Chicken
I’m glad you are happy now with the basic theory of turn performance.
But before you set yourself up to win beer from others who may not have got it sorted, stick a caveat in that you are talking low speed low power aircraft.
Please be aware that this basic theory diverges from reality as speed increases. At 150 kts you would be pushed to measure the difference between theory and practice. By 200 kts if you were good enough you could show the difference, by 300 kts the difference will be so great as to make you wonder what happened to the theory.
The reason is of course that air is not incompressible (as we always assume it is for basic aero stuff) At what speed (or mach number) we must start to modify our ideas is a rather variable feast as some topics are more affected than others. Sticking with our turning topic, a good old fashioned straight winged jet like the Meteor would DEMONSTRATE that the min radius turn was achieved at circa 240 kts but the max rate at circa 350 kts.
This difference between theory and practice was the result of the available CL max reducing as compressibility effects came into play. Hardly Concorde speeds eh?
Never forget the value of min radius compared with max rate when you are trying to miss an obstacle – like the ground at the bottom of a loop…..or a pylon at 12 o/c on a nav ex.
Sorry to go on a bit but the grandchildren were snowed in so I had the afternoon off.
JF