The Physics of Spin in Table Tennis

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The Physics of Spin in Table Tennis

Guest author Jonathan Roberts continues his explanation of the Basic Physics and Mathematics of Table Tennis/Ping-Pong.

A ball that is spinning is always easier to return than a ball that is not spinning because a ball that spins has stability at range. The frontiersmen of America had worked this out and used it with their rifles. If you look down the barrel of a rifle, you'll see it has what are called 'lands' down the barrel. These are grooves cut into the barrel that twist in one direction, causing the bullet to spin. This gives the projectile stability at range. Without the lands, the projectile would stray off course after about 50 meters and certainly by a hundred. For history buffs, rifling was discovered and exploited during the American War of Independence.

To understand spin, an understanding of what's known as air speed and relative air speed is required.

Air speed: This is simply the speed at which an object moves through the air. A top pennants player can smash the ball at about 200 kilometers per hour. This is the speed of the ball relative to a stationary object (the table, the umpire's chair …, as long is it isn't moving, or else you start to get into the beginnings of Einstein's Theory of Relativity, which I'm NOT going into here). If the air itself is moving, then relative air speed is used.

Relative Air Speed: This takes into account any wind that the ball is traveling through. If for instance, you were to smash the ball (with an air speed of 200 km/hr) into headwinds of 10 km/hr, then the relative air speed would be 210 km/hr. If on the other hand you had the wind blowing behind you at 10 km/hr, the relative air speed would be 190 km/hr.

When wind occurs at an angle you introduce what's known as a vector term. This means the angle of the wind only partially affects the ball.

The mathematics is as follows:

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Air Speed and Relative Air Speed

(c) 2005 Jonathan Roberts

The above triangle shows a vector diagram of the direction (the angle, Ø, or Theta) and velocity (the length of the line) the wind is blowing. Through this diagram, a number can be derived to represent the wind speed on the ball.

Sine Ø = Short line ÷ Direction the wind's blowing
Direction and magnitude of wind = Short line ÷ Sine Ø

This isn't really an important factor in table tennis, as wind speed is usually negligible, due playing indoors, unless you have a fan on in the same room.

To fully understand the concept of spinning the ball, a look at what happens when topspin, underspin and sidespin is applied to the ball must be analyzed.

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A Heavily Stylized Topspun Ball

(c) 2005 Jonathan Roberts

The ball will tend to come off the table flatter and faster than if it was just blocked back. The ball also has a tendency to drop suddenly, Think of the effect a high loop has on the ball. This is an extreme example of topspin in use.

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A Heavily Stylized Underspun Ball

(c) 2005 Jonathan Roberts

The ball will tend to float on to the other side of the table. It has a tendency to stay high for longer. When it bounces, the ball tends to kick up off the table. A late chop taken far from the table that just clears the net will demonstrate this.

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A Heavily Stylized Sidespun Ball

(c) 2005 Jonathan Roberts

With sidespin, the ball will tend to curl either left or right. This is clearly demonstrated in service. A forehand pendulum serve will tend to curl away to the opposition's left, whereas a backhand sidespin serve will tend to curl away to the opposition's right (assuming you're a right hander).

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Why Does Spin Behave the Way it Does?

(c) 2005 Jonathan Roberts

To fully understand the dynamics of spin, the relative air speed in relation to the ball's speed must be examined. If you spin the ball (in the diagram below it is top spun), then at a certain point, it will have a minimum relative air speed. At the point where there is a minimum relative air speed, a slight vacuum occurs.

A Topspun Ball Moving Through the Air
In the above diagram, the wind is in quotes, because it is created by the direction the ball is traveling. It's the same as riding a bike on a still day. It will feel as though there is a breeze in your face. The arrows on the ball indicate the direction the ball is rotating. When the arrows point in the same direction as the 'wind direction' a slight vacuum will form.

Nature doesn't like vacuums and will tend to try and fill it. The way this occurs is by surrounding objects filling the void. In this case, it is the table tennis ball. The ball will tend to drop into the vacuum. This explains why top spun shots will drop quickly.

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An Underspun Ball Moving Through the Air

(c) 2005 Jonathan Roberts

With underspin, the vacuum forms at the top of the ball, and 'sucks' the ball upwards. The same principle applies with sidespin, except the vacuum forms on the side of the ball, sucking it left or right, depending on the spin put on it.

Also, a slight vacuum forms at the rear of the ball, due to its motion. There is no technique that can overcome this, it's the nature of anything in motion (i.e. even a snail sliding across a leaf will have this vacuum). The only thing that can be done is to use a new ball.

Don't like this explanation? Then try this one on for size.

Next: Return to the Basic Physics and Mathematics of Table Tennis/Ping-Pong - The Physics of Reaction Speed