Chapter One when heavy, wood racquets were replaced with modern, light racquets at the end of the 1970S. When you strike a ball coming towards you, the ball tends to push the racquet head backward as your arm swings forward. Alternatively, the head slows down while your hand is still accelerating. Light racquets get pushed backward more than heavy racquets. A sudden twist 0f the arm or wrist, repeated many times, can result in tennis elbOW and Other injuries. The problem is magnified by the factthat light racquets need to be swung faster to pack the same punch as heavy racquets, so the impact shock is likely t0 be greater, especially if you miss-hit the ball near the tip 0f the racquet or near one edge. Some caution is therefore needed in choosing a light racquet. lt might feel great for a few months, but you might notice that your arm is get- ting sore. If that is the case, try a heavier racquet tO see if it helps. IDEAL RACQUET WEIGHT ln any bat and ball sport such as tennis or baseball, the bat or racquet is typi- cally about five or six times heavier than the ball and about one-fifth or one- sixth the player's arm or arms (Figure 1.12 ). A tennis ball weighs 57 grams and a baseball weighs 145 grams. A tennis racquet weighs about 340 grams, and a baseball bat weighs about 1 000 grams. One arm weighs about 2,000 grams, and two arms weigh up t0 6,000 grams for a heavy man. There are several reasons for this six-to-one ratiO. The weight Of a bat or rac- quet acts tO SIOW down the speed that you can swing your arm. The effect is relatively small for a six-to-one ratiO or for any ratiO greater than six-to-one. When a bat or racquet strikes a ball, the speed of the outgoing ball depends on the speed of the bat or racquet, and it also depends on the weight 0f the bat or the racquet. A heavy racquet striking a ball at a certain speed generates greater ball speed than a light racquet swung atthe same speed. ltturns out that the best weight ratiO is about six-to-one. If the racquet is t00 heavy, then it can't be swung quickly Furthermore, the ball speed off a 500-gram racquet is almost the same as the speed off a 600-gram racquet. Atthe other end 0f the scale, the ball speed off a 200-gram racquet is nearly twice the speed 0ff a lOO-gram rac- quet. But you can't swing a l()()-gram racquet twice as fast as a 200-gram rac- quet t0 make up the difference because your arm is already about 2 OOO grams and limits the speed at which your muscles can swing it. There is another reason why a six-to-one ratiO iS about ideal. When you swing a racquet, your upper arm first. After your upper speed, it starts tO SIOW down while your forearm speeds up. The racquet also speeds up, but just before you hit the ball, your forearm slows down. That way, 34

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

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

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 Match Point Box 1.2 continued Groundstrokes. A different result is obtained fo 「 a groundstroke where heavy both Figures l.8 and l.9. For example, racquets have an advantage over light rac- doubling the racquet weight from 200 quets in terms of ball speed 0 仟 the rac- grams t0 400 grams will increase the quet for a given effort. The result is shown rebound power from O. ワ to 0.44 for an in Figure l.9. Players rarely use maximum impact with a 57-gram tennis ball. effort to hit a groundstroke, so it was Serve. Experiments show that swing assumed in these calculations that 」 oe speed decreases as SWing 、 Neight increases used half his maximum effort to swing his for a maximum effort SWing, as in a first racquet at half his maximum swing speed. serve, according tO the graph shown in 比 was assumed a 0 that the ball was Figure l.8. Everyone has a different maxi- approaching at 40 mph and that 」 oe hit mum SW ・ ing speed fO 「 any given SWing- the ballin the middle ofthe strings.ln that weight, but if the swingweight is doubled, case there is a ー O mph increase in outgo- then the swing speed will decrease by ing ball speed when the racquet weight is about ワ percent for all players, at least for increased from 200 tO 400 grams. racquets between IOO grams and 500 Alternatively, 」 oe could decide to swing the grams in weight. Doubling the racquet 400-gram racquet upwards at a steeper weight from grams to 20 grams will angle than the 200-gram racquet, in which make no measurable difference at all to case the outgoing ball speed 0 仟 bOth rac- swing speed, but ワ percent is the average quets would be about the same, but the measured result for almost all racquets Of 400-gram racquet would generate more practicalinterest and for a range Of differ- topspin. ent players 0f different strengths and abilities. Adding the racquet speed to 70 the rebound speed gives the serve speed results shown in Figure l.8. The serve speed is a maxlmum at a racquet weight 50 of about 300 grams, but there is on ツ a tiny drop in serve speed at 250 grams or at 400 grams. Consequently, there is almost nothing tO be gained by using a heavier or lighter racquet, at least in terms Of maximum serve speed. Groundstroke 80 0.8 Joe'S outgoing ball speed 0.6 (JöM0d pu コ 0q9 区 ) dY 4 0 0 60 Rebound power ()P scale) HaIf 」 oe ・ s max racquet speed 0 30 lncoming ball speed = 40 mph 90 汚 0 200 250 300 350 400 450 500 Racquet weight (gm) Figure 1.9 Effect 0 「 weight on groundstoke speed. 20 -0.2 23

Racquets relative impact speed at any given impact point (usually measured using a stationary racquet). Exit speed: the speed of the ball when it leaves the strings. lt is composed 0f the rebound speed plus the racquet speed. Swing speed: the angular speed 0f the racquet ⅲ degrees per second as it iS swung in an arc centered at some POint Of rota- tion such as the wrist, elbOW, or shoulder. Maximum rebound point: that spot on the racquet fror れ which the ball rebounds fastest off a s ⅱ on の ) racquet. Maximum power point: that point on the racquet from which the exit speed is greatest Off a swinging racquet. THE COMPONENTS OF "POWER ”・ EXIT SPEED, REBOUND SPEED, RACQUET SPEED There are two components t0 the speed of the ball 0ff the racquet—the rebound speed and the racquet speed. Essentially, the ball rebounds at a cer- tain speed from a platform moving at its own speed. You add those two speeds together, and you have the exit speed 0f the ball off the strings. The rebound speed is determined by the racquet's structure, and the racquet speed is the result of the player's ability to swing the racquet. Most people have difficulty conceptualizing the separation Of a hit intO these tWO components, SO a little explanation iS necessary. The rebound speed is very simply demonstrated (Figure 1.3 ). If you drop a ball from, say, 20 inches ont0 a specific location 0f a stationary hand-held racquet (this is a requirement) , it will rebound a certain height. The ratiO Of the rebound height to the drop height gives the fraction of energy return. If you take the square root Of that fraction, you have the ratiO Of rebound speed tO the impact speed. This ratio is usually about (times IOO equals 40 percent) for an impact in the middle Of the strings (a little more for a heavier racquet, a lit- tle less for a lighter one). This means thatthe ball will rebound with 40 per- cent of the speed that it had just before impact. The higher the ratio, the more rebound speed the racquet imparts at that impact location. If the rebound speed ratio 0f Racquet A is O. 4 and that 0f Racquet B is O 爵 3 , then Racquet B has a more powerful" rebound component at that impact point. For that rea- son, from now on we will refer tO the rebound speed ratiO as the "rebound 1 3

Chapter One Match Point Box 1.2 Maximum Effort Power Even though rebound power provides a are shown in Figures に 8 and に 9 fo 「 a play- convenient measure Ofthe intrinsic POW ・ er er whO we call 」 oe. 」 oe is strong, but not of a racquet, and even though players tend super strong. He iS using various racquets tO adjust their swing speed tO suit the shOt that vary in weight and swingweight, but that they are trying to make, the question each is 69 cm long, and each has a balance point 353 mm from the end ofthe handle, arises as tO hO 、Ⅳ much power a given rac- SO the racquets are equally head-héavy. quet can deliver when the player uses 訓 the effort he or she can muster. 旧 that The racquets are strung with the same case, not on レ rebound power, but a 0 string at the same tension and have the swingweight, will determine the final ball same headsize and stiffness. 旧 that case, speed. That is the sort Of power that ten- the swingweight is proportional tO the niS authorities are worried about. げ some- racquet weight. げ the racquet weight is one can make a racquet that iS SO power- doubled, then so is the swingweight. fulthat 150 mph serves become common, Rebound power SO increases as racquet then the game oftennis will be in trouble. weight increases, but it is not exactly pro- に is doubtful that this will ever happen. portional tO racquet weight. に is relatively easy tO calculate rebound power for an That is not to say that a seven-foot giant will not come along one day and belt impact in the middle ofthe strings because down every first serve at 150 mph or so. energy losses due tO frame vibrations can then be ignored. The result is shown in But what if your average six-foot weal<ling could do it? Even if he could, then it is likely that 95 % of first serves would then be a fault because the margin for error 、 wou 旧 90 shrink almost tO zero. have done some inter- esting calculations concern- ing the variation Of racquet power with racquet weight 70 or swingweight for any play- 比 60 er, based on the assumption that the player exerts max- lmum or near maxlmum effort. These calculations Serve 0.8 0 maximum serve speed 0.6 ( 」 0M0d pu コ 09a 比 ) dY っム 0.4 80 」 oe maximum racquet speed 0 Rebound Power ()P scale) -0.2 50 90 巧 0 加 0 250 300 350 400 450 500 Racquet weight (gm) Figure れ 8 Effect 可 weight on serve speed. 22

Racquets 40 mph 20 mph Just before impact 64 mph 」 ust after impact Exit speed ニ 24 + 40 = 64 mph Rebound speed ニ 0.4 x 60 ニ 24 mph ReIative impact speed = 20 + 40 = 60 mph Racquet speed = 和 mph lncoming ball speed = 20 mph Rebound power = 0.4 Figure れ 6 Racquet and ba 〃 hitting each other. the racquet closer tO the axis. However, all locations Of the racquet move because these parts travel in a bigger circle relative tO the axis than dO parts Of farthest from the axis are moving faster than those closer. ThiS iS obvious bination Of these, creating circles within circles). Those parts Of the racquet as the axis Of rotation) located at the wrist, elbow, or shoulder ()r even a com- being swung in an arc, which is a segment Of a big circle with its center (known same speed. On all swings, except very short punch volleys, the racquet is the most power. That is because all parts Of the racquet dO not move at the erful point on the racquet is not the best point tO hit if you want a shot with attained if the ball hits the racquet at that point. lt is ironic that the most pow- quet is stationary. But that does not mean that the greatest exit speed will be The rebound speed is always greatest at the maximum rebound point if the rac- CHANGES WITH RACQUET SPEED THE MAXIMUM EXIT POWER POINT speed) to the rebound speed and you have the exit ball speed. That's easy Just add the speed of the launch pad atthe rebound point (racquet quet from which it rebounded to get an exit speed of 64 mph. tive tO the racquet, just as it did above, tO which we add the speed Of the rac- the relative impact speed is still 60 mph, so the ball rebounds at 24 mph rela- If the racquet is traveling 40 mph and the ball 20 mph, as ⅲ Figure 1.6 , then

Racquets ing balls 0f different weight. If you can throw a 57-gram tennis ball at 60 mph, then you can throw a 145-gram baseball at about 55 mph, even though it is 2.5 times heavier than a tennis ball. Your throw speed is limited mainly by the weight 0f your arm, which is a 1 飢 heavier than a tennis ball or a baseball and therefore has a much larger swingweight. (See Match Point Box 1.2 for more discussion on the influence Of weight on swing speed. ) We are now able tO state what is meant by racquet power when you are com- paring one racquet tO another. RACQUET POWER DEFINED AS REBOUND POWER Because, for most any given racquet, you can change your swing speed for any given shOt situation, and because you must change your swing speed in differ- ent situations (). e. , serve, volley, groundstroke, etc. ) , and because the actual effect on swing speed of a change in weight is small, we will consider the prop- erties Of the racquet that increase the rebound power as being 1 れ OSt important in the racquet's contribution [ 0 power in actual game situations. Except in an all-out first serve, those properties that make the racquet easier or harder [ 0 swing tend t0 be ignored or overridden by the player, and thus are not proper- ties that dictate certain power results without exception, as rebound power does. The major benefit Of using rebound power as the prime indicator of power is that it is independent Of effort, swing speed, and stroke situation. lt is inde- pendent 0f the ability, style, technique, and temperament of the player. So, however fast you choose tO swing your racquet, and whatever effort it may take, the racquet with the greatest rebound power will usually hit the ball fastest (except for a maximum effort serve, as explained in Match point Box 1.2 ). If you wantto hitthe ball even faster, then simply swing faster, because there is nothing stopping you from doing so, exceptthe need to getthe ball ⅲ the court. Rating racquet power by rebound power is not perfect, but it is the most practical and useful measurement considering the way most players actu- ally use and interact with their racquets. We are leaving swing speed up tO the player and considering the racquet mainly as a rebound platform. Because most Of the time the player has a 、 swing speed override" option at his or her disposal, we will consider the racquet's contribution tO power in に rt れ s Of its rebound PO ℃ r. 21

Chapter One TabIe I. ー Rebound Speed vs. Racquet Speed lncoming Rebound Speed Racquet Speed Exit BaII Speed Contribution Contribution Speed (mph) TO Exit Speed ( % ) TO Exit Speed ( % ) (mph) 30 90 60 66 30 54 30 96 Racquet Speed (mph) 0 (volley) 30 30 60 90 (serve) 0 5 「 4 8 5 -6 っ ~ 4 5 6 0 The calculations assume 0 rebound power 0 「 0.4. is your racquet in the outcome Of your shOts. The faster you swing, the pro- portionately 1 れ ore important iS the racquet speed. Or, in Other words, the faster you swmg, your racquet is less important tO the speed Of your shOts. lt is alSO true for any given player that he or she would probably do better with a heav- ier racquet for volleys (ignoring maneuverability) , a moderate weight racquet for groundstrokes, and a lighter racquet for serves. Unfortunately you can't change your racquet between ShOtS. The second part Of the answer tO the objection is the 1 れ ore important—the rac- quet does not S10 Ⅵ , down enough tO cancel gains in rebound power and cause exit speed tO decline. This is true for three reasons: ( 1 ) except for a first serve, the player can almost always swing faster if he wants t0, ( 2 ) it has been exper- imentally shown that the actual decline in racquet speed with a heavier racquet is quite small, and ( 3 ) the increase in rebound speed and decline ⅲ racquet speed virtually cancel each other. As a result, for any given effort, there is lit- tle or no decline in exit speed for an increase in weight within the range Of rac- quet weights on the market. And if there is, the player can swing with slightly greater effort anyway.. The reason is that the main constraint in swinging faster is the weight (swingweight) of the arm, not of the racquet. The difference ⅲ weights between any tWO racquets is relatively very small compared tO the weight of the arm and thus has very little influence on racquet speed. ln fact, experiments have shown that the racquet speed varies as l/(swing- weight)0 ・ 27 for maximum effort swings. Consequently, if the swingweight of a racquet is doubled (). g. , from 300 t0 600 grams) then the maximum swmg speed decreases by only about 17 percent. A similar effect occurs when throw- 20