# Spin reduction & bouncing ball

## Main Question or Discussion Point

Hi!

I'm from sweden so my english isnt very good, well over to the physic questions:

I'm qurrently making a tabletennis simulator, I'm almost done but there are two problems I havent been able to find solutions to.

In the program as it is now the spin of the tabletennis ball is constant, I wonder how much does the ball spin decreas during its time in air. Is there any equation on this ? Or some book / website thats explains this, i have search a lot but almost everyone seems to "ignore" this fact.

And the second thing is that i havent really figured out what happends to the ball when it bounces on the table, more than that i have calculated the coefficient of restitution.
Its speed in the horizontal direction must lose speed also (if the top spin speed isnt very high) but how much? And the spin rate of the ball must change also, how much? Any website or books or tips anyone can give me ?

Well I'm hoping for some answers they would be highly appreciated.

sorry again for the bad english

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I hope you're taking into account air resistance. That's what makes the spin decrease during its time in the air. Air resistance is also responsible for other components in the motion of the ball. The force is air resistance is proportional to the velocity. The constant of proportionality for a small object like a ping pong ball is 6(radius of the ball)(pi)(fluid viscosity of air). In SI units, the fluid viscosity of air is approximately 1.78*(10^-5) (kg/m)/s.

I hope you're taking into account air resistance. That's what makes the spin decrease during its time in the air. Air resistance is also responsible for other components in the motion of the ball. The force is air resistance is proportional to the velocity. The constant of proportionality for a small object like a ping pong ball is 6(radius of the ball)(pi)(fluid viscosity of air). In SI units, the fluid viscosity of air is approximately C (kg/m)/s.
First of all thanks for responding!

Of course I'm taking the air resistance into account as well as the magnusforce, But as far i have done, will they only decrease or increas the velocity of the ball not the spin rate.

Ok well lets see if i understand you correctly:

The decrease in spin rate of the ball is :

Ds = decrease in spin rate of the ball
v = velocity of the ball
r = radius of the ball
pi = pi
C = airs fluid of viscosity

[Ds = v * 6 * r * pi * C] ?

If so, is the decrease in spin rate mesured in Hz or in m/s ?

Thanks again !

If there is a spin decrease it depends only (or almost) on the spin and not on the ball speed.

About the loss of spin due to air friction, I think it is really negligible. Anyhow, a table tennis ball, spends just a fraction of a second before having a chock.
The other problem is more complicated. You can see it in (European) football. When a non spinning ball bounces its horizontal speed changes and it begin to spin. In the next rebound, it accelerates and its spin diminishes. The problem you must solve is what happens to the spin when a ball touches an immobile surface. Begin with the ball at zero velocity and a coefficient of restitution of 1. Consider that a surface touches de other, there is a horizontal impulsion which gives a horizontal velocity to the ball and the same impulsion changes the spin. You can make different assumption about what happens in the moment of contact. It can be a dissipative force due to friction. Forget the velocity perpendicular to the surface, you will treat it latter. I have never made the computation myself and have never seen someone interested on it. Bu sometimes I thought that it could be interesting.

Forget about your English. Mine is not better, but we talk physics, no English literature.