Distance Between Two Planes With Different Turn Radiuses

[rudderrudderrat]

Hi Badmachine,

Suppose you are both flying with an airspeed of V ft per sec.
The distance travelled around each arc in t seconds = Vt feet.
Number of Radians travelled around each respective arc = Vt/R.
Therefore heading change = Vt/R * 180/pi.

For a small time of 5 secs assume the heading changes are also small.

So plane A's heading change = Vt/10,000 * 180/pi. ....(AH)
Plane B's heading change = Vt/20,000 * 180/pi. ....(BH)
So the change in heading of aircraft B relative to aircraft A = (BH)-(AH)

i.e. If you are in aircraft A and in 5 secs you change your heading by 15 degrees, then aircraft B will have only changed heading by 7.5 degs

Since you both start on the same heading then the separation after 5 secs = about half of 5*V* sin{(BH)-(AH)}

For small angles you could use 1 in 60 rule, so separation after 5 secs = about half of 5*V*{(BH)-(AH)}/60

Approximately.