John Farley,
You are quite right. We have terrible problems down here knowing when to replace functions with their inverses when applying formulae out of english books. The local zoo had a similar problem when they brought out some pommie bats. Poor buggers wore their teeth out in a couple of months trying to hang on in the bat cave.
I was looking at something else with the cos; 1/tan thing.
JF's formula for r is V/10G, where G = 1/cos(a) (V in knots, r in ft)
The theoretical r is (V * 6080/3600)squared / 32.2 tan(a)
So the fractional error in the JF formula is (JF radius - Theoretical radius) / (Theoretical radius)
That error function reduces to
1 - (cos(a)/10) / (2.852 / 32.2 tan(a))
And as a approaches 90, cos(a) / tan(a) approaches 1. That was the cos; 1/tan matter I noted.
So as a approaches 90 degrees, the error approaches 1 - ( 0.1 / .08857), or 12.9%. That is the 13% limit you originally cited.
Dan Winterland
JF's formula is within 13% of correct in the range 51 to 90 degrees bank. It is spot on at 62.5.
Its a very good method if you are low, fast and busy showing off, or engaged in a tactical exercise. Like in JF's old playground.
Don't think it would suit you. Sounds like your nomogram and tables will be hard to beat in your case.
John, Had a great Xmas. Thank you.
ET