The rotational inertia is of the form
K*M*R*R.
In the limit, a small wheel is a solid object and K = 1/2. Large wheels put more mass at the rim and begin to approximate a hoop, K = 1.0. Not only does the mass get larger, but the ratio of mass at a distance tends to do this too (K goes up).
The wheel must also get heavier because the stresses to perform similar maneuvers are higher.
Interestingly, radius has nothing to do with this discussion of acceleration and drops out of the equation.
T = I * alpha
The gear ratio must change to keep the same ground force and free speed, so force is constant not torque.
F * R = I * alpha
Pluggin in the inertia
F * R = K*M*R*R * alpha
Then relating rotational acceleration to linear acceleration
F * R = K*M*R*R * A / R
Then dividing through by radius gives
F = K*M * A
If M goes up faster (proportionally speaking) than K, then acceleration must go down. Per prior logic, K and M generally move upwards together when scaling the same "spoke" type design.
These effects should be in the noise compared to the reflected inertia of the motor (through all of those gears) and the associated losses. Also keep in mind that most teams use chain drives to keep the wheels on each side moving together. The inertia of the chain is more signifficant? And it has the oposite effect, causing large wheel drive trains to have a lower effective rotational inertia. I expect all of this to be in the noise... now I'm just waiting to be surprised by the results Ether's calculations.
