Summary

Given a constant initial speed, plot trajectories of a projectile for varying launch angles. Rotate the printer such that the angle of rotation corresponds to the launch angle (from 0 to pi/2).
First try, might be errors.

How I Designed This

Work in Progress

            <div><p>Read about this in Hestenes' mechanics book.<br>Asked ChatGPT-4 to generate an STL for it. The prompt for ChatGPT was as follows: </p><p>" I want you to to generate an STL file suitable for 3d printing, describing a particular sort of paraboloid of revolution. Regarding 2d Projectile motion:<br>For a given initial speed, using polar coordinates (r, theta, and phi), ...<br>for each radial angle of printing, you assume that's also the angle of elevation of a projectile (launched with a constant speed for all angles), and you make each "angular slice" (in the radial direction) trace the trajectory of such a particle.<br>You could just print it for angles between 0 and pi/2. Assume that the maximum range (i.e. at pi/4) is 10cm.   Go. "</p><p>...It generated a Python file (see attached files) which could then be used to generate the STL. I edited the Python a bit to increase the resolution. </p></div>

Paraboloid of Revolution - Projectile Trajectories