Ugh, just got off the phone from a friend of mine with a masters in physics. I'm sure I'm not the only one starting down the painful math road of calculating accurate trajectory planning for small basketballs. I'm posting this in the hope it will help others or that others here who know more than me can contribute back.
According to my friend the problem is both very simple and very hard and he was unsure which terms would have a large enough impact to be relevant. In fact, that is ultimately the crux of the problem. If we account for everything in the equation then we are going to be far more accurate either way so I'm working from that assumption though I'm not sure if it's feasible.
To that end, we need to know quite a few things starting with the ball diameter, density, and mass (does someone have the weight of the ball measured accurately?). He was uncertain but he did feel that with the light weight of the ball the wind resistance might actually matter. Unless someone has access to a wind tunnel and wants to share results we are going to be guessing this one in part because determining the coefficient of friction for a pebbled surface seems exceptionally difficult. At best, we can use the friction coefficient for something like rubber to air and calculate it for a 7" diameter sphere at the temperature/pressure of the playing field.
This paper says drag through the air on a full size basketball is negligible:
http://www.phys.ubbcluj.ro/~evintele...na/Baschet.pdf
But then it gets shot down a bit here:
http://www.wired.com/wiredscience/20...n-basketballs/ You can see in the graph at the end here that air drag has a huge impact on a baseball:
http://wps.aw.com/wps/media/objects/...cs/topic01.pdf
Another potential nasty problem is the Magnus Effect. This is what happens when something is spinning and creating lift. This is one my friend felt we could likely ignore due to the low spin RPM though it's also one of the easier ones to do:
http://en.wikipedia.org/wiki/Magnus_effect
So what is everyone else currently looking at? How deep down this rabbit hole are you going? Thanks!
-Mike