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Originally Posted by seg9585
Not to overcomplicate things, but a (acceleration of ball) is not a constant "g", but a summation of acceleration due to gravity, Drag, and Lift.
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Yes, that's been discussed at great length here on CD.
There's a paper
here that someone posted a link to a few weeks ago which discusses the effects of air friction and magnus effect, and concluded that it would be reasonable to ignore them.
I don't know whether or not I agree with that conclusion, but I suspect that even if those effects were included, other factors such as variations in ball mass, size, compressibility, surface texture, and location of center-of-mass relative to center-of-volume, and air currents and atmospheric pressure would play a role... not to mention the effect of variations from shot-to-shot in the launcher itself.
Bottom line: in this application, equations are useful for getting a ballpark estimate.
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Change in gravity is a function of Y.
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You weren't seriously suggesting changing "g" with height of the ball should be considered, were you? I didn't see a smiley face at the end of that.
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calculating the final position would require iteration or an ODE solver.
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With air friction and magnus included, the DE would be non-linear, and it's unlikely that an ODE solver could find a closed-form solution. The only way to solve would be numerical ("iteration", most likely rk4).
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Maybe this could be a good student summer post-build season project
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I think there have been a couple of attempts already that have been posted here.