Calculating angle needed to return spin

[Eggroll451]

In the case of table tennis, would you be able to use calculus to find the angle needed to return a ping pong ball with a certain spin. So if a ping pong ball is hit at you with a top spin, what minimum or maximum angle do you need to return it.

 

[pixel01]

Theoretically yes, but there are so many variables to carry it out. Your rubber properties, the surface of the table, the friction of the surface of the ball itself and the linear speed of the incoming ball etc.. I also play table tennis and see that to receive that spinning ball, you have to adjust the angle very flexibly.

 

[rcgldr]

As mentioned it depends on the elasticity of the table tennis rubber. How much of the energy is returned in the form of reversing the spin, and reversing the velocity?

With a given table tennis rubber, then the issue is the velocity (speed and direction) of the stroke, and the angle of the blade. With elastic table tennis rubber, against heavy top spin, it is possible to hold the blade still and simply angle the racket face downwards, and the ball will be returned with quite a bit of speed and top spin. The amount of speed and top spin returned will then be determined by the nature of the table tennis rubber.

Top spinning against back spin is more interesting. With enough blade speed, and striking the table tennis ball while it still has an upward component of velocity (still rising), both the blade angle and the stroke motion can be less than 20 degrees from horizontal.