Modeling Ball Shooters

[BBray_T1296]

Hard to understand your exact setup, but if you only have one wheel and a backplate you must account for spin.

The part of the ball touching the wheel can only have a linear speed equal to that of the wheel at best. Assuming zero slippage, the part of the ball contacting the wheel is at the wheel's speed, and the part of the ball touching the back/compression wall is zero, and thus the actual velocity of the center of mass is half the wheel speed.

Also your energy calculations need to include spin. If it has a large spin it has non-negligible rotational kinetic energy