tough one, it will be heavily related to weight distribution and the surface you are on as turning a tracked vehicle requires slippage. as a side note I have seen dozers with independent control of either track spin in place.
a good estimation assuming that neither track is moving backwards (this still might model that case, but im not sure of it):
let one tracks speed be v1 and the other v2 let W be the width from center of track to center of track let R be the turn radius.
(v1+v2)*W/(2*deltaV)=R
as for force required it would increase as the tracks got longer because the greater motion and the greater area but I doubt deriving the basic integral would give a number that is meaningful.