This is my first post. 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 the trajectory that takes into account the air resistance, initial velocity, initial height, initial angle, etc. 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. 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++). Thanks!
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I’m a mechanical engineer who writes software for a living. Before moving to tech startups, I worked for Lockheed Martin writing simulation software for rockets. I’ve got some chops in this area.
My professional instinct is that there is no such thing as a “grand unified equation”. In fact, this is a hard enough problem that there might not be very good theoretical models for this even if they are correct: for instance, one of your equations will have to be the lift generated from the frisbee, which will depend on its cross-section, speed, angle of attack, and assumptions about the properties of the air. Unless you’re going to put your frisbee in a wind tunnel, this equation will be, at best, an approximation.
It gets worse in the real world: will you be launching the frisbee where there is wind? Then you can kiss your models goodbye, because as casual frisbee players know, the wind is a huge disturbance. Your models can be fine, but the real world can be brutal to them.
The way this complexity is handled in the real world is that almost all systems have feedback: a pilot can correct for the wind, or a rocket’s computer removes disturbances from differences in air density. Unless you put a microcontroller with control surfaces on the frisbee, you’re just not going to get far with your open loop prediction – which I’m sure is the trap they’re setting for you by making it a frisbee competition.
There is a solid engineering way to approach the problem. Give Newton a boot and do they physics equations yourselves.
This is the empirical modeling process: launch a frisbee across a matrix of pitch and roll angles, launch speeds, frisbee spin speeds, etc… and backfit a model to your results. This can be as easy as linear interpolation of the results of your table, so that any combination of input variables can generate a prediction.
It’s not guess and check, because you populate your tables ahead of time, so can make some sort of prediction about the results. You will get much better information faster than trying the idealized models, though you will have to keep going to fetch your frisbee 🙂