 12 kn at the indicated altitude. Therefore, at the true air speed of 498 kn, the average ground speed was around 510 kn.

According to the FI [1], the speed recorded by the military data was between 494 and 529 kn and the “registered” (geometric) altitude was between 31,100 ft and 35,700 ft. These values are not far from the proposed values of 510 kn and 36,000 ft. The deviation is likely due to the inaccuracy in obtaining speed and altitude information from the military radar data.

The times for the start and end of the four segments are shown in Figure 2 for the reconstructed path. In this way, it is possible to compare the position of the aircraft with the radar data at these times. It can be observed that for the first three segments, there is an offset between the radar data (underlying black) and the reconstructed path (yellow). The offset corresponds to about 35 s of flight time. For the fourth segment south of Penang, there is little or no offset. One explanation is that this offset is due to a delay between the time the radar contact was acquired at the radar head in Kota Bharu and when it was stored at the Kuala Lumpur ATC, although the detailed knowledge of how the data are aggregated and stored is not known.

A radar site estimates the distance between the radar head and the aircraft by measuring the round trip time for the transmitted radio signal and relating the time-of-flight to a distance based on the speed of light. As such, the radar is measuring the range between the radar head and the aircraft rather than measuring the distance along the ground. The radar range is sometimes referred to the “slant range” as it represents the hypotenuse of a triangle, where the altitude and the ground distance are the legs. The radar range and the distance will differ when the aircraft is at a distance that becomes comparable to the altitude of the aircraft, in which case a straight path towards and from the radar head will be appear on a radar screen as curved.

The effect of radar slant can be seen in Figure 2 as the aircraft approaches Kota Bharu around 17:34. The solid yellow line represents the reconstructed flight path, and the curved dotted line represents the slant range. The predicted slant range follows the trend of the radar data, as represented by the underlying black line. This suggests that the flight path truly was straight as it passed Kota Bharu.

 

Change in Direction from Northeast to Southwest

The military radar data presented in Figure 2 of the ATSB Report [4] from June 26, 2014, are used to reconstruct the path of MH370 after passing IGARI. The military data from the ATSB report are used as an overlay, and the coast of Malaysia is used for registration of the overlay. The result is shown in Figure 3.

The path is assumed to follow a trajectory towards BITOD at the last recorded ground speed of 473 kn until a sharp turn commences at around 17:22:52. The military data show an impossibly steep turn that would indicate that the graphical representation in the figure is not accurate or the radar data has been misrepresented. It is possible that the sharp radar track is actually crossing radar tracks from two separate aircraft. These hypotheses merit further investigation, and will be the subject of future work.

After the steep turn, the path is reconstructed with the assumption that the plane is flying at M = 0.84 and FL340. For this portion of the flight, this corresponds to a true air speed of 498 kn and a ground speed of 505 kn. The turn represents a rate of about 1 deg/s, which at 498 kn corresponds to a bank angle of about 24.5 deg. This is within the allowable limits of automated flight for a B777.

Figure 3. Military Radar Data for Left Turn after IGARI

Northwest Path over the Malacca Strait

On March 21, 2014, officials from Malaysia made a presentation to the next-of-kin at the Lido Hotel in Beijing. Several photographs were taken of slides from this presentation, including a slide presented by a Lieutenant General from the Malaysia Royal Air Force which showed an image of the military radar data over the Malacca Strait [5]. Here, we rely upon the work of Ron Belt [6], who performed an earlier study of the radar data over the Malacca Strait and extracted the radar data from this slide and produced several helpful figures.

In Figure 4, one of the figures from [6] was used as on overlay, where the waypoints VAMPI, MEKAR, PENANG, and LANGKOWI are used for registration. Using a speed of M = 0.84 and a cruising level of FL340, turns were adjusted to match the radar data. The ground speed averages 502 kn over this interval, and the calculated position at 18:22:12 UTC matches the position of the last radar point on airway N571.

Figure 4. Radar Data over the Malacca Strait

Conclusion

After MH370’s turn back towards the Malay Peninsula, the flight path recorded by civilian primary surveillance radar (PSR), civilian secondary surveillance radar (SSR), and military radar are consistent with a flight at a Mach number (M) equal to 0.84 at an altitude of FL340. With this assumption, some anomalies that were identified include an impossibly sharp turn to the left after passing IGARI, and timestamp inconsistencies as recorded by the PSR data from Kota Bharu. As MH370 likely flew at efficient cruise speeds and altitudes during the time it was captured by radar, fuel consumption models that assume fuel flow rates based on LRC conditions during this time interval are likely accurate. For instance, at FL350 and LRC conditions, the Mach number would vary between 0.838 and 0.834 over this interval [3].

Acknowledgements

The author wishes to thank fellow IG members Mike Exner, Don Thompson, Sid Bennett, Barry Martin, Richard Godfrey, Tom Kenyon, and Henrik Rydberg for reviewing this report and providing insightful comments.

References

[1] Malaysian ICAO Annex 13 Safety Investigation Team for MH370, “Factual Information, Safety Investigation for MH370”, March 8, 2015, updated April 15, 2015.

[2] Barry Martin, Meteorological data for March 8, 2014, http://www.aqqa.org/MH370/models/NCEP/GDAS_FNL/gdas2014030800f00.txt

[3] Boeing, “Flight Crew Operating Manual, 777-200ER, Trent892”, June 16, 2008.

[4] Australian Transport Safety Bureau (ATSB), “MH370 – Definition of Underwater Search Areas”, June 26, 2014.

[5] Don Thompson, “Analysis: Malaysian Radar Surveillance Capabilities”, June 18, 2014, http://bit.ly/TUDM_ADS

[6] Ron Belt, “Analysis of Malaysian Radar Data”, May 29, 2014.

 

Over recent months, despite apparent silence, the Independent Group (IG) has continued to explore and debate possible interpretations of the data available with regard to the flight and loss of MH370. It is only occasionally that some understanding develops that is deemed worthy of the investment of time needed to prepare something for posting/publication here. Continue reading MH370 Flight Path Model V15.1 →

Optimal Gliding Descent Scenarios for MH370

Geoff Hyman, Barry Martin and Sid Bennett
14 July 2015
(Updated 15 July 2015)

 

Introduction

In this note we focus on the final descent of the flight of MH370 and explore the implications of an assumption that the last stage thereof was executed in the form of a glide rather than a spiral descent.

Glide scenarios are of interest because they may assist in the identification of an outer boundary of the search area. Whether MH370 descended in the proposed manner is not resolved here. On the other hand, lack of success in terms of finding the aircraft within the current priority area further raises the interest in plausible alternatives.

On best-available interpretations of the available satellite and flight simulator evidence, optimal glide scenarios represent extreme cases and would not be considered to be the most likely ones to have actually occurred. However, as long as glide scenarios, in some form, are a reasonable possibility, the implications for the search area merit further consideration.

This study was motivated by a proposal that, if under (human) pilot control, MH370 could have continued on an efficient gliding path after passing the 7th arc (00:19:29 UTC; all times herein are UTC). Previously [1] we explored an apparent anomaly in the BTO/BFO observations associated with the re-log-on event at 18:25 and SATCOM handshake transmissions shortly afterwards, concluding that an offset track might have been the cause. Such scenarios would have required human input after the time of final primary radar contact. Combining such considerations with the analysis reported in [2] provides a motivation for the scenarios examined here.

The present study considers a scenario involving events subsequent to 00:11, but there are only two satellite observation pairs available: at 00:11 and at 00:19:29. Inmarsat engineers [3] are confident that the corrected 00:19:29 BTO is usable. The assessment of alternative flight paths after 00:19:36 is problematic because no further BFO or BTO values were recorded. The current simulations are computed in 15 second time increments and are divided into two parts: the first is for the period with satellite observations, from shortly before 00:11 until 00:19:30; and, the second is an extrapolation of the position at 00:19:30 to the end of the flight.

The likelihood of MH370 having executed a simple glide descent, resulting in the aeroplane being ditched at considerable distance from the 7th arc,  is conditional upon rejecting the validity of the BFO at 00:19:29 as it is presently understood [3].  The BFO measurement is a part of the handshake during a re-log-on event with the Inmarsat ground station at Perth and we do not have sufficient comparative data to determine whether the BFO anomaly referred to by Inmarsat for the log-on sequence at 18:25 should be considered in this circumstance as well.  Further data from the ATSB relating to the log-on events would be welcome, including comparable data from similar flights. If the BFO measurement during the re-log-on (at 00:19:29 ) were to be determined to be valid, then the descent scenarios could be complex, and less efficient, with shorter ranges and/or reduced times aloft.

One consideration was the conflicting initial assessment of the location of the intersection of the flight path with the 7th arc. Subsequently, our group has reported a number of studies that strongly suggest that the location of that intersection is quite well established. This intersection may be some appreciable distance from the final location. However, with due recognition of the uncertainty of the descent trajectory, this still facilitates a more focused review of the future search area.

The current report also incorporates improvements to wind modelling, informed by [4]. It also includes refinements to deal with the brief period for which only one engine was operating.

 

Optimal Glide Scenarios

We consider two possible types of optimal glide scenario: maximum range and maximum endurance. The associated altitude profiles for speed and descent speeds are based in the relationships given in annex A below. These profiles are based on a drag model for the airframe alone which does not account for drag contributed by windmilling powerplants.

For the one engine inoperative (OEI) case the single engine thrust also needs to be incorporated. However this only applies to a brief period of the descent and is not reported here.

In Figure 1 we show a distribution of likely flight directions at the commencement of the glide stage. For the maximum range scenarios there are two modes (or peaks), while maximum endurance scenarios show a single peak.

Our previous studies indicated that the most likely flight azimuth, prior to the 6th arc, was 186 degrees True (i.e. six degrees to the west of due south). It appears that, after the second engine flame out, the aeroplane probably made a turn to the left through an angle of at least 20 degrees; alternatively our speed assumptions during the loss-of-power event might be too low. For both sets of glide scenarios the median azimuths are similar, the main differences being their implications for the distances flown beyond the 7th arc.

Figure 1: Initial direction for the Glide: a) Best Range; b) Best Endurance.

In Figure 2 we give a plan view of the simulated flight paths and the locus of sea level endpoints. The square labelled as IG nominal was reported in [5] as the intersection with the 7th arc, without consideration of a subsequent descent, and is included to assist orientation of this result with respect to previous studies.

Figure 2: Sample Flight Paths and Spread of Probable Endpoints.

In Figure 2 the maximum glide range may be considered as encompassing the region between the lines labelled Mode 1 and Mode 2. The maximum endurance path is shown as a single median line. As the distribution of angles in each case is fairly broad, based on Figure 1, a specific radial vector for the search is not suggested.

 

Summary of Model Inputs and Outputs

In all scenarios our modelled speeds begin to reduce one minute prior to the commencement of the descent. However, the speed reduction process after fuel exhaustion for the first engine does not have time to reach its optimal OEI speed before fuel exhaustion occurs in the second engine.

Our model inputs are listed in Table 1 below, along with the consequent outputs.

In reference [6] (specifically on page 26) the ATSB estimated a glide range of 120 NM for a descent from 35,000 feet. Our Table 2 below shows a comparison between the glide stages for our sample flight paths and the ATSB’s assumptions. The maximum range Mode 1 scenario covers a similar distance and has a similar gradient to the ATSB’s values.  The differences shown are within the errors of our modelling approximations.

The maximum range scenario for Mode 2 has a larger range and a flatter glide path due to the presence of a tailwind in our simulated flight path. The maximum endurance scenario covers a shorter distance, and but has a similar gradient to that of the ATSB report [6].

 Table 1: Summary of Principal Inputs (I) and Outputs (O). 

 

Table 2: Comparison of Glide Ratios with the ATSB’s Estimates [6]. 

 

Discussion

These scenarios excluded the BFO data at 00:19:29, which has been interpreted to be consistent with a rate of climb (RoC) of about
–4500 feet per minute (i.e. a rapid descent), whereas the RoC for the scenarios studied is about one quarter of this value, as is to be anticipated for a glide. As there are no further usable satellite data for later times, the possibility of a less efficiently flown scenario with a steep initial descent cannot be excluded. This would have the effect of decreasing the range that would be flown after fuel exhaustion (i.e. in the glide phase).

 

Conclusion

We have illustrated two glide range descent scenarios: maximum range and maximum endurance. The conclusions support the ATSB’s findings [6] that MH370 could have flown 120 nautical miles beyond the 7th arc. For pragmatic reasons the ATSB appears to have restricted its search area to a band located 40 nautical miles beyond the 7th arc and parallel to it. However a case is emerging that, if under the control of a pilot, the positions of impact could all lie further still from the 7th arc. Again, on best-available interpretations of the satellite and flight simulator evidence, optimal glide scenarios are not the most likely ones to have occurred, and only represent extreme possibilities. Appropriate risk analyses would be required prior to making proposals for future revisions to search area priorities.

 

Acknowledgments

The authors should like to acknowledge the contribution of Brian Anderson in providing assistance in checking the fuel exhaustion times. We should also like to acknowledge the contributions of Mike Exner, Victor Iannello, and other members of the Independent Group (IG) for their comments on an earlier draft. Any errors or omissions remain the responsibility of the authors.

 

References

[1] Bennett, S., Hyman, G. & Martin, B. (May 2015). MH370 Path Investigation Studies: The Implications of BFO and BTO  Data at 18:27 UTC. Independent Group; available from: https://www.duncansteel.com/archives/1699

[2] Anderson, B. & Exner, M. (March 2015). The Last 15 minutes of Flight of MH370. Independent Group; available from: https://www.duncansteel.com/archives/1461

[3] Ashton, C., Bruce, A. S., Colledge, G. & Dickinson, M. (2014). The Search for MH370. The Journal of Navigation, 68 (01), 1–22. Available from: http://dx.doi.org/10.1017/S037346331400068X

[4] (U.S.) National Centers for Environmental Prediction/National Weather Service/NOAA/Department of Commerce, NCEP FNL Operational Model Global Tropospheric Analyses (continuing from July 1999): Research Data Archive at the National Center for Atmospheric Research, Computational and Information Systems Laboratory, Boulder, Colorado. (Updated daily.)

[5] Steel, D. (ed.) (September 2014). MH370 Search Area Recommendation. Independent Group; available from: https://www.duncansteel.com/archives/1023

[6] ATSB: MH370 – Definition of Underwater Search Areas.  External Aviation Investigation AE-2014-054 (26 June 2014; updated 18 August 2014); available from: ATSB: MH370 – Definition of Underwater Search Areas 

[7] Vinh, Nguyen X. (1993). Flight Mechanics of High-Performance Aircraft. Cambridge Aerospace Series. Cambridge: Cambridge University Press.

[8] Pereira, R. L. (2010). Validation of Software for the Calculation of Aerodynamic Coefficients. Degree project, Linkȍping University, Sweden; available from:
http://www.diva-portal.org/smash/get/diva2:329418/fulltext01.pdf 

[9] Jenkinson, L., Simpkin, P. & Rhodes, D. (2001). Civil Jet Aircraft Design. [Data sets] Butterworth-Heinemann; available from: http://booksite.elsevier.com/9780340741528/appendices/default.htm  (accessed 5th June 2015).

[10] Malaysian Ministry of Transport (2015). Safety Investigation for MH370: Factual Information, issued 08 March 2015; updated 15 April 2015; available from: http://mh370.mot.gov.my/

 

Annex A. True Airspeeds and Decent Rates for
Best Range and Endurance

The drag force is assumed to be given by an equation of the form:

…where V is the true airspeed, and z is the altitude. The coefficients are given by:

…where ρ(z) denotes the (ISA) density of air at altitude z and the remaining parameters are as in Table A.1 below.

Table A.1: Parameters Pertaining to the Drag Force

Drag coefficients K and C_d0, reported in [8] and reproduced here in Table A.1., are for the Boeing 777-300 model without operating powerplants, at Mach 0.84 and a Reynolds number of 8.7 × 10^5.

 

Maximum Range Descent

The airspeed which maximises range, in the absence of winds, is given by:

In the absence of engines the steady-state rate of  descent, which maximises range, is [7]:

…where W=mg is the aeroplane weight, and

…is the minimum drag. The glide angle γ_md for this maximum range steady descent is then given by:

 

Maximum Endurance Descent

For maximum endurance (i.e. longest descent time) we can write the following relations (see reference [7]) so as to get the equivalent output parameters as in equations A4, A5 and A6 above: