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Table tennis physics

You hear a lot about it from players and coaches: mass, power, velocity, spin, acceleration, etc.  But my experience is that very few players or coaches know what they're talking about when it comes to the physics of table tennis.  It's all based on their intuition and reality and intuition are notorious for being out of sync in human beings when it comes to complex physical systems like table tennis balls, tables, and rackets.

One example of this is the "more mass equals more power" saying that you often hear from players about the weight of rackets.  As I discussed in a previous blog entry, I don't know of any physics based model of the collision of a ball and racket which supports this view and personally I don't believe it though I know experienced players who do.

Another such item is the "fast hall."  That is, some playing venues are simply faster than others with effects like atmospheric pressure (altitude), humidity, etc., taken into account.  I didn't pay any attention to this until I started playing at the Alameda club last year.  Everything is noticeably slower there than in other bay area clubs.  I play at Alameda almost every Tuesday night and the difference between the play there and at the Berkeley club, perhaps 5 miles away, is quite noticeable.  The Cal gym where the Western and Berkeley opens are played is even faster still.

The differences are of course not enormous but it's the sort of thing that once you notice it it really gets into your head.  Being the consummate EJ (or former EJ, or suspended EJ) I had to restrain myself from going out and buying faster equipment every Wednesday morning because I knew that at the BTTC on Friday my set up would again be fast enough.

Thus the effect appears to me to be real but how is it possible?  It's definitely not the tables since the Berkeley and Alameda clubs have similar high quality butterfly tables.  The next culprit is of course the flooring.  In short, the flooring will have an effect on the bounce of the ball if the impact time of the ball is longer than the time it takes a sound wave in the table material to travel to the floor and back.  Anything shorter than that and the ball will leave the table before any information about the floor is able to get back to it.  The way to imagine this is to forget that the table is rigid, it's not.  Like all materials it flexes and bends in response to a stress, such as an celluloid impact.  When a ball strikes the table a compression wave radiates out from the point of impact, across the table and down through the frame and legs.  This is just a sound wave, the same as in air (although parts of it may be transverse and parts longitudinal) except at a much higher velocity.  How high?  Well the table is a composite body made of a series of mechanically connected steel parts and some compressed wood or wood fiber material.  The speed of sound in steel is something like 4000 meters per second and I would guess the speed through the table material is considerably less, call it 2000 m/s.  A ball impacting the center has between one and two meters of material of differing types between it and the floor, which translates into a round trip sound wave time of something like 0.5 to 1 millisecond.

It is much more difficult to estimate the time the ball stays on the table but one web site I found puts it at 0.7 ms, i.e., right in the middle of the estimated sound wave from ball to floor transit time.  If this estimate is correct (and if you read through the web page you'll see that the author there makes it clear that he's extrapolated a certain model to get this number) then it is possible that the flooring can make a difference in the bounce of ball off table.

So what is the flooring difference between Berkeley and Alameda?  The Berkeley club plays in a traditional gym which has a standard wood basketball floor.  The Alameda club has what appears to be a rubberized floor.  Perhaps it was originally wood (and might still be underneath) but the floor surface itself is probably rubber of some type (perhaps synthetic).  

If this is all correct, and I'm not saying it is, then not only does it makes a difference what the floor surface is but also what's directly underneath the floor.  Is it concrete?  More wood?  Dirt?  Unless you're playing on a steel or diamond floor this effect drops off very rapidly since you don't have get much further away from the impact than a few meters for the material to not make a difference at all.

The 0.7 ms ball on table dwell time estimate is also useful for thinking about a ball and racket collision.   The impact time here must be much longer since nobody swings a big thick chunk of table at the ball (well nobody at my club).  But how much longer?  Ten times?  A hundred times?  Obviously it depends a lot on the racket, a thick hardbat being closer to the table figure and a thin racket with softer inverted rubbers (like mine) being much longer.  Ah well, enough for today, we'll save that one for later.

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