MH370 and Other Investigations

Runway on Cocos Island.

Introduction

Now that the recent search effort conducted by Ocean Infinity has ended without finding MH370’s debris field on the seabed, we continue to re-evaluate the evidence and consider other possibilities.

Many researchers that have reconstructed flight paths assume that the aircraft was on autopilot after 19:41. This leads to flight paths that cross the 7th arc at 26S or further south. Now that the 7^th arc has been searched as far north as 25S and at a width of at least +/-22 NM, we have to consider the following possibilities:

1. There are automated flight paths that end north of the 25S latitude that have not been previously considered.
2. The aircraft was actively piloted after 19:41.
3. After fuel exhaustion, the aircraft glided without pilot inputs and impacted further from the 7^th arc than was searched.
4. After fuel exhaustion, there was an actively controlled glide that ended outside of the areas searched.
5. The debris field was scanned but not detected.
6. The BTO data set was somehow corrupted, and we are not properly interpreting it.

Although we cannot completely dismiss any of these possibilities, and each should be further explored, this article addresses the first in the list.

The challenge in finding automated paths ending further north than 26S is that the reconstructed paths need to curve to the left and decelerate to satisfy the BTO. What follows is one way this can occur while the aircraft is navigating on autopilot with no pilot actions after 19:41.

The automated flight path assumes that the flight computers were programmed to pass near Car Nicobar Airport (ICAO: VOCX) and fly towards Cocos Island Airport (ICAO: YPCC) with an intention to land there. (A route that includes flying towards VOCX, YPCC, and other airports was previously considered by Richard Godfrey.) Here, we assume that after programming the flight computers for a landing at YPCC, there were no further pilot actions. Furthermore, we consider that approaching YPCC, the automated flight plan caused the aircraft to turn to the left to align with the runway, to decelerate, and to fly over and continue past YPCC. This combination of left turn and deceleration is required to match the BTO data.

There are several explanations for why the flight computers might have been programmed for a landing at Cocos Island and then that landing not completed. One explanation is the pilot became incapacitated.  Some possibilities for incapacitation include a physical challenge from crew or passengers, or the aircraft was hit by hostile gun fire leading to rapid decompression of the fuselage. The possibility that MH370 was pursued by a Malaysian fighter jet was the subject of a previous article, and may have relevance.

Assumptions and sequence of events

The reconstructed flight paths are based on the following:

1. FMC was programmed for automated flight between Car Nicobar (VOCX) and a landing at Cocos Island (YPCC) using the LNAV and VNAV autopilot modes at cruise altitude.
2. The FMC was programmed for landing on Runway 15 using the RNVZ15 standard approach with PCCNE selected as the transition waypoint. (The selection of a transition waypoint does not significantly change the results.) In the aircraft’s navigation database, the approach would be defined as: APPROACH RNVZ15 FIX PCCNI AT OR ABOVE 1500 FIX PCCNF AT OR ABOVE 1500 FIX OVERFLY PCCNM 55 RNW 15 FIX PCCNH TRK 152 UNTIL 1500; TRANSITION PCCNE FIX PCCNE AT OR ABOVE 1500 SPEED 210
3. Flying between VOCX and YPCC, the VNAV target speed was either LRC, ECON, the last speed constraint from the flight plan, or a speed selected in a VNAV screen. There was no speed intervention, i.e., the MCP speed window was closed.
4. At the Top of Descent (ToD) about 110 NM from PCCNE, the pilot did not reset the altitude to a lower altitude, which constrained the aircraft to continue at the existing cruise altitude.
5. At about 38 NM from PCCNE, the descent path calculated by the FMC would have reached 10,000 ft. The target speed would have reduced to 240 KIAS in accordance with the FMC’s default speed transition at 10,000 ft, even though there was no change in altitude from the cruise altitude.
6. Approaching PCCNE, the VNAV target speed was automatically reduced to 210 KIAS in accordance with the programmed speed restriction at PCCNE, or the minimum maneuver speed (MMS), whichever is greater, with the aircraft remaining at cruise altitude. MMS was about 210 KIAS.
7. At PCCNE, the aircraft turns towards waypoint PCCNI, and aligns with the runway on a track of about 152°M.
8. Upon passing the runway and the final waypoint PCCNH, the FMC reaches an END OF ROUTE, the plane continues at the cruise altitude on a constant magnetic heading until fuel exhaustion. As the speed constraint for the runway is less than the MMS, the MMS becomes the target in the MCP speed window, and this speed is maintained for the remainder of the flight until fuel exhaustion.

The input variables that were varied are:

• The starting position at 19:41. Since we are constraining the path to a great circle between VOCX and YPCC, only the latitude at 19:41 needs to be specified.
• The VNAV mode, i.e., whether in ECON, LRC, or constant airspeed. If in ECON mode, there is an associated Cost Index (CI), which is based on the cost of fuel and time. For ECON mode at a given CI, and for LRC mode, the optimum speed varies as a function of aircraft weight and altitude. VNAV also commands throttle and pitch so that the speed and flight path adhere to any speed and altitude constraints programmed in the flight plan or selected in the VNAV screen.
• The cruise altitude, which is assumed to be constant until the flame out of the first engine.

As the aircraft passes YPCC on a constant magnetic heading, the magnetic variation tends to slightly curve the flight towards the east as the magnetic variation increases from about 2.4°W near YPCC to about 2.7°W near 22 S latitude on the 7^th arc. On the other hand, after passing YPCC, the wind is initially towards the west at 19 knots and 266°T, but weakens and changes direction towards the east between 16S and 17S latitudes so that at 18S latitude, it is about 10 knots at 81°T.

Results

A range of paths can be generated by sampling the input space and incorporating the uncertainty in BTO values, BFO values, wind, temperature, and MMS. One solution that is shown below is at FL320 and M.819, with a position at 19:41 about 25 NM south of VOCX.

Automated flight path passing over YPCC.

At the time the aircraft reaches the approach waypoints for YPCC, the MMS is about 210 KIAS, and remains at this speed for the rest of the flight. The aircraft would cross the 7th arc at about 22.0S latitude, which places it well north of what was previously searched.

The following table summarizes the flight parameters after 19:41 for this case (M.819 at FL320). The RMS error for the BTO is 26.0 μs and the RMS error for the BFO is 6.4 Hz with a mean error of -5.1 Hz:

Discussion

Ocean Infinity has expressed an interest in continuing the subsea search for MH370 at some time in the future. Options include

• Scanning along the 7^th arc at latitudes north of 25S
• Scanning along the 7^th arc at previously searched latitudes, but at a greater distance perpendicular to the arc
• Re-scanning areas where the detection of the debris field might have been missed

Ultimately, the decision where to search must consider other aspects such as end-of-flight dynamics, drift modeling, surface search efforts, and fuel consumption, none of which were considered here. As such, this article is not a recommendation as to where to search next. Rather, this article was meant to provoke discussion about the possibility of an automated flight ending much further north on the 7^th arc than was previously considered. Also, the article provides additional data for scenarios in which the pilot intended to land on Cocos Island but did not take the actions required for landing.

Acknowledgement

I am grateful for comments received from Mike Exner, Richard Godfrey, and @Andrew.

Update on July 4, 2018

Here are the results for another path, including the results from a fuel analysis. The path assumes that after a hold at Car Nicobar at FL250, the aircraft proceeds towards YPCC at FL320 and M0.8, and crosses the 2nd arc about 53 NM south of Car Nicobar. The following table summarizes the flight parameters after 19:41 for this case (M.8 at FL320). The RMS error for the BTO is 25.3 μs and the RMS error for the BFO is 6.0 Hz with a mean error of -4.6 Hz:

The fuel model is an improved version of a model I developed over one year ago, and is based on the drag-lift curves for a B777-200 that was presented in Ed Obert’s textbook entitled “Aerodynamic Design of Transport Aircraft”, with fuel flow – thrust relationships developed from descriptions in Walt Blake’s Boeing textbook entitled “Jet Transport Performance Methods”. Previously, I found that the model predicted the tabulated fuel flow data for LRC and Holding speeds with an RMS error of about 1%. The present model improves the prediction by introducing a correction factor that forces the calculated fuel flow to the exact tabulated values at the LRC and Holding speeds, and linearly varies the correction factor as a function of Mach number between those speeds. As such, the accuracy of the model between the Holding and LRC speeds should be very high. Also added to the model are calculated flow rates for climbs and descents, which assume full thrust and idle thrust, respectively, with vertical speed and flight path angle (FPA) directly calculated from the thrust and drag models.

The results of the fuel analysis are tabulated in this Excel file, which includes the remaining fuel at one minute intervals from 17:07 UTC until fuel exhaustion. At each time, the fuel flow is calculated as a function of weight, altitude, speed, and temperature. Assuming both engines fail at exactly the same time, fuel exhaustion is predicted to occur at 00:14 UTC. If the right engine fails before the left, the final (left) engine will fail at about 00:17. The predicted time of fuel exhaustion is consistent with our assumed fuel exhaustion at 00:17, considering the uncertainty in the actual flight path, the engine PDAs, and the meteorological conditions.