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Malaysia Airlines Flight 370 |

## Reverse Engineering the Inmarsat Ping Data from Flight 370

In the last few days, two possible southern trajectories of the flight 370 appeared in newspapers and on Internet sites, all without much backstory. News outlets then regurgitated this information without adding anything more informative.

This was a significant information that seems to have led the Malaysian government to conclude that "all is lost" in Indian Ocean. And given the significance the Chinese Government demanded access to the raw satellite data. This request comes as the distraught Chinese relatives of the passengers accused the Malaysian government of lack of transparency and honesty.

A question arises then, perhaps it might be possible to attain a rudimentary version of the satellite data from the available information. This article is a proof of concept exercise at probing that possibility.

What is known at this point is that the two possible trajectories were calculated using the series of pings that the Inmarsat satellite received between 3:11AM and 8:11AM. These pings evidently gave one crucial set of information, which is the inclination angle of the aircraft in relation to the satellite, the angle measured from the orbital plane of the satellite, directly under the satellite being 90 degrees.

One can draw a cone under the satellite with the specific inclination angle of the ping, and where this cone intersects the earth's surface would be a large arc of possible locations of the ping. Everyone following this topic should be familiar with the arc that's been derived at based on the last ping from the airplane, but what hasn't been disclosed to the public is the data on the rest of the pings. So let's see what can be had from the publicly available information.

Methodology

The idea is simple. Assuming a constant flight speed, one can divide the two possible trajectories into equal segments between pings. And again, given that it is not clear if the pings came every 30 minutes or every hour, an hourly cycle can be assumed. This information results in five segments for each trajectory.

The first ping came from a point south of Sumatra where both trajectories originate, at 3:11AM. The widely publicized last ping came in at 8:11AM along the 40-degree inclination arc. From here, one can locate four additional points on each of the two trajectories that are equidistant from one another.

The arc that is centered on the satellite with the radius at one of these points gives the inclination angle for that point; one can estimate the angle by comparing the radius of the arc with other known angles (40 deg, 50 deg...etc.). So it is possible, using the public information, to make a guess at the inclination angles of each of the pings. And since the pings came in at every hour, the air speed is simply the distance the airplane traveled in between pings. This can easily be measured on the map.

The method used was crude. The tools used were just a letter size printout of a map and a compass. Here are a few disclaimers:

1. The original map used was a printout from the CNN website, and the type of map projection used is not known. The assumption was made that for all practical purposes, the map represented a flat surface. In order to achieve any accuracy one must know how the curvature of the earth was projected onto a flat surface.

2. The scale of the map was unknown, other than the rough 1600-mile distance sketched on the map. The distances used for this calculation need to be corrected based on proper map projection.

3. The same change in the inclination angle covers a greater distance the further the ping is from vertical. However, for simplicity, one angular unit projected onto the map was assumed to be constant over the range of inclination angles that the airplane covered. Again, a greater accuracy can be achieved if trigonometric manipulations are used to properly translate the inclination angles to actual surface distances.

Result

The following table is a best-guess dataset of six pings, arranged by the time of ping (AM), the inclination angle (degrees), and the range of possible air speeds (MPH). It is not known with the available information whether the speed was an assumption on the part of the engineers or if it was somehow gleaned from the raw data. There could also be quite a discrepancy in speed due to the mapping projection and the non-linear distribution of inclination angles that were not accounted for in this calculation.

a) 3:11 54.6

b) 4:11 56.0 480

c) 5:11 54.3 480-530

d) 6:11 50.6 480-515

e) 7:11 45.8 480-500

f) 8:11 40.0 480-495

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**TAGS:**- engineering,
- ping,
- malaysia,
- trajectory,
- data,
- inclination,
- inmarsat,
- reverse,
- arc,
- 370
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