The other point
I am glad that this issue has caused some debate.
I have read the discussion here gusts and ground features, which is a TOTALLY different issue.
The devil here is in the detail. As for the fact the earth is moving though space at a zillion miles an hour, is all quite true. But so is everything around us. For simplicity, we can look at forces require to change things, in relation to the surface of the earth. I know this is simplistic!!!!
I think Book Worm has Newton I & Newton II a little confused. He mentions the momentum, but the aircraft with 60KIAS in the 60kt headwind has ZERO momentum, it only has inertia.
Ascend Charlie is quite right, the aircraft that turns out of wind has overcome its INERTIA and gain MOMENTUM some how. If this was a Super Cub, at 60KIAS a 60-degree bank turn is totally sustainable. This would equate to a rate 4.5 turn, and a 180-degree turn would take 13 seconds. Not even a Super Cub could gain 120KTS in 13 seconds. That bit of science is easy.
The stone on a string example seems to be a question of conservation angular momentum.
The bit I can't get my head around, is the forces in the turn. The Super Cub at ZERO groundspeed has NO momentum to overcome. Here centrifugal/centripetal forces don't apply. Therefore, with the aircraft banked, the horizontal component of the total reaction is unbalanced!!!
Does anybody have any ideas if the conventional rate/radius maths applies? Conventional logic tells me that with no centrifugal force to overcome, incredibly high rate/low radius turns are possible!!! Also, what effect would these unbalanced forces have on angle of attack?