The actual dynamic tyre diameter of a driven wheel is not a function of the engine torque only. The main influencing parameters are the wheel load, the tyre characteristics, the air pressure in the tyre, the ground (road) characteristics, the vehicle speed and the tyre rotational speed. When considering engine torque, the driven tyre has some slip in the contact surface between tyre and ground. E.g. in case of a standard car tyre and a standard try road, the slip value may reach about 1-3% of the tyre rpm; mostly depending on the vehicle speed and the acting driving torque.

If you want to build up a model to cumpute the dynamic tyre diameter as a function of the engine torque (besides the other influencing parameters), you have to consider the complex interaction of tyre deformation in the contact surface with the road. You could use a finite element based approach, including a tyre model and a ground model.

Kind regards,

Mario

If you just want to calculate the required tyre dimension for given driving condition and engine operating point, you have to consider the engine torque and speed, the overall gear ratio of the drive train and the forces of driving resistance. These forces are calculated by summation of the air drag force, the rolling resistance, the climbing resistance and the acceleration resistance. For more information see the attached excerpt of my lecture script "Automotive Engineering".

Kind regards,

Mario

1. Record transmission and final drive gear ratios.

2. Weigh the vehicle.

3. Find a suitable incline.

4. Using 2 and 3, calculate the force needed to hold the vehicle at a standstill on the incline.

5. With the vehicle placed on the incline, release the brakes, and hold the vehicle at standstill using the clutch. When the vehicle is steady, record the engine torque. (The engine rpm are irrelevant.) Note: Do not do this for excessively long else you burn the clutch.

6. Multiply the engine torque by the total gear ratio found in 1. This is your torque transmitted to the driven wheels.

7. Divide the torque calculated in 6 by force calculated in 4. This is your effective tyre radius.

I guess what Michal Vojtisek-Lom states is a logical method to find out the dynamic rolling radius of the tire from the engine torque and tractive effort on vehicle. however, this method would still give unrealistic values. because a vehicle operates in a wide range of engine torques and tractive efforts. 

On the other hand, I am not clear what is your objective. Is it only a theoretical deduction of tire diameter irrespective of vehicle speed? if yes, then the approach given by Michal Vojtisek-Lom is ok.

If you want to evaluate the dynamic rolling diameter of the vehicle under dynamic condition, at range of vehicle speeds, with a given tire, (that is to estimate the variation of change in dynamic rolling diameter), then you need to have a hybrid approach of the methods discussed in various answers here.