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. A careful reading of the ATSB report of June 26 (and the August 18 revision) may yield an answer that is good enough for most people.
Diagrams in news organisations graphics published in March and April vary widely in what they show and appear to be artistic impressions. These should not be relied on in any way.
ATSB report. August 18 2014
The Australian Transport Safety Bureau released a revised version of their June 26 report.
ATSB report. June 26 2014
The Australian Transport Safety Bureau release a 54-page report "MH370 - Definition of
Underwater Search Areas" which goes into greater detail than any prior official report and shows much more of the calculations that were performed on the Burst Frequency Offsets to calculate probable final position of MH370.
In particular the appendices describe some equations that were used.
A small extract from the report
Raw Satellite Data. May 27 2014
The raw satellite data was made available on 27/5/2014 in response to requests from relatives of the passengers. This shows burst timing offsets (BTO) and Burst Frequency Offsets (BFO) for communications between the Inmarsat ground station and MH370.
ATSB document. May 26 2014.
The Australian ATSB released a factsheet that outlines what is known and reiterates the general description of how the tracks were calculated:
taking the maximum speed of the aircraft into account, the rings can be reduced in length to arcs – there
are some areas of the rings it simply could not have reached.
There are a large number of speeds and headings that can be
consistent with a BFO recording. These are limited, however, by the operational constraints of the aircraft.
Candidate paths of different speeds were created which met the BTO ring location/time constraints and
the predicted BFO values of these paths have been compared with the recorded values. The better the
match, the higher the probability that the path was close to that of MH370.
Release of raw data from satellites. May 27th 2014
On May 21st 2014 CNN reported that the satellite data and description of analysis would be published. No date has been specified.
"In line with our commitment towards greater transparency, all parties are working for the release of the data communication logs and the technical description of the analysis for public consumption," Inmarsat and the Malaysian aviation officials said in a joint statement.
Inmarsat Statement. March 24 2014
On March 24th 2014, 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.
From INFORMATION PROVIDED TO MH370 INVESTIGATION BY UK AIR ACCIDENTS INVESTIGATION BRANCH (AAIB)
Malaysian Defence Minister statement. March 21 2014.
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.
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.