How Wide Should the MH370 Search Area Be?

At a press conference earlier this month, Australian officials released a new report updating the scientific rationale for their continuing search of the southern Indian Ocean, which is expected to wrap up no later than June, 2016 after the expenditure of an estimated $130 million. “We have a high level of confidence that we are searching in the right area,” declared Assistant Minister for Defence Darren Chester.

As a result of this new analysis, the width of the area to be searched has expanded: from 20 nautical miles inside the 7th arc and 30 nm outside, to 40 nm inside the arc and 40 nm outside.

The key piece of data deployed to justify this reassessment was the newly announced finding that that the satellite data unit (SDU) requires only 120 seconds from fuel exhaustion to first log-on attempt, rather than the 220 seconds cited in earlier reports.

Assuming that the plane was operating as a “ghost ship” without a conscious pilot at the controls, its final moments played out like this:

  • 00:11:00 Transmission from SDU to [ground station]. Hourly ping as previously described.
  • 00:17:30 Approximate APU start time. APU requires approximately 60 seconds to provide electrical power.
  • 00:18:30 Approximate time of SDU power restoration. SDU required approximately 60 seconds after power application to begin transmitting a log-on request.
  • 00:19:29 SDU initiated log-on request. SDU began log-on process to satellite system.
  • 00:19:37 Log-on request complete. SDU successfully logged onto satellite system.
  • 00:21:06 Expected IFE [Inflight Entertainment System] set up of first ground connection. IFE set up request did not occur.

Here’s a nice visualization, from page 11 of the report:

End of flight sequence
Click for full size. Credit: ATSB

A shorter log-on time for the SDU means that the plane must have run out of fuel later than originally believed, and therefore would have been higher and/or faster at time of the 7th ping. The important question is: what are the implications of this new timeline for how far the plane could have traveled after it sent the final ping? Here are a few different ways of looking at the problem.

#1: Historical data. On page 14 of the ATSB report we read: “A large sample of previous accidents was reviewed including the results of an analysis commissioned by the French investigation authority the Bureau d’Enquetes et d’Analyses (BEA) during the search for flight Air France 447… The BEA found that in the case of an upset followed by a loss of control, all the resulting impact points occurred within 20 NM from the point at which the emergency began.” Of course, by the time MH370 reached the 7th arc, its loss of control had been underway for two minutes, so the impact distance should be even less than this.

#2: Simulator data. From page 13 of the ATSB report: “The aircraft behaviour after the engine flame-out(s) was tested in the Boeing engineering simulator. In each test case, the aircraft began turning to the left and remained in a banked turn… The final position of the
aircraft was within a region defined by 10 NM forward and 10 NM left of the position where the flame-out occurred. Therefore, relative to the arc location, it was determined that 10 NM forward and 10 NM behind the arc would encompass the simulation impact area.” To take into account various uncertainties, the ATSB felt justified in adding an additional 10 nm in either direction, resulting in, once again, an endpoint no more than 20 nm in either direction.

#3: Stochastic Analysis. Back in May Brock McEwen conducted a stochastic analysis of MH370’s final path using the data current at the time. Asked to rerun his numbers using the new SDU reboot time, he produced the chart below (note that the label “Distribution DESCENT RATES” should actually read “Distribution of DISTANCE from impact point to 7th arc (FL0), in nmi.”

Brock stochastic model update
Click to enlarge. Source: Brock McEwen.

The key rectangle to look at is the light blue one, which refers to the area shown marked off in the thick baby-blue line below. As you can see, it encompasses the core “fried egg” of the probability distribution published in the ATSB’s report:

SIO Search Overlay 2
“Search Zone 2” is demarcated by the thick baby-blue line.

According to Brock’s calculations, the number of paths that hit the 7th arc and have endpoints 20 nm beyond the arc is invisibly small. Similarly few paths hit the 7th arc and wind up 5 nm within the arc.

#4: Assumption of functioning IFE. All of the above methods assume no more than a second-engine flame-out two minutes before the 7th ping. There is, however, a constraint that can be considered. The new ATSB report says on page 10 that an IFE system transmission was expected at 0:21:06, or 97 seconds after the 7th ping. But that never happened. That means that either someone turned off the IFE after 18:28, or the plane had hit the water by then (or was in a very unsual attitude, which let’s assume would be bad enough that the plane was about to hit.) Traveling at 500 knots, a plane can go no further than 13.47 nautical miles in 97 seconds.

#5: The ATSB Approach. In addition to #1 and #2 above, the ATSB paper considered what it calls “basic trajectory analysis of an uncontrolled but stable aircraft…. this analysis included constant and increasing bank angles, but did not include variations in speed or pitch angle.” It is not clear what exactly this analysis exactly entails, or how valid it might be; one would expect that increasing speed and downward pitch would naturally be part of a terminal spiral. At any rate, this methodology produced scenarios in which the plane wound up as far as 40 nm from the 7th arc. The ATSB acknowledges the inherent weakness of this approach: “ Due to the generic nature of this analysis it was given a lower weighting” in calculating the final probability distribution.

Putting all of the above together, the ATSB concluded that in all likelihood the plane hit the water within 20 nm of the 7th arc, yielding a total width of 40 nm. It calls this area the “highest priority width.” In addition, it designated a “secondary priority width” extending out another 20 nm based on “possible uncertainty in the simulation results and the trajectories from the turn analysis.”

The official search area has been redefined to match the results of the ATSB analysis; three ships are now tasked to search a box that stretches nearly 400 nm along the 7th arc and 40 nm on either side.

This strikes me as a remarkable state of affairs.

The report issued by the ATSB on December 3, 2015 is 28 pages long; its data and reasoning were further explicated in a densely erudite book by analysts at Australia’s Defense Science and Technology Group that is 128 pages long. Yet the broadening of the search area, which will entail the expenditure of tens of millions of dollars, is justified only by a fleeting invocation of “possible uncertainty.” This is hand-waving.

Continuing the search beyond the 40 nm “highest priority width” is not justified by the ATSB’s own analysis. Most of this region has already been searched; a remaining 5 nm-wide strip on the inner section of the 7th arc could be accomplished in short order. The ATSB should fulfil its duty to search the area suggested by its analysis. If the plane is not there, then the ATSB’s initial assumptions were incorrect. This will be a crucial piece of information guiding future efforts to solve the mystery of MH370.

148 thoughts on “How Wide Should the MH370 Search Area Be?”

  1. For some reason they think abnormal flight would have normal flight envelope, so they assume someone might have wanted to use cruise speed and straight line to get as far as possible or to spare fuel, which is ridiculous at best.

  2. @StevenG, Bear in mind, however, that while indeed the flight after 18:25 was anything but normal, it was conducted using the same equipment as everyday flights. And so it’s worth bearing in mind that the 777 autopilot does not include a mode that provides for a curving flight path, that is to say, you can’t command the plane to maintain a 1 degree bank. (You can have it follow a magnetic heading, which in this case would produce a slightly curving path, but not enough so to take it out of the SIO search area.) One could command the plane to make a series of turns to approximate a curved path, but the question this would raise is: why? Why fly a curving path over remote ocean in the middle of the night?

  3. @Jeff

    One could apply your question to:

    1) why turn West at Igari ?

    2) why fly over the Malay peninsula ?

    3) why fly NW into the Adaman sea ?

    4) why execute a turn South into the SIO ?

    My link above provides my answer to your question, and the above. Is the answer correct? Don’t know, but it is better than invoking Occam’s Razor or declaring ” that is the way pilots like to fly airplanes”.

  4. @DennisW, The answer to all four questions is the same: because whoever took the plane wanted to go that way. Why did they want to go that way? We don’t know. But the way this portion of the flight was conducted is entirely consistent with normal airliner navigation: flying straight from waypoint to waypoint, then making turns.

  5. @Jeff

    The radar data as presented does not support waypoint navigation. That conclusion was impressed on the Lido Hotel data, by assuming that the graphic was made in haste and manipulating waypoint data to fit. What the Lido Hotel data actually shows is a last contact at 200nm on a 285 degree radial. Fitting a waypoint conclusion to it is another example of a logical leap that has absolutely no basis in fact.

    Likewise the turn left was executed before Igari. There are so many waypoints out there that one can easily pick a path that aligns with them if you are willing to sweep minor unexplained variations under the rug.

    I can construct a waypoint path along the South Coast of Sumatra for that matter. IG members challenged me to construct a path satisfying BFO and BTO, and I wasted time cleaning up my data for that exercise. Actually I am glad I did. It was the right thing to do.

  6. @Jeff “entirely consistent with normal airliner navigation”

    Or, MH370’s actions might just be consistent with normal airliner design. What if the left was shut down near IGARI due to an emergency (just blowing the fire extinguisher would do that and also kill fuel and electric power)? What if lots of rudder trim was dialed in to keep the plane flying straight at 500+ kts in the descent? What if, at bottom of descent, the plane levels off and all that now-excess trim turns the plane northwest? What if the plane eventually gets into an upset situation further up the Malacca Strait and the autopilot takes over?

    Yeah, lots of What If’s but maybe . . .

  7. @Oleksandr,

    The description I have provided is for the automatic operation of electrical power; if there is manual intervention through switching then the system operates differently.

    Selecting Bus Tie off for example now inhibits Right Mains ability to feed Left Main and also Right Transfer to feed Left Transfer if necessary.

    The RAT will deploy as soon as both Transfer buses fail to ensure power to the Standby bus; the APU autostart then occurs.


  8. George / Oleksandr,

    Personally, to take Kate’s testimony down just once again, dust it off, and put it back up, I think there could be something within Kate Tee’s two sightings, but seemingly impossible to prove, but something may be there. Oleksandr I do see how you want to use it for supporting evidence. Her original sighting horrified her, the cockpit windows almost gaping like big black holes, could be the military plane coming down to have a look at her/yacht, or….NOT. And George isn’t the underbelly of MAS fleet a light grey or is it tan? In my Wikipedia it looks grey. I think as far as the eyewitnesses go, she is the most credible, she was in the right place at the right time, but still too far away from the object(s) to see any logos or other distinctive markings, it’s all too “iffy.” Back up on shelf for now.

    I still would love to know what MH88 did or did not hear as far as shelved items go.

  9. @Susie (and all)
    thanks and to U2; here is another wonderfull documentary about Boeing 777 and most important message seems to be the “Working Together” approach, open and frank communication, taking risks and encouraging discussion of problems early, over the globe, with respect to local cultures – if this is how America wants to lead by example, then OK 🙂 Here in EU HQ we have still many things to fix this way… and I am sure the 777 engineering spirit CAN be applied to anything else, yeah

  10. @jeffwise

    “Why fly a curving path over remote ocean in the middle of the night?”

    Why fly a Beijing-bound flight into SIO at all?! I can totally imagine a person ready to hijack an airliner and able to get over malaysian peninsula unchallenged to not really adhere to straight paths or classic ABC piloting.

    FWIW the primary goal could be Cocos then for whatever reason going to Christmas Island after realising Cocos is a bad idea.

    But I’m quite sure that whatever the plan was it had an airfield included and there are only two reachable in SIO after you do a SE turn.

  11. @StevanG, I fear that you are conflating two different kinds of baffling behavior. To explain, allow me to draw an analogy. Let’s imagine that you get a call from the police early one morning. They tell you that they’ve arrested your wife for driving 120 mph on I-15. Apparently she’d been driving all night heading for Vegas. Oh, and one more thing: she’d been driving from the back seat. She’d put a cinder block on the accelerator and was using one of those supermarket grabber sticks to hold the wheel. Now, as you sit in the bathtub trying to process, there are two different kinds of question marks to chew over. First, what I’d call the “inscrutable”: why the heck would your wife want to go to Vegas? As far as you know, she doesn’t like to gamble and she doesn’t like magic shows. So it’s impossible for you to say what her reason was, but it’s easy for you to imagine that she did have a reason–for instance, you never really asked her how she felt about shrimp cocktail. At the same time, there are other aspects of the mystery that are even harder to get your head around: the “baffling.” Assuming you do want to drive all night at high speed to Vegas, why would you want to do it from the back seat? It’s dangerous, difficult, and tiring. Hardly anyone ever drives cars from the back seat. In fact, you can’t think of a single reason for doing this.
    If one is to consider the possibility that the plane flew toward Christmas Island, then we are left to confront both these kinds of mysteries. The inscrutable: why would anyone steal a large airliner and go to Christmas Island? And the baffling: why would they fly it in such a way as to approximate a broad, steady turn, for hours and hours–something which, as far as I know, no airline pilot has ever done, ever?

  12. @Jeff

    There are waypoints with which to navigate the general route I described. I was more concerned with feasibility than an exact route profile. There are a number of airfields along that route which could accommodate a 777. The fact that the plane went down near Christmas Island does not mean that was the intended destination all along.

    The reason for the path along the coast of Sumatra was to kill time while negotiations were ongoing as I explained in in more detail in a previous link.

    Your metaphor is flawed from the get-go, BTW. There is absolutely no way to know why a woman might do anything.

  13. @Jeff

    I am frankly amazed that the DSTG people would author a “book” on their analytics. The fact that Springer is apparently going to publish it is not surprising. Springer has become the National Enquirer of “science” publishing. My guess is there is a clause in the contract with Springer that makes publication contingent on finding the aircraft very near where the authors claim it to be. What that means, of course, is that the likelihood of the book being published is very small.

    It is actually nice to be retired. If I were still employed, there is probably no way I would risk a resume stain by sticking a pin in a map based on the information we have.

  14. @jeffwise
    Thanks for the “dummy down” analogy where I finally found full conprehension of subject matter, it had a brilliance of it’s own!

  15. @Jeff: “why would they fly it in such a way”

    I’m equally curious about why a P51 pilot would perform a barrel roll down the front straight at the 2014 Reno Air Races. It crashed into the spectator stands with great loss of life. It just makes no sense at all . . . . . unless the plane broke.

  16. @Bruce

    I have a better metaphor. A biologist, a physicist, and (Jeff + IG team) are told they are looking at an empty house. They all observe one person entering the house. Time passes, and they all observe two people emerge from the house. They are asked to explain.

    Biologist – single organism reproduction took place

    Physicist – Either initial conditions or observables are flawed

    Jeff+IG – If now one person were to return to the house it would be empty again.

  17. @Jeff

    I have no idea why you keep reverting to the stable curving path theme. I used it simply to demonstrate feasibility. I guess I will have to derive a path based on waypoints to get you out of your rut.

    That will be simple relative to reconciling the current search area with:

    1) no debris associated with MH370 has ever been found there either on or below the surface

    2) there is not a single plausible explanation for how the aircraft might have arrived there

    3) drift modeling is not compatible with that terminus (read Brock’s work)

    You are living in a glass house, but you do have a lot of company.

  18. @DennisW, You’d like me to read Brock’s work? That’s a great idea, can you recommend a web site where I might do so?
    Seriously, though, it does your theory no favors to say that it’s got fewer problems than the current search area. By all means, derive a BTO-compatible path that passes through waypoints, I’m keen to see it.

  19. In regards to a curving versus path, it comes down to available navigation. If a fire did indeed sever a majority of data and control lines, then all navigation is unavailable and only the curved path remains.

  20. Oz,

    A long time ago I took a flight from Schiphol to Singapore. I can’t recall what exactly Boeing model it was, but they kept us for 4 hours locked in the cabin due to a “electronics glitch”. At certain moment the captain announced they had to shut down the whole electrical system of the aircraft for roughly 1 minute. It was unforgettable experience – silence and darkness. Only dim emergency lights were on, apparently fed independently. Soon after that the captain announced they took a decision to replace a faulty unit, which took them an hour or so. Thus I am pretty sure there are electronics glitches that require complete de-powering in order to be repaired.

    Are you saying that manual isolation of the left bus, followed by the shut down of the left engine, followed by manual switch of the left bus “on” would also cause similar effects: drop in the altitude and reboot of SDU?

  21. Jeff,

    RE: “There is no failure mode that puts a 777 on a stable curving path.”

    Absence of evidence is not evidence of absence. Are you sure about the absence of other stable failure modes besides a correctly working AP?

    For example, TOGA is a stable mode, isn’t it? B777 manual says that TOGA remains engaged until any further human input. What does happen if there is no human input for the next 5 hours? So far I have heard only comments from Gysbreght with regard to TOGA.

    Also, how can we be sure that both the engines were operative? Yes, it would be sub-optimal regime of flight, but I haven’t seen fuel-endurance curves for this case. I will not be surprised if the fuel-endurance curve for a single engine mode “touches” the 7th arc at around 100E.

  22. @Oleksandr,

    Selecting the Left generator off with Bus Tie isolated (off) and then selecting Left generator on will definitely cause an SDU power up or reboot as you state.

    There is no need for the engine to have shut down for flight level change; simply input the new altitude to the AP or if not in AP push on the column.


  23. @Jeff

    Yes, it (tidied up flight path) has to be done I suppose, tedious and boring as those types of analytics tend to be. It won’t happen before 2016 or my better half will execute me.

    In the meantime, I offer the narrative linked below for people here to think about. The narrative is general, and does not refer to any particular terminal theory, but rather addresses questions I have seen asked relative to the recently published DTSG analytics.

    I have purposely disabled comments in that blog since I prefer to keep the conversation centered here.

  24. @Bruce, It does come down to available navigation–and, as I’ve pointed out, a curved path is not available. This is why the IG and the ATSB have been so steadfast in basing their calculations on straight, fast flight: it is very hard to imagine the plane flying any other way. Once the current search area is ruled out, the remaining options look very, very strange.

  25. @jeffwise

    I can’t see the analogy in your post, I have never stated pilot was operating the plane from a strange position.

    I don’t say it was a constant curved path but if he did this on a whim I can totally see him changing the goal during the flight.

    Thus changes in direction and/or altitude and/or speed. The fact BFO&BTO fits constant speed&altitude (with some margin of error) could very well be just a coincidence.

    Imagine this, thief steals an item and disappears, you have one path leading to nowhere which would fit some data points if he went constant speed and you have another one where he could hide that require change of speed and direction, something happens to him along the way (gets eaten by a grizzly let’s say) and you find his remnants on the second path (flaperon drift analysis) but still continue to search only the first one since you believe he would for some reason want to go only straight.

  26. @Jeff

    So the plane flew straight from Igari to the FMT? There is substantial evidence to contradict a straight path during that portion of the flight.

    The hole you are digging just gets deeper and deeper.

  27. @DennisW, Yes, that’s right: to the best of our knowledge (the radar data is obvs sketchy), the plane flew straight between turns between IGARI and its disappearance from radar.
    Let me be clear: yes, you can approximate a long-term curving path by making a series of turns, as I have said. But there is no autopilot mode that produces a gradually curving path. (Before anyone jumps on me here, I acknowledge that a magnetic heading will produce a curved path, but in this particular set of circumstances the curve will be gentle and insufficient to take the plane out of the current SIO search area.)
    Also bear in mind that at this point only extremely, extremely sophisticated hijackers could have guessed that BTO/BFO data could be used to generate flight paths retroactively, so it’s off the table to postulate that someone plotted a curving, slow path in order to mislead searchers into thinking they’d taken a fast, straight path.

  28. @Jeff

    “the plane flew straight between turns between Igari and its disappearance from radar”.

    I had to read that a few times to get the intended parsing. What I think you are saying is that the path between Igari and the FMT is a series of straight line segments. Sure, I accept that, but the path itself was far from a continuous straight path (geodesic). My path was curved for analytical convenience (Actually I was lazy and modeled it as straight line segments between arc crossings.) BTW, I have never invoked magnetic heading plus windage to explain any path. As I said, that path was done to demonstrate feasibility as requested by some IG person whose login I forget. I left it at that since the purpose was served.

    I will clean it up to satisfy waypoint navigation, although that seems like an exercise that I would normally assign to “people”, but I don’t have “people” anymore.

  29. Jeff,

    “Magnetic heading AP” terminates at around 32S if I recall correctly. Similar magnitude of the residuals BTO and BFO as for the “classic” AP. The respective trajectory was curved. Then what? Failure related to the engines and/or electronics appears to be more plausible than magnetic heading from my point of view.

  30. Oz,

    Yes, that is true.

    However, I am looking for a reason, which can explain all the coincidences and math: a number of variants of my CTS models converge at nearly 50-60% of the max thrust (output from the residual minimization model). A single working engine is the first thought I had. And now I think this can somehow be related to possible dive at 18:22 and SDU reboot at 18:25.

  31. @Jeff: “no autopilot mode that produces a gradually curving path”

    Actually, the most basic of autopilot modes is that of a simple wing leveling. When operating as a wing leveler, the autopilot has no input from a heading bug or electronic nav receivers. It merely keeps the airplane flying straight or some semblance thereof. And just like the guy lost in the desert, the long-term track is a curve as there is nothing to convey “straightness”.

    MH370 was deaf, dumb, and blind — and pilotless.

  32. @Jeff: The B777 autopilot is an excellent device that works quite well, even in the face of adversity. Wing leveler mode is not a choice available to the pilots. In fact, no choices were available to the pilots because the control panel died, just like so many others that had their cables severed. Wing leveler mode is also not an explicit choice within the autopilot electronics but it was forced upon it when the data feed from the ADIRU and, perhaps, the SAARU went away.

    No, the wing leveler mode is not an autopilot option — it’s the default.

  33. Bruce Robertson: Can you please explain how the wings are maintained level with no ADIRU input?

  34. @VictorI: The SAARU (Standby Air Data and Attitude Reference Unit) provides the basic information that enables the autopilot to “keep the dirty side down”.

  35. @Bruce Robertson: You proposed that both the ADIRU and the SAARU might not be available, yet the plane would fly with wings level as a default autopilot mode. How could it?

  36. @VictorI: We have to consider the possibility some of the SAARU inputs as being compromised. Tying in with the flash fire scenario, those system wires that aren’t severed may be intermittent.

    I do see MH370 as a broken airplane, unlikely to fly for seven hours at near max altitude and speed.

  37. @Bruce

    Long term stats still show only 20% of airline crashes due to an issue with the airplane. I would not bet into those probabilities. Also the lack of communication lowers that 20% dramatically, only a small fraction of mechanical failures would entail a complete malfunction of all coms. An even smaller fraction of aircraft failures would allow the plane to keep flying until fuel exhaustion.

    Said another way, you are beating on a very dead horse. I don’t even feel sorry for people advocating an aircraft issue in the case of MH370. The probabilities are overwhelmingly stacked against it given the circumstances surrounding this incident.

  38. @Jeff

    You know what?? I just do not care any more. This is my last post (or any other Input) forever relative to MH370. My SO is tired of it, and so am I.

  39. @DennisW
    Don’t do that…..could be your “SO” got a bit sideways with the unpredictability of women comment, but of course, no way to know. Hang in there.

  40. @DennisW

    whenever I feel frustrated about the way this search is conducted I just remember the people on those search ships who also might suppose they are searching in a ridiculous area but they still have to do their job in a very risky environment, their frustration sure has to be at least one notch higher

  41. Dennis — every blog has three horses ass’s….if you leave, that will only leave Jeff and myself….so….have a nice christmas…a sufficient number of martini’s…and we will talk to you next week…o k (besides, you still have to explain what “bifurcation” means..) merry..merry…oh and remember…it’s a woman’s perogative to change her mind; it’s a man’s perogative to change it back….

  42. @George

    I struggled to find a better term than bifurcation – the division of something (in this case possible flight paths) into two branches. It is the best I could do.

    My interest has actually shifted from finding the aircraft (which is extremely unlikely IMO) to studying the debilitating effects of intellectual sunk cost.

  43. @susie

    Thanks. My SO has a PhD in EE, is an excellent mathematician, and spent the vast vast majority of her career employed by a navigation company. She certainly has a much better grasp of the problem statement, which is actually pretty trivial from a physics and math standpoint, than any of the posters here or at the DSTG for that matter.

    Unlike Jeff’s wife, she actually agrees with me (relative to the limitations and interpretation of the data). Her frustration stems from an inability to grasp why I get so annoyed. She is, as usual, correct.

  44. Quick question regarding the Pings.

    How many known hops occur between the source and destination and logging of time? Anybody know the protocol? Is it simple IP based or a a lower level time code?

    I ask because I have a theory that has been knawing at me and occasionally evidence appears that only seem to collaborate the theory. Accept for the Ping round tripping. However, in my experience, this can be an unreliable method for determining geographical distances given that processing time, traffic and the number of hops can have a significant impact.

  45. I’m curious, has anybody ever tested actual SDU Bias’ while an SDU was stressed or having had a fresh reboot? Would these older satellites have inherent abnormalities during such occurrences on an aircraft?

    They seem to be making a lot of assumptions with regard to the SDU Bias of MH370 being a constant. They use previous SDU Bias numbers from a normally functioning aircraft… STATIONARY AND ON THE GROUND!

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