John Farley,
I was curious to see why your V squared/10G formula works. I would have liked to use it on a C172, except I can't find the G meter.
So I tabulated theoretical and JF methods in the range 5 to 85 degrees bank, 100 to 450 knots, and calculated the differences.
Here are three cases
AoB 20, 1.064g, 200kt. Theoretical r 9743 ft, JF r 3759 ft.
AoB 40, 1.305g, 300kt. Theoretical r 9509 ft, JF r 6894 ft.
AoB 60, 2g, 150kt. Theoretical r 1152 ft, JF r 1125 ft.
For us mortals who get really worried above 60 AoB, your formula is not so good. At 30 AoB, your error is 43% the WRONG way.
The two methods break even a little over 60 degrees, then the JF approach is 11% safe at 80 degrees (5.76g), and 12.4% safe at 85. So we can see where you used to play.
Lastly, why is your formula so good in the 60+ range ?
(Dan Winterland, I promise I will go fishing immediately I have posted this).
Answer: The cosine of an angle asymptotically approaches 1/tan of the same angle as the angle approaches 90. And the g load is related to cos(AoB); the turn radius to tan(AoB)
Gone fishin.
ET