4 ms·
Any physics experts know what the actual optimal shape is? I imagine it would be a pretty gnarly problem to work out.
by yissp 7y ago
Any physics experts know what the actual optimal shape is? I imagine it would be a pretty gnarly problem to work out.
- gshdg 7y agoWell, IIRC, theatrical lights use parabolic reflectors to focus a non-point source into a point on a lens, so that might be a good place to start.
- lonelappde 7y agoLight and sound gets to ignore gravity.
- justinator 7y agoHaha well light can, if far enough away from a black hole!
- deleted 7y ago[deleted]
- baddox 7y agoI was wondering how you could get an analytical solution, but I think you’d have to define the problem much more rigorously to do so. As he mentions in the video, different basketball paths can contact the same point on the backboard from any number of angles, so it seems fairly clear that there is no perfect solution.
- contravariant 7y agoIf you fix the position of the 'thrower' and just throw them at ridiculous speeds so gravity doesn't matter you'd end up with a hyperbolic backboard. So annoyingly for an 'optimal' solution you'd need to specify where people can throw from and how fast. Frankly you might as well just use a hyperbola with one foci on the hoop and the other on the middle of the court, or maybe a point slightly higher than the court itself as the balls will be coming in at a lower angle (or maybe even a downwards angle?).
- CrazyStat 7y agoWouldn't you rather want an ellipsoid with the thrower at one focus and the hoop at the other?
- deleted 7y ago[deleted]
- contravariant 7y agoI may have gotten things the wrong way around. You definitely want whatever conic has the foci in the right spots.
- shawnz 7y agoDon't forget about spin as well, which can significantly change the trajectory due to the Magnus effect
- mannykannot 7y agoI would guess that if there is enough spin for the Magnus effect to be significant, it would also be significant with respect to the rebound, as the surfaces in contact are not frictionless. On the other hand, I am not sure there is much spin in most basketball shots, and, given a backboard designed without taking it into consideration, there would be no incentive to add spin.
- tomjakubowski 7y agoBackspin is an essential part of a reliable jump shot, and topspin is employed on finger roll layups close to the rim.
- mturmon 7y agoBetter to account for gravity first, no?
- mannykannot 7y agoI do not think you can make definite claims about optimality without putting it in the context of some probability distribution over all possible incoming trajectories etc.