Tuesday, February 25, 2014

A Lesson in Simple Mechanics

Before we start with today's lesson, here's a pop quiz. Which of these balls are not like the others?

The answer is in the photo further down the page. Skip down to it if you wish, but you are also welcome to continue reading first.

Today's lesson is about speed and spin in table tennis.

We don't measure speed correctly. In attempts to promote the sport, people sometimes cite numbers which attempt to illustrate the challenges involved in playing table tennis, and one of those numbers is the speed of the ball. Where does table tennis rank in a list of the fastest sports, or the fastest racket sports? How fast does a table tennis ball actually travel? 100 miles per hour is a high number cited; 60 mph might be more reasonable.

I believe that giving an answer in miles per hour is inadequate or counterproductive. Table tennis is clearly one of the fastest sports, and this is clear not by looking at ball velocity, but by looking at time: how much time a player has between shots, or how many shots are completed per second. A tennis ball has a higher velocity than a table tennis ball, but in table tennis there is less time between shots. It's the short amount of time that puts stress on the player, not the high velocity of the ball. Table tennis has far more shots per second than tennis, racquetball, or squash; and by that measure table tennis is the faster sport.

Similarly, we don't measure spin correctly. People cite spins in the range of 9,000 rpm (revolutions per minute), but how does rpm affect the player?

Spin is a little more complex than speed. Let's look at the primary ways that spin affects a player:
  • The spin causes the ball to curve; more spin causes the ball to curve more.
  • The spin kicks off the opponent's racket; more spin causes the ball to bounce off the racket more sharply.
In both cases, using rpm to describe spin is inadequate. If you compare a 40mm ball spinning at 9000 rpm with an 80mm ball spinning at 9000 rpm (all else being equal), they will behave very differently. The equator of the 80mm ball is traveling twice as fast as on the 40mm ball, and will jump off a racket twice as hard. It will also have a sharper curve through the air. It's common to use rpm as a measure of spin, but when we consider the effect of spin on a player, what really matters is the linear velocity of the equator of the spinning ball.

Why do we care?

Back in the year 2000, we switched from 38mm balls to 40mm balls. It was a widely circulated fact that the new 40mm ball would have less spin - but only if you were looking at revolutions per minute!

In fact, 40mm balls are not less spinny than 38mm balls in the measure that matters - the linear velocity of the equator. When a player strokes the ball, the tangential energy of the racket is transferred into the ball's spin. The linear velocity of the ball's equator is the same regardless of its size; all that matters is the stroke. No matter the size of the ball (but again, all else being equal), if a player applies 20 mph of tangential speed, the ball's equator will spin at 20 mph, and the ball will kick off the opponent's grippy racket accordingly. So if your goal is to make the ball jump off your opponent's racket, the size of the ball is irrelevant.

The other factor, the curve of the ball through the air, is more complicated. I don't want to get into it too much here; look up equations for the lift vortex of a spinning ball if you want details. But the conclusion is that for a given linear velocity of the equator, a larger ball will curve through the air more than a smaller one. That is, with a larger ball, the effect of spin is more pronounced than with a smaller ball for a given stroke, all else being equal. Intuitively this can be expected because the larger ball has more air resistance.

Didn't read all that? Here's the summary:
  • Table tennis is a fast sport when measured in time, not velocity. Forget about miles per hour and talk about shots per second.
  • For a given stroke, the effect of spin on the ball's bounce off the opponent's racket is the same regardless of ball size.
  • For a given stroke, a larger ball curves more than a smaller ball.

Now for the quiz results.

Another tournament, another surprise. This time it was the TMS Midwest Regional Tournament in the NCTTA College Table Tennis League, hosted at Northwestern University. Instead of bringing the MiniRAE device to test rackets, this time I brought a variety pack of balls.

The correct answer is: The three on the left are non-celluloid, and the two on the right are 38mm. (This was a pretty easy quiz because I arranged the balls this way rather than mixing them up.)

Now, if you forward this article to your friends and say "read this article about the new ball!" you'll spoil the quiz for them. I hope you don't.

As you may know, earlier this month the ITTF approved three non-celluloid plastic balls, made by DHS, Double Fish, and XuShaofa. All three are made in China. The DHS and Double Fish balls are of the seamed variety, similar to the celluloid balls that we use. The XuShaofa ball is seamless, and this fact can be seen in the photos.

Another thing you can see in the photos is the size of the balls. If you believe the rumors on the internet, table tennis after July will be an unrecognizable sport because of how different the poly ball is compared to the celluloid ball, not just in material but in size. Now look at the photos and compare the size of the poly balls with the celluloid balls, and the size of the 40mm celluloid balls with the 38mm balls. Is there a huge difference in size?

There's also a rumor on the internet that my wife owns a patent on table tennis balls. How likely is that? (Hint: I'm not married.)

I only have one of each ball. I measured the diameters and they came out to: 40.03mm, 40.15mm, 40.17mm. The rules specify that the ball shall have a diameter of 40mm, so yes, these balls meet that requirement.

From what I understand, the process of making these balls and getting them approved was not easy. The initial balls submitted to the ITTF did not meet all the required standards, and the manufacturers had to adjust their formulations multiple times. As I had stated before, anyone who played with a prototype ball, and delivered a judgment of "the new poly ball" based on their experience with that ball, will not know what an ITTF approved poly ball plays like until they actually have an opportunity to use one of the new, approved balls. I have a few prototype XuShaofa seamless balls, and they play differently from the ITTF approved XuShaofa seamless ball.

Back to the tournament. I wanted players to perform a blind test on these balls, to see if they could detect a difference between the poly balls and the competition celluloid balls. Upon arrival I knew this would be difficult because the matches were being played using orange balls.

Plan B involved finding players who had been knocked out of the competition. Gabriel Skolnick had been drawn into the quarters against his brother Micaiah and lost, and he was willing to hit with me just for fun, because once in a while officials like to play too. The seamless XuShaofa ball has a different sound that I knew he would detect, so I only brought out the Double Fish and DHS balls. We countered. He looped, I blocked. He looped, I chopped. I looped, he blocked. Then I told him what was up.

Gabriel's teammate, Felipe Morita, had lost to Micaiah in the semis. (Micaiah would eventually win the Men's Singles event with a series of upsets.) Gabriel grabbed Felipe and they tried the poly balls. As teammates, each would be familiar with how the other plays, and this would be a better test than hitting with me.

The verdict? Both players agreed that when they tried the poly ball, they didn't notice anything unusual; it was just like a celluloid table tennis ball. When they switched to the celluloid ball, they noticed a subtle difference. When comparing the balls side by side, the flight of the poly ball was slightly different from the celluloid ball. But the feel of the ball on the racket was the same.

For reference, Felipe and Gabriel are better players than I am, but they're not world class. As more people test the new balls I'm sure there will be different impressions reported, and I can't presume to know how the game will develop as a result of the introduction of these new balls. This is just a single test.

I expect that the ball factories started production of these balls shortly after they received word that they were approved. Even so, it may take some time before new balls reach our markets. Now that I've seen that it's not a drastic change, I'm not in a terrible hurry to get them. At some point things will change, and I have hope that it will be okay.