I'm the lead programmer on a FIRST robotics team, and this year's competition is about throwing Frisbees. I was wondering if there was some sort of "grand unified equation" for Frisbee trajectory that takes into account the air resistance, initial velocity, initial height, (lift... It has to fly at max 50') etc. and solves for the required angle to reach a specific distance (angle will be the only manipulated variable).
Basically, I would like to acquire data from an ultrasonic rangefinder, the encoders that determine the speed of our motors, the angle of our launcher, the rotational force (should be pretty constant. We'll determine this on our own) and the gravitational constant, and plug it into an equation in real time as we're lining up shots to verify/guesstimate whether or not we'll be close. Probably other variables, as I was informed on StackOverflow. There is no wind.
If anyone has ever heard of such a thing, or knows where to find it, I would really appreciate it! (FYI, I have already done some research, and all I can find are a bunch of small equations for each aspect, such as rotation and whatnot. It'll ultimately be programmed in C++.)