Modeling Ball Shooters

[Tom Line]

This is actually a two part question with some observations from the past year. Initially, when we were discussing different ways to shoot the ball we modeled the system using basic Newtonian physics. You can find a very similar spreadsheet here using some of Ether's formulas.

While the ball flight characteristics follow the flight estimates very closely, what doesn't fit out expectations is the actual shooter mecahnism and the losses when shooting the ball.

In 2012, our shooter ran from 4000 to 6000 RPM using two 550's and a AM CimSim. That gave us a ballpark to setup for this year. However when you do the math and assume a minimum of slip, here are the number got:

Shooter Wheel Diameter .1016 M
Release Height .4064 M
Release Angle 75 degrees
RPM required to approximately hit the target: 2400 RPM.

In reality, we required an input RPM of 4675 to make this shot (from the defenses). These losses seem astoundingly high. We have close to 170 degrees of wrap on the wheels and we use 2.5" of compression. We have flywheels on the system - 2 .1016" diameter 3 kg aluminum disks with the centers lathed out.

Unfortunately I never captured the exit RPM of the shooter, but I did a simple energy conservation calculation (angular momentum etc) and those numbers also suggest we shouldn't need nearly that large an input RPM. I can only assume that the major loss in the system is the compression of the ball and friction - but I wouldn't know how to begin to model that.

My next question involves choosing the gear ratio for a shooter system. Obviously you want minimum spin-up to the maximum speed you're going to use. How do you make a guesstimate of what the unloaded speed of your shooter system is going to be, though? Clearly it will be much less than the gear-reduced free speed use to friction.

We got to where we needed to be through iteration of a number of motors and transmissions. However, I'd like to be able to make first approximations computationally.