Tennis Science for Tennis Players

Introduction

Why Another Book on Tennis?

This book will not make you an instant champion; it will help you to play as well as your physical endowment allows. There is no substitute for athletic ability and practice, but there are many things that will help you to win more points—without the drudgery of long hours of lessons, practice, and hard work. In addition, taking an understanding of all the laws of nature onto the tennis court with you will add to your enjoyment of the game.

You do not need knowledge of science or engineering to use the material presented here. In order to profit from this book, it is not necessary that you understand, or even read, the explanations of the physics. You are free simply to accept what is recommended here, just as you do when you learn tennis or take lessons. You never ask the pro why you should keep a firm wrist or why you must follow through with every stroke.

Written for tennis players, this book is based on work that has been done in the laboratory and on a computer at the University of Pennsylvania over a number of years. Some of the information has been published in four rather technical articles for physicists in the American Journal of Physics (June 1979; September 1981) and The Physics Teacher (November 1984; April 1985).

This book gives advice on three aspects of the game that determine and shape one another: equipment, strokes, and strategy. Most important is the matching of these three things to your own ability. Because Bjorn Borg strings his racket at 80 pounds, you should not necessarily do likewise. Because Jimmy Connors throws his whole body into every shot, you are not required to do so also. And because some top pro blasts his first serve and eases up on his second, you need not feel compelled to do the same. All the best professional players have tuned their equipment, developed their strokes, and calculated their strategy to fit their own physical abilities and temperaments—not yours—so you should not blindly copy them.

This book lays no claim to being The Compleat Handbook of Tennis. It covers only a limited number of topics, but it does so from a different point of view—that of a scientist trying to tell you how to take advantage of the laws of nature to win more points and, as player or spectator, to enjoy the game more. Tennis has developed through years of trial and error. No group of scientists, engineers, and players has ever attempted to determine the underlying scientific principles of the game and then to construct strokes and strategies based on their analyses. Professional teachers and books on tennis answer all the how to questions, but they do not try to answer the why questions (and they certainly do not bring the how to and why together, as here). The pros have learned tennis by taking lessons from other pros or coaches, and a set method of teaching tennis has been developed. It is basically an arbitrary series of rules and drills, and it works. Up to now, very few people have stopped to think about the basic science that governs the game, and no one has yet published a book of this type.

Strokes are not emphasized in this book. Almost every book on tennis will tell you more than you probably want to know about how to hit a backhand, how to manage the mechanics of the overhead. Instead, this book stresses the proper choice of equipment, strategy, and ball trajectory because scientific analysis of these subjects gives meaningful results that can be translated into specific actions that you, the tennis player, can take advantage of and appreciate. Several additional topics are included, even though they lead to no specific recommendations, because they are appropriate and interesting, and because the information cannot be found anywhere in the tennis literature.

A few of the concepts advocated in this book are contrary to accepted tennis lore. These new ideas are not arbitrarily fashioned; they are derived from the application of the basic laws of physics to the game of tennis. In addition, many of them have been tested in the laboratory, with computer models, and, of course, wherever possible, on the court. Ten years ago, many of the ideas in this book would have been dismissed by the tennis establishment as wrong. No one had done controlled experiments, and the accepted lore was based on anecdotal information. There was no doubt in most players' minds that tighter strings and a flexible racket gave more power. Today we know better. With the revolution in tennis racket technology and design that began ten years ago, manufacturers and designers of rackets developed a new understanding of tennis. Now it is necessary that players and tennis teachers also come to a new understanding of the game. That is what this book is all about.

Chapter 1

The Importance of the Strings

There is a famous advertisement in many tennis magazines that points out that the ball never touches that very expensive, hightech tennis racket. The ball only touches the strings. That is why this book will start by discussing the strings.

1.1 Strings and Stringing

What tension should you string your racket at? Should it be 50 pounds? Or 55? Or 62? Or 73? How can you determine what tension is optimum for a racket, a style of play, and the strings that are in use? When players decide to have an old racket restrung—or even to get a new one—they usually ask for the same tension that they have been using. If they are at all unhappy about their present game, they may think about trying a different tension. Unfortunately, if they ask someone in a sports store, a teaching professional, a friend, or a good player what tension they should try, they will usually not get good advice because most people do not understand the physics of the strings.

Some of the Problems

Th re is more to the strings and stringing than just the tension. Not long ago, when a racket was strung, the head sizes were all the same, the string spacing was uniform, and specifying the tension was about all one had to do. Now there are a variety of head sizes and stringing patterns. A tension of 65 pounds in a standard size racket plays very tightly, while 65 pounds in an oversize frame may play loosely. How do you compare rackets with different size heads? How do you compare rackets where the space between the strings (string density) is different or nonuniform? You can buy rackets where the strings are twice as far apart as in the standard racket, and there are rackets where the spacing is half that of the standard. In addition there are rackets with three sets of strings instead of the familiar two. When you use a different gauge of string, how does that change the way the racket plays? What is the difference between gut and synthetic strings?

Some Answers

The way the racket plays, with respect to the strings, can be determined by examining how much the string plane deforms when a force is applied to the racket face. If you push on the strings with a known force and measure the deformation of the string plane (how much it moves perpendicular to the plane of the strings), you will know approximately how the racket will play. This measurement automatically takes into account the size of the racket head, the density of the stringing pattern, the tension, and most of the other variables that can be involved. You can either take a single measurement with a single force pushing on the strings, or you can measure the string deformation for many values of the force, as is shown in Figure 1.1.

GENERAL RULE I:

Rackets will play in a similar manner if they are strung so that their curves of string plane deformation versus force are similar.

By measuring the string plane deformation or deflection, therefore, you can compare a Prince (oversize racket) strung with 15-gauge nylon with a Wilson Kramer strung with 16-gauge gut and know how the strings in one will play relative to the other. Some tennis shops have a device to do this (for example, the Sports Pal Flex II Tension Tester), or you can do it yourself (as was done to obtain the data used in this book) with a set of weights and an accurate ruler. Figure 1.1 shows several different rackets tested this way. It is obvious that the strings in the old Spalding Smasher strung at 20 pounds of tension deflect a great deal more (for the same applied force) than, for example, those of the Prince, which was strung at 76 pounds of tension.

GENERAL RULE II:

If you increase (or decrease) the tension of the strings in proportion to changes in the length of the strings in the head, the string plane deformation will be similar to first order.

Figure 1.1. The String Plane Deformation versus Applied Force for Several Rackets. As the force being applied perpendicular to the face of the strings increases, the deformation of the strings increases. The greater the tension (divided by string length), the less the strings will deform for a given applied force. This figure shows rackets with string tensions ranging from 20 pounds to 76 pounds.

As an example, an 8-inch-wide head (which is the old standard size racket), strung at a tension of 55 pounds, will have a string plane deformation similar to that of an oversize 10-inch-wide frame (which is 25 percent larger), strung at 69 pounds (25 percent greater), if all other things (such as string density, gauge, and so on) are the same. This means that in order to change from one frame size to another while retaining similar playing characteristics from the strings, the tension divided by string length must be kept the same. This is why the oversize racket is strung at higher tensions.

For small string plane deformations (hitting the ball softly), the principal variables that determine the string response are the tension divided by string length and the density of the stringing pattern (number of strings per inch in the weave). For moderate hits (larger string plane deformations), the elasticity of the strings begins to affect the way the racket plays. The harder the ball is hit, the more important the elasticity of the strings becomes. The more elastic the strings are, the larger the string plane will deform for a given applied force, and the straighter the curve of string plane deformation versus applied force will be (the less the curve will turn over or level off at large forces).

1.2 Power from the Strings

The reason you go to the trouble of using a strung racket instead of simply a wooden paddle is so that you can get power. You want the ball to leave the strings with a high velocity without your having to swing the racket at a very high speed. Strings allow you to do this. The tighter you string your racket, the more it feels like a wooden board, and the less power you will get. That last statement bears repeating:

Tighter strings mean less power; looser strings mean more power.

The physics of this is clear and easy to understand. Then why do so many people think just the opposite? They see many of the top players get tremendous power from their rackets, which are strung tightly. Borg strings his racket at 78 pounds, so they conclude this is why his balls have great pace on them. Nothing could be further from the truth. It is because Borg and the other top players can hit the ball so hard that they can afford to string their rackets tightly to gain other advantages; they sacrifice some of their power in doing so.

Why Loose Strings Give More Power

By design, a tennis ball does not store and return energy efficiently. A ball dropped from a height of 100 inches onto a hard surface rebounds only to a height of about 55 inches. Indeed, that is the official specification for the manufacture of a tennis ball. This means that about 45 percent of the energy that the ball had has been lost (100 – 55 = 45).

Strings, on the other hand, are designed to return between 90 and 95 percent of the energy that is fed into them. To give the ball the maximum energy (that is, the highest speed) when it is hit, the strings, not the ball, must store the energy by deflecting. The strings return almost all of the energy that they store when they deform, while the ball only returns about half the energy when it is hit and deforms. If the strings have a lower tension, they will deflect more (that is, store more energy), and the ball will deform less (that is, dissipate less energy). The larger the string plane deformation, the less the ball will deform. Try dropping the ball on the ground (equivalent to infinitely tight strings) and comparing the rebound height to that when the ball is dropped from the same height onto a racket lying on the ground (supported around the head, not by the handle alone). The ball will bounce back considerably higher in