How to determine Initial velocity of the ring as it leaves two shooter wheels?
Honestly there are so many variable beyond a simple ball or disk shooter, modeling everything may just prove to be too much work for the pay-off when easier methods exist.
I would measure it empirically from a prototype (high speed video from a phone and a background scale reference).
From there you can make a look-up table or calculate out your n-degree polynomial.
Sorry if that’s not the answer you were looking for, but every shooter will be different, modeling will be difficult.
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If you ignore variables like compression, air resistance, magnus effect, and so on, I’ve been using a few tools to get rough estimates of initial velocity:
Flywheel shooter calculators like ReCalc generally appear to assume a single wheel being used (in a traditional hood shooter configuration). If you look at intake calculators though (I use the one in the JVN Design Calculator) and compare 1-sided vs 2-sided intakes, you can see that adding a second side basically doubles the speed an object travels through it (in the case of a ball, this is because the motion isn’t being translated into rotation anymore when you add a 2nd side), thus you can roughly assume that adding a second side to a flywheel shooter has roughly the same effect as doubling the radius of the shooter wheel (which would also roughly double the exit speed) for the purposes of initial velocity calculation using flywheel shooter calculators.
There’s lots of other variables to consider of course (mass, spin up times, etc) that this method is not suitable for, but it seems to be a good way to get a ballpark estimate of velocity at least.
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