[Rick TYler]

We rejected a catapult early on because of the inherent limitations of rate of fire. Spinning wheels or belts have such an obvious advantage in fire rate that we didn't seriously consider a catapult for long, although some students did some interesting math on one.

So, this is just FIRSTnoodling, and not a serious design proposal. I'm also not going to do the math, so forgive me for that, please.

I agree that one of the problems with catapults is the waste of energy involved. A lot of energy is used accelerating the arm, which is then usually wasted at the end of the stroke. How does this calculus change when the arm weighs essentially nothing? You could build a very stiff launching arm three feet long of hand-laid carbon fiber and fiberglass on a foam form that would weigh about about six ounces. If you molded a CF/glass dish on the end for the ball it might add another two or three ounces. I wonder how the math would work out if a pneumatic cylinder pushed on a 6-inch lever arm driving a 30-inch throwing arm on the other side of its ball bearing pivot? I have to get back to work, but perhaps some enthusiastic physics student wants to work out the numbers.