The Last 15 Minutes of Flight of MH370
Report prepared 2015 April 24
Determining what happened to MH370 during the last 15 minutes of flight is difficult, given the limited information available, yet it is important to arrive at some estimates of the aircraft altitude and path during this time. The path is needed in order to establish where the end point might be.
At the time of the Independent Group’s (IG) September 26 statement last year, the information available to help with the analysis of this period was limited to the satellite-derived BTO and BFO data at 00:11 and 00:19 UTC (on 2014 March 08), and the expectation that the engine failures with fuel exhaustion would not occur at precisely the same instant in time.
It was expected at that stage that knowledge of the engine Performance Degradation Allowance (PDA) figures would provide evidence as to which engine failed first, and also enable the remaining flight time before the second engine failed to be determined. Unfortunately the PDA information has not been made public by Malaysia Airlines.
The analysis of several simulation runs in a certified B777 level 4 simulator showed that knowing which engine fails first, and hence being able to determine the direction of the Thrust Asymmetry Compensation (TAC) deflection at the time of the second engine failure, is not a predictor of the flight characteristics of the aircraft following the second engine failure. Hence, knowing the PDAs is not immediately helpful in this regard (i.e. knowing which engine first ran out of fuel is not a necessity here). Rather, the flight characteristics, and in particular the propensity of the aircraft to bank into a turn immediately following the second engine failure, is a function of precisely how the aircraft was trimmed immediately before the first engine failure. The simulator trials showed that seconds after the second engine failure the TAC is reset to the cruise rudder trim position.
We know that each B777 aircraft is subtly different (as are most other aircraft) with respect to rudder trim in particular. One might say that they may be slightly ‘bent’ in terms of aerodynamics. Some require a little left trim, some a little right, and some require neither in order to fly straight. In addition, individual pilots often adopt slightly different regimes in order to manage the trim (TAC) requirements. Without knowing how this particular aircraft handled historically – and even if we did know – it may not be possible to say with certainty if the aircraft would depart into a turn to the left or to the right following the second engine failure.
In performing the analysis presented in this paper I have made the following necessary assumptions:
- There was no manual intervention to control the aircraft during the last 15 minutes of flight;
- The aircraft was flying on autopilot during its passage south over the Indian Ocean until the second engine failure;
- The flight path is similar to the path discussed in the IG statement dated September 26 (and also a number of other independently-derived flight paths ending at similar latitudes, so that the precise flight path taken over the Indian Ocean is not significant here);
- The B777 level flight simulator runs previously studied by the IG (per Mike Exner) deliver a valid representation of how MH370 would be expected to have behaved near the end of its flight.
With the release of the Factual Information statement by the Malaysian Safety Investigation Team on 08 March 2015 [reference 1], new information became available which enabled more analysis of the fuel consumption rates and better estimates of the engine failure timings, without requiring specific knowledge of the PDAs. This at least enables us to say with some certainty that it was the Right engine that failed (ran out of fuel) first.
When the first engine fails the TAC is immediately set to trim the aircraft to fly straight, and the auto-throttle increases thrust in order to maintain air speed and altitude, as far as possible.
The ATSB, in its 26 June 2014 report , described the Satellite Data Unit (SDU) power up process and concluded that the 0019:29 log-on would have occurred three minutes and 40 seconds (+/- 10 seconds) following the second engine failure, and that the autopilot would have been disengaged for this period due to the interruption in electrical power. The SDU boot-up and final log-on is assumed to be a result of an automatic Auxiliary Power Unit (APU) start due to the loss of both electrical generators driven by the jet engines. The time required for the entire process, from loss of the second engine until the log-on, is 3m40s. This time was confirmed during the B777 flight simulator trials mentioned previously.
Note that the APU is supplied from the left main (fuel) manifold, and will continue to run only for as long as there is sufficient fuel in the fuel lines to the APU (given that the fuel tanks are empty, resulting in the jet engine failure). It is not surprising therefore that the final communication received from the aircraft was at 00:19:38, a possible cause being complete loss of power again, as the APU shut down. (An alternative explanation for the incomplete log-on might be mis-direction of the satellite communications antennae due to a spiral dive; however the receiver power indications provided by Inmarsat  remain stable throughout all signal exchanges, and so this possibility seems less likely.)
The possibility that the aircraft impacted the sea at or very shortly after this time (00:19:38) should not be ignored: an implication of this would be that at that time the aircraft was at a low altitude, affecting the calculated position of the 7th/final ping arc, and therefore the search region for wreckage on the sea floor. Taking the aircraft altitude to be near zero at this time rather than at 35,000 feet has the effect of shifting the 7th ping arc by about 10 km to the northwest; this is discussed in more detail below.
A separate analysis of the fuel data is being undertaken within the IG  and it is sufficient to recognize here that the rate of fuel consumption rate for both engines combined for the remainder of the flight, from 17:07 through to 0019:29, is an average of about 6,072 kg/hr, (13,386 lbs/hr), and hence significantly lower than that shown for the take-off and climb phases of the flight as reported in the Factual Information , Appendix 1.6B. It is expected that the difference in fuel consumption rates between the two engines will be lower too (information in the Factual Information report indicates differences of 1.9 and 1.3 per cent, for take-off and climb: reference 4), and for the purpose of the ongoing discussion I have assumed, based on a simplified analysis, that this difference is 0.8 per cent. Using this figure it is possible to deduce that the Right engine failed close to, and perhaps a few seconds before, 00:11 UTC on 2014 March 08.
Flight path after the first engine failure
The simulator trials mentioned earlier illustrated clearly that following the first engine failure the auto-throttle increased thrust in the remaining engine, altitude was maintained, and the (longitudinal) pitch increased as the speed reduced so as to provide adequate lift. The deceleration observed was noted, and the Indicated Air Speeds (IAS) were converted to True Air Speeds in Knots (KTAS) for illustration in Figure 1, below. The observed trend is linear, with a deceleration of approximately 19 knots per minute. (dy/dx = -0.315 ´ 60 = -18.9). A deduction from this result is that the aircraft would still have been well above the best single engine speed and would have continued to fly at the same altitude for some minutes after the engine failure.
Figure 1: Deceleration after first engine failure
The flight dynamics are such that although drag and the available thrust are lower at higher altitude, the minimum drag speed also increases. Hence, coincident with one engine failing, we would expect deceleration to commence immediately and a reduction in altitude to begin as the minimum drag speed is approached. This was not observed in the simulator trials commencing at FL350 (Flight Level 350, nominally 35,000 feet but in actuality the geometric altitude depends on the atmospheric temperature and pressure). In fact the speed continued to decrease (below the minimum drag speed) without a descent being automatically commenced, but the ensuing part of the simulator trial was perforce cut short by the failure of the second engine. The speed (and time) at which MH370 would have begun to descend is therefore unknown from the simulator trial.
Turning back to what we know about the actual flight, the BFO at 00:11 suggests that at that instant the aircraft was descending at about 250 feet per minute. Together then, the BFO descent rate, the estimated time of the Right engine failure, and the simulator trials, may all be reconciled if the altitude was greater than FL350, in which case it is possible that a shallow descent commenced just prior to 00:11.
The appendices in the ATSB report  provide an indication of possible vertical descent rates resulting from loss-of-control events at high altitude. Descent rates of greater than 20,000 feet/min have been observed.
At the rate of speed (and altitude) reduction observed in the simulator trials, and because the aircraft is observed to be within a normally-expected flight envelope, it seems clear that the aircraft would still be close to FL350 (or higher) at the time the second/Left engine failed, at 00:15:49 (+/- 10 seconds). If, as a result of total loss of control at that time (autopilot failure due to interruption of electrical power) it happened that the aircraft impacted the sea at 00:19:38, the average descent rate would have been about 9,500 feet/min, which is well within the observations referenced in the preceding paragraph.
An immediate conclusion should be drawn at this point. Taking a conservative view (conservative, that is, in terms of the plausible distance travelled from the 6th ping arc at 00:11), the 7th arc position calculation should assume that the aircraft was at or near sea level (the surface of the reference ellipsoid) at time 00:19:38, and hence only a little above sea level at 00:19:29, and descending rapidly. At the latitudes of interest this will position the 7th arc at a distance of about 56 nm from the 00;11 arc along the 186 deg (from True North) azimuth in the vicinity of a latitude of 38 degrees South.
Assuming that the deceleration is a linear function, as observed in the simulator trials, the distance travelled from time 00:11 until the Left engine flames out can be calculated. For a range of speeds at 00:11, and assuming that at that time the aircraft was exactly on the 00:11/6th ping arc, the distances are illustrated in Figure 2, below.
Figure 2: Distance travelled from 00:11 before second engine failure
Assuming a ground speed of 480 knots at 00:11 (equivalent to a wind-corrected KTAS of about 500 knots), and noting that this is likely to be an optimistic value since various IG path models suggest ground speeds between 429 and 455 knots at this point, and with a linear deceleration of 19 knots/minute, the ground speed at 00:15:49 would have been 389 knots, and the distance travelled from the 6th arc at 00:11 is 35nm (nautical miles). On an azimuth of 186 degT this will put the aircraft 21nm short of the 7th arc calculated at sea level for when the Left engine fails. Continuing with that rate of deceleration in a straight line (allowing for the effect of wind following the second engine failure), the total distance covered before 00:19:29 is 56 nm, which is just on the 7th arc calculated at sea level, but 6nm/10km short of the 7th arc at FL350.
Continuing deceleration after the Left engine fails is not a certainty. It is possible that the speed may increase, since it is governed primarily by the relationship between the drag and the component of the aircraft weight acting down the flight path. With the assumption that there is no further deceleration after the Left engine fails, then in 3m 40s the distance covered is 24 nm and hence the aircraft is capable of reaching the 7th arc calculated at sea level, but still not capable of reaching the (FL350) 7th arc at 00:19:29, on the 186 degT azimuth.
As a comparison it is useful to test the outcome assuming a lower ground speed, say 429 knots (rather than 480 knots) at 00:11, and assuming the same rate of deceleration. In this case the ground speed at 00:15:49 would be down to 338 knots, and the distance travelled from the 6th arc at 00:11 would be only 31nm, which is 25nm short of the 7th arc calculated at sea level. In order to reach the 7th arc in a straight line on the same 186degT azimuth, a linear acceleration of approximately 50 knots per minute would be required, reaching a ground speed of 485 knots at 00:19:29. This seems unlikely, and indicates a likelihood that the speed at 00:11 was greater than 429 knots. Perhaps even more likely is the possibility that the aircraft turned towards the 7th arc at the time of the second engine failure.
Flight path after the second engine failure
Observations from the simulator trials suggests that following the failure of both engines the aircraft will bank into a turn almost immediately. The direction of the turn, and perhaps the rate of the initial turn, is a function of precisely how the aircraft was trimmed immediately before the first engine failure, and this is of course unknown. However, the observation that the aircraft may not be capable of reaching the 7th arc if that is assumed to be at 35,000 feet (as discussed above) may help in reaching a conclusion here.
For example, if the aircraft banked and turned to the right after the Left/second engine failed, then with the speed profile examined above, commencing at 480 knots at 00:11, it would not be possible to intercept the 7th arc until after 00:19:29, and even then the turn radius would have to be greater than about 48nm to intercept the arc at all.
Alternatively, if the aircraft banked and turned to the left after the Left/second engine failed then an intercept with the 7th arc at 00:19:29 is possible, but only if the turn radius is between 8 and 10 nm. At the assumed speed at which the turn commenced the required bank angle is approximately 15 degrees. Figure 3, below, illustrates these possibilities.
Figure 3: Illustrating possible tracks after second/Left engine failure
The simulator trials illustrate that after entering a banked turn, even one with a bank angle as shallow as 15 degrees, the aircraft does not recover to a wings-level attitude. Rather, over a period of about three minutes, and interspersed with possible phugoids, the bank angle will continue to increase until the aircraft enters a spiral dive. At that point the bank angle may have increased to 90 degrees, the aircraft may have rotated through three complete turns, the aircraft speed with respect to the air would exceed the normally-allowed maximum operating speed (VMO), but not necessarily have increased beyond maximum Mach operating speed (MMO) at that altitude so that it would likely not have suffered severe structural damage, and the descent rate would be up to 15,000 feet/minute. A high-speed uncontrolled impact with the sea would be inevitable.
Note that a descent rate of 15,000 feet/minute at the airspeeds of interest requires an aircraft track dipping only about 20 degrees below the horizon. More extreme descent rates are certainly possible.
Based on this analysis one may conclude that:
- It is only with ground speeds greater than about 440 knots at 00:11 that it is possible subsequently to reach the 7th arc at sea level at all;
- Following the Left/second engine failure, the aircraft very likely entered a turn to the left, a turn which developed into a spiral dive over the course of a few minutes resulting in a high speed impact inside the 7th arc as calculated for sea level.
It is clear from this analysis that establishing precisely where the 7th arc is located is very important from the point of view determining the path of the final few minutes of flight, and the underwater search strategy to be used. Based on the corrected BTO (18,400 microseconds) at 00:19:29 provided by the ATSB (2), the advisable position would be to establish the 7th arc at the surface of the reference ellipsoid (i.e., sea level) and not at high altitude (say 35,000 feet) the distinction between these shifting the 7th arc by about 6nm/10km.
I thank members of the Independent Group (IG) for the active discussion, and contributions, which have greatly helped me to present this analysis and to arrive at the above conclusions. It is hoped that these will assist the official search teams in their identification of where to concentrate their efforts to achieve the highest likelihood of timely success.
 MH370 – Definition of Underwater Search Areas, 26 June 2014 (updated 18 August), ATSB Transport Safety Report.
 The Search for MH370, Journal of Navigation, September 2014, authors Chris Ashton, Alan Shuster Bruce, Gary Colledge and Mark Dickinson (Inmarsat).
 Fuel Burn Analysis, spreadsheet by Mike Exner, April 2015. (Note that this link to Exner’s spreadsheet was added on 2015 June 20.)