I can't comment on the math, it is interesting reading but not too practical when your in the saddle and about to turn downwind.
What I believe in and what I used to drum into students is this:
The aircraft doesn't know or care where the ground is or how fast it is going over the ground. All it knows is the air coming at it, and it will perform according to that. Forget the ground, set the power and attitude to give sufficient airspeed and performance and voila!, one shouldn't hit the ground. Scan the bloody instruments!
In my opinion, all turning downwind accidents are in some way related to the pilot letting the ground come back into the basic performace equation.
We are flying AIRcraft not GROUNDcraft eh?
