# Computer model yields two possible flight paths of MH370 in South Indian Ocean

Martin Vegter
• Computer model yields two possible flight paths of MH370 in South Indian Ocean Martin Vegter

I am reading this article on the NY Times, where they show two possible flight paths of the missing flight MH370 in the South Indian Ocean:

I am wondering how they can come up with such specific paths, when the only information we have are those two arcs (those arcs are not paths, rather the last satellite ping happened somewhere on the arc).

How can anybody create a computer model with just this information? Or does it mean that the modelers have more information available than the general public?

• The "related article" specified in your link has this to say:

Searching one possible flight path, Australia said it would focus its efforts in a specific stretch of the southern Indian Ocean, using computer models of the plane’s possible flight path that take into account undisclosed satellite data, wind conditions and ocean currents and some assumptions about how fast it was flying and how much fuel it had left.

So yes, apparently they have more information than the general public does.

• My personal guess: I think what they've done is to start a line where from where the plane was last known, and then intersected it with the arc where the distance would have been correct at cruise speed with reference to the time.

Example with just some values. Since the arc radius and time was known, one would be able to draw a line which would show a constant speed. If it was not a constant speed, the line would have to bend left/right to account for it, which does not appear to be the case in the provided image.

This is based upon the following:

• 'A signal was sent out every hour'. In other words, they got several data points.
• Based upon that, they would have points for the arc radius at set times.
• They might assume that the aircraft has a constant speed. Because of this, they should see if the data points lie on the a straight time, since the only variable is the distance.

I'm pretty sure that the two lines is based upon the fact that they know the uncertainty at the final position, and in my opinion it suggests that the aircraft flew a constant course from the last known radar fix where it originates.

• how they can come up with such specific paths

The correct answer currently is that we (the general public) do not know exactly how these tracks were calculated.

The specific lines in your graphic were probably invented by graphics artists employed by NYT and based on vague verbal descriptions.

On March 24th, Inmarsat stated that a new analysis of the records of satellite handshakes with MH370 were able to use doppler effects in the signals together with an analysis of similar satellite handshake data from other Malaysian 777s to determine that MH370 flew into the Indian Ocean and ruled out flight paths to the previously described northern corridor.

On March 21st, a little light was shed on this process by a statement attributed by New Straights Times to Malaysian Defence Minister and acting Transport Minister Datuk Seri Hishammuddin Hussein.

"The investigations team received the complete raw Inmarsat satellite data, which included the six handshakes at approximately 3 pm on Wednesday, March 12."

"This type of data is not normally used in investigations of this sort. It is only because we have so little other information to go on in this difficult and unprecedented situation that the data is being used.

"Upon receiving the raw data, the Malaysian authorities immediately discussed with the US team how this information might be used. The US team and the investigations team then sent the data to the US, where further processing was needed before it could be used.

"Initial results were received on Thursday, March 13 at approximately 1.30 pm, but it was agreed by the US team and the investigations team that further refinement was needed, so the data was again sent back to the US.

"The results were received at approximately 2.30 pm on Friday, March 14 and presented to the investigations team at a high-level meeting at 9 pm on Friday. The UK AAIB, who had also been processing this data independently, presented their results - which concurred with ours and those of the US team – at that meeting.

"The Prime Minister was briefed on this satellite information at 8 am Saturday, March 15 and publicly announced it at the press conference at Saturday lunchtime.

(my emphasis)

Obviously the above does not describe the actual calculations involved. However it does confirm that the satellite data had six handshakes (presumably at hourly intervals up to 08:11).

The graphic below, illustrates one idea for how these track might have been deduced. It is a result of speculation rather than a reporting of information actually provided by the people who made the calculation.

The graphic suggests that the NTSB calculated possible paths based on data that is not public and that the NTSB were able to assign probabilities to those paths. As far as I know, neither Inmarsat, the NTSB nor the Australian government (or it's agencies) have made public the data or method of calculating these tracks.

The graphic below suggests several Inmarsat pings were used (the example shows 01:11, 02:11, 04:11, 05:11, 06:11, 07:11 and 08:11 but these are probably speculation).

So far as is publicly known, there was no ping at 09:11 or later which suggests the flight ended between 08:11 and 09:11. This is broadly consistent with maximum fuel range of the aircraft. The labelled NTSB solutions suggest that NTSB calculated that no other constant speed (and heading?) tracks fit the data.

source Scott Henderson

which says ...

For a constant speed track, distance between ping arc intersections will be equal.

NTSB solutions are based on constant speed straight track. Curve in track shown due to map projection

A later version of this graphic adds a disclaimer saying that the tracks and zones are not accurate and are symbolic only.

We do know that NTSB sent staff to Malaysia to assist in the search. We know that Inmarsat provided data to the investigating teams.

• I provided a potential mathematical solution on deriving the flight paths using the ACARS data on 17 March (before the possible flight paths were published by the authorities) on CNN's iReport: http://ireport.cnn.com/docs/DOC-1108312

The key to finding MH370 without the aid of the transponder data but with regular attempted ‘handshakes’ from the ACARS satellite is by a process known as “vector addition”. If the last handshake with the ACARS satellite took place at 8.11am as reported then depending on the frequency of the previously attempted handshakes (half hourly or hourly, there seems to be some discrepancy in the reported frequency) a set of flight route models can be easily constructed giving a high probably of the final location based on the accurate last known location at 2.40am. Therefore, depending on the frequency of the ACARS handshakes there should be at least 6 and up to 12 vectors that could be mathematically solved.

Assuming a constant speed for the first probability model, each time the ACARS handshake occurs it gives only a footprint angle on the Earth (as has been shown on the reported 8.11am ACARS ping map; 40 degrees). The next time it handshakes another angle is indicated. At a constant speed only two possible headings are possible to ‘join’ the ACARS isogons (for the plane to get from one ‘angle’ to another). If MH370 was heading in generally the same direction or arcing across the sky, (even if there was some tacking back and forth like a yacht) only one of the possible vector solutions will be valid.

If the vectors from the last known location at 2.40am were systematically added together the final solution at 8.11am will bisect one of the two arcs provided by the authorities. Subsequent models at different average speeds and taking into account routes that would more effectively avoid radar detection would refine the models to a few high probability scenarios and narrow down the search area considerably.

It’s simple mathematics but there is no indication the authorities are using it.

As RedGrittyBrick has pointed out this is almost definitely how the flight path was estimated. The reason for the two flight paths is probably illustrating the two end member solutions based on the accumulated error using this technique (the more times you add one vector to another the more error can be introduced). Hence the two predicted flight paths diverge.

The reason for the confidence by the authorities in the southern Indian Ocean route is that the mirror set of solutions would need MH370 to pass straight over India and Pakistan; and they have emphatically denied this could have taken place.

Therefore there is the highest probability that MH370 ended up in the region of the southern Indian Ocean they are currently searching.

I am somewhat saddened that these probability models were not derived within days MH370 went missing and that at least 7 days were wasted searching in other areas.

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