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pnachtwey
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I would like to know if there is an easy way to calculate the speed and spin on the ball after a serve. The server must toss the ball straight up so it drops straight down and without spin so the initial conditions for the ball are easy. Assume the paddle is moving horizontally at 1 m/s and is flat or the normal direction of the surface of the paddle is straight up. When the ball hits the paddle the paddle generates a impulse on the ball. I am interested in the spin and speed caused by the tangential impulse.
The vertical calculations are easy. There are speed after impact formulas that take into account the coefficient of restitution of the impact and the conservation of momentum. See the speed after impact formulas
http://en.wikipedia.org/wiki/Coefficient_of_restitution
There are studies that indicate that the tangential coefficient of restitution for a paddle in ball is in the range of 0.5 to 0.6 but assume 0.5 to keep things simple. See this
http://www.ittf.com/ittf_science/SSCenter/docs/199408014%20-%20%20Tiefenbacher%20-%20Impact.pdf
If one assumes the mass of the paddle is essentially infinite compared to the ball the tangential COR will mean that if the paddle is traveling 1m/s horizontally when then the surface of the ball will be traveling 1.5m/s horizontally after impact. However, that is the surface of the ball and not the ball itself. Some of the surface speed will be due to spin and the rest will be due to the motion of the center of gravity of the ball.
My question is how is the impulse that generates spin and speed divided up? Assume the ball weighs 2.7gm and the paddle weighs 200gm for calculations.
I have looked all over for conservation of angular momentum examples but they all have to do with simple examples of skaters extending and retracting their arms, not conserving angular momentum around a impact point or center gravity of two objects.
Does anybody know of a good example on the internet that is similar or better yet, know how to solve this problem themselves? When I start thinking of the conservation of angular momentum around a point in space I see triple integrals and that is messy. I have mathcad and can do the math if necessary (eventually) but there must be a simpler way.
I am hoping that someone knows an easy way to calculate this or can point me in the right direction.
Thanks for reading this far
Peter Nachtwey
The vertical calculations are easy. There are speed after impact formulas that take into account the coefficient of restitution of the impact and the conservation of momentum. See the speed after impact formulas
http://en.wikipedia.org/wiki/Coefficient_of_restitution
There are studies that indicate that the tangential coefficient of restitution for a paddle in ball is in the range of 0.5 to 0.6 but assume 0.5 to keep things simple. See this
http://www.ittf.com/ittf_science/SSCenter/docs/199408014%20-%20%20Tiefenbacher%20-%20Impact.pdf
If one assumes the mass of the paddle is essentially infinite compared to the ball the tangential COR will mean that if the paddle is traveling 1m/s horizontally when then the surface of the ball will be traveling 1.5m/s horizontally after impact. However, that is the surface of the ball and not the ball itself. Some of the surface speed will be due to spin and the rest will be due to the motion of the center of gravity of the ball.
My question is how is the impulse that generates spin and speed divided up? Assume the ball weighs 2.7gm and the paddle weighs 200gm for calculations.
I have looked all over for conservation of angular momentum examples but they all have to do with simple examples of skaters extending and retracting their arms, not conserving angular momentum around a impact point or center gravity of two objects.
Does anybody know of a good example on the internet that is similar or better yet, know how to solve this problem themselves? When I start thinking of the conservation of angular momentum around a point in space I see triple integrals and that is messy. I have mathcad and can do the math if necessary (eventually) but there must be a simpler way.
I am hoping that someone knows an easy way to calculate this or can point me in the right direction.
Thanks for reading this far
Peter Nachtwey
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