# Tennis Ball Pitching Machine

I'm trying to design a automatic tennis ball pitching machine for my senior design project. I will be using two spinning wheels as the launching mechanism. So far I've found the initial velocity after the ball leaves the two spinning wheels (v = 33.398 ft/s). This velocity was found by using the equation R=v^2 sin⁡2θ. Right now I'm having trouble figuring out the forces while the ball is in contact with the two rotating wheels.

One rotating wheel:
Diameter - 6 inches
weight - 1.5 lbs
circumference = 1.57 ft

Tennis ball:
weight: 0.026 lbs
diameter: 2.7 inches

So far the equation I've been using to try and solve this is:
mv_1+∑▒〖∫_(t_1)^(t_2)▒Fdt=mv_2 〗

My professor told me I need to find the forces involved while the ball is in contact with the two wheels so I can calculate the torque needed and select a motor.

Also I've found the rpm's that the wheels would need to be spinning for the ball to have the exit velocity needed to be 1299.36 rpm.

I've also added a picture trying to illustrate my problem and what I've done so far.

Thanks in advance for any help!

#### Attachments

• visual depiction pitching machine.jpg
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cjl
You'd have to make some fairly rough approximations to get a decent estimate of the force. However, I don't think that's really needed. With wheels of reasonable mass, the energy to launch the tennis balls will come from the stored kinetic energy of the wheels, not directly from the motor. So, a better analysis would be to determine how much energy is transferred to the tennis ball during launch, and then calculating how much the wheels will slow down in the process. If the analysis shows that the wheels will slow down too much, then increase the mass of the wheels until it is not a problem. Once that analysis is done, the motor can be selected based on the mass of the wheels.

how could I calculate how much energy is transferred to the ball during the launch? Can I accomplish this through equations and calculations or would I need to actually purchase parts and test this to get more data?

rcgldr
Homework Helper
On some of these "pitching" machines the wheels can rotate at different speeds, in order to put a spin on the ball. There are table tennis machines that also use two wheels, but sometimes spins one of the wheels backwards (with the other going forwards much faster) in order to generate a lot of spin. I don't think you can get that amount of spin in tennis though, so just a difference in speed (as opposed to opposite spinning) would be enough to give top spin and back spin (slice).

would like to see the final design of your http://www.sportsmachineshop.com/" [Broken].

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