After 10 years since flight Malaysian 370 (MH370) disappeared, it is time to reflect on what has been attempted and what conclusions can be drawn from this case. This Boeing 777 disappeared on the 8th of March 2014 with 239 people on board and has not been found yet (Fig. 1). Chances are that it will never be, since the search operations were abandoned 7 years ago after spending AUD198 million (€120 million). How wisely were these funds been spent?

The data sheet of the aircraft (Fig.1) is presented in Table 1.

On 8 March 2014 there was this aircraft accident all over in the news. The flight from Kuala Lumpur to Beijing did not reach its destination and disappeared in the Gulf of Thailand, after uneventfully reaching the cruise flight level (Fig. 2). As an aerospace engineering professor with some experience in aviation safety, my students expected me to explain this accident as I usually do. This time, I found myself incapable of explaining anything. It was a mysterious case. The only detail which caught my eye was the location of the disappearance, a waypoint called IGARI. It was hardly a coincidence that this was a handover point between the Malaysian and the Vietnamese ATC. This detail increased the probability of an intentional act. It did not look like an accident to me. When I checked the transcript of the radio communications, I noticed that one of the pilots reported twice their cruise flight level to the Malaysian ATC. This was unsolicited, unusual, and looked suspicious. The controllers knew this level, they had cleared the flight to climb to this level, and they saw the flight level on their secondary radar screen. What was the purpose of these useless transmissions? Maybe to reassure the controllers that everything was fine with the flight, just minutes before everything will turn to quite the opposite. On 10 March 2014 Mr. Azharuddin Abdul Rahman, chief of the Malaysian civil aviation, presented hijacking as one of the hypotheses for the first time, but later many details converged to this scenario: hijacking of the aircraft and mass murdering of the occupants. This was no accident. it was a carefully planned hijacking, mass murder and hide of the evidence as far as possible, in the most remote and uncirculated area. At the time, this hypothesis was not at all popular, most people including experts believed in an accident scenario: engine failure, structural failure, and fire were the most circulated. The structural failure hypothesis was fueled by the previous involvement of the aircraft registered 9M-MRO (S/N 28420) in a minor accident. Later, when the continuation of the flight was evident, the only accident scenario still compatible with the new evidence was a hypoxia case similar to the Helios flight 522 (14/08/05). However, such a scenario can happen during climb with a gradual depressurization left unnoticed, whereas the communications at the cruise flight level proved that people were breathing ok. So many facts have converged to the intentional act hypothesis lately, that the accident scenario has now been left with zero probability.

The aircraft was last on radar near IGARI point in the Gulf of Thailand South China Sea on 8 March 2014 (the orange dot in Fig. 3), so the search and rescue operations started on 8 March 2014 from there, in the orange circle, Fig. 3. After a couple of days, the Malaysian authorities released a stunning detail: the flight continued, and it was tracked for 1 hour by the military primary radar in the Malacca Strait, Andaman Sea. However, no military jets were scrambled to intercept it and the flight exited the coverage area, flying to north-west to the Andaman Sea.

On 15 March 2014, the INMARSAT satellite communications company announced that MH370 was in connection with their Indian Ocean satellite for 6 hours, flying to an unknown direction and thus covering in excess of 2000 Nautical Miles. This increased the mystery and the theoretical search area to a staggering 66.9 mil. sq. km (Fig. 3). They made public the raw satellite communication data. This provided a great opportunity for my friend Prof. Cristian Constantinescu and me and to calculate. Initially we wanted to try to calculate just the direction of flight. There were two potential directions consistent with the data, one to north and one to south. The direction to the south made no sense because there were no airports along that corridor, so we placed our bets on the north. Amazingly, the southern corridor matched the data 10 times better than the northern corridor. In the Research section I explain how these calculations were performed.

Our first results were published on aviatia.ro portal in Romanian on 20 March 2014 [B13], with a conclusion that the southern route was more probable, contrary to logic since there were no airports on that path. We repeated the calculations many times because we did not trust our own results, especially because the costly search operations were taking place so far away from where our calculations indicated the final point of the flight, south of the Broken Ridge. My take in that article is still valid today: why was MH370 left to fly one hour in the Malaysian airspace without any radio contact, without being intercepted by the air force jets? It is a lesson to be learned very early from this tragedy, confirming the importance of the air policing of the skies.

On 3 April 2014 the search moved to the Indian Ocean, west of Perth, Australia, based on the first trajectory calculations of the INMARSAT radio signals. These calculations were very approximate, assuming constant Ground Speed of the aircraft and ignoring local weather. On 14 June 2014 the search area moved more to the south, but still north of the Broken Ridge. After repeating our calculation many times, on 31 August 2014 we submitted to the Joint Agency Coordination Centre (JACC) our first paper [A1], which was later presented in September at an international conference in Bucharest. This is our <letter> and the <mail exchange> with the JACC, they acknowledged to receiving the paper, but showed no further interest into our work. However our calculations pointed to a location 750 NM to the south of the current search area, south of the Broken Ridge. However, on 14 October 2014 they moved the search area south of the Broken Ridge for the first time, probably as a consequence of the results of the INMARSAT team (Ashton et al), published in the Journal of Navigation [A2]. Both our results and the INMARSAT team’s results indicated the final point of the flight south of the Broken Ridge. So the search area was finally right after 8 months of search operations in other hopeless areas. It was 7 months too late for the expected life of the ULB batteries, leaving the research team without an important underwater acoustic homing signal. I find this hard to explain: based on the INMARSAT radio signals published in March 2014 it was obvious that the airplane crashed south of the Broken Ridge, but the search efforts were wasted for 8 months in areas with a low probability. Why did this happen? I am sure it was not an intentional act, as conspiracy theorists enthuse about. Rather, I believe it was the result of a bias in the mindset of the JACC experts.

Fig. 4 illustrates a synthesis map of the search areas, and as you can see there is a huge effort to cover 120,000 Sq. Km. along the so-called 7th Arc. This search was abandoned after 3 years after spending €120M, mostly north of Broken Ridge, where we believe it was unplausible to find anything. My conclusion by looking at this map is that there has been a bias towards the North in the minds of the search experts, attributing more probability to the Northern places. Here is this example of the red-yellow-green arc: red denotes “highest probability”, yellow “medium” and green “lowest probability”. After the brilliant paper of Ashton et al INMARSAT team was published in the Journal of Navigation [A2], the JACC moved the search south of Broken Ridge for the first time, as you see in magenta colour. Still, the hashed area shows more probability attributed to the north and less and less to the south, where our first [A1] and our second papers [A2] indicated.

Of course the search operations were extremely difficult, I do not want to blame anyone. It is easy to criticise from the armchair, with hindsight information. You might be surprised that the surface of Mars is better charted than the Southern Indian Ocean. Yet, these mistakes demonstrate how important an unbiased approach is. The circumstance that the search operations took place in a hostile environment demand even more careful planning of the search areas and better use of available information.

In July 2018 an inconclusive Accident Investigation Report was released [B4] – Fig. 5. From this report I selected this detail in Fig. 6: the Pilot In Command of this airplane practised flights in his home flight simulator very far to the South of the Indian Ocean. Fig. 7 represents the 7 points entered manually in his Flight Management Computer at home, and interestingly they match the trajectory calculated and published by us before these data were made public. Points 6 and 7 seen here down, were entered manually as Latitude and Longitude, in an area no airplane would go, being the most remote area from any airport and from any circulated routes.

Fig. 5 – The Malaysian ICAO Annex 13 Safety Investigation Team for MH370, Safety Investigation Report Malaysia Airlines Boeing 777-200ER (9M-MRO) 08 March 2014. Kuala Lumpur, Malay published on 2 July 2017 [B4]

The breakthrough in this case was made possible by INMARSAT through their early public release of the handshaking signals, the famous 7 pings exchanged between the SATCOM transceiver on board of the Malaysian 370 and the INMARSAT Indian Ocean geostationary satellite. The SATCOM transceiver was left without business because the ACARS had been cut off, but nevertheless, it maintained its readiness to communicate by pinging the satellite from time to time, in principle one-hour time intervals. There are 7 pings usable to locate the aircraft. After the Air France 447 accident in 2009, INMARSAT decided to log not only the carrier frequency shift (so-called Burst Frequency Offset or BFO), but also the Burst Timing Offset (BTO) which provides the distance between the satellite and the aircraft, in case such a communication signal would be ever used for tracking an aircraft, as attempted in the Air France case (Fig. 8). In our research we privileged the BTO and calculated just using the BTOs, we disregarded the BFOs. This is something we did differently from other teams. The positioning using BFOs in this case is an ill-conditioned problem due to the high angle (over 60°) between the aircraft Ground Speed vector and the direction to the satellite. If BFOs participate in a BFO-BTO data fusion, the accuracy is worse than if we rely just on the BTOs.

As early 15 March 2014 (one week after the disappearance), INMARSAT released their data in raw format, allowing us and all other teams to calculate. As I mentioned, our first results were published on aviatia.ro portal in Romanian on 20 March 2014, with a conclusion that these first results pointed to the southern route, which we found contrary to logic because there were no airports on that path. We repeated the calculations many times because we did not trust our own results, especially because the costly search operations were taking place so far away (Fig. 9). In June 2024, CNN released a piece of news on an American team who calculated a place not far from our results [B1], and this gave us the courage to come forward. This paper called Possible Trajectories of the Flight Malaysian 370 [A1] was sent to JACC on 31 August 2014. JACC coordinated the search efforts in the Indian Ocean.

On 18 September 2014 we did a keynote plenary presentation of this paper in the INCAS Aerospatial international conference in Bucharest (Fig. 10). We did not expect its publication in the conference proceedings, because plenary presentations in this conference are usually left out of the proceedings, but to our surprise, it was published in January 2015. In the meantime we co-opted our aerospace engineering master student Barna Jakab in our team and did a much better version. In November 2014 we submitted this new paper to the AIAA Journal of Navigation Guidance and Control. They rejected it immediately, so fast that I took it as even without reading it). The reason given was that the paper did not correspond to the scope of the journal. I found this appalling: the greatest mystery of aviation to be solved by an innovative navigation method did not correspond to the scope of the JNGC. At least we were lucky with a fast rejection. Usually, these rejections take ages. We decided to supply the article to the Journal of Navigation on the assumption that at least they could not claim that the subject does not interest them, since the Ashton et al paper had already been published.

The Indian Ocean INMARSAT satellite was rather old, low on fuel and slightly off the Equatorial orbit. The orbit correction required more fuel than the satellite can afford to burn at that stage of the life cycle. Instead of appearing as a fixed point in the sky, it appeared to oscillate along a curve illustrated in Fig. 11 and this complicated the calculations.

In our first paper [A1], we provided scientific proof that the southern corridor was 10 times more probable than the northern corridor, as seen in the diagram Fig. 12. Both corridors were compatible with the radio signals, but the quadratic sum of errors for the 7 pings was ten time smaller i.e. better fitted to the south than to the north. This was our method based on BTOs and flight simulations but in the paper of Ashton, Schuster-Bruce et al [A2], they provide a BFO based proof (Fig. 13). The INMARSAT team’s method [A2] uses BFO + BTO to make a compelling demonstration that the southern corridor is more probable from the INMARSAT data.

In Fig. 13 you see the major turn in the Andaman Sea, the vertical line in blue. This was the turn to an unknown direction, but Ashton’s team did a straight-line flight simulation of the pings for a northern flight (in red) and a simulation for a southern flight (in green). The actual signals in blue fit perfectly to the southern corridor. There is a minimum there when the aircraft crosses the Equator. Please, keep in mind this diagram because we will discuss later the weak signal team ideas and findings. These pings are aligned in what seems to be a straight-line flight. The turns would look like vertical variations such as those in the Gulf of Thailand and in the Andaman Sea. So this also serves as proof that the multiple turns hypothesis assumed by the WSPR team [A20] [A21] is a fantasy.

Fig. 14 illustrate our second paper called Reconstructing the Malaysian 370 Flight Trajectory by Optimal Search, also published in the Journal of Navigation [A3]. We did a total search among 34 million simulated trajectories and found 38 solutions with a Quadratic Sum of Errors lower than 25 km for this 6,000-km flight. The errors represent distance discrepancies of the latest 6 Burst Timing Offsets. After the flight disappeared from the primary radar at a point called 18_22, it continued to fly for a number of minutes (TTT) before taking a major turn in the Andaman Sea. The new track TK, the Mach number M, and the Flight Level FL are the other unknowns of the search. We searched for all possible values, but soon the algorithm converged to the underlined ranges of values: TTT between 5 and 17 minutes, TK between 183° and 193°, Mach between decimal 82 and decimal 89 and Flight Level between FL340 and FL430. The INMARSAT signals best fitted the fastest and at the same time the highest trajectories. What we did differently from other teams was that we considered the weather at the time and at the place of the flight, and our flight simulation considered all the automated flight modes in the Flight Management System and the Autopilot. The last ping (the 7th) was a half ping and it indicated when the fuel-starved aircraft ran out of power. We confronted that moment with the result from our engine simulation, integrating the fuel burn over the duration of the flight. The errors for the 38 solutions were remarkably low, within plus or minus 2%.

We attempted a high fidelity simulation using the weather and the flight dynamics of the aircraft and a turbine engines simulator. At the time, we were the first team to consider the local weather at the place and at the time of flight.

These are the main features of our method:

• wind vector field at the time and place of flight
• temperature
• pressure
• B772 flight dynamics
• RR Trent 892 engines
• Flight Management System (all modes scenarios)
• Auto Pilot (all modes scenarios)
• Asymmetric engine out at fuel starvation
• Engine-out gliding trajectory
• INMARSAT-3 IOR orbital dynamics
• Ping signal propagation (ionospheric refraction)

In this virtual environment we performed a multimodal optimization by total search covering 34 mil. possible trajectories. A refined search narrowed down to 42,240 more promising trajectories, and we selected 38 solutions with quadratic sum of errors < 25 km, which is remarkably small for a 6,000 km flight. We selected the 25 km threshold because that corresponded to the inherent errors of the radio signals.

Our paper [A3] was written between August – November 2014, it was submitted to the Journal of Navigation on 13 January 2015 (after the AIAA JNGC rejection), it was accepted after an intense peer review process on 1 July 2015, and finally published online on 30 July 2015 and in printed format in January 2016. One of the objections of the reviewers was why did we consider the influence of the wind? Is it so significant? The probable FMS mode maintained constant Mach. They made us repeat all the calculations without using the wind information, and the results degraded one order of magnitude. The quadratic sum of errors increased from under 25 km to 190 km. That convinced our reviewers that the wind adds value, and they approved the paper after several months of discussions. Although this process incurred a major delay in the publication of our paper, we were grateful to the anonymous reviewers, because they were quite competent and addressed many issues, helping us to improve the paper. In particular they spotted our assumption error about the 7th ping from our previous research [A1]: the 7th ping corresponds to the both engine out moment and not to the moment of the aircraft impacting the water. We initially assumed the latter because we could not believe that the SATCOM transponder was not connected to the RAT powered essential bus.

Fig. 15 is a diagram of the simulated Ground Speed for one of our 38 solutions. We considered the weather, and consequently, the Ground Speed is far from constant. Most other researchers and experts at the time assumed the aircraft’s speed was constant. To the left, you see the turn in the Andaman Sea and how the Ground Speed suddenly drops due to the turn from a tailwind into a headwind. At the right side you see the sudden drop in Ground Speed due to the loss of power.

Fig. 16 illustrates our published results, our 38 solutions with a Quadratic Sum of Errors of less than 25 km for this flight. In red you see an envelope of all possible crash locations.

We were very disappointed that in 2017 the search was abandoned. Although we were both early and accurate in our research, our papers were not taken seriously. The proof that our calculations were accurate is provided by the ATSB themselves. In 2017 the ATSB published their final report on the search [B3]. We took the liberty to superimpose our own findings on this map in Figs. 17, 18, and 19. Our area is that yellow footprint and the blue dot is our initial calculation in early 2014.

Fig. 18 – The Heatmap of the MH370 end of flight positions as published in [B3]; on that background, our research results were added: [A1] as a blue dot and [A3] as a yellow footprint, the envelope of our best fitted 38 solutions

The Royal Institute of Navigation though took us seriously, and we are so grateful for receiving the Richey Medal from His Royal Highness Prince Philip of Edinburgh himself in London, as the best scientific paper published in the Journal of Navigation in 2016 [A3]. It was published online in July 2015 and in print in January 2016.

This was the greatest honour and professional recognition for me and my team, Professor Cristian Constantinescu and Barna Jakab. At the same time, the paper itself received no relevant citations, although both the Davey book in 2016 [A5]  and the ATSB report in 2017 [B3] indicated identical results to ours. This means that the results were obtained independently and thus confirmed twice.

Fig. 20 B – The Richey Medal 2016

The recognition of our work is a mixed bag: the large scientific community and the search operation experts decided to ignore our work, whereas the Royal Institute of Navigation and the Journal of Navigation found our work relevant. In the next Research section, we analyse all the relevant published research between 2014 and 2024, to draw a conclusion on how well did our scientific community fulfill its duty to debunk the largest mystery in the history of aviation. The search operations and the final investigation report obviously represent costly failures of the aviation community. The question is did we learn anything from this failure? More on this in the Impact and Lessons Learned section.

In 2024, having finished the work for my most important book [A26], I could afford to dedicate time to this 10 years time mark, and participated as keynote speaker in three MH370 events:

• 10 Years After – Malaysian 370 Webinar with RIN on 27 March 2024
• EASN Research Webinar: 10 Years of Research into the Malaysian 370 Lost Flight on 17 May 2024
• RIN Annual Meeting Invited talk: MH370 Disappearance: 10 years on, London, 18 June 2024

In preparation for these three events, I got together with my team mates Cristi Constantinescu and Barna Jakab and reviewed what happened in the past 10 years. This site section is a follow-up of these efforts. As a general conclusion, we were stunned to find that our 10-years old work is still relevant today in the MH370 case. Self confidence has never been our strong point, and we have never believed that our work really mattered. We have always expected to read scientific papers much better than ours. However, the most important scientific results confirmed ours.