How We Can Tell How Fast MH370 Was Flying

– November 22, 2014Posted in: Aviation
Early Inmarsat route calculation, from Ashton et al.

Early Inmarsat route calculation, from Ashton et al.

A week after MH370 went missing, the Malaysian government dropped a shocker: Inmarsat, the satellite communications provider, had recorded signals from the plane that allowed them to calculate the plane’s distance from the satellite about once an hour for nearly six hours.

At first, the Malaysians only released a rough sketch of the final arc: two matching fragments of a circle, 3000 miles in radius, that stretched from Kazakhstan in the north to the remote Indian Ocean in the south. This in itself was a major step forward, in that it drastically reduced the numer of possible places the plane could have gone. But even more enticingly it suggested that if we had the numerical values for all the pings, and could figure out what speed the plane was flying at, we would be able to identify the route that the plane was taken and thus its precise final destination.

The scientists at Inmarsat recognized this immediately, and as Chris Ashton et al relate in their paper in the Journal of Navigation, they quickly plugged in the most logical speed value — typical airliner cruise speed, around Mach 0.83 — and concluded that the plane flew either to the middle of Kazakhstan or almost directly south into the Indian Ocean. (See image above.) As a result, the Malaysian government submitted a request to the Kazakh government asking that it be allowed to set up a search operation in the country, and planes were dispatched to search the ocean surface near the southern potential end point. Hopes were high. After satellites spotted what appeared to be floating material in the southern ocean, Australian Prime Minister Tony Abbott told his country’s parliament that it was a “potentially important development.’’

Of course the idea that the plane flew straight and fast, as airliners typically do, was just an assumption. Theoretically, it could have flown from ping ring to ping ring at any number of speeds along any number of routes, including straight, curvy, and zig-zag. Most of these alternatives would have resulted in the plane winding up at a lower latitude. And indeed, within a few days the authorities abandoned the southernmost search area and started scouring a section of the ocean much further north. The decision to shift the search zone appears to have been heavily influenced by a second set of data also derived from the handshakes exchanged between the plane and the satellite: the so-called BFO (“burst frequency offset”) data. After much head-scratching, Inmarsat believed that they had come up with an algorithm that allowed them to understand the physical implications of this data, and it told them that a) the plane had definitely gone south, not north, and b) the plane had not been flying straight and fast, as initially supposed, but instead taken a slower and/or meandering course and wound up about a thousand miles from the initial search area.

Frustratingly, for those of us who were watching from the sidelines and eager to understand what was going on, neither Inmarsat nor the Malaysians were willing to either release their numerical data nor to explain their BFO algorithm. We just had to take their word for it. Which was enormously frustrating, since it seemed tantalizingly plausible that if we had the data and understood the physical processes that generated it, we would be able to mathematically solve for the location of the plane. Et voila: mystery solved.

Finally, after much pressure from the public, the Malaysians did finally release most of the Inmarsat data in May; the following month, the Australian Transport Safety Bureau (ATSB) released a report which explained how the then-current search area had been arrived at and explained in some detail how the BFO algorithm worked.

Many independent experts, including members of the Independent Group, leapt at the chance to finally get under the hood of the BFO algorithm and see if they could reach their own conclusions about where the plane went. In time, however, their optimism faded. In turns out that the BFO data offers only a very imprecise gauge of a plane’s location or direction of travel. To test the algorithm, for instance, scientists working for the search effort compared BFO data received from a known flight with the plane’s actual path. They found that, of the thousands of possible paths that matched the BFO data, even the one that most closely matched the actual flight was hundreds of miles off in places.

We seemed to be almost back to where we started: we had a set of ping rings that showed us seven quite accurate (within 10 km, the ATSB estimates) arcs along which the plane must have been at seven moments in time, but with only vague intimations of where along those arcs the plane actually was.

Gradually, however, without much fanfare, it has become clear that other, non-BFO techniques can provide insight into how MH370 was traveling after it disappeared from radar, and these in turn offer a strong suggestion about where the plane went.

  • Geometrical. The distance between the ping rings, especially in the middle portion of the flight between 19:41 and 22:41, is consistent with straight-line flight.
  • Aeronautical. Jet planes are remarkable forms of transportation, but they are efficient only in a fairly narrow range of speeds and altitudes. That is to say, they are happy when flying high (35,000 to 42,000 feet) and fast (Mach 0.78 to Mach 0.84, give or take, which translates to 450-484 knots at 35,000 feeet). At those altitudes, there is nothing for them to bump into, except for an occasional thundercloud. So airliners tend to go from here to there in a pretty close approximation to a straight line. As an addendum to that thought, I would like to add that airliners (so I’m told) are not that easy to hand-fly at 35,000 feet, the way one would hand-fly a single-engine Cessa at 5,000 feet; airline pilots generally let the autopilot steer the plane, and an autopilot can keep a plane essentially glued to a very, very straight line. So to recap: airliners spend most of their time flying high, fast, and straight. This is especially true over the open ocean, and extra especially true if one’s purpose is to fly to the remotest corner of an ocean one can find. There is simply no reason to, say, suddenly turn five degrees to the left before proceeding ownward. That’s not to say that one can’t, or that it’s physically impossible, to make some random turn in the middle of nowhere for no reason. It’s just very hard to think of a reason why someone would do that. So we’d expect MH370 to have flown south in a straight line. Oh, and this is especially true, of course, if the pilots have taken a poison pill, been hacked to death, or succumbed to hypoxia. In such cases we would definitely expect the plane to fly south in a straight line, unless before they lost consciousness someone programmed a zig-zag series of waypoints into the autopilot just to flummox investigators in the future. Again, not impossible, but not very likely-seeming, either.
  • Historical. As described in my post “What We Know Now,” several people have traced the radar track that MH370 followed before it disappeared from primary radar in order to calculate what speed the plane was traveling at. Richard Godfrey’s calculated average groundspeed is 504 knots, which translates into an airspeed of 496 knots. This lies at the fast end of the normal operational speed range, suggesting that the hijackers were in a hurry to get somewhere.
  • The Brian Anderson technique. In the same post I describe a technique IG member Brian Anderson devised to estimate the speed of the plane between 18:28 and 19:40, based on an inferred point of closest approach to the satellite. The technique yields a best fit at about 494 knots.
  • Ping-ring Gap Inference. One of the peculiar features of MH370’s flight to the south, which presumably began some time after 18:22, is that the early portion of that flight, accordiing to the ping rings, was nearly tangential to the ping rings. As a result, if you start from any given point on the 19:41 ping arc, and head for a point that is, say, 450 nm away on the 20:41 ping arc, you will find that there is a very small angular distance between that course, and a course that intersects the 20:21 ping arc 500 nm away. This is not as true later on; as the plane moves progressively away from the satellite, its course becomes less tangential to the ping rings, and the distance traveled less sensitive to the angle of the course. The surprising upshot of all this is that, so long as you start with a reasonable speed between 19:41 and 20:41, you always wind up traveling at more or less the same speeds during the next two intervals: about 510 knots during the first interval, and about 505 knots during the second. In essence, the plane’s ping rings don’t just narrow down where the plane was, they actually tell us how fast it was moving.

I believe that this last technique has not been described before so I’m going to go into a bit more detail. As an example, let’s look at three routes based on recently published models (two by IG members, one by Ashton et al). In each case, I drew the line on Google Earth, then measured the distance between the points where this line crossed the ping rings. (There are numerous sets of ping rings available to choose from, all slightly different; I chose rings built from calculations supplied by Richard Godfrey, but I’ve also tried other sets of ping rings as well, the results are broadly similar. Note that each of the models was constructed different sets of ping rings, and the initial segment in particular is highly sensitive to the location of the rings, which is why the early speeds vary so widely.) Here are the results:

Three possible routes southPing Ring Speed Diagram
Note that this technique doesn’t allow you to learn anything about the speed prior to 20:41. However, as noted above, Brian Anderson’s technique suggests a speed between 19:40 and 20:40 of about 494 knots, and Malaysian radar data allows us to calculate a speed prior to 18:22. All of these speeds are very approximate, yet they seem broadly consistent with groundspeeds in the vicinity of 500 knots.

What kind of speed mode could underlie this observed pattern of speeds? There are basically three options: constant Mach, LRC, and ECON. Constant Mach is self-explanatory; the plane will maintain a constant Mach number, which corresponds to a lower true airspeed as the ambient temperature decreases. LRC, or long-range cruise, is a calculated Mach number that decreases as the weight of the plane decreases due to fuel burn. Finally, ECON speed is calculated based on input fuel and time costs and takes into account temperature, weight, and headwinds, but unfortunately is complex in ways that we can’t model so will have to leave off the table for the time being.
As the plane flies to the south, all of the factors will tend to make it gradually fly more slowly over the ground. Prevailing tail winds turn to head winds. The temperature decreases. And the plane grows lighter as the fuel burns off. Yet the speeds we’ve derived from the ping rings don’t show much of a decrease until the very end. Thus in my estimation a constant Mach mode offers the best fit, as seen below:

Post-Diversion speeds
A couple of points to observe:

  • The speeds derived from the spacing of the ping rings are consistently about 10 knots faster than Mach 0.84. If the technique I’ve described is valid, that implies that the hijackers were, in the vernacular, hauling ass.
  • There are a lot of uncertainties involving this technique, so I would caution against putting too much weight in the details. For instance, the ping rings are only accurate to about 10 km; moving the 20.41 ping ring 5 miles inward would reduce the speed during the preceding interval by that many knots, and increase the speed of the subsequent interval. The headwinds calculations are also a huge source of uncertainty, since we don’t know how accurate the data are or, more importantly, where exactly the plane’s track actually ran.
  • I am reluctant to read too much into the discrepency between 19:41-20:41 and subsequent intervals because it is derived using a different technique.
  • Having said that, it may be significant that the speed is 10+ knots too high for the two hours before 22:41, and 10 knots too low afterward. (I repeat: “may be”!) If there were in fact a marked slow down during this interval, it could be due to a) a pre-programmed change in heading or engine thrust setting b) much stronger than estimated winds aloft, most likely associated with the southern jetstream, or c) the plane was actively being steered during the final 90 minutes.

This latter line of reasoning may have been what led Emirates’ Tim Clark to say that he thinks the plane was under control until the end.