Expert: Paul Soderman - 6/21/2011

Question
Dear sir,

i have question regarding to turn rate and radius.

in my research, the equations for level turn rate and rate are

w = (g(n^2-1)^1/2)/v    and
r = v^2/(g(n^2-1)^1/2)

the only value i don't have and wondering is n, which indicates load factor.

i know n = 1/cos(bank angle) = L/W

but I don't have bank angle though...

the conditions I have are

- flying at 25,000 ft
- steady level turn
- speeds
- weights
- etc

so the point of my question is how do I find the value 'n'

Thank you

Answer
Jay - Your equation for w looks odd to me.  My book (Perkins and Hage:  Aircraft Performance Stability and Control) gives W = gRL sin(phi)/V^2 where R = turn radius, L = lift, phi = bank angle, V = velocity, W = weight.

In any case, you need more information to solve your problem.  You need bank angle to get L or you need to compute L from the experimental or assumed lift/drag polar; i.e., from the equation:

Cd = Cdf + CL^2/(pi AR e) where Cdf is drag coefficient at zero lift coefficient CL, AR is aspect ratio, e is Oswald's efficiency factor that accounts for the variation of parasite drag with angle of attack.  Solving for CL you can find L given a velocity V, altitude (density), and wing area. The drag coefficient is related to the power available and power required:  PA = PR = DV where D = drag.  In other words, your bank angle and load factor depend on lift, which must be computed for the conditions of the aircraft.  Many different turn radii can be flown depending on the lift pulled by the aircraft and the power of the propulsion system.
Paul