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 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

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 1.2 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

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

Racquets tO touch the strings, string dampeners were used tO dull the sound Of impact, and players just hit four balls with racquet A and then racquet B. If they could tell thatthere was a difference, they couldn'ttell which racquet was the high- er or lower tension. some might guess one way, some the Other. ln Other words, the immediate feel Of power and control in a racquet is not obvious. A player's opinion 0f a racquet is formed by his interpretation 0f what he feels, and that interpretation can hinge on the littlest Of things that have nothing tO dO with the racquet's actual performance, such as the sound Of the strings. ln a sense, the sound tells him how he should feel aboutthe racquet. One last example is one that demonstrates hOW players can be fOOled intO thinking they have hit a ball faster, when they have no [. Players sometimes get the feeling that the ball comes off the strings faster than usual or with less effort than usual. The effect is probably psychological rather than a genuine increase in racquet power for several reasons. ln general, tO hit the ball you have to hit it harder by swinging the racquet faster. The result is usually felt as an increase in the force on the hand and arm. However, you can get an increase in that force just by hitting the ball at a different spot on the strings. Conversely you can get a decrease in the force, for the same ball speed, by hit- ting the ball ⅲ the middle 0f the strings. A decrease ⅲ the force on your arm, for the same ball speed 0ff the strings, might give the appearance 0f more power, when in fact there is no change in power at all. The only way t0 know for sure is to measure (a) the speed 0f the racquet, (b) the impact point on the strings, (c) the speed 0f the incoming ball, and (d) the speed 0f the outgoing ball. No one has ever done that. These examples can be multiplied many times over, but the point is that the player creates a perception 0f the facts ⅲ his mind and acts accordingly. A play- er can have all the facts wrong but still make all the correct stroke adaptations and be a great player. If you ask that player why he is great and how and why he hits the ball so fast and accurate, you will get a very confident answer, but one that might not be bestto pass on t0 any other player as the how and why of the forehand (though you still may wantto copy his forehand). RACQUET FEATURES COMBINE WITH STROKES The other complication when talking about racquet features is that they pro- duce different results for different players. When we talk about increasing or decreasing power or control, we are talking about certain properties Of the rac- quet. put any racquet int0 a player's hand, however, and the result may be more or less power and control with respect tO hOW and where the player is 7

Chapter One 、 'This racquet hits with a lot of power," or 、、 This racquet has a 10t of power. Such usage Of the word power" is not the scientific meaning at all and can cause a lOt Of confusion When people 、 VhO are unfamiliar With tennis vocabu- lary try tO make heads or tails out Of players' conversations or what is written ⅲ the literature. When a player says, 。、 I want a racquet with a 1 飢 of power," he means one that can make the ball go very fast. The belief is that the racquet has a property called power" and that some racquets have more Of it than Oth- ers. ln a sense this is true, but the problem is that there is a large amount Of misinformation and confusion when it comes tO nailing down exactly what racquet power is and what affects it and by how much. 嶬気 h those difficulties ⅲ mind, we boldly go forth to try to shed some light on the ubiquitous but misunderstood concept Of racquet power. TO dO SO, we need tO define S01 れ e terms. S01 れ e Of these terms we have had tO COin ourselves because there is no player-friendly vocabulary, and most 0f the terms available for use in discussion are intimidating scientific terms that have no meaning tO players. SO if we use a term as if it iS common parlance, it most probably is not the case at all, at least not yet. On the Other hand, some words may be used in common parlance, but we define them slightly differently so that they have a precise meaning with respect tO power. The vocabulary Of power consists Of the following words and phrases (Figures 1.3-1.7 will show these terms in action): Power: The racquet's intrinsic ability to hit the ball fast for a given effort. lncoming ball speed: the speed of the incoming ball just before it hits the racquet strings. Relative impact speed: lncoming ball speed plus racquet speed. lmpact point: The contact point on the racquet where the ball and racquet collide. Racquet speed: the speed 0f the impact point on the racquet immediately before the racquet hits the ball. Rebound speed: how fastthe ball rebounds from the surface of the strings, relative tO the racquet speed before impact. Rebound power: the ratio of the ball's rebound speed to the

Racquets If the swing speed is slow, then the difference in speed between one impact point and another will not be great, and it may or may not be enough tO com- pensate for the IOSS in rebound speed between the points and thus may or may not result in faster exit speed. The general rule is that the slower the swing speed, the lower in the racquet will be the maximum power point, and the faster the swing speed, then the higher ⅲ the racquet will be thatlocation (up tO a point, anyway). For strokes Of moderate speed and above, that location is usually somewhere between the middle and tip of the racquet head, but exact- ly where will depend on the swing speed. TechnicaIIy, the maximum power point changes for every swing speed. However, a general rule of thumb applies: for maximum exit speed, if you SWing SIOW, aim lower•, if you SWing fast, aim higher. COMPARING RACQUET POWER lt would seem that if you want tO maximize power, all you would have tO do is choose the racquet with the greatest rebound power at the location where you typically hit the ball for a certain kind 0f shot. This is indeed true, but before we can make rebound power our OffiCial definition Of power, we first must slay a persistent objection tO using this power comparison criteria. That objection states that if the easiest and most effective way tO increase the rebound power Of a racquet is tO increase the weight ()r 1 れ ore correctly, the swingweight, as we will see later) , then the gain ⅲ rebound power will be more than lost due い a decrease in racquet speed, and the exit speed will actually end up being less. The answer い this objection is twofold: first, the result of the tradeoff between more rebound power and less racquet speed depends on the stroke, and second, the objection is incorrect tO begin with. Let's address each of these. First, even assuming racquet speed does decline with increased weight, the consequence 0f this depends on whether the ball is going faster than the rac- quet or not. The faster the ball speed compared t0 the racquet speed, the more the contribution of rebound speed compared to racquet speed. SO for volleys and slow swings, a heavier racquet with a higher rebound power at the impact point will likely add t0 exit speed, even if the racquet speed is less. For very fast swings and serves, any slowing of the racquet due to extra weight will like- ly decrease the final ball speed. Table 1.1 shows these relationships. ln general, the slower you swing compared t0 the incoming ball, the propor- tionately more important iS rebound power (and hence weight) [ 0 your exit speed. Or, in Other words, the slower your swing, the more important tO you 19

Racquets and feel. There are seemingly hundreds 0f technologies ⅲ the marketplace, but virtually every one 0f them is ⅲ some way directly or indirectly addressing weight and stiffness. But weight and stiffness can be combined ⅲ so many dif- ferent ways that each racquet feels different from the next. lt all depends on how much weight you put where and how stiff that material makes the frame. Knowing this, it iS a 10t easier tO compare racquets by assessing the weight- and stiffness-related consequences Of any new technology as compared tO another. Often, weight-related technologies can be approximated simply by adding lead weight. Similarly, any technology or design that affects the stringbed stiffness can often be approximated by raising or lowering tension, which, along with material and gauge, changes the stringbed stiffness. Any effects on the stringbed 0f big- ger headsize, large grommets, free moving string, extended strings, spring- loaded strings, cushioned strings, etc. , can be approximated by raising or 10W - ering tension. MOSt Of these technologies are designed tO soften the stringbed for any given tension compared tO an identical racquet without them. You can do the same thing by keeping your present racquet and lowering the tension. The same is true with the strings themselves. Any change in playing perform- ance (not including durability) due tO a change in material, construction, gauge, or pattern can be approximated by raising or lowering tension. All stringbed and string technologies alter the force and time 0f impact. That is all. This is accomplished by changing the stringbed stiffness. lt does not matter how you change the stringbed stiffness, only that you do. Stiffness is stiffness no matter hOW you get there. At the risk of putting the carriage before the horse, we will first discuss the benefits—power and control—before we discuss the features—、 veight and stiffness. lt's just 1 れ ore interesting tO know where we are going and work back- ward than tO work our way up tO an unknown destination. POWER power is probably the most talked about characteristic Of racquets. Manufacturers talk about 、、 ultimate power," players marvel at the feel of effort- less propulsion, and the governing bodies cringe at the prospect 0f faster and faster serves ruining the nature Of the game. ln the tennis vernacular, power" is generally used t0 mean one 0f two things—ball speed 0ff the racquet or the ability of the racquetto make the ball go fast. Thus you will hear players say,

Chapter One Rebound power is the power" that is available due simply t0 the racquet's existence and that iS always available on every swing, ShOt, and situation that the game Of tennis can throw at you. REBOUND POWER THE SUM OF ALL RACQUET PROPERTIES The magic Of rebound power is that lt is the result Of the combined influence of all the frame's physical parameters. The effects of the racquet's mass, bal- ance, swmgweight, flex, headsize, pattern, string, and tension are each accounted for in measuring rebound power. The rebound iS the consequence of the effects of all of these things, as well as every other feature designed into the construction and stringing Of the racquet. A racquet with a higher rebound has a more powerful combination Of these factors at that impact location than a racquet with a lower rebound. If you had a map 0f the stringbed showing the rebound power value at one-inch locations radiating out frOI れ the center Of the racquet, you could compare the power Of every racquet in the area Of your impact zone (indicated by where you find ball fuzz on the strings 0f your rac- quet) ・ Such a rebound power map shows the results of the different flow of energy ⅲ a racquet for each impact location. When the ball strikes a stationary, free- standing or hand-held racquet, the energy 0f the ball is divided between rac- quet translation (linear motion) , rotation, twisting, and bending. Each Of these motions siphons 0ff energy, making it unavailable for propelling the ball. The energy that is left over (elastic energy stored in the stretched string and com- pressed ball) is used t0 rebound the ball off the strings, though about 25 per- cent 0f that energy is lost ⅲ the process also. ln general, lighter, more flexible racquets and stiffer stringbeds result in more energy being wasted and less tO propel the ball. Also, as you move out from the center of the stringbed, rebound power declines, more SO for smaller head racquets than larger ones. Rebound power is actually tricky [ 0 measure accurately without special equip- ment, but the concept is incredibly simple, and quickly lays t0 rest any "which racquet is more powerful" debates. lt is astonishing that the intrinsic, Off-the- shelf power Of the racquet at any given stringbed location is revealed SO com- pletely and accurately by such an unimpressive, simple, slow collision as the drop test shown in Figure 1.3. NO on-court, 。、 realistic" situations are necessary tO determine a racquet's built-in power—the power that is available in every single hit of the ball, independent 0f swing speed. 24