Calculating Rate Of Separation Between Two Arcs

[Badmachine]

Homework Statement

Is there a formula for calculating the rate of separation (per degree) for two planes beginning at a common point, traveling at the same speed, performing turns with two different turn radiuses?

Homework Equations

See linked image for better understanding (separation values for image were measured):

http://i224.photobucket.com/albums/dd121/88Badmachine88/CircleRadius-1.jpg

The Attempt at a Solution

 

[ideasrule]

The formula can easily be derived with some geometry. I don't know what the formula is or where on the Internet you can find it, but if you want to try deriving it, I'll be glad to help.

 

[Badmachine]

Thanks. Not sure where to begin.

The turn radiuses in question:

a) 54,795 feet at 545mph

b) 34,546 feet at 545mph

The difference between the two radiuses:

54,795 - 34,546 = 17,410.

The separation seems to become exponentially larger. Also, the difference in distance traveled means the plane traveling the smaller circumference completes its 360 turn before the other.

 

[ideasrule]

To start, try assuming that at the time the first vehicle has turned by "a" degrees, the second vehicle has turned by "b" degrees. You can easily find "a" and "b" given the time it took the vehicles to reach those angles.

Now, draw a few triangles on your diagram and proceed from there.