# Physics of Tennis Racquets

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Tennis racquets with old type of strings did not allow power and control over the racquet at the same time. To get a powerful stroke player had to hit the ball with the area of racquet closer to the tip of the racquet (toe). To obtain control and to reduce vibration of the racquet, player had to hit the ball with the area of racquet called “sweet spot”, located around the geometric center of the head. NASA’s 1973 Skylab 3 mission showed that tapered strings can move the “sweet spot” from the center of the racquet toward the position of greater power.

The NASA research on spider webs, which was meant to find the solution to reduce the vibration on space stations, unexpectedly benefited tennis. NASA’s Skylab, the first U.S. space station, in 1973 carried out the experiment with the space born spiders Anita and Arabella, to learn from spiders how to construct low vibration space stations.

Soviet space station Mir had serious problems with vibration. Every use of exercise equipment caused the entire station to shake. Spiders are well known for making their nets capable to absorb the impact of their pray. According to the book “The Web of the Spider” by Laura Barr Lougee [3], spider webs are made in such a way to keep all tensions in balance. The NASA research showed that the change in diameter of strings changes the stability of a network. This property of strings was used to improve the performances of tennis racquets.

It is hard to define “power” of racquet. According to [4] power could be defined as

1. racquet bounce (high coefficient of restitution)
2. high swing weight (high angular momentum)
3. low work (racquet which gives the greatest ball speed with a given player effort)

The easiest way to understand power is the coefficient of restitution (COR). The maximum power occurs when the COR is the greatest.

The coefficient of restitution is the ratio of the differences in velocities before and after the collision. COR is defined as difference in the velocities of the two colliding objects after the collision, divided by the difference in their velocities before the collision.

COR = coefficient of restitution

= linear velocity of the racquet mass center before impact

= linear velocity of the ball before impact (will be negative according to our convention that away from the player is positive)

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### Popular Essays

= linear velocity of the racquet mass center after impact

= linear velocity of the ball after impact

From the coefficient of restitution formula, it follows that

To find the coefficient of restitution in the case of a falling object bouncing off the floor, or off a racquet on the floor, we can use the following formula:

where: is rebound height

is initial height

According to [5], the highest coefficient of restitution (power) is near the tip of the head.

COR

COR (center of mass): .74162

COR (near the throat): .63246

COR (tip of the head): .7746

Sweet spot is the position of optimum vibration. When the ball hits the sweet spot player does not feel the impact of the ball, because a minimal kick or jar is transmitted to the player's hand. The strings absorb the vibration that increases stability of the racquet in the player's hand and player has more control over the racquet.

“The sweet spot is determinative of the force from impact: the higher the sweet spot, the lower the Impact Force acting at the racquet's mass center, and the more positive the Impulse Reaction” [5]

NASA Research

Dr. David Noever a research scientist at the NASA Marshall Space Flight Center in Huntsville, Alabama, used two space born spiders, Anita and Arabella in Skylab 3 mission to study the way in which spiders span their webs in space. The objective of that experiment was to learn how to make a low vibration network of strings in outer space. The resulting network would be used in the construction of future space stations. The outcomes of the research showed that spiders born in space, in microgravity conditions made their webs with treads of different diameters. In contrast, spiders on the Earth make trends of the constant diameters.

The March 1995 issue of NASA Tech Briefs in the article “Improved Tennis Racquets Have Tapered Strings” explains some results of the Skylab 3 mission experiment

“Research found that changing the diameters of strings could radically change the stability of a network against vibration” [6]

Strings of different diameter have different properties. Thicker strings are stronger than but not as elastic as thinner stings.

In old wooden frame racquets the sweet spot was at the geometric center of the racquet. But new method of tapered string made it possible to move the sweet spot toward the toe of the racquet.
According to Racquet Research web site [1], longer distance from the hand to the sweet spot is better. This improves the performance of the racquet by combining the stability and controllability of the racquet and power.