[KrazyCarl92]

To understand how to prototype a flywheel design you should first understand the physics behind them. The fly wheel is intended to convert the angular momentum of the wheel to linear momentum in the ball. Ideally, the change in angular momentum of the fly wheel (decrease) is equal to the increase in linear momentum of the ball.

The formula for angular momentum is L = Iw, where L is the angular momentum, I is the moment of inertia (of the wheel in this case) and the w (actually omega) is the angular velocity of the wheel. The formula for linear momentum is P = mv, where P is momentum, m is the mass of the ball, and v is the velocity of the ball. Since the moment of inertia of the wheels and the mass of the ball don't change, we are simply concerned with the angular and linear velocities. Increasing the change in angular velocity of the wheels will in turn increase the change in linear velocity of the ball. One way to do this would be increasing compression between the backing and the wheels. This will transfer more of the energy stored in the angular momentum of the wheels to the balls, which is what you are looking for. The wheels should slow down significantly when the balls go through the shoot.

The more the wheels decrease in velocity, the farther the ball will go. More torque applied to the wheels via the motor will help with reload time (getting the wheels back up to speed after firing), but may not do much for increasing the distance or speed.

(My explanation above ignores the effects of angular momentum increase in the ball due to spin, but it still holds mostly true I believe.)