Here are my thoughts in trying to maintain a constant tangential velocity between different FOV's, this could be be totally wrong and these are just my thoughts.
The following equation describes how to convert a screen width (W) to its respective arc length (L) at a particular FOV (theta):
L = W + W[(theta - 2sin(theta/2))/(2sin(theta/2))]
The following equation constructs a circle with a particular circumference ( C ) from the previously calculated arc length (L) at a particular FOV (theta):
C = (360/FOV)(L)
The following equation describes the factor increase (X) from a circumference of a circle constructed at a particular FOV to a circumference of a circle constructed at a relatively smaller FOV, basically the factor increase from C1 to C2:
X = (C2 - C1)/C1
The equation for tangential velocity (V) is:
V = (radius)(angular velocity)
and since circumference is linearly related to radius:
C = (2)(pi)(radius)
Therefore if the constructed circles circumference increases by a factor of X from 1 FOV to another, then the angular velocity must decrease by a factor of X from 1 FOV to another. Vice versa.
These are just my thoughts at attempting to match tangential velocities between 2 FOV's, and like I stated at the beginning of my post, I could be totally wrong.
Thx for reading. ( :