Occam’s Razor is Overrated

conspiracy theoryMartin Dolan, chief commissioner of the Australian Transport Safety Bureau (ATSB), is plagued by conspiracy theorists. According to an article in the Sydney Morning Herald, since the disappearance of MH370, “conspiracy theorists have been busy trying to solve the mystery themselves. Many have contacted Dolan.”

“You’ve got this big mystery and everyone wants to know the answer and everyone wants to help,” the SMH quotes Dolan as saying. “It’s unhelpful, for the sake of the families more than anything else, in the sense that it has the potential to undermine confidence in what we are doing.”

I feel somewhat guilty for being one of those peanut-gallery denizens who have tormented him. Along with my fellow obsessives in the Independent Group, I’ve been straining my brain for the last eight months trying to make sense of the strangest aviation mystery in history. Yes, I’d like to be helpful; yes, I’d like to know the answers. And yes, I may have unwittingly undermined confidence in what the ATSB was doing, for instance by publicly saying that I thought they were looking in the wrong place. (Though, to be fair, they were in fact looking in the wrong place.)

Nevertheless, I must take issue with one aspect of the article’s characterization of my subculture: the use of the term “conspiracy theorist.” Now, look: I get it. My wife says that I remind her of the Kevin Costner character in “JFK.” I ruminate about the intracacies of a famous case and try to piece them together in a new way that makes more sense. I’m obsessed.

There’s a big difference, however, between true grassy-knoll conspiracy theorists (or 9/11Truthers, or the-moon-landing-was-faked believers) and MH370 obsessives like me. It’s this: there is no default, mainstream narrative about the missing Malaysian airliner. There is no story that officials and all reasonable people agree makes sense.

This isn’t the result of laziness or incompetence. It’s just that the data is so strange.

A lot of people don’t get that. Ever since the mystery began, certain voices have been invoking the principle of Occam’s razor, saying that when we try to formulate a most likely scenario for what happened to the plane, we should choose the answer that is simplest. People who are making this argument are usually in favor of the argument that the plane suffered a massive mechanical failure and then flew off into the ocean as a ghost ship, or that the pilot locked his co-pilot out of the cockpit and committed suicide. However, as I’ve argued over the course of several earlier posts, neither theory matches what we know about the flight.

Instead, I’ve argued that an accumulation of evidence suggests that MH370 was commandeered by hijackers who had a very sophisticated understanding of airline procedure, air traffic control, avionics systems, military radar surveillance, and satellite communications. In other words, what happened on the night of March 7/8 of this year was a intentional act. And when it comes to human schemes, Occam’s razor goes out the window. Instead of simplicity, we should expect complexity, not to mention red herrings and any other form of subterfuge.

Whenever I hear Occam’s razor invoked, I inevitably find myself thinking of something that Sarah Bajc said on CNN. Bajc’s partner, Philip Wood, is one of the missing passengers, and she has been very open minded in considering alternative explanations to what happened that night. “There are 40 crazy stories that you could tell about MH370,” she told the anchor. “And one of them is going to turn out to be true.”

I’ve come to think of this as the Bajc Postulate, which I think should replace Occam’s Razor in situations like this. It goes like this: “When trying to unravel human deception, don’t expect simplicity.”

Remember Operation Mincemeat? In 1943, a fisherman found the body of a British officer floating in the sea off the Spanish coast. The authorities turned the corpse over to German intelligence, who discovered that it carried a number of secret documents, including one indicating that the expected Allied assault from North Africa would target Sardinia, not Sicily, as widely expected. The authenticity of the documents was vouched for by every detail of the body, its clothes, and the accompanying possessions, which included several love letters, a photo of a fiancee, a bill from an exclusive tailor, and a theater ticket stub. Either this man and his belongings had all been elaborately and meticulously forged, or he really was who he seemed to be: Occam’s Razor. Hitler himself was utterly convinced. And yet, of course, the whole thing was a ruse, an elaborate deception cooked up with painstaking care by British intelligence. Hitler shifted three divisions to Sardinia, the invasion landed at Sicily, and the war was that much closer to being over.

I think it’s distinctly possible that MH370 represents a deception crafted at the same level of complexity.

In my mind, the crux is what happened at 18:25. Until that moment, the plane had been on radio silence for nearly an hour. After following a zig-zag path along national airspace boundaries, it had reached the limit of military radar coverage and had disappeared. But then, mysteriously, the satcom system reconnected to the Inmarsat satellite overhead. For it to do this, the hijackers would have had to either climbed into the electronics bay or carried out a complex procedure in the cockpit that few people outside of Boeing itself would now how to accomplish. All this, to no evident purpose: no attempt was subsequently used to communicate via the system.

Other things were odd about the 18:25 logon. The frequencies that the system transmitted over the next few minutes were inexplicable to the scientists at Inmarsat. Though the electronics of the system are perfectly understood by the equipment’s manufacturers, they cannot explain how the frequencies were produced. Investigative efforts within the IG suggest that there was another mysterious aspect to the satcom’s behavior post-18:25: when a pair of incoming calls was received at 18:41, the system was unable to pass the calls through. We’re not sure why, but the most likely cause is that errors in the system’s configuration prevented it from aiming the satellite dish correctly.

By 19:41, the satcom system seemed to settle down and transmit at stable frequencies. If taken at face value, these frequencies indicated unambiguously that the plane was flying south. Yet the ATSB has never able to completely make sense of these values. As I wrote last week, it has proven frustratingly difficult to make the two distinct halves of the Inmarsat data—the timing and the frequency data—match up in a way that makes sense.

Regardless of these difficulties, most reasonable people share the conviction that, regardless of what particular track the plane happened to fly, it definitely flew south into the most remote reaches of the southern Indian Ocean. I’ve examined the data myself, and come away convinced that, indeed, the frequency data unequivocally supports this conclusion. But no one knows why anyone would do this. One popular notion is that the hijackers had a destination in mind, but something went wrong, they became incapacitated, and the plane flew on autopilot until it ran out of fuel and crashed. This scenario is certainly possible, but as I recently pointed out, a new speed-analysis technique suggests the plane was under deliberate control until the very end.

So if they weren’t incapacitated, why were these very motivated, very sophisticated hijackers flying a perfectly good jet off into the middle of the ocean? As I see it, there are two possibilities:

  • The hijackers were very sophisticated, but for some unknown reason chose to fly the plane off into the middle of the ocean, or
  • They were very, very, very sophisticated, and not only survived, but managed to cover their tracks in a way that has fooled absolutely everybody — and turning on the SDU was an essential part of their plan. This explains why there has been no debris found, why there was no radar track over the southern Indian Ocean, and why Inmarsat has been baffled by the BFO values.

This kind of thinking would have been considered outlandish a few months ago, but the more time goes by without any trace of the plane turning up, the more reasonable it is starting to seem. No less an industry eminence than Emirates CEO Tim Clark, whose airline operates the largest 777 fleet in the world, recently told Der Spiegel: “We have not seen a single thing that suggests categorically that this aircraft is where they say it is, apart from this so-called electronic satellite ‘handshake,’ which I question as well.”

To accomplish a disappearing act, the hijackers would have had to have pulled off a plan that the authorities not only couldn’t anticipate beforehand, few could wrap their heads around it afterward. A plan so devious, it would literally be —

Inconceivable

What could such a plan have been? Frankly, there’s no way we can be sure. Until the plane is located, and the black boxes are found, all we can do is speculate. But some speculation runs in accordance with the facts, and some runs counter to it. Over the last few months, I’ve pieced together a narrative that I think matches well the facts we do know, explains some otherwise baffling conundrums, and basically ties together a means, a perpetrator, and a destination. (Which, paranthetically, is something that no one else, official or amateur, has yet attempted.)

In the past, I’ve invited others to share their “conspiracy theories,” and I tip my hat to the very, very few (two) who’ve had the courage to take me up on my offer. For the most part, their efforts were met with skepticism, but polite skepticism, and that reaction has emboldened me to press forward with my own big reveal. I hope that some people will find it thought-provoking, perhaps even convincing. I expect that a great many will find it, yes, inconceivable, perhaps even outrageous or even offensive. Remember, it is speculation, not a statement of fact; but if we don’t risk trotting out our speculations eventually then we will never get any closer to figuring out the truth.

If you care to dive down my rabbit hole, click below:

The Spoof, Part 1: Why (A Speculative Scenario)

The Spoof, Part 2: How (A Speculative Scenario)

The Spoof, Part 3: Where (Not a Speculative Scenario)

The Spoof, Part 4: Motive

The Spoof, Part 5: People on the Plane

The Spoof, Part 6: MH17

And that’s all there is for now.

450 thoughts on “Occam’s Razor is Overrated”

  1. @Cheryl

    MH370 is in the ocean South and East of Christmas Island where it ran out of fuel on the approach to make a landing there. That scenario fits all the facts, including BTO, lack of debris, lack of primary radar sightings, and the mental state of Captain Shah.

  2. @myron

    There is a major static current (not wind driven) that would carry debris in that area toward Africa. Plus that no one has ever looked for debris in that area.

    @Jeff

    Christmas Island sits precisely on the last ping ring.

  3. Cheryl: The Joint Investigation Team (JIT) that has had Brock pulling his hair out is indeed an international team of experts divided into three sub-teams. These teams cover airworthiness, operations and human factors (psychology, pathology and survivability). With the exception of psychopathology on the part of the crew, it I am unable to identify a dedicated team within Malaysia that is actually pursuing an ‘investigation’ into the how and the who besides the Royal Malaysian Police.

    Again, from an external perspective, the ‘investigation’ is being pursued as a civil aviation crash, rather than an investigation into a hijacking. One could imagine that there are any number of US, Malaysian et al intelligence and law enforcement agencies that have looked into the incident, but my point is that the messaging from Malaysia is that this is ‘an unfortunate incident and a mystery’ rather than an incident involving a hijacking. The messaging in turn is indicated by the silos associated with the investigation, with a dedicated criminal investigation silo apparently missing from the mix.

    There is a basic assumption here among many that the loss of MH370 involved a hijacking. Meanwhile, the Malaysians, after the better part of a year, have gone completely silent regarding any criminal dimension to the loss of the aircraft. This simply does not make any sense, unless, of course, there is some large, multilateral effort to pursue something behind the scenes.

    We could reduce it all down to a question of probability: is it more likely that Malaysia is obfuscating/not pursuing a criminal investigation; or there is something larger, multilateral investigation being quietly pursued behind the scenes?

    Nihonmana has alluded to the involvement of ISIS, for example, which would perhaps involve a quiet effort to pursue the perpetrators. I would rather argue that the search for MH370 has been bureacratized to the point where we can now clearly discern that the criminal investigation has somehow been left out of the mix. This aspect of the overall investigation would be pursued by the Malaysian authorities – yet, there isn’t any dedicated team in the alphabet soup that can be identified as being charged with such, other than the RMP.

    The world outside of Malaysia would appear to have grown quiet on the issue. Within Malaysia, there has always ONLY been quiet, unless you want to include the highly publicized enquiry by the RMP into the origins of the mangosteen cargo. You follow me here?

  4. @Dennis W, I confess that I’ve avoided wading into the mathematics myself, instead relying on ping ring kmz files cadged off of Barry and Richard. But Christmas Island is more than 100 nm from any of their 0:19 rings, in the backwards direction.

  5. Jeff, I tried to explain the same thing to Dennis some time back. Still waiting for some real data on his track to Christmas Island, assumed flight speeds, coordinates for “ping ring” crossings, and supporting data. Still waiting – – – – Christmas Island is also more than 70 nM inside the 00:11 ring. So the aircraft flew there, then turned around and tracked back toward Christmas Island ? Show us some numbers Dennis.

  6. @Flitzer

    You can construct a flight path to anywhere on the last ping ring by making arbitrary assumptions about flight path and ROC. That has been reinforced above with respect to a Northern route. The Christmas Island route would be even simpler. I will construct one if it will make you happy, but it truly is irrelevant. The only relevancy is the final BTO value.

    That fact that Christmas Island lies slightly inside the ping ring is consistent with the West to East wind that day, and a South to North landing approach. A logical approach would be from South of the Island and slightly East crabbing back into the West wind. That is the way airplanes conduct an approach. The Christmas Island runway is doable for a skilled B777 pilot, a light load of fuel, and a meticulous approach.

    Hey, I don’t have a dog in this fight relative to where the aircraft turns up. I am simply pointing out logical and consistent alternatives. I fully support Jeff’s hypothesis as well, and proposed it as a flyer myself early on in Duncan’s blog. If you have any serious issues with Christmas Island, I would love to hear them, but you are nit-picking now.

  7. @Denis: “by making arbitrary assumptions about flight path and ROC”

    On that basis MH370 could be anywhere within fuel range. Just choose a termination point you fancy and speculate on how it got there. That’s a big help.

    Two definitive sources for wind on the day show it to be light, about 10 knots, from the South East, thus favouring an approach to Christmas Island from the north.

    Forget Christmas Island. There is not one piece of evidence that leads you there.

  8. The Tu-160 drone sounds attractive but it would need to get in very close to Malaysian radar would need knowledge that the Indons were asleep? Does the lack of radar data also preclude this?

  9. @ MuOne:

    “All the spoofers needed to do is to alter the BFO to hide the actual path.”

    No, that is not sufficient. They need to know the ping rings to generate BFO’s that make sense.

    The BFO is calculated in the ground station. In Jeffs scenario, the highjackers spoof the navigation data that are fed to the SDU, and thereby alter the calculation of the AES Doppler compensation. The spoofed southern path data that are fed to the SDU must produce approximately the same BTO as the northern path actually flown by the airplane. Therefore the highjackers must understand the path reconstruction from BTO and BFO. If they just feed an arbitrary southern path to the SDU the BFOs will be incompatible with the BTOs.

  10. Gysbrecht – If the measured BFO is not actually real, how do we know what makes sense? No test flight, one very limited model, and a bunch of numbers we can’t replicate and no plane has ever flown that route. It’s all tied to the model, and how good it is, am I right, or way off?

  11. @ Matty Perth:

    The logged BFOs are incompatible with the logged BTOs if, for example, the path reconstructed from them does not reach the 7th arc, or requires airplane speeds that the plane cannot possibly have achieved.

  12. Gysbrecht – OK, the point I’m trying to articulate here, if the logged BFO’s aren’t the real deal, if they are generated by the hijackers own model, then would it be a jawdropping surprise if Immarsta’s model roughly matched it? And a rough match is what they got?

  13. 1/2

    Why am I thinking ISIS?

    Nihonmama
    Posted September 13, 2014 at 4:43 PM
    MH370 Search Area Still Too Far North, Independent Experts Suggest (UPDATED)

    “In May 2013, an unmarked Dornier en route from the Maldives to Singapore was forced down in Banda Aceh, Indonesia. Turns out that plane was a U.S. Special Ops “Wolfhound” https://twitter.com/nihonmama/status/506945975143763968 The claim was that they ran out of fuel. Really.”

  14. @ Matty – Perth:

    ” And a rough match is what they got?”

    They got a nearly perfect match within +/- 1 Hz.

  15. 2/2

    The “Wolfhound mentioned in the previous post was en route from Male to Singapore.

    If they were using a Great Circle route, the plane (should) have flown across Indonesia, way south of Banda Aceh
    http://www.gcmap.com/mapui?P=mle-sin

    So unless it didn’t have overflight rights, why did that Wolfhound ‘run out of fuel’ way out of its way, over Banda Aceh?

  16. Perfect match – across the whole route? I thought some of the points were fairly disparate?

  17. @ Matty – Perth:

    The imperfect matches of some proposed paths result from dogmatic assumptions regarding autopilot use, so called ‘human factors’ that merely imply the absence of human activity.

  18. @ Matty-perth:

    Perhaps I should retract my last post. This exchange has drifted a long way from the point I was trying to make: That the highjackers must have known of the BTOs in order to create a credible spoof of the path.

  19. @Gysbryght, I disagree. There is poor agreement between BTO and BFO values, which is why there is internal dissent within the ATSB about where to look.

  20. @ jeffwise,

    A few days ago I posted some “perfect fit” paths. The objection one could raise against those paths is that they do not fit the basic autopilot modes under the dogma of human inactivity after what the IG calls the Final Major Turn (FMT), or a programmed waypoint after the FMT.

  21. @Nihonmama

    Yeah, I read that piece. He even quotes me in it 🙂 Thx.

    @Jeff

    There can be an arbitrary number of perfect fit paths if one discards a fixed autopilot mode. Not to say the plane was being actively flown, simply that a pilot was inputing AP changes. Perfect fit in this context could even be expanded to include reasonable uncertainty bounds on the BTO and BFO data.

    @Fltizer

    Do you have a link to the actual surface wind stats on the morning in question? All I could find were average stats which greatly favored a West wind in March.

  22. @ jeffwise:
    “Can you repost?”

    Sure:
    https://www.dropbox.com/s/g8zlioyjem5xh2n/BFOtracks_11.jpg?dl=0

    The purpose of the graph is to show the sensitivity to Fixed Frequency Bias of paths calculated to match the BTOs and BFOs .

    I’m less well equipped to produce paths that match autopilot modes, winds, magnetic declination etc, but I think that my path for FFB=149 Hz, or the Inmarsat “Reconstructed” path, could be massaged to match those with minimal BFO errors if one allows for a “Final” track correction between 18:40 and 19:41.

  23. @Flitzer & @Dennis W
    Dr. Ulich’s Sept. 25 White Paper list winds and direction at each handshake along his route. The winds for the last three handshakes were 40kts or more from 242° to 269 deg.

  24. Dennis: The easiest and most helpful wind data is here – – http://earth.nullschool.net/#2014/03/07/2100Z/wind/isobaric/250hPa/orthographic=-260.33,-18.71,791/grid=on

    Click on a spot to get lat/long and wind vector.

    Modify the date within the URL for a different time. Left-click and drag to reposition the centre. Zoom in and out using the mouse wheel. Clicking the “earth” button in the bottom left corner brings up a small control panel with clickable options.

    While this is a simulation, the data behind it is real.

    Lauren H: See the link above. Dennis is looking for surface winds in the vicinity of Christmas Island.

  25. Dennis: How do you find your point of intercept on the 00:11 ping ring?

    There are at least 2 possibilities (i) a calculation of speed and distance based on some assumed start point, or (ii) some wild guess.

    In what direction was the aircraft tracking at that instant?

    The BFO allows you to calculate that using your assumed speed and a knowledge of the satellite parameters etc.

  26. @Gysbreght,

    Maybe I should have said “effect the alteration of BFO”. I guess the only accessible way for hijackers is the AES based doppler compensation (discounting a perp’s satellite shielding the INMARSAT sat, intercepting signals and modifying frequency up there, or maybe a large truck parked in front of the Perth receiver doing something similar).

    A simple AES based means of spoofing would possibly be a simple inversion of the LAT input and maybe a constant 180 degree offset on heading/track. That would easily ensure a spoofed frequency correction consistent with the N/S mirrored (LAT-spoof = -LAT-actual) path.

    To me layman the mechanics of such a spoof sound rather simple (cut cables, plug in prepared inversion circuit, done). Come to think of it, such a spoof would not be very sophisticated either, but a rather obvious thing to do. One wouldn’t even need to know about BFO and frequency correction to get it “about” right.

    Not sure though, if the “mirrored path” input, would produce the BFO N/S fan effect.

    Cheers
    Will

  27. Flitzer,

    As I have said many times, you can get to any point on any ring by making assumptions relative to speed, heading, and ROC. There is no unique solution. An assumed starting point leads to an assumed intercept which becomes the next assumed starting point for the next intercept calculation. The only hard limitations are aircraft max/min speeds, and fuel range.

    There is no data between BTO and BFO reports, so any changes in speed or heading between reports are not knowable. Without assuming a fixed AP mode (which I do not assume) there is not much you can say except that the aircraft is somewhere on the BTO ring at that time.

    If the AES did not pre-compensate for aircraft horizontal Doppler we would have more to work with.

    Thanks for the link. I will check it out.

  28. Dennis: Yes, I understand all that. What I am hoping that you might provide is your intercept point on the 00:11 ring, and your headings, speeds etc derived from the BFO that lead you to the Christmas Island conclusion.

  29. And here’s another re MH17:

    Evidence being removed from the MH17 crash (crime) scene BEFORE investigators arrived:

    https://twitter.com/nihonmama/status/493519942222757891

    When I asked VICE reporter Simon Ostrovsky if he could post that footage in its entirety, got no response.

    The men you see in the video are from the “Ukrainian Ministry of Emergency Situations”

  30. Flitzer_Flyer: My ‘guess’ is that Dennis W’s conclusion re Christmas Island is conceptually/logically as opposed to mathematically derived. I realize that you are attempting to goad him into providing a proper proof of derivation, but an alternative test would be whether such a conclusion can fit the data and then assigning a reasonable probability to the same – as he has been arguing. If one assumes that the conclusion is largely based upon the premise that the aircraft would have had an intended destination, then we can start by assigning higher probability to the conclusion of an island as the intended destination, as opposed to ‘somewhere’ at sea. Meanwhile, we could assume that Dennis W has other reasons to support his conclusion. And, yes, assigning probability as to the location is largely guesswork constrained by reason.

    If, however, as you and Jeff have been arguing, the data does not SUPPORT such a conclusion, then It gets tossed. I would imagine that Dennis is now engaged in such a process; he’ll probably toss it himself, with your continued help.

    It would perhaps be good to remind ourselves that the data set and the various analyses are but maps of the flight trajectory. While they do present the best means du jour of locating the debris, they are, ironically, not the reality of its location.

    BTW, one grosser example of a conceptual route to the location of the debris that would not be derived from an analysis of the Inmarsat, radar and wind data would be for the location of the aircraft/debris to be identified by a whistleblower with information re the same.

    Meanwhile, what entity is actually investigating the criminal/potential hijacking side of things? Is this, too, to wait until the flight recorders are recovered?

    “Had the acute-angled rabble been all, without exception, absolutely destitute of hope and of ambition, they might have found leaders in some of their many seditious outbreaks, so able as to render their superior numbers and strength too much even for the wisdom of the Circles.”
    Edwin Abbott Abbott, Flatland

  31. Flitzer,

    Stay tuned. I am at my ranch, and my computer with Octave (which has those analytics) is some 200 miles away at a different location. We are experiencing a major storm in NorCal at the moment, so I am not sure when I will get back to the Mac. Probably early next week.

    I am not trying to avoid your question.

    Rand,

    That was an eloquent post.

  32. TIME OF FINAL MAJOR TURN (FMT)

    On December 7th in this blog Michael Exner indicated that he believed the “Final Major Turn”, or FMT, was in progress during the BFO data sequence at 18:39-18:41 UTC. He also indicated that the “heading at 18:41 was ~200-210 degrees”, and that “calibration of the C-channel BFO data provided the clue.”

    On December 8th, Michael Exner then posted a link to a short paper on the FMT timing. This paper (“MH370 Final major Turn Timing” by Michael Exner, Richard Godfrey, and Sid Bennett) claims that “the FMT started and ended close to 1840UTC” and “the start and end times are probably accurate to +/- 30 seconds.”

    The timing of the FMT is an important consideration in predicting the location of 9M-MRO at the 7th arc.

    In this post I will present five reasons why I believe these claims by Exner et al. are unsubstantiated by the BFO data.

    To begin, let me summarize the BFO data prior to and at the time interval in question:

    1. There are 4 BFO values between 18:28:06 and 18:28:15 that range from 143 to 148 Hz with a mean value of 145.5 Hz and a (very rough estimate of a) standard deviation of 2.4 Hz. The standard deviation of the mean is 2.4 / SQRT(4-1) = 1.4 Hz. These BFO values appear consistent with the WNW bearing indicated by the radar track prior to the FMT.

    2. There are 39 BFO values between 18:39:55 and 18:40:00 that range from 86 to 90 Hz with a mean value of 87.7 Hz and a standard deviation of 1.1 Hz. The standard deviation of the mean = 1.1 / SQRT(39 – 1) = 0.2 Hz. These BFO values appear consistent with a SSW bearing indicating that the FMT is complete, or nearly complete. Indeed, that is the subject at hand, whether or not the FMT is complete or is still underway at 18:40 UTC.

    3. There are 6 BFO values between 18:40:03 and 18:40:53 that range from 86 to 90 Hz with a mean value of 87.3 Hz and a standard deviation of 1.8 Hz. The standard deviation of the mean = 1.8 / SQRT(6 – 1) = 0.8 Hz.

    4. There are 6 BFO values between 18:40:55 and 18:40:56 that range from 87 to 90 Hz with a mean value of 88.8 and a standard deviation of 1.2 Hz. The standard deviation of the mean = 1.2 / SQRT(6 – 1) = 0.5 Hz.

    Thus we have the following four BFO data means:

    18:28:10: 145.5 +/- 1.4 Hz,
    18:39:57: 87.7 +/- 0.2 Hz,
    18:40:28: 87.3 +/- 0.8 Hz, and
    18:40:56: 88.8 +/- 0.5 Hz.

    Note that these error bounds are one sigma and they only represent the apparent noise over the short time scales of each data set average. The next question is, what other effects (besides read noise) will cause changes in the BFO, and on what time scales do they occur?

    First, we know that the satellite velocity (both with respect to the aircraft and the ground station) near 18:40 produces rather linear positive BFO changes (approximately +195 Hz from 18:28 to 00:19) with a slope of 0.56 Hz / minute. So we first need to remove this satellite-driven slope from the BFO data near 18:40 to leave the aircraft-only uncompensated portion. We can estimate the approximate total slope at 18:40 by simply taking the difference in the measured BFO means at the two ends – at 18:40:56 and at 18:39:57. This gives us a total (aircraft and satellite) measured slope of 1.1 +/- 0.5 Hz and thus an aircraft-only slope of 0.5 +/- 0.5 Hz over this period of 59 seconds.

    The critical parameter in fitting a (partial) turn to the BFO data is the BFO slope. The change in BFO during a turn depends primarily on the change in aircraft heading. The rate of change of heading is the aircraft turn rate. Thus the time rate of change in BFO (= the BFO slope) is driven by the aircraft turn rate. Zero slope means zero aircraft turn rate. High BFO slope means high aircraft turn rate, etc. Another way to visualize this relationship is that the BFO slope depends on the curvature of the aircraft track. Zero slope means zero curvature (i.e., no turn).

    The aircraft-only slope near 18:40 is 0.5 +/- 0.5 Hz. This one-sigma result is not statistically very meaningful. It cannot be used as proof that a change in BFO (or a turn) occurred at all. The true change could very well have been zero. Even if this extremely small change is real, it is probably due to causes other than a turn.

    There are at least two aircraft-driven effects besides read noise that can affect the BFO data on time scales of a minute or less. The first one is the “steps” that are produced in the AES TX frequency compensation algorithm due to the use of look-up tables rather than continuous trigonometric functions. According to Michael Exner, these steps may be on the order of +/- 2 Hz. During the ~1 minute of BFO data at 18:40, the aircraft bearing is changing by 35 degrees (according to the paper by Exner et al.), and one would expect multiple steps to occur during such a significant bearing change. There is no evidence of any steps (~4 Hz peak-to-peak) occurring in the data near 18:40.

    A second effect is the uncompensated Doppler shift due to aircraft Rate of Climb (ROC). I find it quite remarkable that the BFO is so constant during the ~1 minute period of the 18:40 BFO data. Note that for MH370 the BFO will change by approximately 1 Hz for a ROC of 1 foot per second (= 60 FPM). For all the BFO values to be within +/- 2 Hz means that the ROC’s were constant within less than +/- 2 feet per second. I believe this fact implies (1) that the VNAV autopilot must have been engaged, and (2) it is unlikely that a turn was underway. On the first point, it would seem to me that not even a highly skilled pilot could maintain such a steady altitude using manual vertical control. On the second point, I believe it is improbable that, even with altitude being controlled by the VNAV autopilot, ROC could be held constant within +/- 2 feet per second while the aircraft is in a turn and banked at 15 degrees or more.

    I conclude that, even if there is a very small aircraft-driven slope in the 18:40 BFO data, it is more likely to be caused by small altitude fluctuations at a constant bearing than by the aircraft turning.

    Next, let me turn to the amplitude and the sign of the BFO slope caused by an aircraft turn. In this case, the complete turn shifts the BFO from ~145 Hz at 18:28 to ~89 Hz at 18:41 UTC. Thus the complete turn shift is -56 Hz. However, the measured shift during the 1 minute near 18:40, when the turn is supposedly underway, is only +0.5 Hz. Why is it so small, and why is it positive when the turn should produce a negative slope? Again, I conclude that there is no evidence of a turn occurring during the 18:40 BFO sequence. It appears that the turn parameters given in the paper by Exner et al. are actually fitting BFO read noise with small ROC contributions and are statistically insignificant.

    One final point is that, since all the 18:40 BFO data are from the C channel, any BFO slope during this ~1 minute period is unaffected by the fixed frequency bias (FFB). It is also evident from the C-channel BFO data near 23:14 that the C-Channel FFB is very close to the R-Channel FFB because using the same FFB for both channels results in good BFO model fits. Thus the -56 Hz drop in BFO from 18:28 to 18:40 is not materially affected by any slight difference in FFBs of the C Channel and the R Channel.

    CONCLUSIONS

    My analyses of the BFO data do not substantiate the claim that the Final Major Turn was underway at 18:40 UTC. The principal arguments against this claim are as follows:

    1. The variations in BFO near 18:40 are dominated by read noise and probably include small aircraft Rate of Climb Doppler shifts.
    2. The BFO slope at 18:40 is statistically insignificant.
    3. The BFO slope at 18:40 is of the wrong sign and is too small to be caused by an aircraft turn in progress.
    4. No “steps” in BFO are apparent as would be expected during a major turn.
    5. The presence or absence of a turn-in-progress effect in the 18:40 BFO data is not affected by the C Channel FFB value.

    The Final Major Turn appears to have been 100% completed before 18:39:55 UTC. It was begun at some time definitely after 18:25:27.

    It does not now appear possible to ascertain the turn time between 18:26 and 18:39 using BFO data alone, unless one uses at least some of the data from 18:25:34 to 18:28:15, which Inmarsat says MAY be unreliable. Is it possible that some of these data are actually accurate but difficult to interpret because of a simultaneous climb and turn?

  33. Bobby, Mike:

    A Suggestion:

    I have a 18:30 turn – straight path to Bobby’s final location (touches 19:41)

    I have a ~ 18:43 turn – straight to Mike’s final location(touches 19:41)

    For Mike’s new 18:38 analysis and path
    there is a small turn before / at 19:41.

    This suggests that Mike’s final location
    needs to be revised (towards Bobby’s)

    As an initial guess try (~ 5/13) of the difference with yours.

    or Bobby (~ 8/13 to Mike’s) and Bobby’s
    turn completion time to 18:38.

  34. Yap’s BTO&BFO Calculator shows that if the track changes from 220 degrees at 18:39:55 to 184 degrees at 18:40:56, the calculated BFO reduces by 10 Hz.

  35. @Gysbreght,

    Your high-resolution plots of the 1840 BFO data may indicate the presence of a BFO artifact. I am referring to the “steps” that may occur in the AES TX frequency algorithm (this is not confirmed). The algorithm may employ look-up tables for the trig functions used to calculate the aircraft frequency compensation term. This frequency term is typically hundreds of Hz in magnitude, so “quantized” trig functions (sine and cosine, etc.) with limited precision, if present, would introduce “saw-tooth” approximations to the precise trig functions. The result will be a sawtooth waveform superimposed on the “full-precision” curves.

    Looking at your last graph of BFO values, near 18:39:56.85 there appears to be a fairly obvious 3-4 Hz step upward followed by a ~3 second ramp down period. If one assumes this step is real, then the actual single-read BFO noise w.r.t that sawtooth would be significantly less than 1 Hz RMS. The quantization of the BFO data with 1 Hz precision also makes tiny 1 Hz steps. The RMS contribution due to 1 Hz quantization is 1 / SQRT(12) Hz so it is not the dominant single-read noise component.

    If the period of the ~3 Hz steps in this data set is on the order of 3 seconds, then all the remaining data are probably affected as well, but the data are just too sparse in time to identify plainly the “phase” of the sawtooth pattern across the entire data set.

    That “first step” looks pretty real to me.

  36. @Gysbreght,

    ALL BFO LOVERS:

    Following Gysbreght’s lead, here is a link to a plot I made of a sawtooth waveform overlying the BFO data near 18:40 UTC.

    https://drive.google.com/file/d/0BzOIIFNlx2aUX1g0c1hxRW5YN2s/view?usp=sharing

    The sawtooth waveform has a 4.0 Hz amplitude, a 3.29 second period, and a phase that is zero at 18:39:59.95 UTC. I just did an eyeball fit.

    The sawtooth appears to match the BFO values quite well over the entire data sequence.

    The most remarkable thing about this plot is the fact that a “constant period and constant phase” sawtooth waveform actually manages to fit the data over the full 61 second extent of this data sequence. If the apparent period and phase stability is real, this would seem to imply a very stable transition rate from one line in a look-up table to the next line. This would also imply that the temporal rate of change of the look-up table argument (perhaps an angle related to the projection of the aircraft velocity toward the satellite) was also stable during this one minute period. I’m thinking there might be a possibility of making a judgment regarding whether or not a turn was in progress during this data sequence. IF ALL THE ABOVE IS TRUE, I would think that a turn in progress would not produce sawteeth with constant period and constant phase over a full minute of time.

    As Bill O’Reilly says, “Where am I going wrong?”

  37. @ Dr. Bobby Ulich,

    Truly fascinating! But if you ask me, are you perhaps trying to read too much into the limited data?

    Did you ty the same for the sequence 23:14:01 – 23:15:02 ?

  38. So in laymsn’s terms what does this say about the turn ie: was there a lot shaking of the aircraft during this turn or was it a turn at all ???

  39. Thank you Bobby and lets not forget the 1/2 offsets Andaman Island and East side Of Andaman Sea for your 23:14 23:15 as previously stipulated for sequenced order along with Channel use and Offsets per TZ shifts from Incident area and Straits to Andaman Sea … using CIA TZ layout for UTC stationary Sat Overlay TZ Local Adjustments pic.twitter.com/amyTg5CXx anf UTC throw offs in the millaseconds corresponding appropriate Data Field and sequence.

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