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:
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:
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.
@Gysbreght, Is it that you feel that finding flight-simulator waypoints in the SIO would be incriminating for Zaharie, or you just don’t believe the story that these were in fact found by the FBI?
@All,
I have been following this blog for several months now and never posted. It would seem that Jeff’s account has been hacked recently without a change to his password and someone with a beef with Jeff is posting comments alongside of the real Jeff — especially given his comment to “ban himself” and the recent out of character reply to @RetiredF4. These are interspersed with lucid replies which is what leads me to think his blog account has been hacked without a change to password.
Thought I’d suggest this before too many more people get confused/upset at “Jeff”‘s posts.
@Julie, Thanks, yes, this is the case, I appreciate your concern. I’m working on fixing the situation.
Though… the reply to RetiredF4 was actually from me. What part of it did you find out of character?
Hi all,
My first post on this board. I’ve been following Jeff since the very beginning and I keep scratching my head as much as you guys do about the MH370.
I just want to ask if anyone has ever taken into account that, should whoever was in control of the flight wanted to take the airplane as far as possible before fuel starvation (for whatever reasons), a very good way of achieving that would be by shuting down one of the engines and descending the airplane to Long Range Cruise level for single engine, flying the remaining at long range speed. This would imply a lower cruising level and a lower TAS. Anyone ever ran this scenario in numbers?
Regards and sorry for the drift!
@Jeff, thanks for the reply. It posted my comment then saw the earlier replies indicating same posted while I was typing. Sorry for the repeat!
@Jeffwise
I’m so glad you’re ok. I really thought you had flipped. Understandable enough, the pressure and responsibility of managing a forum like this must be formidable.
@ISM: “Anyone ever ran this scenario in numbers?”
Yes, and it doesn’t work like you suggest.
@Jeff, just saw your second question now! I must have gotten the posts mixed up, the really out-of-character reply was the one just before JS suggested you’d been hijacked. It was full of inline replies about being a “dictator” and seems to have been deleted now.
@Julie, Oh, good, thanks for clearing that up.
@Rob, No, haven’t cracked up yet!
@Jeffwise
I just want to say I’m glad you are ok. Keep up the good work! This blog is doing a valuable service.
@ISM
Hello.
In a way it was discussed a few weeks ago.
I was suggesting the possibilty of a left engine shut down causing the SDU-reboot before FMT and then what range, speed and altitude it could have on one engine till end of flight.
I also suggested lower speed and altitude which possibly could have resulted in a more nrthernly crash area.
The conclusion was the reboot could not have happened by a left engine shut down and must have been done by human intervention and fuel consumption would be ~the same as with two engines running.
With that a one engine flight after FMT was kind of left undiscussed further.
I don’t know. Maybe you spark some interest in the idea again.
@ROB Reformed, Thanks, I appreciate that. FYI I’ve had to set your comments to manual approval because it looks like “Greg Long” was spoofing you, too.
@Rob
And still no nexit for me 😉
Question; was the outboard flap section send directly to Canberra instead of first to Malaysia as the other pieces?
@Jeffwise
No, got to admit that was the real me there!
Just got caught up in the talking dirty episode. I really thought you had flipped! Call me naive. Anyway, promise not to use rude words from now on.
Thanks
Rob
@Ge Rijn
I’m not sure about that. All I know is it’s on it’s way to Australia.
@jeffwise:
RE: “Gysbreght, Is it that you feel that finding flight-simulator waypoints in the SIO would be incriminating for Zaharie, or you just don’t believe the story that these were in fact found by the FBI?”
No, I don’t feel that finding flight-simulator waypoints in the SIO would be incriminating for Zaharie. It depends on the waypoints, and to what use they have been put. Zaharie reportedly had built a home-made flight simulator, its hardware components connected to a Personal Computer running a purchased “Flight Simulator” software package. Most likely that software package was an orphan of the Microsoft Flight Simulator program. The program probably has a facility for building a database of waypoints, similar to the navigation database used by, e.g., a Honeywell Flight Management Computer installed in real airplanes. The user doesn’t have to input all those waypoints, he just clicks on the ones he wants to plan a route. In a selectable display mode, waypoints in the Honeywell data base within range are displayed on the Nav Display as the flight proceeds, whether they are part of a flight plan or not. It would probably work that way also on Zaharie’s home-built simulator.
No, I don’t believe either the story that these were in fact found by the FBI. That story has been around ever since the harddrive was sent to the FBI for examination. That these early rumours were recently refuelled by ‘reputable’ journalists doesn’t justify public condammnation of a generally respected person by journalists like yourselves. I’m truly disappointed by your following the generally quite ignorant “Zahari did it” apostles on this blog.
@Jeff
Can we please reset to @ROB?
I only went to ROB REFORMED because I thought you had put a block on ROB.
I need to talk to Ge Rijn
@Rob Reformed, Sure, you can go back to @Rob. If you want to communicate with Ge Rijn off line I can pass your email address to him.
@Ge Rijn
All I know is that it’s on it’s way to Australia. Perhaps I can say more next week.
Jeffwise
Ok, send him my original email address, the ROB address.
”First officer Hamid was not exactly a newbie. He had a B777 type rating and was fully qualified to pilot a B777. He may have had little experience on the B777, but his training on systems was recent and still fresh in his mind. Any unusual handling of those systems does not require ‘experience’. It needs to be figured out in advance from the books. He was undergoing line training.”
Just to make a comparison. The fact that you passed for your drivers license doesnt mean that you will safely complete a highway trip without an instructor for the first time.
Actually the chances of something unusual happening is much higher. And we know something very unusual happened on MH370.
Hmm…
@Jeff Wise
Before I give you permission to do that I rather first hear what it’s about from @Rob on your blog. Thank you.
GE Rijn
Fine by me. All I can say is the flap is on route to Australia. That is all I can tell you.
@All
In a 2 plane diversion theory the Inmarsat data is created by 2 aircrafts.
In this scenario the first part of the Inmarsat data (16:00 UTC to 17:07 UTC was indeed transmitted by MH370. I believe at 17:07 MH370’s SDU was permantly switched off at this time and was never rebooted at 18:25 UTC.
What happens at 18:25 UTC is that the SDU on the decoy UAV is switched on and it is this unit which is transmitting the ISAT data from 18:25 UTC onwards using the same AES ID as MH370. I believe the firmeware on this unit was reprogrammed to transmit the same AES ID as MH370.
In this case Inmarsat would have no clue that this part of the ISAT data was being transmitted from another aircraft and would just assume it was coming from MH370. The only proof we have that theses signals were coming from MH370 is this easily spoofed hex address code (AES ID) which was embedded in each data packet recieved, which tells them the aircraft ID. Even Inmarsat has stated publicly that is indeed a possibility that some sort of spoof like this is possible with their network.
If you look at the ISAT data this way you can see how MH370 may have been able to fly somewhere else while another plane crashed in SIO.
@ir1907: You miss the point, which is whether he needed experience in a B777 to divert a B777 to the SIO. He had flown an A330 for more than a year and that is not so different from a B777. Before the A330 he had flown a B737.
@Jeff Wise @Rob
I hope you are alert to protect my privacy.
Especialy this time. I feel it’s still ‘spoofy’ on your blog.
If @Rob has something to discuss with me he can do it here. If it’s realy important to discuss more private then I can give him another Email adress anonymously passed through via your blog not publisher here by you.
@jeffwise,
A spoof, huh.
@Ken S,
Why would someone spoof a plane’s address only to crash one or both planes into the sea? A spoof-to-steal t theory has some logic to it. A spoof-to-crash?
I started to type a reply, but @Gysbreght:Posted July 16, 2016 at 9:47 AM did it for me.
For too long, this deliberately piloted event has been based on Zaharie bias. I might add on little evidence. Show me the money. Flight sims aren’t even small change.
On another note, I found Fugro Discovery in port last week and a Qantas napkin on a train. We don’t have a train line anywhere near an airport, nor Thirsty Point. Come back Matty-Perth and Olaksander.
I’m going bush for a month shortly and there is no internet where I’m going, only desert and Camels. Hope I don’t miss something valuable whilst gone.
Welcome back @Rob.
@Ken S
As I understand you well in your scenario the decoy plane had to be a B777 too?
The flaperon was identified as coming from MH370. The other identified parts only sure coming from a B777.
Do you suggest two B777’s crashed? One in the SIO and MH370 near the Maldives?
With the flaperon coming from MH370 and the other debris from the other B777?
@JS
My belief is that MH370 was a military style operation and a sophisticated hijacking by some powerful Government.
My belief is that there was senstive military technology cargo on-board that plane ( not listed on cargo manifest ) that was being smuggled into China on-board MH370 and this other state did not want this technology falling into the hands of the Chinese.
I believe the perpetrators wanted to mask their involvement in this hijacking and make it look like a tragic accident and frame the pilot.
Ge Rijn
Ideally the perfect decoy plane would be another B777-200ER that looked identical to MH370. One such airplane would be N105GT (formerly 9M-MRI) which was being stored in hanger in Tel Aviv back in 2014. Interestingly in 2015 is was officially listed as dismantled
In this case the plane would had to have been equipped with a type of BUAP device ( Boeing Uninterruptible Auto Pilot) so it could be flown completely by remote control.
However if the piece on Kangaroo Island is a piece of this decoy aircraft then it cannot be a B777 but it could be some other type of unknown military UAV aircraft which has a similiar airframe to a B777.
At this point I really don’t know the exact type of aircraft this was yet. It is still a mystery to me at this point.
@Ken Goodwin – Thank you for doing the calculation showing the minor difference between right wing and left wing air speed during a banked turn. Question – If the right wing hit first wouldn’t that indicate a right turn?
@DennisW & @jeffwise – If a pilot chose to go up and down and make many turns, those maneuvers would have wasted fuel and the plane could not have flown 5h55m after last radar and still have met the ping rings. IF the a/c did fly straight after the FMT there are a limited number of combinations of speeds and altitudes that support the ISAT data. (See Grysbreght graph from May 2015.)
As for a motive: A life insurance policy that excludes suicide BUT pays treble damages if loss occurred due to an accident on a common carrier. Remember Rajib announced that this was an “accident.”
@jeffwise
“merit less” “calling shenanigans ” “lunks” …….ouch! 😀
I do take it that I am not everyone’s favourite “troll” in these parts 😛 so thanks for those plaudits dude.
On the contrary …..regarding the evidence …theres plenty but I sure don’t wanna exceed my flight envelope and get blown to smithereens by a “banned” projectile from you Jeff.
Just to say that I love this blog for I find it strangely addictive though I am not a chronic follower. You are doing a great job man handling all and sundry including riff raff like me ;D and I tip my Stetson off for that. Wonderful moderating!
And hope my “shenanigans ” or this one or an earlier missing one doesn’t get me banned. Thanks for the space Jeff, you are good folk just like all the others here seeking closure for the NOK with their own theories and lines of enquiry. Good luck to all.
Me? I will stick with mine as it best fits all the ‘verifiable’ data from my perspective but I guess I will quit harping on that angle ( unless clarification is sought) as everything has been made sufficiently clear on that score except to @Dan Richter, for all its worth KAL 1983 flew a full 12 minutes after impact and so therein lies your answer to 370’s garbled coordinates.but thats about it regarding my theory.
I will keep reading though, rest assured.. Thanks once again for the space, Jeff.
@Lauren H: “Question – If the right wing hit first wouldn’t that indicate a right turn?”
Revisit the amateur video of the Ethiopian B767 ditching/crash naear the Comores.
Yeah forgot this……..welcome back @ Rob. Good to have you back 😀 Hope @Oleksandr , @Matty Perth @ rand and @ Matt return too.
And here’s hoping @Brock @ Alsm and @ Susie revert to their regular selves….been MIA lately guys.
@Rob
The Pemba outboard flap was handed over to Malaysian authorities yesterday. There’s a photo of the piece added. Bit strange to me; it’s just lying outside on a street. I would expect they would handle it more carefully:
https://twitter.com/h1ppyg1rl
@KenS – a drone such as the UAV Avenger seems like it could fly as far and as fast as a B777. Perhaps It took on the same sdu identification as mh370 as well. I suspect it actually didn’t crash but stopped spoofing mh370.
@All
A very clear video of the Pemba-piece:
https://www.youtube.com/embed/msXHjpt6WDo
@MH – I wrote on 7/13/2015, “a MQ-9 Reaper drone (Max: 435 Knots, 50,000 feet, 18 hours)”
@MH
Yes, some people have suggested to me that possibility, that the decoy did not crash in SIO but it simply stopped transmitting at 00:19 UTC and then conrinued on to some airbase, like Diego Garcia.
I however believe that some plane did crash in SIO because I see possible evidence of this in the imagery data which leads me to believe this.
Borh options are possible.IMO.
@Wazir Roslan,
You have interesting ways of reasoning with interesting conclusions. The main danger with your approach is that you may find what happened to MH370. Following the clues rather than re-processing official technical info may have this unwelcome effect. I would be glad to discuss your ideas via my Google mailing account dreamer371, mine make me scared.
One of my predictions was no more debris would turn up. That is why the absence of interest.
IMHO – no more debris would come ashore because that is all “they” dumped in the IO to “support” the “crash scenario” after the actual aircraft was “dismantled”.
@Ken S
You, and most others, have an over-rated opinion of US military technology. It is clunky. The best and the brightest engineers do not flock to the military industrial complex or their suppliers. Why should they when they can get stock options and get rich working for any number of silicon valley companies? I routinely turned down requests to even bid on military contracts – you have contract managers sniffing your butt all the time and then you are stuck having to support and provision an obsolete system for some 30 years. All that for a tightly controlled cost plus profit margin. Why even bother?
The military equipment we did provide turned into a nightmare. You could not even find replacement semiconductors still in production and had to scrape around boneyards to find spare parts.
The main US military heavy bomber is still the B52 which was first produced in 1952. That is a 65 year old subsonic airplane 🙂
Trust me, there is nothing in the military arsenal short of a nuclear weapon that would be worth the trouble of stealing.
Back in the 80’s the military figured out that it was cheaper and better to buy COTS (Commercial Off the Shelf) hardware. It did not work out for them for the same reasons as above. Try finding a paper tape reader or 5.25″ floppy drive to service some old COTS equipment bought by the military. They went back to old Source Control Drawing procurement method and made sure 30 years of support was written into the contract award.
A striking example of COTS procurement is the Condor Cluster, a US Air Force supercomputer built out of 1,760 Sony PlayStation 3s running the Linux operating system. Sony disabled the use of Linux on the PS3 in April 2010,[10] leaving no means to procure functioning Linux replacement units. The Air Force was screwed.
@DennisW
Well , if you can’t see this possibility in this theory I won’t try to convince you. At this time I could only offer you speculation on this 2 plane diversion theory with regards who did this, and why, so without any proof you certainly have the right to dismiss my speculation
But I am very certain that whoever did this, for whatever reason, used a drone to decieve us, and if that is true, you better rethink your opinion Dennis.
@Ken S
The two plane diversion theory simply lacks a plausible motive. I agree that if someone wanted to divert the aircraft and make it look like it disappeared into the SIO, then the two plane method is probably the simplest and easiest to implement.
IMHO – the pilot suicide theory doesn’t sound plausible until there is some solid evidence. As far as I know nothing has been made public.
@Lauren H,
Do you have a source for those drone specs? I’m seeing a max speed of 260 knots and a max duration of 14 hours, with a much lower cruise speed. Considering it’s a turboprop, 435 knots sounds a bit unrealistic.
@DennisW
Yes, if you are an organization, that has deep pockets and you don’t mind losing the cost of a drone, and you have the technical capability to fly drones that travel as fast as a B777, then this would be the simplest way for them to spoof the ISAT data. This is how they would do it if their intent was to make a modern commercial airliner just vanish.
@Ken S – which drone has those capabilities?