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Calculation of Spin of Ball in Table Tennis

  1. Aug 7, 2012 #1
    Hi !

    I am working on the modelling of the Table Tennis game.
    Can I calculate the Spin of the Ball after hitting without using any camera and any vision system.
    I know the velocity of the ball before and after the hitting in all directions (x,y,z) and velocity of the racket as well.
    Is there any mathematical formula or relationship to find the spin of the Ball after hitting ?

  2. jcsd
  3. Aug 8, 2012 #2

    Simon Bridge

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    You need to know how spin is given to the ball ... iirc it's from oblique striking with the bat: the ball rolls a bit along the bat. Sort of.

    You'd need to model that. But the short answer is: yes.
  4. Aug 8, 2012 #3


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    The rubber sheeting on a table tennis paddle is quite elastic in both normal and parallel to surface reactions, resulting in a lot of spin. If the paddle isn't moving the tendency is to reverse the spin on the ball. So even a motionless paddle can return top spin against a heavy top spin if the paddle is angled downwards enough to keep the ball from going high or long. The wood also affects the normal (perpendicular to surface) reaction so the math would be pretty compicated.

    There was a previous thread here about table tennis physics, and I think there was a link to some article that examined the amount of spin involved. I seem to recall maximum top spin speeds over 100 rev/sec (over 6000 rpm).
    Last edited: Aug 8, 2012
  5. Aug 8, 2012 #4
    I think the spin of the ball (or the change of angular velocity) is due to the friction. You should consider angular momentum in this case.
  6. Aug 8, 2012 #5


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    You'd need to know the "tangental" coefficient of restoration (parallel to surface) of the table tennis sheet. Note that this value changes somewhat depending on circumstances (for the same type of table tennis sheet).

    If reversing the spin, such as top spin versus top spin, the surface speed of the ball as it leaves the racket will be greater than the speed of the racket surface. As mentioned above, the racket can be held motionless mostly face down (called a block) against a heavy top spin shot (loop) and the ball will leave with both a lot of speed and a lot of top spin.

    I found the previous thread that has some links to articles about this.

    Last edited: Aug 8, 2012
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