Calculating Rate Of Separation Between Two Arcs

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Homework Help Overview

The discussion revolves around calculating the rate of separation between two planes that are initially at the same point but are turning with different radii while traveling at the same speed. The context involves geometric relationships and the implications of differing turn radii on separation distance over time.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss deriving a formula based on geometric principles, with one participant expressing uncertainty about how to begin the derivation. The original poster provides specific turn radii and speeds, noting the increasing separation and the implications of completing turns at different rates.

Discussion Status

Some participants are exploring geometric approaches to derive the necessary formula, while others are questioning how to initiate the derivation process. There is an acknowledgment of the complexity involved in the relationship between the turn radii and the resulting separation.

Contextual Notes

The discussion includes specific values for turn radii and speeds, which may influence the calculations. There is an emphasis on the geometric relationships and assumptions regarding the angles turned by each vehicle over time.

Badmachine
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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

 
Last edited:
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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.
 
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.
 
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.
 

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