paper: Ball Trajectory Calculations

[JesseK]

The motor speed shown is free speed, yet the trajectory calculations show that only a % of that maximum speed is used due to torque loss in the gearing. The reasoning behind this is that these balls do not compress without a substantial amount of force, thus I was unable to figure out a way to properly calculate a torque load. Hence I had to throw that idea out for this FTC game and estimate the trajectory based on the old-fashioned method that gearbox losses determine maximum speed. The idea behind the bottom of the sheet with feeder speed really comes from my watching the success of many 06/09 shooters who had feeder systems that were just as fast as the shooter wheels. In experimenting with the wiffle balls, the same principle holds true that the shooter only accelerates the ball by a certain amount, and the only way to consistently get that acceleration (thus overcoming the inconsistency in ball-shooter contact) is to have a high feeder speed.

Additionally, I don't know of the equations to calculate losses from wind, nor do I know where to find it or any of the constants for the medium (air), ball properties, etc. So I left wind resistance as a percentage so it's intuitively simple to adjust after some experimenting. I'm also not great at Excel, so the preferred method of drop down boxes and lookup tables for the topspin/backspin/no spin will have to be implemented when I have time.

I am working on a "mother of all spreadsheets", due out at the end of FRC competition season 2010. The hope is that I can take what I've done with JVN's drive train calculator and extend it into arms, elevators, etc. The new ones will attempt to graph position as a function of discretized time based upon the inputs and our favorite physics equation v = a * t (or ... v(k+1) = a(k) * h + v(k) ...). The hope is to be able to graphically relate power, time, and systems engineering-type requirements to really make the design portion of the build season fly.