Hi.. this is from the aviation formulary website.. Hope it helps..
In a steady turn, in no wind, with bank angle, b at an airspeed v
tan(b)= v^2/(R g) v= w R where g is the acceleration due to gravity, R is the radius of turn and w is the rate of turn.
Pivotal altitude h_p is given by
h = v^2/g With R in feet, v in knots, b in degrees and w in degrees/sec (inconsistent units!), numerical constants are introduced:
R =v^2/(11.23*tan(0.01745*b)) (Example) At 100 knots, with a 45 degree bank, the radius of turn is 100^2/(11.23*tan(0.01745*45))= 891 feet.
The rate of turn w is given by:
w = 96.7*v/R (Example) = 96.7*100/891= 10.9 degs/sec
The bank angle b_s for a standard rate turn is given by:
b_s = 57.3*atan(v/362.1) (Example) for 100 knots, b_s = 57.3*atan(100/362.1) = 15.4 degrees
A useful rule-of-thumb, accurate to ~1 degree for speeds less than 250 knots, is b_s= v/7 (v in knots).
The pivotal altitude is given by:
h_p = v^2/11.23 (Example) At 100 knots groundspeed the pivotal altitude is 100^2/11.23 = 890 feet.
