Rate/Radius of turn

[splitS]

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.<br>
<br>
Thanks,<br>
Bill Straus<br>
wstraus@interquest.de

 

[dano]

SplitS<br>
Here are some basics (you must have had this in flying school):<br>
<br>
m - the mass of the plane<br>
g - gravitational acceleration<br>
L - lift force acting on the airplane (perpendicular to the wings plane)<br>
V - airplane velocity<br>
R - radius of turn<br>
phi - roll (bank) angle<br>
rot - rate of turn (radians per second. multiply by 57.3 to convert to degreesper second)<br>
<br>
The lift force vector is tilted, with the airplane, by the bank angle phi.<br>
The weight of the airplane is balanced by the vertical component of the lift:<br>
mg = L cos(phi) (1)<br>
The centrifugal force is balanced by the horisontal component of the lift<br>
mV**2/R = L sin(phi) (2)<br>
<br>
where V**2 means V squared. Devide (1) into (2)<br>
<br>
V**2/Rg = tan(phi) (3)<br>
<br>
The rate of turn is actually the yaw rate V/R which you can get from (3):<br>
<br>
rot = V/R = tan(phi)/gV (4)<br>
<br>
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.<br>
<br>
I hope this helps...

 

[knoxj]

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

 

[buzz41]

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 &quot;=~&quot; for &quot;proportional to&quot;.

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.

 

[Basiliscus]

http://flighttest.navair.navy.mil/unrestricted/FTM108/

Chapter 6.