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Technical Tennis


Foreword Several years ago, the two authors 0f this b00k and I wrote an encyclopedic tome with the imposing title The Physics の ld 阨 c ん 1 司 0 可 阨 れ ⅲ s. Even though thousands of copies 0f this book have been sold and are still selling, and in spite Of the fact that it was a Scientific American BOOk Club selection, it is not for everyone, and only the 1 れ OSt motivated have read it fror れ cover tO cover. 从 市 0 ever thought there was so much science to hitting a fuzzy yellow ball? Butthere is, and it is all there ⅲ its 435 , 8.5 ' ' x 11" pages, including many hun- dreds Of graphs, charts, diagrams, and formulas. lt is a tremendous reference bOOk, textbook, or self-teaching manual, but it is not a casual read. What is needed now is an up-to-date, reader-friendly book that covers the technical parts Of tennis in a far less comprehensive and technical manner. lt needs tO be written SO that a tennis player can pick it up, read it, and under- stand it. This is that bOOk. lt is written for tennis players and tennis fans, not engineers, scientists, over-motivated super-achievers. lt iS still meaty intellectual adventure, but all the technical language has been translated t0 people-speak within its human-sized 160 pages. lt addresses questions such as: When you want a bit more power in your game, should you go tO a heavier racquet or a lighter one? ・ What are the advantages of a racquetthat has a bigger head? ・ What effect does string tension have on your game, and hOW does it affect power and control? ・ What is the difference between gut strings and synthetic strings? ・ What is the importance Of string thickness? What is a 、 、 fast ” court and what is a "slow" court? ・ Should you adjust your equipmentto match the court speed? ・ When buying a racquet, what features should you look for? ・ If you want to put more spin on the ball, what should you do? ln my many years of playing tennis and studying tennis, I have heard a 10t 0f anecdotal answers tO these questions. ThiS bOOk gives you the answers that sci- ence and technology provide. HOWARD B RODY Physics Department University Of pennsylvania

Technical Tennis


Preface effect if they did. Understanding why a ball bounces as it does on a topspin, backspin, or sidespin shot enables you t0 ready yourself, get ⅲ position, and anticipate your return Of the shOt. lt eliminates the frustration Of being caught flat-footed and clueless time after time. lt enables you tO make intelligent cor- rections in your game. But most of all, knowing what actually happens during the hit, flight, and bounce of the ball and why れ happens is just plain fun. To be able to explain hOW and why the court, racquet, and air affect the speed, spin, and direction Of the ball—the very essence Of tennis—and thus why strokes, tactics, and strategy have evolved as they have, is a rush matched only by being able to actually do these things. Knowledge and performance combine to provide a much deeper and enjoyable tennis experience, if not a 1 れ ore successful one as well. For readers WhO are interested in the technical and scientific aspects Of tennis or are Just plain curious or are looking for an extra understanding that 、 vill give strokes and shots meaning, this b00k has been written especially for you. lt contains the results Of many years Of investigation and many experiments designed tO extract the secrets Of hOW and why tennis balls, racquets, and strings manage t0 behave the way they d0. We still don't know everything there is tO know ・ about the subject, but we know a lOt more than we used tO know.. For example, we know very little about players' perceptions 0f equip- ment properties and why they are SO Often quite different from actual measure- ments Of those properties. Likewise, we don't know why one player has a favorite string or racquet and another will think that particular strlng or rac- quet is the worst he or she has ever played with. N0t knowing all the answers makes the search an adventure, finding them out is exhilarating, and applying them raises the level of the game. Many people have contributed t0 this b00k in many ways. Ⅵ で thank all 0f them profusely, especially Howard Brody, Ron K0hn, Paul Metzler, Greg Raven, Kristine Thom, Ron Waite, Nancy Crowley, and our wives Voula and Susan.

Technical Tennis


Chapter One Go 脩 swing TenniS SWing Wrist cocked at 90 at 5 ね 代 of swing ↑ CIub pulls wrist around in line with forearm Wrist cocked at 90 。 Figure ー 」 3 The ロ 「 m slows down as the club 師 racquet speeds up. That way, energy is transferred 〇 m the ロ 「 m tO the club 0 「 racquet. A tennis serve is like an upside-down go / 「 swing. Each acts as 0 double pendulum. The wristis locked at the start Ofthe swing ⅲ 0 「 de 「 tO accelerate the club 0 「 the racquet, but the wrist should be relaxed just before impact. BALANCE POINT AND PICKUPWEIGHT At one extreme, the balance point Of a racquet is something that many players either haven't heard about or regard as a useless technical detail. At the Other extreme are professional players whO can be very fussy about the location Of their balance point. The balance point has a strong effect on hOW the racquet feels when you hold it ⅲ your hand, and it has an indirect effect on the way the racquet feels when you swing it. That's why professional players are so fussy.. They bring ontO the court five or six identical racquets, each with the same weight and with exactly the same balance point. If one Of the racquets has a different balance point, the player will notice it immediately. The balance point can be located simply by balancing a racquet across the width of the racquet using the edge 0f a ruler, or a long rod or tube. The bal- 36

Technical Tennis


TechnicaI Tennis Racquets, Strings, Balls Courts, Spin, and Bounce Rod ( 「 055 ( 「 0M0 記 Lindsey Racquet Tech Publishing Vista, Ca 鼾 0 「 nia , USA

Technical Tennis


Chapter One F ↑ Pickupweight = 700 gm F 2 = 900 gm Racquet at rest Weight = 300 gm Figure 1.15 ln 0 「 de 「 t0 h01d ロ 300-gram racquetin 0 ho 「 レ 〇 n / position, you need to push up with 四 u 「 first finger (FI) and down 砒 the butt end ( F2 ). The total upward 厄 て e is 3 〇 〇 grams, but the racquet Ⅳ Ⅲ "feel" heavier than 3 〇 0 grams because the forces FI and F2 are each ロ lotlarger ロ n 3 〇 0 grams. That's because the torque due to FI ( / 〇 〇 0 gm x / 〇 cm distance 0 butt end) has to balance the torque due to the racquet weight ( 3 〇 〇 gm x 34 cm distance を om balance point tO butt end) tO stop the racquet 「 Otat ⅲ g. vince yourself of this, hold your racquet horizontal and put a weight (your car keys, for example) first on the handle and then atthe tip of the racquet. SWINGWEIGHT Swingweight is another one 0f those technical details that a player usually doesn't worry about unless he or She iS serious about tennis. professionals should definitely worry about it because their livelihoods depend on having exactly the right equipment. Even though two nominally identical racquets might have exactly the same weight and exactly the same balance point, they will feel differentto swing if each has a different swingweight. BaIance point and swingweight each depend on how the weight is distributed through the racquet and, therefore, on whether the racquet is head-light or head-heavy. Figure 1.16 details a simple example that explains the difference between weight, balance point, and swingweight. Consider a rod that is the same length as a racquet (say 700 (m) and that weighs 280 grams. The balance point will be ⅲ the middle of the rod, 350 mm from each end, if the rod has its weight uniformly distributed along its length. lt will feel the same to swing regardless of which end you hold. Now suppose we add 20 grams so the rod weighs 300 grams. Being heavier, the rod will feel heavier to hold. We can add the extra 20 grams anywhere we like, and it will still weigh 300 grams. However, the balance point and swingweight each depends ⅲ different ways on where we putthe extra 20 grams, and this will affect the way it feels to swing the rod. Consider four cases: 38

Technical Tennis


Chapter Three Ba 騰 and Bounce 旧 the blink of an eye 0 bouncing ball slows, changes its spin, slides across and bites intO the court and st 「 ings, squashes and stretches, and rebounds. The very nature Of the game depends on this 5-millisecond sequence Of events. BALL BASICS BALL HISTORY TenniS balls were used many centuries ago in France When they were made from leather and filled with wool or cloth. HoIIow rubber tennis balls were used for the first Wimbledon Championships ⅲ 1872 , but by 1875 they were covered ⅲ white c10 市 stitched 0m0 the ball because of their better playing characteristics. Almost nothing has changed since then, apart frOI れ the compo- sition of the rubber and the cloth. If you remove the cloth from a modern ten- nis ball, you will have almost exactly the same 40-gram, 51-mm diameter rub- ber ball that was used for the 1872 Championships. ln some respects the old rubber ball is easier to play with because it feels a 10t lighter, butthe bounce and flight through the air are a bit erratic. A 40-gram ball is not a whole 10t lighter than a 57-gram ball, but ⅱ feels a whole lotlighter because a rubber ball without its clOth cover is much SOfter. The force on the strings, transmitted through the racquet tO the arm, is therefore a 10 [ smaller. RULES ABOUT BALLS There are more rules in the game of tennis about tennis balls than there are about tennis racquets, strings, or courts. You can play with a five-pound brass racquet strung with fencing wire on an uphill cow paddock according to the 87

Technical Tennis


( hap 「 Two GENERAL RULES OF DWELL TIME tip is lighter than the 山 roa し strings and about 5.5 ms near the throat. That's because the ms near the racquet tip, about 5 ms ⅲ the middle 0f the ・ Contact time for a bounce on a handheld racquet is about 生 5 racquet. is a big increase in the speed of the ball or the speed of the ball or the racquet, although there is a slight decrease if there ・ Contact time does not depend significantly on the speed of the Contact time increases if the mass Of the racquet increases. ・ Contact time increases if the mass Of the ball increases. lncreases ・ Contact time decreases if the stiffness Of the string plane ・ Contact time decreases if the stiffness Of the ball increases. 86 playing conditions, Journal 0 「 SPorts Sciences, 23 , / 65 ー / 7 / ( 2005 ). R. Bower and R. Cross, String tension effects on tennis ba 〃 rebound speed and accuracy during Science and Medicine ⅲ Sport, 6 , / 2 〇 引 ( 20 〇 3 ). R. Bower and R. Cross, Player sensitivity tO changes in string tension ⅲ ロ tennis racquet, 丿 n /. 0 「 3 , 刀 9 ー 230 ( 2 〇 〇 の . R. Cross, C. Lindsey and D. Andruczyk, 比 bo 「 砒 0 「 / testing oftennis strings, Sports Engineering, performance, 5P0 s Engineering, 3 , / / / - / 22 , ( 200 の . R. Cross, Flexible beam analysis 0 「 the effects 0 「 string tension and frame stiffness on racket Jenkins, W00dhead, Cambridge, ( 2003 ). R. Cross, 砒 e ⅱ ロ / s and Tennis Strings, Chapter 8 ⅲ MateriaIs ⅲ sports equipment, Ed. M. H. Brody, Tennis Science 「 0 「 Tennis Players, University 0 「 Pennsylvania Press, / 98 /. So na Beach, USA ( 2002 ). H. Brody, R. Cross and C. Lindsey, The Physics and Technology ofTennis, Racquet Tech PubIishing, Further Reading

Technical Tennis


Strings 0 て : ロ ■ 1 ■ 1 ■ ー 000 83 Federation. ) (Courtesy ofthe University 0fSheffield, England and the lnternational Tennis no spin 砒 0 90-degree angle. Filmed 砒 2 , 40 〇 frames/second ( / 2 frames = 5 ms. ) Figure 2.9 Time series 0 「 b ロ 〃 impact with 0 head-clamped racquet 砒 9 〇 mph with

Technical Tennis


Chapter Fo 町 Baseline angle 8 inch Net 39 feet Figure 4 」 8 Can you aim 0 ba 〃 within one degree?lt takes practice, but that's whatis needed to get ロ / 0 mph return to land within u 「 feet ofthe baseline. Slowing down the return (hitting 0 "moon ba ″ " higher over the net) gives you ロ 「 ge 「 range 0 「 good angles and hence ロ better chance 0 「 success. Throwing 0 tennis ball intO 0 one fOOt wide bOX 0 「 bucket 20 e 亡 ロ Ⅳ ロ / ロ / SO requires one degree accuracy. ls that any easier? feet away from the net (see Figure 生 18 ). Of course, you have t0 getthe speed righttoo. Hitting the ball 3 mph t00 fast without topspin sends the ball 生 5 feet over the baseline or three feet beyond the baseline if you hit with 30 revolu- tions/second of topspin. The moral of the story is that it is better い hitthe ball with topspin, and you need lots of practice to get the angles and the speeds just right. If you still have trouble, then watch the professionals ⅲ action. They usually have trouble t00 , although some of them can strike a purple patch at times and get the ball to land within one foot 0f the baseline at least half the time. At other times they seem to have trouble getting the ball to land pastthe service line. They know hOW tO dO it, and can dO it on the practice court, but tennis is a mind game as much as a game 0f skill. Physics can tell you whatto d0 and why, and practice makes perfect, but if you have justlostthe first set and your opponent is full Of confidence, then it's time tO rethink your game plan. Further Reading H. Brody, R. Cross and C. Lindsey, The Physics and TechnoIogy ofTennis, Racquet Tech PubIishing, 50 / ロ n ロ Beach, USA ( 2002 ). H. Brody, Tennis Science 「 Tennis PIayers, University 0 「 PennsyIvania Press, / 98 /. R. D. Mehta and J.M. PaIIis, The aerodynamics 0 「 0 tennis b ロ ″ , Sports Engineering 4 , / / / ー / 89 ( 20 田 ). 5. R. Goodwi 〃 and 51 Haake, B ロ 〃 spin generation 厄 「 oblique impacts with 0 tennis racket, ExperimentaI Mechanics, 44 , / ー ロ ( 20 〇 4 ). 152

Technical Tennis


Chapter Two S n95 Many technologies affect stringbed performance, including headsize, string pat- terns, suspension systems, and string materials, 90U9e and construction, bUt Ulti- mately they 0 Ⅱ come down to one thing—making the st 「 ingbed so 幵 e 「 0 「 stiffer. STRINGSANDTHE MODERN GAME TO date, trial and error have reigned in choosing strings. 、 /lOSt tennis players use nylon strings. Up t0 about 1990 most professional players preferred natu- ral gut because they liked its feel and performance. ln recent times, most pro- fessionals have switched tO using polyester strings. The reason is hard tO pin down, but polyester seems t0 suitthe modern style of game played by profes- sionals. lt is not necessarily the best string for recreational players. Natural gut is made from the long intestines Of COWS. lt is made frOI れ the thin stretchy membrane known as the serosa which surrounds the intestine and which allOWS the intestine tO expand and contract as a COW digests its meal. The intestine Of a COW is long enough tO string a tennis racquet, but the serosa is tOO thin tO make even a O. 8 millimeter (mm) diameter string. lt takes three COWS tO make a thick enough string for one tennis racquet. ()f you are SO inclined, you can even go tO the butcher and get your own serosa sausage skin and make your own gut. ) The process takes a few days 0f cleaning, twisting, drying, and polishing, SO it iS expensive. However, the result iS a string that iS more elastic than any man-made synthetic, and it hOldS its tension better than any synthetic. The main problem is that it is not as durable and tends t0 break more easily, especially if れ gets wet. lt is a string that has a SOft feel that some players still prefer. 59