Hi Gysbreght,
I tried to understand your equation from post #21. Unfortunately I failed.
But I can try to better explain my understanding :
I think up to the term DeltaFup + deltaf_comp we have a common understanding.
Of course it's kind of artificial to split DeltaFup into (D2aircraft + D2Satellite), yet I don't see any reasons not to do so. In contrary it's very helpful because the terminal applies deltaf_comp to compensate for D2aircraft only. The terminal doesn't know about D2Satellite because it supposes the sat to be stationary. Actually splitting into these two components is the natural thing to do, if you take the earth at rest as frame of reference.
With DeltaFup = (D2aircraft + D2Satellite) we can write:
DeltaFup + deltaf_comp = (D2aircraft + D2Satellite) + deltaf_comp = (D2aircraft + deltaf_comp) + D2Satellite
For a given aircraft position D2Satellite can be calculated from the angle between line of sight and sat velocity vector. The calculation is the same as for D3 aka DeltaFdown, only that instead of the coordinates of Perth the coordinates of the aircraft position are taken (and of course the L-Band Frequency).
Now deltaf_comp almost cancels out with D2aircraft, but just almost so, because the terminal's assumption of the sat position is not accurate (it supposes the sat position to be above the equator). That causes the terminal to calculate an inaccurate line of sight and thus an inaccurate line of sight speed.
(D2aircraft + deltaf_comp) is what I called "miscompensation" before. It depends on the offset of the sat from its geostationary position and on the aircraft velocity vector (mainly the component of the aircraft velocity that is parallel to the offset of the sat from its geostationary position i.e: its north/south component).