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

Racquets MISTAKES WHEN BUYING A RACQUET There are several common mistakes that you can make when buying a racquet. The first one is tO choose one because you liked the advertisement you saw in a tennis magazine or because some new high-tech feature appeals tO you. By all means try it if you like the sound 0f it, but don't forget t0 compare it with a few others. Another mistake is tO buy the racquet that feels best in the tennis shop. Hitting the air with a racquet is not a good way tO find out hOW the racquet behaves when you hit a tennis ball. There is no shock, no vibration, and no sense Of feel or power when you swing at the air. Don't buy a racquet because your favorite player uses it or because your friend uses it. Racquets don't dO all the work. You have tO match the racquet tO your own strengths and playing style in order t0 find one that works best for you. Try the same brand as your favorite player or friend if it appeals to you, buttry a few other brands as well. Players often decide thatthey want a racquetthat is both light and powerful, a perfectly natural ChOice. Here again, it is better tO try hitting with a variety 0f racquets before buying one. You might find that a 250-gram racquet is indeed light but a 300-gram racquet also feels light and delivers a bit more povver. The last mistake is tO buy the cheapest or the most expensive racquet because 0f its price. Maybe the best one for you is indeed the cheapest or the most expensive, but price alone is not a good way い choose a racquet. There are 10 ト Of good racquets in the medium price bracket. The most expensive racquets tend t0 be the new high-tech models that everyone wants t0 try because they are new. Sometimes they are indeed very good, but it is really up t0 you t0 be the best judge of that. THREE TYPES OF RACQUET Racquets can be classified as being suitable for beginners, recreational players, and serious competition players. Different folks have different strokes and ben- efit from different types Of racquet. Serious competitors and professionals gen- erally use a moderately heavy and flexible frame with a relatively small head and narrow cross-section—about 20 millimeters ( 1 れ 1 れ ) in the direction per- pendicular t0 the string plane. Recreational players tend t0 prefer lighter and 3

Contents The Six 、、、 Weights" of a Racquet . Racquet Weight Light vs Heavy Racquets 旧 e Racquet 、 Weight BaIance Point and Pickupweight Swingweight Twistweight . Spinweight Hiftingweight ( 、、 Effective Mass") STIFFNESS (FLEX) . Racquet Stiffness . Measuring Racquet Stiffness . Match Point Box l.4:Vibration Comparison between Racquets .. 46 Racquet Vibrations, Sweetspot, and Feel .. 48 Vibration Dampening .. 50 Shock & the Center of Percusson .. 引 Match Point Box l.5:The Difference between Shock and Vibration CUSTOMIZINGA RACQUET ... 56 Match Point Box l.6: Customizing Weight, Balance, & Swingweight .. 57 Further Reading .. 58 STRINGS .. 22 STRINGSAND THE MODERN GAME .. 59 .24 .25 STRINGBED STIFFNESS Static & Dynamic Stringbed Stiffness .62 Effect of String Materialand Gauge on Stringbed Stiffness Effect of StringTension on Stringbed Stiffness . Effect of String Pattern on Stringbed Stiffness . Effect of Headsize and Stringbed Suspension System on Stringbed Stiffness FOREWORD . PREFACE ー RACQUETS INTRODUCTION Choosing a Racquet—the Basics Mistakes When Buying a Racquet Three Types of Racquet . Racquets and Player Psych010gy Racquet Features Combine with Strokes Selecting a Racquetls Art & Science ... 9 Care of Racquets RACQUET PROPERTIES . POWER The Components of 、、 Power": Exit Speed, Rebound Speed, Racquet Speed Match Point Box 凵 : Effect of Grip Firmness The Maximum Exit Power Point Changes with Racquet Speed Comparing Racquet Power . Racquet Power Defined as Rebound Power Match Point Box l.2: Maximum Effort Power . Rebound Powerls the Sum ofAII Racquet Properties . Power and Energy Loss Match Point Box l.3: Maximum Theoretical BaII Speed . 25 The Bad News: Rebound PowerValues Aren't Readily AvaiIabIe .. 26 CONTROL . Rebound Control WEIGHT Weight and Apparent 、 Weight 8 0 「 ) 4 ー 8 っムつ」 . V っコっ LO -4 4 ー 5 ) 4- 4 ・ 4 ・ .. 55 .. 66 . .68 .. 27 . 27 . .28 .. 28

Chapter One will usually be slightly different. One might be 320 grams with a balance point at 340 mm, and the other might be 325 grams with a balance point at 345 mm. A racquet technician will be able t0 add mass here and there to make each of these racquets ()r all 6 if you are a professional) almost exactly the same. Sometimes a bit Of trial and error is needed. lt is easy to add small strips of adhesive lead tape before a restring so they are hidden out of the way under the bumper strip or under the gnp. Adding weight to the tip of a racquet makes the racquet harder to swing, but it adds power tO the racquet head SO you don't need tO swing the racquet as fast anyway. If your problem is that you hit the ball t00 early, then adding weight atthe tip might help t0 fix the problem by slowing down the tip. If you tend to hitthe ball t00 la に then one solution (besides buying a lighter racquet that swings faster) is either to take weight off the tip or add weightto the han- dle. That way your forearm will slow down a bit and give the tip of the racquet a chance t0 catch up. Adding weightto the handle simply slows down the han- dle end compared to the tip end. To hit the ball properly, the handle end and the tip end both need t0 be ⅲ the correct spot when you contact the ball. That might require a change in swing style or timing or it might be possible to fix the problem simply by adding weight to the racquet. There is a third location where extra weight can be of benefit. That is, at the 3 and 9 0'clock positions on the frame (the tip being at 12 0'clock). The advan- tage Of adding extra weight at these locations is that it is located farther from the long axis and hence it increases the twistweight Of the racquet (see 、、 Twistweight" section). Further Reading H. Brody, R. Cross and C. Lindsey, The Physics and Technology ofTennis, Racquet Tech Publishing, 50 n ロ Beach, USA ( 2002 ). H. Brody, Tennis Science 厄「 Tennis Players, University 0 「 Pennsylvania Press,1 987. R て . Cross, The sweet spots 0 「ロ tennis racquet, 5P0 s Engineering, I, 63- / 8 卩 998 ). R て . Cross,Impact 0 「ロ ba ″ with 0 bat 0 「 racket,Am. 丿 . Phys. 6 乙 692 ワ 02 August ( / 999 ). R. Cross, Customising 0 tennis racket by adding weights, Sports Engineering, 4 コ - 図 ( 20 田 ). R. Cross, Center 0 「 percussion 0 「 hand-held implements, Am 1 Phys. / 2 , 622 ー 630 ( 2004 ). R. Cross, A double pendulum swing experiment: ln search 0 「ロ better bat, Am. 丿 . Phys. 73 , 330- 339 ( 2005 ). R. Cross and R. Bower, Effects 0 「 swing-weight on swing speed and racket power, 丿 ou 「 n 0 「 Sports Sciences ()o be published late 2005 ). 58

Racquets cial rule ⅲ tennis about racquet weight. You could use a 1 OOO-gram racquet if you wanted to, as heavy as a baseball bat, but baseball players don't have to run around with their bat chasing after the ball. lt doesn't hurt tO try a heavier racquet tO see if it makes any difference to your game. The simplest way t0 d0 that is t0 add some lead tape t0 the tip and/or the handle or to borrow another racquet. You might find, for example, that you struggle t0 swing the racquet comfortably, or you might find that you can get a bit more power ⅲ your shots. Ten grams added to the tip of a racquet will feel quite different [ 0 an extra 10 grams ⅲ the handle. The effect is described in the section on swingweight. LIGHT S. HEAVY RACQUETS If a heavy and a light racquet are each swung atthe same speed, the ball will come Off the heavy racquet faster because the heavy racquet has more momen- tum and 1 れ ore energy that it can transfer tO the ball, and it will lose less ener- gy. However, heavy racquets might not be swung as fast as light racquets. There is, therefore, not a big difference in maximum power between heavy and light racquets. ln general, racquets tend い be swung at medium tO fast pace rather than maximum possible speed because players need [ 0 make sure the ball goes in. ln that case heavy racquets Offer a bit more power and control than light racquets because they don't need tO be swung as fast tO achieve the same ball speed. Outgoing ball speed is a combination 0f rebound speed and racquet speed. The rebound speed is really a measurement Of hOW much energy iS lOSt in the rac- quet and ball collision. The higher the rebound speed, the less energy is lost. The energy available tO use and lose comes from the mass and the motion of the ball and racquet. During the collision, both the ball and the racquetlose energy. The heavier the racquet, the more energy the racquet has available at a given racquet speed and the less energy it loses during the collision. Top players are generally stronger and fitter and can make better use of a heav- ier racquet by swinging it faster than the average recreational player. Conversely, if a player needs to getthe racquetto the ball quickly, a light rac- quet will help. For that reason, even professionals use racquets that are much lighter than they are capable of swinging. ln theory, a heavier racquet should help to reduce arm injuries. There is anec- dOtal evidence from veteran coaches that arm and shoulder injuries increased 33

Chapter One Bu mperguard gm Stri ngsl 5 gm Grommets gm Raw frame 227 gm Paint and decals 田 gm HandIe 30 gm Grip 20 gm End cap gm TotaI racquet weight = 340 gm Figure れ The weights Ofthe individual components 0 「 tOt ロ / racquet weight. About ha / 「 0 「 the raw frame weightis just glue (resin) weight. The weight 0f most racquets varies from about 250 grams t0 about 360 grams, with the majority being around 300 grams. Figure 1.11 shows the components that contribute tO the overall weight Of the racquet. The trend over the years has been toward lighter racquets because most players prefer racquets that are easy [ 0 SWing and easy tO carry ontO and around the court. On the Other hand, professional players tend t0 prefer heavy racquets because heavy racquets are generally more powerful and because professional players are generally fitter and stronger than recreational players. There is no correct or 、、 best" racquet weight. Even some professionals play very well with light racquets. ln that respect you should play with a racquet that feels just right ⅲ terms 0f its weight. Obviously, if you weigh more than 180 pounds, you can swing a heavier racquet than a young child. There is no offi- 32

TECHNCAL TEMIIS 日合こロリ ETS , ST n65 , 日 A 乢 5 , こロリ日 TS , SP れ合 n ロ日ロリ n こ E ROD CROSS & CRAWFORD LINDSEY HELPING TENNIS PLAYERSIN THEIR QUEST FOR THE PERFECT RACQUET Wh0tis the single most important vorioble in rocquet performonce? What kind of racquet, strings, and swing produce the most power? HOW d0 YOIJ creote maximum spin? Where on rocquet sh0Uld YOU hit the b0 Wh0t racquet and string feotUres combine f0 「 the most ( on 加し comfort, ond feel? HOW d0 YOU affect the bounce, speed, spin, and troiectory 0f the b0 旧 0 your odvantoge? This b00k answers these and 0ther elUSive equipment and performonce-related questions 市 at h0 perenniolly 可 0 胆 ed hockers ond experts alike. This informative primer will help turn h0Uß 0f mindless proctice int0 0 focused 叩 p 0 加 n 0f principles affecting the impoct, ond flight of the . Rod Cross and ( 「 0M0 「 d Lindsey 0 「 e ( 0 耐 ho 「 s of 廂 P and 0 加 / 0 灯砌 which wos 0 Scientific American B00k ClUb selection. R0d Cross is an associate professor at the University of Sydney, AUStroIio, ond is one 0f 加 world's most prolific researchers in the field 0f tennis physics. wf0 「 d Lindsey is the editor-in-chief 0f ( qlJ 就 5P0 ホ加面 5 mogazine and has written extensively on the technology ond science 0f tennis. 術 05 加 0 肌 4 t0 Ⅷ d 師加市四「確 ofsfrings 側側側 of 所劬 Technical Tennis provides Ⅷん 0 確加 ma 加 n ん「 ( 00 訪 and p 毎部 0 e. ″ / 側Ⅷ舷加 enhance / 側「 game, $ book 0 市 0 e 卸 of / 側 rl . " ー釖耐Ⅷ ( 0 翩側 age い rna 加祠席ん de 耐加 0 旧 " 動 00k provides 0 wonderfuloverview 0f ev 町加 0 朝ⅲ e ( な 0f 加席 . ″な昭 practical and written in 0 cleor and ( 側 ( mannerto わ p 毎師 0f 0 ″ e な . ん加 g 0 肌 4 リ就 wnning 0 ″加 the ( 側市 , ma s 訂 0 0d this 6 側 k ! " ー E. Pwl Ro 計劬の川 an 四加厮 e ( 衂川り e 昭加 m USA $12.95/Canada $ 17.95 旧 BN 0-9722759-3-2 ( の ( ,corn Racquet Tech PubIishing An imp 「 int Of the USRSA www.「acquetTECH.com

F Swingweight = 700 gm F 2 Racquets = 2000 gm Weight = 300 gm Figure れ Swingweight. The sum ofthe hand forces must now not only support the racquet ()s in Figure /. / 5 ) , but ロ / SO accelerate around an axis at the butt end Ofthe racquet. That requires more force and makes the racquet feel heavier. TWISTWEIGHT Sometimes, when you hit a forehand or backhand, the ball will drop into the bottom of the net. There are several reasons why this may happen, including the factthat you didn't hit the ball hard enough, or you hitthe ball downward instead of upward. Alternatively, you may have hitthe ball below the center of the strings toward the bOttom Of the frame. ln that case the racquet will tend tO twist SO that the racquet face points down toward the court instead Of fac- ing toward the net. The twisting effect is caused by the ball pushing on the bot- tom half of the strings. There is no such twlsting effect if you hit the ball in the middle of the strings or anywhere else along the axis of the racquet (the line extending from the handle t0 the tip 0f the racquet). The racquet will twist ⅲ the opposite direction if you hit the ball near the top of the frame or anywhere in the top half of the strings, ⅲ which case the ball will tend tO fly over the baseline. The amount Of racquet twist increases if you hitthe ball farther away from the axis of the racquet. The amount of twist also depends on hOW easy it is tO twist the racquet. ln general, light racquets twist more easily than heavy racquets, and racquets with a small head twist more easily than racquets with a large head. ln fact, that is one of the reasons that large head racquets became so popular when they replaced wood racquets. Because large heads twistless, it became easier to keep the ball ⅲ play.. There are tWO things you can do to a racquet い reduce the twisting effect. One is t0 add lead tape to the 3 and 9 0'clock positions on the frame. ln other words, you need tO add the extra weight as far away from the rotation axis as possible. That will increase the 、 'twistweight" of the racquet. If you add t00

Racquets Match Point Box 1.3 Maximum TheoreticaI BaII Speed 『 the racquet was petfect and lost no energy, and ifthe ball was a 0 perfect and lost no energy,then the maximum possible serve speed tO racquet speed ratiO would be 2. O. 旧 other words, the serve speed would be twice the racquet speed. に is impossible tO dO any better than that according tO the laws ofphysics, no matter what is done tO improve the racquet frame or the strings. However, the factor 0f2.0 here so requires the racquet to be infinitely heavy. Such a racquet would sink tO the center of the earth as soon as it was constructed, and it would suck in the sun and the moon while it was at it. For racquets around 300 or 400 gm, and for perfect racquets and balls, the maximum theoretical serve speed tO racquet speed ratiO is around に 5. 旧 practice, the serve speed to racquet speed ratio is typically about に 4. M0dern racquets are therefore almost as powerful as they can be, given that the rules specify that balls must lose energy in every collision. That being said, the easiest way to hit the ball faster is still simply to swing faster. Every player has more ⅲ reserve than any amount of fiddling with the rebound power can deliver. But for any given racquet, the rebound power is the way tO compare racquet power. POWER AND ENERGY LOSS 、、 More powerful" actually means less energy loss. So, although racquet adver- tisements are constantly singing the praises Of "more powerful" racquets, these racquets have no propulsion system. AII the energy that is possible is present before the impact. That is the energy of motion in the racquet and ball approaching each 0ther. The impact does not produce energy; it only loses it. Designing a powerful racquet is all about limiting energy loss, not about pro- ducing energy. And that is what is measured ⅲ rebound power. The primary reason the ball rebounds faster on a racquet with a high rebound power is that the extra weight limits these extraneous 1 れ 0 ⅱ ons and thus creates a 1 れ ore sta- ble platform from which the rebound can take place. If you lay a racquet on the court and put your foot on the throat area so that racquet can't recoil or vibrate, then the rebound power will increase tO about 0.9. That is, the ball will bounce い about 80 percent of the drop height (rebound power is the square root of the bounce height ratio). This provides a rather dramatic demonstration Of the fact that rebound power is strongly 25

Racquets Balance POint in string area Head heavy 360 mm →ー Head light 340 →ー Balance point near top of handle Figure ー」 4 Balance point. lfthe balance point is n10 「 e than halfthe racquet length as measured を om the end Ofthe butt, the racquet head-heavy. / 戸朝 s located 砒 less than halfthe racquet length, the racquetis head-light. ance point is roughly half way along the racquet and is measured from the butt end of the handle (Figure 1.1 の . Most racquets have a balance point between 310 mm and 390 mm from the butt end. If the balance point is more than halfway along the racquet, the racquet is said to be head-heavy. If it is less than halfway, the racquet is head-light. If the racquet is head-heavy, it means either that the head is heavier than the handle or that weight ⅲ the head has been shifted towards the tip, or weight in the handle has been shifted away from the butt end. The difference between a head-heavy and head-light racquet is easy to feel just by holding each racquet horizontally ⅲ your hand. You can't feel the difference if the racquets hang down vertically. If the racquet is vertical, all you feel is the weight. ln a horizontal position you feel a combination of the weight and the balance point. The weight you feel ⅲ this circumstance is called pickup- weight" because this is the approximate position which you pick up the rac- quet and hold it. A head-heavy racquet will feel heavier than a head-light rac- quet even if bOth racquets are exactly the same weight. That's because the weight of a head-heavy racquet is shifted further away from your hand, so you need to use a firmer wrist to hold the racquet horizontal (Figure 1.15 ). To con- 37