3D-Physics of a Rubber Ball (Squash)

Question

I'm trying to simulate the environment on a Squash Court on Android with my own physics and using OpenGL for visualization. Basically, its about a rubber ball bouncing around in 3d, not just on the floor but also on the walls.

What I'm not quite sure about is what kind of physical concepts are altering the movement of the ball or how much they are.

• Obviously there's gravity...
• Also, air friction, but I'm not sure how to calculate air friction of a rubber ball that is roughly 40mm in diameter. I've tried different formulae but I wasn't happy with them (eg. some were linear to speed and some were quadratic lol) and I was missing some material-dependant constants.
• Then there's the normal force applied from the solid shape on which the ball bounces. I don't think I need to alter any values as the normal force is "taken into account" by changing the ball's direction. I mean, if the solid shape where the ball bounces is vertical, normal force is zero but the ball still changes direction. Correct?
• Now, every collision reduces the kinetic energy as it emits sound and warms the ball. I assume that this reduction is greater if the ball hits the solid shape on a tighter angle. Is there a way to quantify it? So far, all I could do was use values "to make it look like it might be".
• Furthermore, I suspect that the angle at which the ball hits the shape is not equal to the angle in which it leaves the ball. Obviously, if the ball hits at 90° (orthogonal), then it will leave at 90°. On the other hand, if the ball hits at, say, 45°, it might leave at 30° (compared to the solid shape eg. the floor).
• There is spin which I have not spend much thought on but if anyone knows where I might find something about that I'd be greatful.
• Other forces/effects on the trajectory of the ball...??

Thanks in advance :)

Edit: To summarize, I am looking for (1) an applicable formula that represents air friction with possible constant values depending on the rubber-ball-scenario, for (2) a confirmation that my way of handling normal force is correct, that (3) a way of quantifying energy loss of the ball in a collision, (4) how (if) the angle after the collision is altered, with regard to the incoming angle, and lastly (5) how to handle spin.

Answer 1

That this question is quite broad makes it quite difficult to answer, but the basic physics that would go in to it could be summarized as:

1. Gravity - As long as the ball stays within moderate height (within the squash court), this could be treated as a constant.

2. Air Resistance -

   Also, air friction, but I'm not sure how to calculate air friction of a rubber ball that is roughly 40mm in diameter.

   This is not an issue since smaller objects having smaller surface areas does not suffer much air resistance. But this does have an effect in the long run. Below is an example of a bullet (much higher velocity than a squash ball). While bouncing on the ground, air resistance will reduce the horizontal range of the ball (its parabolic trajectory) and will effect the game!
   The equation connecting velocity of motion to the force (linear) is as follows:
   rho is the density of the medium, Cd is the drag coefficient and A is the drag area ().

3. Collisions - Refer to inelastic collision in 2D and extend it to 3D. You'll simply need to calculate energy loss from this collision. Sound, and heat effects are a bit of an overkill. Sound is pre-set in the game anyways, and heat is visible in the expansion of the material, and for a 40 mm ball that is next to nothing.

4. Spin - believe it or not, spin could be one of the most toughest things to calculate compared to other parameters above. We know angular momentum isn't conserved when there is a torque. Thus, inorder to calculate the rate of change of ang.momentum (ang. acceleration), we'd need to calculate moment of inertia and thereby the torque, or forget Newton's method and set up the whole thing with Lagrange's equations instead(Makes it a lot easier). But, if you could build a system of spin for the ball itself, then it would be quite easier to keep track of it while it touches a surface (at any angle) and calculate the torque right away.
   Note: There is something called a Magnus effect that you might want to look in to (overkill).

5. Rolling - Similar to spinning, but a much simpler equation depending on the rolling-friction and moment of inertia of the ball. (I can't give a link due to lack of reputation)