MH370 Flight Path Model version 13.1
by Richard Godfrey
Preface by Duncan Steel: The Independent Group (IG) has continued its robust analysis of the available information and data regarding MH370 for some months. Typically around 50 email messages are exchanged each day across the 18 members, some being more active than others; I have, due to other concerns, been one of those less active. All I am saying here is that the IG has been working away, we hope pro bono publico, even though our efforts might not be widely apparent.
From time to time various people have asked whether any updates on progress in respect of the above will be published, and my response has been that the problem is that the complexity of getting a detailed, agreed report ready when there is a substantial number of people working on a variety of aspects of the analysis proves to be difficult; and, should all ongoing work be halted so as to provide a full discussion of what has been done, that would stymie progress. It is hoped that when the flight recorders of MH370 are found, and what actually happened on that fated flight is uncovered, we will be able to compare our analysis (and necessary assumptions) with reality. In the meantime the efforts are directed towards refining our ‘best guess’ at the aircraft’s end point based on the information available. It is lamentable that many important pieces of information continue to be concealed by the authorities (see Section 5 of this Progress Report).
The IG is not generally concerned with arguing with others about who is right and who is wrong, but it is interested in looking at other ideas and suggestions if those have promise of providing new insights and ideas with respect to the analysis of the available information. This is not a competition, with a prize for the winner: it is a human tragedy that needs a resolution.
Various members of the IG have developed distinct but similar models for the flight of MH370, making use of the BTO and BFO data, and also (to varying extents) constraints imposed by aircraft performance limits such as the available fuel, the plausible engine performance degradation since new, the air temperatures, the wind fields, the modes of the autopilot, and so on.
What is described briefly below is version 13.1 of the model developed and maintained by Richard Godfrey (Frankfurt, Germany). As I wrote in the preceding sentence, the description is very brief, and as Richard himself noted to me, “A user’s manual has not been written.” However, those of ability will be able to look inside Richard’s model (which is in the form of an Excel spreadsheet) and explore how it works, what the assumptions and technical relations are, and so on.
But: caveat emptor.
Notes from Richard Godfrey:
The model is simply an Excel spreadsheet without any description of the purpose, approach, assumptions, calibration, calculation methods, simulation methods, sensitivity analysis, findings, etc.
The spreadsheet should open at the first sheet, which is labelled “Key Points”. This is the one to look at. One can ignore all the other sheets as they just support various further investigations.
This modelled flight path for MH370 is one of many possible solutions. The methodology is generalised, but in this version a particular set of conditions has been assumed:
(1) The auto pilot was engaged and had waypoints such as ISBIX and S35E90 programmed, hence a constant track for the final segment of the flight after the final major turn southwards.
(2) The auto throttle was engaged and the air speed followed Victor Iannello’s simulation equation for Mach speed.
(3) The True Air Speed (TAS) is calculated from the Mach speed taking the air temperature into account.
(4) The Ground Speed is then calculated from the TAS taking the wind fields into account.
Please allow me to acknowledge the many contributions from members of the IG with data, calibration methods, calculation methods, simulation methods, checks, reviews and comments.
The model version 13.1 is available here.
A KMZ file showing this modelled route is available here.
A KML file containing labels for the times and so on along that route is available here.
Here (below) is a visualization of the modelled flight path, with the ping rings, as set up in Google Earth:
Here (below) is a visualization of the modelled flight path across the Malay Peninsula, up the Malacca Strait and the southern end of the Andaman Sea and then the final turn southwards near 18:40 UTC on 2014/03/07. The georeferenced insert with an orange background is derived from a photograph of a slide projected onto a screen at the families’ briefing at the Beijing Lido Hotel late in March, our only source for the primary radar tracking of MH370 through to 18:22 UTC; the actual radar-derived positions have not been made publicly available except in this slide.
Here (below) – courtesy Mike Exner – is a comparison between the end point indicated by the model described in this post (i.e. that point labelled ‘RG’) and various other end-point derivations based on a variety of models. The violet lines indicate recent navigational tracks taken by the search vessels; the green line is the 7th ping ring calculated for zero altitude above the WGS84 Earth ellipsoid; the red line is the 7th ping ring calculated for an altitude of 35,000 feet.