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Rate/Radius of turn

Rate/Radius of turn

Rate/Radius of turn

(OP)
This may not seem like the most difficult question to many of you. I'm a military pilot with a general engineering background. I'm looking for a fairly simplified formula to graph radius and rate of turn as a function of velocity and bank angle. Any help would be greatly appreciated.

Thanks,
Bill Straus
wstraus@interquest.de

RE: Rate/Radius of turn

SplitS
Here are some basics (you must have had this in flying school):

m - the mass of the plane
g - gravitational acceleration
L - lift force acting on the airplane (perpendicular to the wings plane)
V - airplane velocity
R - radius of turn
phi - roll (bank) angle
rot - rate of turn (radians per second. multiply by 57.3 to convert to degreesper second)

The lift force vector is tilted, with the airplane, by the bank angle phi.
The weight of the airplane is balanced by the vertical component of the lift:
mg = L cos(phi) (1)
The centrifugal force is balanced by the horisontal component of the lift
mV**2/R = L sin(phi) (2)

where V**2 means V squared. Devide (1) into (2)

V**2/Rg = tan(phi) (3)

The rate of turn is actually the yaw rate V/R which you can get from (3):

rot = V/R = tan(phi)/gV (4)

Dont forget to multiply rot by 57.3 if you want it in degrees per second. The beauty of the result is that R cancels out which means that rot depends only on the speed and the bank angle.

I hope this helps...

RE: Rate/Radius of turn

There are plots of these in a book I think is titled "Handbook for Naval Aviators". Published by the Government. This is very good reference for pilots and others concerning practical aerodynamics. - jk

RE: Rate/Radius of turn

splitS, the fighter jock is now a stock broker or in real estate, surely. This way dead thread is in it's 3rd year. I didn't notice right away. But, not for naught, here are some relationships that might interest that I did a day or so ago, thinking the thread was current:

You said simplified, right?

Here is some maneuver math without the numbers. I used "=~" for "proportional to".  

radius =~ V^2 ( constant bank angle )

rate of turn =~ 1/V (constant bank angle )

rate of turn =~ tan(bank angle) ( velocity constant )

Derived :

rate of turn =~ 1/V * tan(Bank Angle)

radius =~ V^2 * 1/tan(Bank Angle)

Of course limits imposed by lift/drag are not here.

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