Is there a formula for calculating the pivot point of an aircraft while turning on the ground?
The pivot point will be where an imaginary line through the rear wheels and an imaginary line perpendicular to the front wheel intersects.



So if θ is the steering angle and d is the distance between the front wheel and a point halfway between the rear wheels then 

X = d • tan(θ)

will give you the distance from the point between the rear wheels to the pivot point.