Angle of Bank rate 1 = 1/10xTAS+7
There's your TAS
The formula is a rule of thumb. It
works quite well but I'm there’s no precise mathematical formula behind it.
But, for a given bank angle, if you
change the TAS you change both radius of turn and rate of turn.
Or looking at it another way, if you
fix the radius of turn, then if you change either rate or TAS then the other
one must also change.