Brercrow
Seriously? Whats wrong with the diagram?
In diagram A) you say VG = VA +/- W: Therefore difference = 2W.
In diagram B) you say VG = W +/- VA : Therefore difference = 2VA.
In A you use the aircraft’s velocity as a reference, in B you use the Wind vector as a reference.
In the link you posted #201 The Downwind Turn, “Ft” is Zero. It does not exist. There is no FWD / AFT acceleration on the aircraft. There is only a centripetal acceleration towards the centre of the turn in the moving air mass (i.e. relative to the aircraft wing). The ground velocity changes by the vector addition of wind + aircraft's instantaneous heading and airspeed.
If you don't understand the difference then I can't help you.