How We Know Where MH370 Went

DSTG report 1

One of the most misunderstood insights into the riddle of MH370 is how the plane’s final path can be derived from Inmarsat BTO data alone.

Recall that the data, which was generated after someone on board caused the Satellite Data Unit (SDU) to re-logon to the Inmarsat Satellite 3F-1 over the Indian Ocean at 18:25, comes in two flavors. The first, the Burst Timing Offset (BTO) data, reveals how far the plane is from the satellite at a given time. This can be mathematically converted into a set of “ping rings” along which the plane must have been at a given time. The BTO data is very well understood and fairly precise, providing an accuracy of within 10 km.

The second, the Burst Frequency Offset (BFO) data, is more more complicated and much fuzzier than the BTO data; its inherent uncertainties are equivalent to a position error of hundreds of miles. It doesn’t have a single physical correlate but is related to how fast a plane is going, what direction it is headed, and where it is located.

For a time after MH370 disappeared, searchers hoped that they could combine these two data sets to identify the area where the plane issued its final ping. After months of work, however, they determined that this would be impossible. The BFO data is just too vague. However, along with the bad news came some good: it turned out that by the clever use of statistics they could figure out where the plane went using the BTO data alone. The methodology developed by Australia’s Defense Science and Technology Group (DSTG) and explained in an ATSB report entitled “MH370 – Definition of Underwater Search Areas” released last December.

Many independent researchers do not understand the technique and believe that it is invalid. For instance, reader DennisW recently opined that “The ISAT data cannot, by itself, be used to determine a flight path. One has to invoke additional constraints to derive a terminus.” But I believe that the DSTG position is correct, and that one does not need to invoke arbitrary additional assumptions in order to calculate the plane’s track. I’ll explain why.

First, some basics. Imagine that you have two ping rings, one created an hour after the other. For the sake of simplicity, let’s say the rings are concentric, with the later ring’s radius 300 nautical miles bigger than the earlier one’s. Let’s further assume that the plane crossed some arbitrary point on the innermost ring. If that’s all we know, then the plane could have taken any of an infinite number of routes from the first to the second. It could have travelled radially directly outward at 300 knots. Or, if traveling straight at 400 knots, it could have turned left or right at an angle. Or, it could have traveled faster than 300 knots on any number of meandering paths. So, the fact of the matter is that this simple understanding of the plane’s situation indicates that it could have traveled by wide number of paths and speeds to a wide range of points on the second arc.

However, there are some pecularities of commercial aviation that narrow the possibilities considerably. The most important is that planes can only travel in straight lines. They can turn, but in between turns they will fly straight. Knowing this vastly reduces the number of paths that MH370 could have taken between 19:41 and 0:11. It could not of simply meandered around the sky; it must have followed a path of one, two, three, four, or more straight segments.

Through the marvels of modern computing, researchers can generate a huge number of random routes and test them to see which fit the observed data. It turns out that if the plane flew straight in a single segment, the only routes that match the data are those that are fast, around the speed that commercial jets normally fly, and end up over the current search area. If you assume that the flight involved two straight segments, it turns out the ones that fit best are those in which the two segments are nearly in a straight line and are also fast and wind up over the current search area.

If you suppose that the flight after 19:41 involved a larger number of segments, your computer’s random generation process will be able to come up with valid routes that are neither straight nor fast, and do not end up in the current search area. But to come up with such routes, the computer will have to generate many, many others that do not fit. So it is extremely unlikely that by random chance the plane would have happened to travel a slow, curving route that just happened to “look like” a straight, fast route.

“Well,” you might object, “presumably whoever was in control didn’t fly randomly, they had a plan, so modeling by random paths isn’t appropriate.” But a plan of unknown characteristics is equivalent for our purposes to a random one. After all, there is no imaginable reason for someone to fly a plane over empty ocean in the dark at a slower-than-usual rate, making slight turns every hour or so. (Before you say that they might have done it to throw searchers off their trail after the fact, bear in mind that whoever took the plane would have had no way to know that Inmarsat had started logging BTO values a few months before, let alone imagine that they would be able to conduct this kind of analysis.)

When DSTG ran the math, they came up with a probability distribution along the arc that looks like the image at top.

Worth noting that the peak of the curve, and the lion’s share of the area under it, lie in the southern half of the search box, but it also has tails that extend past the box in either direction.

When the search of the seabed began, many expected that the plane would be found in short order. When it wasn’t, the burning question then became: how far out from the 7th arc should we search? A one-dimensional question had now become a two-dimensional one. Based on past loss-of-control accidents and flight simulations, the ATSB decided that an out-of-fuel 777 with no pilot would enter a spiral dive and impact the surface within 20 nautical miles. Mapping the two probability distributions (i.e., where the plane crossed the 7th arc, and where/how far it flew after that) yielded the following probability distribution:

DSTG report 2

I believe that we have to take the image above with a grain of salt, as I don’t think it is really possible for a plane to fly more than 40 km by itself. It’s generally agreed that the only way the plane could have plausbily gone further than that is if the pilot was conscious and actively holding the plane steady in a glide, in which case it might have gone as far as 100 nm.

A few months before the ATSB publlshed this analysis, a further set of information about the impact point of MH370 became availalble: the plane’s right-hand flaperon washed up on Réunion Island. Reverse-drift analysis was performed by several independent groups to determine where the flaperon might have started its journey. The German institute GEOMAR came up with the following results:

map_mh370_figure_0516_en_a74ba7fb33 small

As you can see, the probability distribution hardly overlaps at all with the probability distribution derived from the BTO data; it only touches at the northeastern corner of the search box. Drift analysis performed by other groups reached a similar conclusion. Using a branch of mathematics called Bayesian analysis, it’s possible to take two probability distributions and merge them into a single one. I’m not a mathematician myself, but intuitively one would surmise that given both the BTO and the drift-model data sets, the new peak probability are should lie somewhere between the northern end of the current search box and Broken Ridge.

The ATSB report disagreed, arguing that the drift analysis

… made no meaningful changes to the ATSB search area due to the relative weighting of the significance of the drift analysis in comparison with the analysis based on the satellite data. While this debris find is consistent with the current search area it does not provide sufficient information to refine it.

What this means is that the ATSB considers the BTO data and its analysis “hard” and the reverse-drift analysis “soft,” because the random motion of ocean currents introduces a large amount of uncertainty. However, the reported also noted that “if additional debris is identified it will be included in the analysis to provide further information on the location of source areas.” Indeed, after the report came out other pieces of debris were found, and drift modeling of these pieces be used to refine the search area. Indeed, after I published last week’s guest post by MPat, reader Ge Rijn pointed out:

Over those 20 years in MPat’s model only 7 out of 177 buoys landed in Australia. Those 7 all passed the search box under 36S… [this] points clearly to the trend the more south you go under ~36S the more likely it becomes buoys (debris) will land on Australia and the more north you go above 36S the less likely it becomes buoys~(debris) will land on Australia. This is also because the more south you go under ~36 the currents tend to go further east and the more north you go around 36S the currents tend to bend stronger to the north avoiding Australia. And this is exacly what the facts about found debris shows us till now.

Note that 36 degrees south is just shy of the northern end of the current search area; as Ge Rijn observes, historical drift data suggests that if the plane had crashed south of this latitude, debris should have been found in Australia, which it obviously hasn’t.

The size and species mix of barnacles growing on ocean debris could provide clues as to which waters it floated through; oxygen isotope analysis can provide information about the temperature of the waters that it floated through. As far as I know, no such analyses have been conducted. For a long while now, the ATSB’s weekly update reports have included the phrase “In the absence of credible new information that leads to the identification of a specific location of the aircraft, Governments have agreed that there will be no further expansion of the search area.” The fact is, though, that further information is available, and it could be used to determine which of the two possible explanations is more likely: that the plane passed over the current search area and was held in a glide, or crossed the seventh arc further (but not too much further) to the northeast.

489 thoughts on “How We Know Where MH370 Went”

  1. @VictorI:

    Thanks for the link. How inexcusably stupid of me forgetting to mention the transsonic effects. Apart from that the paper doesn’t seem to be in conflict with my statement. Figure 30 for a B767 shows how the flutter-limit dynamic pressure increases with reducing Mach, i.e. reducing TAS.

    The associated text states: “The main objectives for the high-speed wing testing were to determine experimentally the effect of Mach number on flutter characteristics …”.

  2. @VictorI: “In addition, the ground speed observed by the radar prior to 18:02 is relatively high and implies that the aircraft would have been at low altitude. This is likely to result in poor fuel efficiency, …”.

    I regard that merely as evidence of the authors ignorance in the field of airplane performance.

  3. @oriondt

    Thank you for confirming. Things were a bit ‘spoofy’ lately here and still seem to be. So I just asked..
    And thanks for your post some time ago on the ‘blue panel’. It set some things in motion again IMO.

    Question; are you able (and willing) to perform a forward Adrift model with a significant amount of ‘ducks’ starting from a box between 36S and ~28S along the 7th arc? And offcourse to find out where those ‘ducks’ will land after ~18 months?

  4. @Ventus45 – mobile phone connectivity:

    There are some experiments here on low speed cell phone connections (at less than 150 knots – max altitude = about 6k feet) and also some user experiments trying to connect at commercial aircraft heights and speeds (only connecting on approach, less than c. 250knots and around/less than 2.5k ft – scroll to end of second link):

    The conclusion appears to be that, even with CDMA, you would need a (single?) cell mast at a good distance from the aircraft to avoid doppler and also to avoid the phone constantly switching to other, nearer masts (before the call has had time to connect) due to the speed of the aircraft and the number of masts.

    So connecting over an urban area with many cell masts at such high speed might be problematic, more likely to connect over rural areas with less but higher-powered masts, but general user experience suggests it’s still unlikely?

  5. @Victor: thanks – but this means that the DSTG-reported speed variations you once dismissed as unrealistic are now what you ask us to RELY upon as evidence of path feasibility.

    If you are asking us to reverse our position on the reliability of the DSTG-reported speed variations this fundamentally, I suggest you provide supporting evidence for such a reversal – e.g. a flight simulator log of a path which both descends enough to facilitate a telco ping near Penang AND covers the requisite distance in the requisite time.

    As it stands, I believe the only support you’ve provided for this position reversal is “CNN reported that anonymous US officials confirmed the co-pilot cell phone ping story, and I believe them”. Many of us don’t, for many obvious reasons.

  6. @Brock McEwen: I am not asking you to RELY upon anything. Nor am I asking you to BELIEVE anything. At most, I have courteously tried to explain to you my line of thought.

    You’ll have to show me where I said the speed variations in the DSTG report were unrealistic. My memory is that I have been trying to understand the speed profile and I have asked both Malaysia and the ATSB for the radar data precisely because the data conflicts with a constant Mach number, high altitude flight, which is what I concluded in my radar report published before the DSTG was released.

    I have explained to you that there can be a descent and a climb with no loss of average TAS other than concerns about flutter from overspeed. I don’t know how to better explain it so I won’t try again. Perhaps you should ask somebody else.

    As for the cell phone connect, I gave you a link to a New Straits Times article that also made reference to this, so it is not just CNN. I am confident that this story is true for a number of reasons. You choose to not believe it. That is your choice. My agenda is not to persuade everybody here that I am right.

    Many here also don’t believe that the FBI found coordinates in the SIO on the pilot’s computer simulator, despite repeated claims from a variety of sources. I expect more will be known about this soon. And then the two camps will form–one accusing the pilot, and one accusing the FBI for framing the pilot. My guess is that you will be in the latter.

  7. @Middleton

    I encountered both your links while researching the use of cell phones on the flights associated with the 911 incident some time ago. There is another confusing fly in this ointment. No point in dredging up the pros and cons of that experience. Suffice to say the FBI puked all over themselves several times.

    My point here is that the links you reference specifically refer to tests attempting to make calls and the success rates at various speeds and altitudes. Hamid did not make a call. No one ever claimed he made a call. What is claimed is that his phone registered with a network. This is a much different and far less stringent circumstance than completing a call over the network. To my knowledge no testing has been done relative to network registration from aircraft. Also the studies you link are classic examples of pedestrians trying to do science. Neither “study” attempted to do what is known as a “tower dump” to get registration information. Tower dumps are often used by law enforcement agencies to track who was present at various events such as demonstrations. Some of our intelligence agencies even use their own portable base stations known as IMSI-catchers to collect this data.

    So while your links are interesting, they are not really relevant to the problem statement. I do suggest you read some of the vast body of “literature” available relative to the 911 cell phone calls, especially for Flight 93.

  8. DennisW: Exactly. One would need to have the cooperation of the telephone company to determine if a phone registered on the network. The ability to complete a call is requires a better and longer duration signal.

  9. @DennisW

    I have always wondered why didn’t investigators check for cell registrations of the F/O cell phone with other cell networks in Malyasia, Thailand, Indonesia, and Maldivess. The technical possibility that F/O’s phone may have at least registered on other cell networks is real so why didn’t investigators pursue this avenue of investigation more throughly? Why didn’t they check with all cell providers in the area? Why is it that it’s always seems to be the US officals telling us this info and not the Malaysians or the actuel Telco company who providied us the data which recorded this alleged cell number registration?

    This whole story stinks!

  10. @DennisW said:

    ‘So while your links are interesting, they are not really relevant to the problem statement. I do suggest you read some of the vast body of “literature” available relative to the 911 cell phone calls, especially for Flight 93.’

    Dennis, thank you for your suggestion. I do understand the difference between attempting to make a call and whether the cell tower actually registered the connection, whether or not the caller thought it had. And although it was a while ago now, I can confirm I have read a fair bit on the events and ‘investigations’ of 911 and also on the alleged cell phone calls made from flight 93.

    There seemed little will then for the authorities to gather/provide factual information on whether cell phones had actually connected to towers, and we have a similar situation now.

    Until (if) that information (data) is made available in this case, then the best we have is the other side of the ‘experience’, if you like: what is the likelihood of connection, based on things such as range of cell masts, spacing, height and speed of the aircraft.

    It is fine to decry ‘non-scientific’ approaches (that yet might still glean some information or stimulate ideas) when you have actual ‘scientific’ data. Until then you have to assess possibilities and likelihoods based on what data / information (or estimates, guesses, approximations, modelling …) you do have.

    That is, after all, largely what has been happening here (and in other places) for the last 2 years, and still is. And so those links (which were meant to extend/add to the post made by Ventus45) were to some (whatever) extent informative as a starting point for some people in thinking about the issue and certainly not out of place here.

    If they are not useful to you, then you do not have to read them. For others they may be helpful in thinking about possibilities.

  11. @Ken S

    It is hard to know what has been done and what has not been done. You might recall hearing stories relative to no messaging or calls from passengers in the boarding area prior to the flight or from the plane before takeoff. This claim is apparently not true.

    One has to be very careful about adding things to your “box of truths” relative to this event.

  12. @Middleton

    Sure. I have no beef with your links or your intentions. My comments were meant to inform people here that there is far more to the story, and to not form conclusions based on the truly anecdotal work of amateur investigators.

  13. @DennisW. “It is hard to know what has been done and what has not been done.”.

    Yes, this is exactly the problem, the lack of transparency and information with regards to the criminal investigation and exactly what they have done to investigate this potential crime.

    We were promised at the end of 2014 by then Transport Minister, H2O that they would release a report on the criminal investigation in the near future, that never happened.

    For all we know they may have just treated this incident like an accident and have done nothing to investigate this as a crime or pursue finding other potential data and evidence.

  14. @Middleton – phone connectivity

    Those links are interesting.

    Not my field, but I have dug out one of dad’s old textbooks on the subject (he is in his mid 80’s in a nursing home and beyond providing useful info / insight unfortunately).

    Will take a few days to try and get my head around this.

  15. @Ken S

    Yeah, I am feeling, and have felt for awhile now, that there are people who know a lot more than they are telling. I am not trying to sound like a conspiracy theorist here. Just my deep down gut feeling that I have great trust in.

    We definitely need a polarizing event right about now. We have a lot of smart people resident here, but we often have trouble agreeing that the sky is blue on a clear day. Sometimes that is healthy and sometimes that is an impediment. Not sure how I would characterize it at the moment.

    The latest comments by the Fugro top guy relative to searching in the wrong place are so typical of the garbage we get fed on a daily basis. People have been saying the same thing all over the blogs for some time now. Suddenly when someone with an official “standing” in the search makes that comment it is big news, and then the bozo comes to the wrong conclusion relative to where to expand the search. Don’t these people at least try to stay current with the latest thinking and what lead to that thinking? Very frustrating.

    I have been very critical of the ATSB in general and Dolan in particular. There is just no one I actually trust who is anywhere near a decision making position relative to MH370. Where and who are the leaders? It seems like everything gets decided by a committee of unidentified people who cannot be held accountable for some objectively very poor decision making.

  16. @AM2

    Much the same but with a significant difference as earlier statements:

    ‘The search will not end but be suspended upon completion of the 120.000 square kilometre search area’

  17. VictorI posted July 21, 2016 at 10:21 AM: “@Gysbreght: Evasion and fun, although the conversation was mostly about the capabilities of the aircraft and the pilot. ”

    It must have been fun. Zooming up to 43,500 ft is not evasion of radar.

  18. MH370 Tripartite Meeting:

    “Ministers were provided with an update on the status of the underwater search and the Annex 13 investigation.”

    Nothing on the criminal investigation.

  19. One question is when and what will be the next investigation report? An interim? If so and like the last one there may be little information disclosure, including on the criminal investigation or the flaperon condition. Indefinitely?
    Presumably there are some rules.

  20. @David: “second affirms the ATSB view that the aircraft was in a high rate of descent”

    How convenient!

  21. @Gysbreght

    The steep descent comment was made to deflect the recent statements of Paul Kennedy of Fugro.

    The meeting was essentially a choreographed “check box”. Everyone knew what the decision was going to be long before the meeting took place.

    What we now have is a cancelled project (you can use the word suspended if it makes you feel better). I’ve been part of a few of those over the years. The mood is always – let’s tidy things up, archive what we have done, and move on. There is no enthusiasm left relative to the initial project objectives.

    It is over. Don’t expect to hear anything further relative to drift studies, bio-analytics, or feet on the street criminal investigation results. There is no appetite to toss any more time or money at this morass. My expectation is that the “final report” will be a few pages referencing the more detailed stuff we already have without the release of anything new or the additional data people here have been requesting.

  22. @Ge Rijn

    As I recall, to do the adrift study one only need to click locations on the map to drop a virtual ducky, then view the results.

  23. [Malaysian transport minister Liow Tiong Lai] said all data and information collected from the flight, search and debris of MH370 would be released to the public.

    “It is in a very big volume, so it will take some time,” he said.

    Notice that he did not commit to releasing any conclusions from the criminal investigation, which they are trying to bury. For those wanting full transparency regarding rumors such as the data found on the pilot’s computer and the cell phone connect at Penang, the evidence from the criminal investigation is where to turn.

    Look at the France’s frustration in receiving evidence from the criminal investigation from August 2015:

    French investigating judges opened a probe after the Boeing 777 disappeared last year, a standard procedure in France because four of its citizens were on board. But Malaysian officials haven’t shared evidence from their criminal investigation into the flight’s disappearance with the French, said a spokeswoman for the Paris prosecutor’s office, which has been helping manage the French investigation.

    “We’ve been asking for information from the Malaysians for a long time,” the spokeswoman said.

  24. @orion @others

    Yes, I tried it several times but the program doesn’t open on my computer. Still running on XP may be the problem..

    Watched back on the Deltares study Maarten van Ormondt and Fedor Baart did using the HYCOM model.
    They took 2 starting points on the 7th arc starting in march 2014. One in the current search zone and one more north at ~20S:

    Clearly the starting point in the current searchzone results in quite some landings in Australia strarting in ~october 2014.
    The northern starting point avoids this but allready in ~october 2014 particles are arriving on the islands Reunion etc. and in ~november 2014 Madagascar, ~april 2015 Tanzania and Kenia but none on Mozambique or South Africa.

    Considering all the other debris finds after the flaperon are done after december 2015 (Mosselbay piece) starting from a location at ~20S the timeframe is much too short.

    And considering many particles from this starting location are arriving well north on Tanzania and even Kenia with barely any particles going south in the direction of or landing on Mozambique and South Africa.

    This all suggests a starting location at ~20S or more northern latitudes is too far north for a possible crash area and a starting location of between 35S and 39S is too far south considering no debris finds in Australia.

    So I suggest the crash area must be well south of ~20S to fit the timeframe and the debris found in Mozambique/South Africa and north of ~36S considering a dividing line of debris landing in Australia.

    I think it would be usefull to repeat this study with a number of starting points between 20S and 36S and find out which starting point(s) fit the timeframe and all the debris locations best.

  25. @retired f4 mentioned this in his earlier comment at 6.56 am

    “The aim is to change the track as expeditious as possible, f.e. in an air to air fight to deny an attacker a shooting solution, to outturn a missile shot or…….”

    Interesting….. Very interesting

    I would put the last bit of the above excerpt with an earlier observation by @ Ge Rijn in a different thread about the likelihood of shrapnel caused damage on one of the debris finds.

    Leaving aside the two above, one has to wonder whether a commercial pilot would undertake a difficult manoeuvre with a civilian craft when he simply could have :

    “………..secondary radar contact, mumbling some garbeled words to simulate some comunication failure and proceed on to Penang unharmed, as anybody would expect him coming in for landing.”

    That he did the unexpected indicates that something was flying into his path hence the desperate evasive manoeuvre. And that comms go off radar that very moment is telling as well.

    Equally intriguing is the fact that a suicidal pilot with a comprehensive premeditated plan would chose to leave his smoking gun simulator unmolested. Probably he didn’t have the heart to trash it as he wanted to it to be his giveaway gift horse.

    It’s the non-consideration of absurdities like these in order to rationalise a patently faulty theory regarding pilot suicide or whatever that has people like @ dah ah justifiably riled up and understandably so. My commiserations @dah ah.

    But then again another absurdity is also glossed over to keep that theory viable. This regarding the pilots brazen “flyby”. There were three radar stations at Gong Kedak, Kota Baru and Butterworth that picked him up on that fabled flyby add probably Kuantan and Alor Setar into the equation, and you have five. And they all tracked and watched him fly by without lifting a finger despite ample tracking time!!

    And talking about such absurdities, the link below is replete with many coming as it is from an ex deputy premier:

    Maybe those obsessed with Zaharie etc etc should check that out too as it throws even more absurdities regarding their pet theory and by default, scapegoat.

  26. Actualy the northern starting point in the Deltares-study is more indicating a 25S latitude.

    So my suggestion would be to make a new studies like this with at least 10 or 15 starting points equaly divided between 25S and 35S.

    I e-mailed Maarten van Ormondt (Deltares) with a request to look at the possibilties of further studies like this.

  27. @all
    one question: knows anybody here PERSONALY somebody related to this incident?? was some NoK active here in forum?? (first time I heard recently @dah ah; who knows if real) and I know the FB of Sarah Bajc only, who is hopefully quite ok now, but everybody is still confused. May be some message thrown at peeople in big volume is bad therapy rather than slowly controlled release.

    Anyway may be good for all to try to focus on real life again, often something is discovered just after search stops, who knows.

  28. @Brock McEwen

    I read your revised drift study. With all respect for your effort but IMO you state nothing new or contributing to narrow a possible search area. On the contrary; you spread, with your excluding 7th arc model and introducing non verified and verifiable Maldives debris, conclusions and suggestions, possible search areas around half of the Indian Ocean. With an obvious intention to focus on your own favorite area; the Maldives.

    I see your approuch as a scholastic approuch. Like the catholic church scholastics defending the earth is the center of our universe in the middle ages.
    Inspite of all the evidence Galileo and Copernicus provided.

    I remember a statement you made in one of your earlier studies: ‘or the model is wrong, or the search area is wrong’.

    IMO back then your model was not wrong but the input was wrong. And it’s becoming clear now the search area was wrong too.

    Now not your input is wrong or your model (excluding the 7th arc) but your assumptions which lead to this practicaly useless outcomes to define a more precise search area.

    Hope you can let go of your assumptions regarding the Maldives. I think your knowledge and scientific background then can be more helpfull.

    I hope you take this as positive critisism.

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