If you want to calculate the LOS
velocity of the aircraft away from the satellite, it's simply:
speed = BFO * c / 600,000,000
Divide the LOS
speed by the cosine of the altitude to get the radial velocity from the subsatellite ground position.
E.g., if the BFO is 250 Hz, then the radial velocity from the subsatellite point is approximately ~320 knots. If the aircraft crossed the last ping arc at 400 knots near where the Chinese ship supposedly heard the pings, then that would indicate a course/heading of about 156.
Which indicates (a) the aircraft probably was not on autopilot, and (b) if the pilot was lost, since it was daylight at that point, he should have been steering east--not south by southwest....
Conversely, if the pilot was
lost, and was steering due east, that would entail that the azimuth from the satellite to the plane was 054, which would place it on the 00:11 LOP over Yunnan Province in southern China....
ETA: If you'll recall, I was able to deduce the radial velocity from the subsatellite point for the last ping ring LOP (00:11 UTC) from the published Inmarsat tracks. The velocities were virtually identical down to 4 significant figures. Then I did the same analysis on the 22:40 UTC ping ring and got radial velocities for both tracks of 280 knots. Then, as an experiment, I took the published Doppler shifts of 250 and 200 Hz using an "effective frequency" of 600 MHz. The predicted radial velocities were within 3% of the measured radial velocities.
Thus, the published BFOs by Inmarsat must all be precorrected, and by assuming a frequency of 600 MHz, one can get the same radial velocities used to construct the Inmarsat flight paths.
[Edited 2014-04-05 09:12:18]