Effective radius of a tire and rolling resistance based on information on velocity and tire pressure

Measure the effective circumference to calculate the diameter. To do this mark the tire, and the ground with paint or a soapstone. Move the vehicle until the mark on the tire contacts the ground again, and mark the ground. Then measure the distance between the marks on the ground. This distance is the effective circumference. C = 2 * pi * r. Solve for r. r = C / (2 * pi).

Rough estimate:

If the car is not moving fast- Let's call the flat contact surface of tire A, and forget about the bending flexure resistance of the side-walls and the leading and trailing edges of this surface. $ A*air pressure = tire load $

So $ A = frac{tire load }{air pressure} $

And from there having the section dimensions of the tire we can calculate the effective radius, which is the distance from a circle section A to its center.

However this can hardly be a good estimate when the car is accelerating and the torque from the wheel is warping the walls of the tire, pinching and wrinkling the attack edge of the flat surface, or the tire is hot after lengthy trip.