What has been attempted 2014-2024

I summarise what has been attempted scientifically in the past decade. The initial breakthrough was the research using the INMARSAT radio signals and flight simulations. We will call them forward algorithms. The debris found since August 2015 allowed the research on backward algorithms, backtracking on oceanic currents. The satellite images database has been searched but the aircraft itself was not found, due to the fact that most of the flight happened in the darkness of a moonless night. However, floating debris has been identified. Also, some unconventional methods have been used.

Scientific research based on:

• INMARSAT radio signals and flight simulations (UHF) – Forward algorithms
• Recovered debris – Backward algorithms backtracking on oceanic currents
• Search in the satellite image database – Multi-static image processing algorithms
• Unconventional methods:
  • WSPR radio ham signals (HF 10 MHz) – Multi-static radio signal algorithms
  • Underwater acoustic signals – Acoustic detection algorithms of the crash
  • Electromagnetic pulses in the underwater cables – Electromagnetic detection algorithms

Here is the total reference list of the 25 scientific papers published in the past decade on Malaysian 370, which try to calculate the trajectory or the location of the crash of this aircraft. Most of them are peer-reviewed. We used a colour code here for the method: INMARSAT signals in red, ocean drift in green, etc. This reference list was put together with help from ChatGPT 4.

All these results are represented on Google Earth. You see here the Broken Ridge. The INMARSAT flight simulation forward algorithms yielded solutions South of Broken Ridge. In magenta you see the last point the pilot entered manually in his flight simulator, as published in the Accident Investigation Report. This is also South of Broken Ridge, but this was meant to be a farther, unreachable point to be used in the Flight Management Computer to define a direction, not a destination. The ocean drift algorithms however converged North of Broken Ridge, and of course, they moved away the attention from our findings back to the initial search areas. We will discuss entropy and why it degrades accuracy. Interestingly there is one recent paper, [A24] in our list, which is based on ocean drift of alleged debris from satellite observations, reducing the entropy accumulation from 16 months plus down to 6 months minus, and that immediately shifted their results South of Broken Ridge, as you see down here. That’s why we believe that understanding entropy is a key issue.

This is a zoom in the area of our results. Here you see our initial finding [A1]. [A2] is Ashton’s team finding, they used the constant Ground Speed assumption which explains why they indicated a position more to the North. Our main research [A3] indicated the rectangular perimeter here, and [A5] in red represents the results of Davey’s team, published by Springer. In hindsight, these are the most credible research papers, based on various algorithms. They are multidisciplinary approaches, based on UHF radio signals, meteorology, and flight simulations.

Why did the ocean drift algorithms not concur with the INMARSAT/flight simulation algorithms?

In red you see the positions indicated by the forward algorithms, and in dark green the centre of gravity for the results by the backward algorithms. The flaperon found later on the Reunion island is shown here in light green and the oceanic currents in the Indian Ocean make a direct link between both these solutions and the African coast.

Ocean drift is not just about oceanic currents! Surface winds do intervene on any floating object, which is pushed by the vector addition of hydrodynamic and aerodynamic drag forces. Surface wind modelling would require the exact moment when the debris landed, which is unknown.

In 2015, we started our own research using ocean drift using the model above, but when we understood the impact of the accumulated entropy, we abandoned it. The final results would have been as inaccurate as the whole Indian Ocean. To our surprise, some published papers did not use a combined hydro- and aerodynamic model like ours, they did just backtrack on the currents. A floating object such as this flaperon is carried by the oceanic currents by the hydrodynamic drag force of the submersed part, but also by the aerodynamic drag of the part above the water, which is exposed to the surface wind. The drift force is a vector addition of the hydrodynamic drag and the aerodynamic drag. The ocean drift is not only about oceanic currents.

Ocean drift is driven by dispersion and entropy prevents a backtracking algorithm from providing accurate results.

Entropy effects accumulated in the 16 months+ time interval degrade the accuracy of the results beyond relevance.

The backtracking algorithms could provide accurate results only if the time interval is small. Accumulated entropy prevents accurate backtracking if the time interval is too large. This is obvious in this simple aquarium experiment: an aquarium is split in two by a wall. Ink is poured in one half. When the wall is removed, the dispersion starts to spread, but for a while, an observer can determine where the ink was poured. After a while, the place is less obvious, but at least the ink-contaminated half initially remains traceable. There is a time limit, however, beyond which an observer cannot say which half was initially contaminated. Backtracking could find any of the halves with an equal probability.

To those who have great expectations from the ocean drift algorithms, I recommend this book. Moby-Duck is the true story of a shipping container full of plastic bath-tub toys which was lost during a storm in the Northern Pacific (Aleutian Islands). After many months, the ducks were discovered in the most remote and unexpected places in the Pacific but also in the Atlantic. This involuntary experiment is instrumental in understanding ocean drift as an entropic phenomenon.

Ocean drift backtracking to the initial location is based on modelling dispersion, which is affected by entropy. You cannot replicate the exact route of any given object. The route is subject to many so-called bifurcations.

If you release a group of separate objects at sea, they will land at different locations, as distant as thousands of miles away from each other. If you release objects far from each other, they might gather in a common place like the Great Pacific garbage patch.

The ocean drift papers either ignore the entropy and indicate a location or an area of the crash or consider it and end up with inconclusive results.

If the time interval between the release of a floating aircraft part at sea and the moment it is recovered is too large (16 months and above), the entropy causes excessive uncertainty in the backtracking results. That is why the INMARSAT-based algorithms and the ocean drift algorithms cannot compare in terms of accuracy or certainty. The only ocean drift algorithms that could provide a clue are those that track debris as observed from satellite images, which reduce the time interval from 16 plus months to 6 minus.

The INMARSAT algorithms themselves have their small share of entropy which intervenes between the 7th ping and the moment of crash, but the time interval of this descent is below half an hour. This atmospheric entropy causes the airplane with neutral controls to get random control inputs, which are unpredictable to our algorithms, so we need to avoid simplistic or speculative assumptions about the place of the crash with respect to the place of the 7th ping. The Independent Group’s claim that somebody flew the airplane manually during this final descent is an exception from the neutral controls assumption, but the active manual controls space of solutions can be included in the random control space of solutions.

Atmospheric Entropy also intervenes in the powerless glide of an airplane with neutral controls.

Understanding Entropy

In our efforts to find solutions to the MH370 mystery we found ourselves in a middle of an international crowd of experts, scientific researchers, pilots, sleuths, and journalists with the same objectives. This competition revealed our weak points (low self confidence, bad access to first hand resources, etc.), but also some aspects which seemed easy for us to understand and surprisingly hard for many others. The most striking example is the understanding of entropy. The entropy means that a system where randomness is characteristic may have many states out of which none is certain, there are many states, each with its own probability. With the passage of time, it is less and less conclusive to understand previous states from the current state, and there is a time limit after which the original information about a particular state of the system is completely lost. To illustrate this, we did the simple aquarium experiment where the dispersion of particles is that entropic phenomenon is taken as a proxy of the ocean dispersion. After a while from the beginning of the dispersion, an observer cannot determine anymore what was the initial state of the system.

We take an aquarium full with water, with a median wall plate splitting the aquarium into two halves. We pour ink in one half to colour the water, then we withdraw the wall plate. The dispersion phenomenon begins, but we are still able to determine which half was coloured after a couple of minutes. There is a time limit to this, though. After this time limit, an observer cannot backtrack visually the drift of the particles to a certain half. Both halves become equally probable to have been coloured at the beginning.

Why Entropy Matters in the Ocean Drift Modelling

When the first debris landed on African beaches after one year and 4 months from the crash, all the people obsessed with MH370 started to analyse if backtracking of these debris can reveal the location where the flight ended and the aicraft disintegrated. We started to do our own analysis based on the ocean currents and surface winds, but we quit this track when we realised that it is not getting us anywhere. In the 16+ months between the crash and the finding of the debris, the inherent entropy associated with the ocean drift phenomenon would make the results irrelevant. The computer model can perform this algorithm and backtrack the debris to the source, but the uncertainty of the result is unacceptable and if we try to calculate for example a 95% probability area of the source, we end up with a massive area where the aircraft could have crashed. So we dropped our research on this path. Now we see that many such papers have been published (see Table 1 and Figure 1). One of them [A12] seems to ignore the entropy altogether. Others take entropy just as to relativise their results (for example [A15]), and others consider the entropy properly, but this deprives the papers of conclusive numerical results, or leads to overextended areas (for example [A17], between parallels S17° and S33°). An interesting paper in this respect is [A25], which provides numerical results covering a large rectangular area, but that is based not on the debris landing positions, it is based on debris spotted much earlier, on satellite images. That makes this algorithm more likely to get relevant results, because the entropy applies to shorter time interval. The aquarium experiment demonstrates that time is a major constraint of drawing numerical conclusions with a decent degree of certainty in an entropic phenomenon.

How Is Entropy Relevant to the Problem of the Powerless Glide

Another instance where entropy is not fully understood is the powerless glide of a Boeing 777 without anyone at the controls. Normally, there is no entropy involved in navigation, guidance, and control of an aircraft, the system is determinist. However, when the powerless glide starts and if no one is at the controls (not even the auto-pilot or basic yaw dampers), the flight dynamics of the aircraft starts to depend on small or large random perturbations, due to the atmospheric turbulence. Even if the air is calm, when descending new layers of the atmosphere are encountered, and they have various wind speeds, causing pitch and bank angles movements, and possibly not-dampened oscillations. Over the duration of the descent, this random inputs in the system induce entropy to the system.

This explains why so many excellent experts in flight dynamics and pilots with tens of thousands of hours of flight did not really understand the phenomenon. Nobody has flying hours experience in powerless glide of an uncontrolled Boeing 777. Moreover, the pilot’s bias is in favour of control scenarios explains why so many pilots joined the Independent Group controlled ditch theory. In the controlled airplane flight dynamics, entropy does not intervene. In the uncontrolled flight of 15 to 30 minutes, the entropy makes the difference. We could say that entropic flight and determinist flight are two different physical phenomena. The whole MH370 flight is determinist, with the exception of the last part, the powerless glide, which is an entropic flight. If you have 20,000 flight hours in determinist flight, it would very difficult to accept or to really understand the entropic flight. We see no other explanation why so many pilots and experts agree with the idea that a powerless B777 falls straight down in a vertical dive at a high angle. One example is the China Eastern Airlines CES 5735 crash on 21 March 2022 which was captured on a camera falling straight down, but that was deliberately controlled into that attitude. As a consequence of accelerating above Mach 1, the aircraft broke apart in flight. This is easy to exclude in the case of MH370 because all the recovered debris are consistent with an impact fracture and none found so far indicates in flight break up, so the attitude of the aircraft when impacting the water was not straight down. In this I agree with the IG and with all experts who favour a 7°-10° pitch down attitude at impact, but I see it as a manifestation of the randomness of the entropy of an uncontrolled airplane, whereas the IG believes that someone was at the controls ditching the airplane. The entropic flight theory includes scenarios where the glide distance would be longer and the aircraft would descend at a lower path angle. Our theory is the entropic flight with no one at the controls, but the controlled ditch scenario is included in the space of solutions.

The ATSB vs. IG Dispute

In [C2] the search operations are reported as marked by a fundamental dispute between ATSB and IG. ATSB considers that (i) no one controlled the aircraft during the powerless descent and (ii) consequently the airplane fell in a vertical spiral dive, more or less straight down. IG considers that (i) the airplane was manually flown during the powerless descent and (ii) consequently the gliding distance was much longer, including some flaps deployment, but also making the location of ditching less predictable by a number of turns the pilot commanded.

We agree with ATSB (i) and disagree with all other statements. As a matter of fact our research is agnostic to the problem of manual control, so even if someone would have controlled the aircraft, the ditching location would fall inside our calculated perimeter. Both ATSB and IG have logic fractures between their (i)s and (ii)s. The misjudgment is caused by ignoring the entropy of the flight by both. The deduction of the ATSB that a close spiral dive is the only scenario of how such a flight ends is wrong, there are more probable states, and the close spiral dive is not even the most probable. The deduction of the IG that if the impact was not at a high angle (like that which occurs in a close spiral dive) it means that someone must have been at the controls reflects the same mistake from the opposite angle. A deduction requires a determinist flow of states, but when the entropy is involved, such deductions lose grounds. A final state is a consequence of many intermediary states, each with a certain probability.

References

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