Constraining Possible Routes for MH370
Duncan Steel, 2014 April 08.
The physicist always asks, “Do I know this?” “How do I know this?” and “Is this still true?” Luis Alvarez (1976)
After the diversion represented by my last post, I now return to the scientific (I hope!) analysis of the information that is publicly available with regard to the path taken by MH370.
In previous posts I have examined how the range of possible flight paths might be narrowed down based on the information that was available to me at the time of those posts. That information has now been expanded with more ping rings being available, through the good work of GlobusMax, and so one would anticipate that with both ping rings (from the ping time delays) and line-of-sight speed/Doppler shifts (de-composed from the Inmarsat Burst Frequency Offset graph by Mike Exner) the range of feasible routes for MH370 could be narrowed down. But, as I will show here, that anticipation might be mistaken, at least in part.
Plausible aircraft tracks inserted into STK
In several previous posts I have been considering, to greater or lesser degrees, the path taken by MH370 during the early part of its flight: through to the final radar detection at 18:22 UTC, the apparent (from the BFO hence Doppler information) rapid turn around 18:25 to 18:29, and then the position somewhere on the 18:29 ping ring. Now I leave behind considerations of that early part of the flight, and consider only the path from 18:29 onwards.
What I do, then, is to assume the aircraft was at a certain position at that time which I will call P_18_29, and examine the possible paths from then onwards. I chose latitude 6.7 degrees N, longitude 95.3 degrees E for that point, just inside the 18:29 ping ring:
From that point I allow paths to go either north or south, although not directly (i.e. they do not start off with headings at either azimuth 0 or 180 degrees). The paths from P_18_29 are defined only by the following requirements:
(a) The assumed speed is to be constant for each path; and
(b) Each path must cross the ping rings for 19:40, 20:40, 21:40, 22:40 and 00:11 UTC at those times and from the inside (that is, the satellite-aircraft distance must be increasing at each of those times).
Note that I am ignoring all effects of the wind, including increasing or decreasing the aircraft speed (i.e. tail or head winds) or changing its path through the air (i.e. cross winds). As I have explained previously: Ockham’s Razor dictates that I should start with the simplest approach.
Note that requirement (b) above is in essence dictated by the BFO/Doppler information, and as explained later I have reasons to doubt its veracity; nevertheless I think that requirement (b) is correct in that the aircraft does indeed cross all the ping rings from the inside from 19:40 onwards. But that presumption is subject to possible disproof.
In a previous post I concluded, based on the information available at that time, that a track going generally northwards at about 250 knots would be a good fit to the Doppler information. With no availability of ping rings other than that at 00:11 UTC I was later able to indicate that the aircraft speed must have been at least 300 knots. As discussed later in the present post, that does not (again) exclude a northerly path. (It does not, also, exclude a path taken with variable speed.)
Before coming to that, I must first present paths that satisfy requirements (a) and (b) above, and only paths with speeds of at least 300 knots will do that, due to the separation in distance and time of the ping rings for 22:40 and 00:11 UTC.
With that in mind I have so far modelled plausible aircraft paths for uniform speeds of 300, 400 and 460 knots, turning either northwards or southwards from P_18_29. That makes six paths in all, as shown in the following image obtained from my STK scenario 3D window:
Here is an expanded view of the northern paths:
(The figures at lower left simply define my effective viewing position in this 3D environment.)
Here is an expanded view of the southern paths:
The small white symbols apparent along each of the paths simply indicate the points at which I had clicked to define effective waypoints in the STK route definitions, these being decided upon by trial and error with the criterion being that the path/route (at constant speed) should reach the appropriate ping ring within a minute of the time defining that ping ring. It is this that leads to the paths displaying sudden angles/heading changes at the ping rings.
I caution again that my ping rings positions were themselves entered by eye, and so may be erroneously placed by 10 km/10 nm, perhaps more.
For the convenience of readers, I will now show also the path locations in the STK 2D window (i.e. as maps):
Line-of-sight speeds for these paths
For each of the six paths shown above I have calculated LOS speeds for the aircraft relative to the Inmarsat-3F1 satellite across the time of the flight between 18:29 and 00:11 UTC. The resultant plots are shown below. In each plot there is included an identical set of six dots, representing the LOS speeds that would be required on the basis of the decomposition of the BFO graph and thus the evaluation of Doppler shifts, which can then be converted into LOS speeds.
In each plot the line showing the LOS speed satellite-aircraft demonstrates fairly-sudden changes or steps. These are due to the angles (or changes in bearing) at each of the ping rings as seen and discussed above. They are not of concern. The actual trend of the LOS speed for a smoothly-changing path would also be smooth, so please ignore the steps and imagine a line that smoothly follows the general trends in the lines.
If you do that you will see that they are essentially identical, whether the paths go north, or south. (And before someone asks yet again: yes, I have included the satellite’s velocity in the calculations.)
An implication of this, if it is correct, would be devastating given that the searches have concentrated upon the Indian Ocean. The implication, of course, is that the LOS speed(s) of the aircraft do not favour one direction (north or south) over the other. Unless I have made a serious error somewhere, the Inmarsat engineers made a mistake in their analysis.
The lines in my plots also have slopes rather higher than that indicated by the BFO/Doppler information (i.e. the six discrete points). I cannot find a solution that will fit the ping rings and the indicated Doppler shift/LOS speeds from the BFO graph.
Further, the fact that all six graphs show essentially the same slope indicates that somewhere amongst the analysis a circular argument has been made.
There is a limited number of explanations for this:
(1) I have made an error somewhere;
(2) Mike Exner made an error somewhere in his de-composition of the BFO graph; or
(3) The Inmarsat engineers have erred somewhere.
Having checked my own analysis multiple times, and also having had access to Mike Exner’s analysis, I am hereby adopting a working hypothesis that (3) is what has occurred. I think there has been some significant mistake made by the Inmarsat engineers in their interpretation of the raw data so as to derive their BFO graph, and either that or some other error has also led to their model for the aircraft’s path – leading to the southern route(s) being favoured over the northern route(s) – being invalid.
We all make mistakes under pressure; and that statement also applies to me, perhaps here. But at this juncture I do not believe that the BFO information is correct.
At this stage of my discussion I insert a little note with regard to some laxity that has appeared in debates on this thread, with me being responsible for some of the lapses (mea culpa). I have already mentioned it in one or two of my replies to comments received.
The DIKUW hierarchy or pyramid (sometimes simply DIKW) should be second nature to anyone who wants to analyse complex situations, or indeed conduct scientific research. I like to think of it this way:
Data < Information < Knowledge < Understanding < Wisdom
There are many little examples that could be given, a frequently-cited one being that you might understand that a tomato is a fruit, but it takes wisdom not to put it in a fruit salad.
In this instance we only have information about constraints the satellite engineers have placed on the path of MH370, we do not have the data. I interpreted the first ping ring graph (issued March 15th) to get the radius of that ring subject to various assumptions, and also pointed out on March 23rd various false assumptions apparently made by the Inmarsat engineers. Later GlobusMax has used publicly-available information (in particular the Google Earth graphic from Inmarsat, made public on March 25th) to derive all the ping ring positions. Mike Exner, aided by Ari Schulman and myself, de-composed the Inmarsat BFO graph to get Doppler shifts and thus the LOS speeds I have used here (i.e. the identical six dots in each of the preceding six graphs).
From the above information we have tried to develop knowledge and thence understanding, in the hope that the wisdom will result to narrow down the search.
But what if the information is false in some way? Without the data we cannot check the first transition, from data to information. And that forces me to assume that in some important aspects the information is wrong.
To some extent my adopted assumption henceforth, until proven incorrect, is that the Inmarsat BFO graph and deductions based on it are false. It may well be that the aircraft went south, but I no longer believe the analysis/information that led to that conclusion.
In coming to the decision to reject the Doppler shift constraints my thoughts have been shaped somewhat by the apparent performance of the Inmarsat engineers both early on (the March 15th graph) and later (the BFO graph itself). The impression I gained from those is not of a professional organisation. Sorry, but that’s the way it is, and I stated at the start of this series of posts that I was trying to give an explanation for each decision I made. Advance apologies to them if they have been correct all along, but paramount at present is finding out what happened to MH370.
A precedent involving a President
The quotation from Luis Alvarez I showed at the start of this post, and also that from that same person in an earlier post, comes from a paper he wrote entitled A physicist examines the Kennedy assassination film (American Journal of Physics, volume 44, page 813, 1976).
One of the things he showed in that paper is that, contrary to all previous assumptions by others, the camera that recorded the famous Zapruder film of the assassination was not running at the nominal 24 frames per second. If I recall correctly, his conclusion was that the framing rate was near 17 frames per second (i.e. it was running slowly, which means that when played back at the usual 24 frames per second it is shown too fast). The way in which Alvarez got suspicious about the film speed is quite surprising: he noted how fast spectators were clapping their hands as the presidential cavalcade approached, and showed that it was quicker than normal human clapping rates. The point is that there is a natural rate (or range of rates) at which we applaud. Do it a little faster and the power required is tiring, and you soon slow down again.
On that basis Alvarez was able to reject some information that had previously been generally accepted, including by the Warren Commission. The data were still valid – you can never argue with data – it was the information derived from the data that was wrong, due to a false assumption and so a mistake in the analysis.
To repeat: The physicist always asks, “Do I know this?” “How do I know this?” and “Is this still true?” In asking myself those questions I have come to the conclusion that there is something fundamentally wrong with the Inmarsat BFO graph, and so I reject it. I may well be wrong to do so.
Where is MH370?
I do not have an answer to that. All I can try to do is to narrow down the possibilities. Paradoxically, if I am correct in what I have written in this post then I have actually widened the possibilities: I do not see a valid reason to favour the putative southern routes over the northern routes.
Dependent upon the speed, the aircraft seems to have ended up somewhere close to the ping ring for 00:11 UTC. Above I have shown fans of arcs (in the north and the south) limited by assumed speeds of 300 to 460 knots. I have no reason to exclude speeds higher than 460 knots, and will likely look at (say) 500 knots tomorrow.
One might presume that the aircraft continued outside of the 00:11 UTC ping ring for several minutes and the reported ‘partial ping’ at 00:19 UTC might represent the engines shutting down, the aircraft descending, or hitting the ground/ocean; I do not know.
One should not assume, however, that the aircraft continued on anything like its previous course once its fuel was exhausted. That is, it might have done so; but unless one has definitive evidence for that (e.g. that the autopilot would have maintained course after fuel exhaustion) I think it best not to assume such a thing.
Indeed I have assumed herein, perhaps incorrectly, that the aircraft continued at the nominal speeds I have given it for each path, and one might easily imagine that not only would it slow as fuel was running out, but also that each engine would have its own fuel exhaustion time and that would result in the aircraft not only slowing but also deviating from its nominal course somewhat.
I note also that I have ignored the effects of the wind at different positions and times on the aircraft. One must start somewhere, and so I started without multiplying complexity by adding in wind factors about which I know almost nothing.
A suggested location for MH370’s crash
I wrote above that I do not have an answer for where MH370 ended up. But I do have a suggestion for where it might be.
Quite early after I began this series of posts I received an off-the-record email message from someone who, through a misunderstanding on my part, I thought to be a Chinese man. In fact later emails revealed it to be an American woman. She has posted comments several times as LGHamilton, but I have no reason to believe that she would want her identity revealed to the world.
LGH drew my attention to a series of three posts on a Chinese website: here, and here, and here. The posts are apparently in Han Chinese (not one of my languages), but Google translates.
The posts, by Dr Yaoqiu Kuang, a professor at the State Key Laboratory of Isotope Geochemistry of the Chinese Academy of Sciences, draw attention to imagery from NASA’s Terra satellite which indicate a smoke plume rising from the Beshtash Valley (about 30 kilometres SSE of the town of Talas in Kyrgyzstan), and also thermal emission from the source location of the smoke. The Aqua satellite, which obtained imagery of the same area a few hours later, showed no such smoke plume.
Whilst the area is fairly densely covered in trees, it is at a high elevation and at this time of year covered in snow, so that a forest fire is contra-indicated. Dr Kuang also indicates evidence for rapid snow melting causing the river in the valley to rise.
The locations of Talas and the Beshtash Valley are shown in the graphic below, and can be seen to be fairly close to the termination of the hypothetical 460-knot northern path I have presented earlier in this post.
A web search from here in my apartment far away in Wellington, New Zealand, fails to indicate any further information with respect to the above suggestion. Perhaps someone has already gone to take a look on the ground and found no evidence of a jetliner crash. If this has not yet been done, given the amount of time, effort and money being spent on scouring the Indian Ocean it would seem to be a sensible step to go and take a look in the Beshtash Valley.
I’d invite readers to alert the mass media to the potential for a scoop as being perhaps the quickest way to get a reconnaissance accomplished. Unfortunately I can proffer no advice with regard to the availability of snowmobiles for hire in Kyrgyzstan.