Help on complicated projectile math for shooter angle calculation

Right now we are working on the projectile math needed to calculate the angle of our shooter. Our shooter is relatively similar to the Unqualfied Quokkas RI3D, with our shooter being placed on a rotating arm. This means that the distance required to shoot to the speaker will be dependent on the angle of our shot.

Given these constraints, how do we calculate the angle of our shooter required to hit the speaker?

Looking at the Wikipedia page for Projectile Motion, the equation to find the shooter angle given a static distance (x,y) is

{\displaystyle \theta =\arctan {\left({\frac {v^{2}\pm {\sqrt {v^{4}-g(gx^{2}+2yv^{2})}}}{gx}}\right)}}

The main difference with our problem is that the x distance and y distance are also functions of the angle, changing with the cosine and sine of the angle. Inputting this change into the function gives us approximately this equation where L is arm length

{\displaystyle \theta =\arctan {\left({\frac {v^{2}\pm {\sqrt {v^{4}-g(g(x + {L\cos(\theta))}^{2}+2(y - L\sin(\theta))v^{2})}}}{g(x + {L\cos(\theta)}))}}\right)}}

However, I have no idea where to begin to solve this equation. I don’t think it’s possible to solve, and there must be a better way to solve this. Does anyone have any ideas?

As opposed to solving for the angle of the arm from projectile motion equations, this can be done by fitting a quadratic to a dataset of the robot’s distance to the goal and the resultant angle needed to score.

The equations above also will not correctly describe the motion of the ring as it neglects the quadratic drag and effect of spin. Plus, the velocity term here is hard to determine.

1 Like

If you do choose to go with a physics-based formula, the one you have will probably be fine. The speaker geometry necessitates a very flat arc, so the linear path through your shooter is basically the same as the parabolic arc after release. This means you can use the pivot point of your shooter as the launch point, and it will probably be good enough.

This topic was automatically closed 365 days after the last reply. New replies are no longer allowed.