Oblique Colllisions between Paddle and Ball

1. Jul 18, 2007

Thomas12357

In my "living room lab", I have observed that oblique collisions between a moving hand-held ping-pong paddle and a stationary ping-pong ball result in various post-collision angles of the ball with the plane of the paddle. The angle is determined by the orientation of the paddle to the hand and arm. I have experimented primarily with a 45 degree impact and with low uniform paddle speed of about 2 m/s. The paddle is moved horizontally in a straight line and its face is approximately perpendicular to the floor at impact. I am only looking at two dimensions, so that the angle of concern is the projection upon the plane of the floor.

Post-collision angles vary from normal to the paddle surface to half way between normal and the direction of movement, and sometimes closer to the direction than to the normal. Such large differences are observable with the eye and are fairly repeatable. Much care must be taken to keep the direction of the paddle and the angle the face makes to the floor constant. Obviously, refined analysis is not possible in the living room. Therefore, I am asking how the mass and torque of the arm and hand are causing this variation. For those of you who are not ping-pong players, let me say that the collision produces a great spin of the ball. Let me also say that perpendicular collisions always result in a normal post-collision angle.

I am a ping-pong player and recently modeled the flight of the ball. Now, I hope to do some modeling of the collision. Thank you, Thomas12357

2. Aug 3, 2007

Thomas12357

I wish to delete my post of 7-18-07 as there is a major flaw in the control of pre-collision speed of the paddle. Consequently, my conclusion that orientation of the paddle to the arm plays a major role in the determination of the post-collision angle is totally unwarranted. The speed of the paddle does play such a major role. Apparently, with certain arm positions I unconsciously moved the arm faster than with others. I apologize with embarrassment over this retraction. thomas 12357

3. Aug 3, 2007

olgranpappy

Don't worry about it. It is nice that you are attempting to investigate this. Cheers.

4. Aug 4, 2007

rcgldr

I'm trying to make sure I understand, the ball is resting on the floor, the paddle face is perpendicular to the floor, but angle 45 degrees relative to the direction of travel.

Assuming you're using a high quality sheet of table tennis rubber on the racket, the sheet has a very high coefficient of friction (well over 5), and a high amount of energy retension (over 70% for mild collisions). The result will be both speed and spin on the ball. Doing this on the floor could affect the trajectory of the ball though, because of "ground effects", and any friction between the ball and the floor.

I made a short video of the stickiness and the elasticity of table tennis rubber (Stiga Innova in this case). The first half demonstrates the coefficient of friction with a comb while the paddle is angled nearly vertical before the comb slips off (something more steady than my hand would have increase the angle a bit more). The second half demonstrates the elasticity, in both bounce and spin reversal. I strike the ball with opposing sides of the paddle, reversing the spin, keeping the ball bouncing near vertical, while the paddle is moving relatively slowly and angled about 45 degrees or less from vertical. The result of the collisions are pretty consistent, the only variation is due to my control inputs.

ttstick.wmv

Another short video of of a few points from a table tennis match.

tt2.wmv

Last edited: Aug 4, 2007
5. Aug 4, 2007

Thomas12357

This Thread Should Be Deleted, in My Opinion

I started this thread on 7-18-07 and in my opinion it should be deleted for the reason I gave in my reply of 8-3-07. However, as it is still "living", I will make another reply to clarify my procedure. I also want to thank olgranpappppy for a suppportive reply and say that Jeff Reid's video robustly shows the high coefficient of friction of a good ping pong paddle.
As I said at the end of the original post, I want to model the initial velocity vector of the ball as it leaves the paddle. I would also like the initial angular velocity of the ball. I need an expression for these results in terms of paddle velocity, collision angle, and coefficeints of friction and restitution. Not simple. Really, this entails a new post, but I don't think I am the one to make it.
I need to clarify what I meant by a "stationary ball." The ball was not on the floor. I used two methods. 1) The ball was dropped a vertical distance of about 10 cm with no spin in front of the moving paddle. It was stationary in respect to the plane of interest. 2) The ball was suspended by 2 m of very thin thread from the ceiling. The thread "weighed" < 0.1 g compared to a 2.7 g mass of the ball. The second, or "pendulum" method clearly showed that the paddle carries the ball about 2 to 5 cm before they separate, as the swing of the pendulum was not in a plane containing the point of suspension and the initial ball position and oriented perpendicular to the floor. Only the first swing of the pendulum was measured, as the projection of the ball upon the floor was an elongated, somewhat elliptical trace which, of course, grew smaller with each swing
Thank you, Thomas12357

Last edited: Aug 4, 2007