Calculation of Spin of Ball in Table Tennis

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Discussion Overview

The discussion revolves around calculating the spin of a table tennis ball after it has been hit, focusing on whether this can be achieved without using visual systems. Participants explore the relationship between the ball's velocity, racket motion, and the resulting spin, considering various physical principles and factors involved in the interaction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that spin is imparted to the ball through oblique striking with the bat, indicating that modeling this interaction is necessary.
  • Another participant notes the elastic properties of the rubber on the paddle, which can significantly affect the spin, and mentions that the wood of the paddle complicates the mathematical modeling.
  • A different viewpoint emphasizes the role of friction and angular momentum in determining the spin of the ball after hitting.
  • One participant points out the need for the tangential coefficient of restitution of the table tennis sheet to calculate the spin, noting that this coefficient can vary under different conditions.
  • There is mention of a previous thread that discussed table tennis physics and provided links to articles examining spin speeds, suggesting that this topic has been explored in more depth before.

Areas of Agreement / Disagreement

Participants express differing views on the factors influencing spin and the complexity of the calculations involved. There is no consensus on a specific formula or method to calculate the spin without visual systems, indicating that the discussion remains unresolved.

Contextual Notes

Participants highlight the variability of the tangential coefficient of restitution and the influence of different striking angles and paddle motions on the resulting spin, suggesting that assumptions about these factors are crucial for any calculations.

Zeeshan86
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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 ?

Regards,
Zeeshan
 
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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.
 
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).
 
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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.
 
Zeeshan86 said:
Is there any mathematical formula or relationship to find the spin of the Ball after hitting?
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.

https://www.physicsforums.com/showthread.php?t=595269
 
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