String tension effects on tennis ball rebound speed and accuracy during playing conditions

The primary aim of this study was to determine whether variations in rebound speed and accuracy of a tennis ball could be detected during game-simulated conditions when using three rackets strung with three string tensions. Tennis balls were projected from a ball machine towards participants who attempted to stroke the ball cross-court into the opposing singles court. The rebound speed of each impact was measured using a radar gun located behind the baseline of the court. An observer also recorded the number of balls landing in, long, wide and in the net. It was found that rebound speeds for males (110.1?±?10.2?km?·?h^?1; mean?±?s) were slightly higher than those of females (103.6?±?8.6?km?·?h^?1; P?<?0.05) and that low string tensions (180?N) produced greater rebound speeds (108.1?±?9.9?km?·?h^?1) than high string tensions (280?N, 105.3?±?9.6?km?·?h^?1; P?<?0.05). This finding is in line with laboratory results and theoretical predictions of other researchers. With respect to accuracy, the type of error made was significantly influenced by the string tension (P?<?0.05). This was particularly evident when considering whether the ball travelled long or landed in the net. High string tension was more likely to result in a net error, whereas low string tension was more likely to result in the ball travelling long. It was concluded that both gender and the string tension influence the speed and accuracy of the tennis ball.     

Elite tennis player sensitivity to changes in string tension and the effect on resulting ball dynamics

Eighteen elite male tennis players were tested to determine their ability to identify string tension differences between rackets strung from 210 N (47 lb) to 285 N (64 lb). Each player impacted four tennis balls projected from a ball machine before changing rackets and repeating the test. Eleven participants (61%) could not correctly detect a 75 N (17 lb) difference between rackets. Only two participants (11%) could correctly detect a 25 N (6 lb) difference. To establish whether varying string tensions affected ball rebound dynamics, the ball’s rebound speed and landing position were analysed. The mean rebound ball speed was 117 km h⁻¹, with only the trials from the 210 N racket producing significantly lower (P < 0.05) rebound speeds than the 235 N and 260 N rackets. This is contrary to previous laboratory-based tests where higher rebound speeds are typically associated with low-string tensions. The anomaly may be attributable to lower swing speeds from participants as they were not familiar with such a low string tension. Ball placement did not appear related to string tension, with the exception of more long errors for the 235 N racket and fewer long errors for the 285 N racket. It was concluded that elite male tennis players display limited ability to detect changes in string tension, impact the ball approximately 6% faster than advanced recreational tennis players during a typical rallying stroke, and that ball placement is predominantly unrelated to string tension for elite performers.     

Tennis racket stiffness,string tension and impact velocity effects on post-impact ball angular velocity

There has been significant technological advancement in the game of tennis over the past two decades. In particular, tennis rackets have changed in size, shape and material composition. The effects of these changes on ball rebound speed have been well documented, but few studies have considered the effects on ball angular velocity. The purpose of this study was to investigate the effects of three factors on post-impact ball spin. Tennis balls were projected at three velocities toward a clamped racket simulating three levels of stiffness and strung at three string tensions. The angular velocity of each tennis ball was measured from stroboscopic images during an oblique impact with the racket. A three-way factorial ANOVA revealed significant (P < 0.01) differences in the post-impact angular velocity for string tension, racket stiffness and impact velocity, as well as two-way interactions between string tension and impact velocity, and between racket stiffness and impact velocity. The possibility of tangential elastic strain energy being stored in the racket and ball was evident in low impact velocity trials. These displayed a post-impact angular velocity where the circumference of the ball was translating faster than the relative velocity between the ball’s centre of mass and the string surface. It was concluded that increasing the relative impact velocity between the racket and ball was the best means of increasing the post-impact angular velocity of the tennis ball.     

The Influence of Tennis Racket Flexibility and String Tension on Rebound Velocity Following a Dynamic Impact

Abstract

The effects of string tension and longitudinal racket flexibility on post-impact ball velocity were investigated in tennis. Six wooden rackets, two with flexible shafts, two with medium and two with stiff shafts were strung with synthetic gut at tensions of 245N (55 lb), 289N (65 lb) and 334N (75 lb).

A pneumatically driven racket-arm was triggered by a stimulus from a photo-electric cell positioned at the exit nozzle of a ball machine so that impact occurred with the racket perpendicular to the path of the ball. New tennis balls were fired to impact each racket at the geometric center of the strings and 5 cm above the geometric center. The average horizontal velocity of the ball, both before and after impact, was determined using stroboscope photography.

A significant interaction between racket stiffness and string tension was recorded for an inward ball velocity of 22.7 m/s and a racket velocity of approximately 6.8 m/s. String tension had no significant influence on rebound velocity for a stiff racket following impact with a moving racket. Medium and flexible rackets produced the highest coefficients of restitution when strung at 245N (55 lb) compared to 289N (65 lb) and 334N (75 lb).     

The dynamic impact characteristics of tennis balls with tennis rackets

The dynamic properties of six types of tennis balls were measured using a force platform and high-speed digital video images of ball impacts on rigidly clamped tennis rackets. It was found that the coefficient of restitution reduced with velocity for impacts on a rigid surface or with a rigidly clamped tennis racket. Pressurized balls had the highest coefficient of restitution, which decreased by 20% when punctured. Pressureless balls had a coefficient of restitution approaching that of a punctured ball at high speeds. The dynamic stiffness of the ball or the ball-racket system increased with velocity and pressurized balls had the highest stiffness, which decreased by 35% when punctured. The characteristics of pressureless balls were shown to be similar to those of punctured balls at high velocity and it was found that lowering the string tension produced a smaller range of stiffness or coefficient of restitution. It was hypothesized that players might consider high ball stiffness to imply a high coefficient of restitution. Plots of coefficient of restitution versus stiffness confirmed the relationship and it was found that, generally, pressurized balls had a higher coefficient of restitution and stiffness than pressureless balls. The players might perceive these parameters through a combination of sound, vibration and perception of ball speed off the racket.     

The dynamic impact characteristics of tennis balls with tennis rackets

Abstract

The dynamic properties of six types of tennis balls were measured using a force platform and high-speed digital video images of ball impacts on rigidly clamped tennis rackets. It was found that the coefficient of restitution reduced with velocity for impacts on a rigid surface or with a rigidly clamped tennis racket. Pressurized balls had the highest coefficient of restitution, which decreased by 20% when punctured. Pressureless balls had a coefficient of restitution approaching that of a punctured ball at high speeds. The dynamic stiffness of the ball or the ball-racket system increased with velocity and pressurized balls had the highest stiffness, which decreased by 35% when punctured. The characteristics of pressureless balls were shown to be similar to those of punctured balls at high velocity and it was found that lowering the string tension produced a smaller range of stiffness or coefficient of restitution. It was hypothesized that players might consider high ball stiffness to imply a high coefficient of restitution. Plots of coefficient of restitution versus stiffness confirmed the relationship and it was found that, generally, pressurized balls had a higher coefficient of restitution and stiffness than pressureless balls. The players might perceive these parameters through a combination of sound, vibration and perception of ball speed off the racket.     

A review of tennis racket performance parameters

The application of advanced engineering to tennis racket design has influenced the nature of the sport. As a result, the International Tennis Federation has established rules to limit performance, with the aim of protecting the nature of the game. This paper illustrates how changes to the racket affect the player-racket system. The review integrates engineering and biomechanical issues related to tennis racket performance, covering the biomechanical characteristics of tennis strokes, tennis racket performance, the effect of racket parameters on ball rebound and biomechanical interactions. Racket properties influence the rebound of the ball. Ball rebound speed increases with frame stiffness and as string tension decreases. Reducing inter-string contacting forces increases rebound topspin. Historical trends and predictive modelling indicate swingweights of around 0.030–0.035 kg/m² are best for high ball speed and accuracy. To fully understand the effect of their design changes, engineers should use impact conditions in their experiments, or models, which reflect those of actual tennis strokes. Sports engineers, therefore, benefit from working closely with biomechanists to ensure realistic impact conditions.     

The physiological cost of velocity coupling during tennis groundstrokes

Velocity coupling denotes a perceptual motor behaviour known to occur during coincidence timing tasks. Individuals have been shown to increase their effector limb speed with increases in stimulus speed during interceptive tasks. However, little is known about the physiological effects of velocity coupling. The aim of this study was to determine the physiological cost of velocity coupling during tennis groundstrokes. Eight male and eight female competitive tennis players volunteered to perform three 4-min bouts of continuous groundstrokes against balls projected from a tennis ball machine at speeds of 18, 22, and 27 m x s(-1) (65, 79, and 97 km x h(-1)) and a frequency of 14 balls per minute, the order of which was counterbalanced. Breath-by-breath pulmonary gas exchange, heart rate, locomotion time, and limb acceleration were measured throughout each of the 4-min bouts. Capillary blood samples (for blood lactate analysis), rating of perceived exertion, and difficulty rating were taken at the end of each bout. Increasing ball speed did not influence the locomotion time between groundstrokes but did result in a bilateral increase in both the mean upper- and lower-limb acceleration (all P < 0.05). Velocity coupling behaviour increased oxygen uptake, blood lactate concentration, heart rate, rating of perceived exertion, and perceived task difficulty (all P < 0.05). It would appear, therefore, that velocity coupling influenced tennis groundstroke behaviour and indirectly modified the concurrent cardiopulmonary and metabolic responses.     

Effect of type 3 (oversize) tennis ball on serve performance and upper extremity muscle activity

This study investigated the effect of the larger diameter (Type 3) tennis ball on performance and muscle activation in the serve. Sixteen male advanced tennis players performed serves using regular size and Type 3 tennis balls. Ball speed, surface electromyography, and serve accuracy were measured. There were no significant differences in mean initial serve speeds between balls, but accuracy was significantly greater (19.3%) with the Type 3 ball than with the regular ball. A consistent temporal sequence of muscle activation and significant differences in mean activation of different muscles were observed. However, ball type had no effect on mean arm muscle activation. These data, combined with a previous study, suggest that play with the larger ball is not likely to increase the risk of overuse injury, but serving accuracy may increase compared to play with the regular ball.     

Tennis

This study investigated the effect of the larger diameter (Type 3) tennis ball on performance and muscle activation in the serve. Sixteen male advanced tennis players performed serves using regular size and Type 3 tennis balls. Ball speed, surface electromyography, and serve accuracy were measured. There were no significant differences in mean initial serve speeds between balls, but accuracy was significantly greater (19.3%) with the Type 3 ball than with the regular ball. A consistent temporal sequence of muscle activation and significant differences in mean activation of different muscles were observed. However, ball type had no effect on mean arm muscle activation. These data, combined with a previous study, suggest that play with the larger ball is not likely to increase the risk of overuse injury, but serving accuracy may increase compared to play with the regular ball.     

A comparison of the ball rebound characteristics of wooden and composite cricket bats at three approach speeds

The primary aim of this study was to compare the rebound characteristics of wooden and composite cricket bats. The rebound characteristics of two 'experimental' bats manufactured from composite material were compared with three English willow bats and one Kashmir willow bat. The bats were tested using a specially designed testing rig, which propelled a 156 g Kookaburra cricket ball at three impact speeds: fast-medium, 67 km x h(-1); fast, 101 km x h(-1); and express, 131 km x h(-1) on to the bats mounted in position so that the ball impacts occurred at the position where the blade of the bats was the thickest. The rebound characteristics of the bats were calculated by measuring the approach and rebound speeds of the ball as it passed through a light beam positioned a short distance away from the point of impact. The statistical software package SAS was used to test for significant differences (p < 0.05) between the average rebound characteristics of the bats. Further, Scheffé's method was used as a post hoc comparison to determine whether differences existed between the composite and willow bats. When the composite and traditional willow bats were compared, the results showed no significant differences between the three average approach speeds, while the composite bats showed significantly smaller rebound speeds and coefficient of restitution at all three approach speeds. Thus, the rebound characteristics of the composite bats were significantly less than the traditionally designed English willow wooden bats and would not enhance performance by allowing the batsman to hit the ball harder, assuming all other factors, such as bat speed, mass distribution and the impact point, were the same for the bats. Further study is required to determine the physical properties of composite and wooden bats to enhance their impact characteristics.     

The physiological cost of velocity coupling during tennis groundstrokes

Abstract

Velocity coupling denotes a perceptual motor behaviour known to occur during coincidence timing tasks. Individuals have been shown to increase their effector limb speed with increases in stimulus speed during interceptive tasks. However, little is known about the physiological effects of velocity coupling. The aim of this study was to determine the physiological cost of velocity coupling during tennis groundstrokes. Eight male and eight female competitive tennis players volunteered to perform three 4-min bouts of continuous groundstrokes against balls projected from a tennis ball machine at speeds of 18, 22, and 27 m · s^?1 (65, 79, and 97 km · h^?1) and a frequency of 14 balls per minute, the order of which was counterbalanced. Breath-by-breath pulmonary gas exchange, heart rate, locomotion time, and limb acceleration were measured throughout each of the 4-min bouts. Capillary blood samples (for blood lactate analysis), rating of perceived exertion, and difficulty rating were taken at the end of each bout. Increasing ball speed did not influence the locomotion time between groundstrokes but did result in a bilateral increase in both the mean upper- and lower-limb acceleration (all P < 0.05). Velocity coupling behaviour increased oxygen uptake, blood lactate concentration, heart rate, rating of perceived exertion, and perceived task difficulty (all P < 0.05). It would appear, therefore, that velocity coupling influenced tennis groundstroke behaviour and indirectly modified the concurrent cardiopulmonary and metabolic responses.     

Differences in ball speed and accuracy of tennis groundstrokes between elite and high-performance players

Abstract

The main aim of this study was to identify and compare ball speed and hitting accuracy of forehand and backhand groundstrokes between ATP professionals (elite) and high-performance youth players when shots were played cross-court and down the line to a target square. Six elite and seven high-performance tennis players volunteered to participate in the study. A Doppler-radar device and a digital video camera, operating at 120 frames per second, were used to measure ball speed and accuracy of forehand and backhand groundstrokes in the respective situation (cross-court and down the line). The results of 1040 measured groundstrokes indicate that the ball speed of the forehand and the backhand ground stroke was higher in the elite group when analysing (1) all valid shots, (2) the six fastest shots, and (3) the six most accurate shots (all P < 0.05). In addition, all players achieved a higher forehand speed compared with their backhand when balls were directed cross-court (P < 0.01). The participants demonstrated similar ability when considering accuracy of their groundstrokes (P > 0.05). However, a group difference for accuracy was identified when considering the six fastest forehand shots (P<0.05), and the forehand cross-court stroke was played more accurately than the backhand cross-court stroke by both groups (valid shots and six most accurate shots, P<0.05). Moreover, there was no evidence that players who impacted the ball faster were any less accurate than those who impacted the ball more slowly. Analyses for participants actually revealed a negative correlation between ball speed and mean radial error (accuracy) for the backhand down the line (r= ? 0.77, P<0.01). According to the results of this study, ball speed seems to be the determining factor that separates elite from sub-elite tennis players.     

Measurements of the horizontal and vertical speeds of tennis courts

Tennis courts are normally classified as fast or slow depending on whether the coefficient of sliding friction (COF) between the ball and the surface is respectively small or large. This classification is based on the fact that the change in horizontal ball speed is directly proportional to the COF if the ball is incident at a small angle to the horizontal. At angles of incidence greater than about 16° it is commonly assumed that the ball will roll during the bounce, in which case one can show that the ratio of the horizontal speed after the bounce to that before the bounce will be 0.645 regardless of the angle of incidence or the speed of the court. Measurements are presented showing that (a) at high angles of incidence, tennis balls grip or ‘bite’ the court but they do not roll during the bounce, (b) the bounce:speed ratio can be as low as 0.4 on some courts and (c) the normal reaction force acts through a point ahead of the centre of mass. An interesting consequence is that, if court A is faster than court B at low angles of incidence, then A is not necessarily faster than B at high angles of incidence. An exception is a clay court which remains slow at all angles of incidence. The measurements also show that the coefficient of restitution for a tennis ball can be as high as 0.9 for an oblique bounce on a slow court, meaning that the ball bounces like a superball in the vertical direction and that slow courts are fast in the vertical direction.     

Tennis ball diameter: the effect on performance and the concurrent physiological responses

The aim of this study was to examine the influence of a pressurized tennis ball 6% greater in diameter (Type 3) than a standard sized (Type 2) ball on performance and the physiological responses to the Loughborough Intermittent Tennis Test (LITT) (Davey et al., 2002). Eight competitive tennis players (males, n = 4, age 24.8+/-3.5 years, body mass 81.3+/-3.1 kg, height 1.74+/-0.02 m, estimated VO2max 54.4+/-2.6 ml x kg(-1) min(-1); females, n = 4, age 26.3+/-3.1 years, body mass 67.0+/-6.7 kg, height 1.68 + 0.02 m, estimated VO2max 49.9+/-3.3 ml kg(-1) min(-1); mean+/-s(x)) completed two main trials of the LITT with either the Type 2 or Type 3 tennis balls to the point of volitional fatigue. The mean time to volitional fatigue was 29.5% greater during the Type 3 trials than during the Type 2 trials (56.9+/-6.4 min vs 40.1+/-3.7 min; P < 0.05). The mean percentage accuracy and mean percentage consistency recorded for the entire LITT were greater for the Type 3 than the Type 2 trials (9.2+/-1.5 vs 4.0+/-0.3% and 61.1+/-0.6 vs 51.3+/-0.6%, respectively; P < 0.01). A significantly lower mean heart rate and blood lactate concentration were observed during the Type 3 than during the Type 2 trials. There was a clear effect of ball diameter on tennis performance and certain physiological responses.     

The effect of ball compression on the match-play characteristics of elite junior tennis players

The purpose of this article was to examine the effect of equipment scaling, through the modification of tennis ball compression, on elite junior tennis players (aged 10 years) within a match-play context. The two types of ball compressions that were compared were the standard compression (the normal ball) and 75% compression (termed the modified ball). Ten boys and 10 girls participated in the study. Participants were stratified into pairs based on their Australian Age Ranking and gender. Each pair played two two-set matches: one match with standard compression balls and one match with modified balls. The characteristics of each match were analysed and compared. The results showed that the use of the modified ball increased rally speed, allowed players to strike the ball at a lower (more comfortable) height on their groundstrokes and increased the number of balls played at the net. Ball compression had no effect on the relative number of winners, forehands, backhands, first serves in and double faults. The results are discussed in relation to skill acquisition for skilled junior tennis players.     

Variability of impact kinematics and margin for error in the tennis forehand of advanced players

The kinematics of the racket and ball near impact in tennis forehands were studied to document typical variation in successful and unsuccessful shots, in order to determine biomechanically meaningful differences in advanced players and confirm models of groundstroke trajectories. Seven tennis players (six males and one female) were videoed from the side at 180 Hz as they performed 40 forehand drives on an indoor tennis court. Vertical plane kinematics of the racket and ball near impact were analysed for sub samples of successful and unsuccessful shots for each subject. Most racket kinematic variables were very consistent (mean CV< 6.3%) for successful shots, so bio mechanically meaningful differences in angles and velocities of the racket and ball (3° and 2 m s⁻¹) near impact could be detected between successful and unsuccessful shots. Four subjects tended to miss long and three subjects missed shots in the net that were reflected in initial ball trajectories. Mean (SD) initial trajectories for long shots were 9.8° (1.4°), while netted shots were 0.7° (1.1°) above the horizontal. The initial ball trajectories and margins for error for these subjects were smaller than those previously reported (Brody, 1987) because players tended to select mean ball trajectories close to one error than another, differing amounts of topspin, or incorrect lift and drag coefficients for tennis balls had not been published when this model was created. The present data can be used to confirm if recent models (Cookeet al., 2003; Dignallet al., 2004) more closely match actual performance by advanced players.     

Physiological responses and bowling performance during repeated spells of medium-fast bowling

The aim of the present study was to investigate the relationship between physiological and performance responses during repeated 6-over fast-bowling spells. Six, first-class, medium-fast bowlers performed 2x6-over spells separated by 45 min of light activity. The 6-over spells were based on the Cricket Australia fast bowling skills test that is a set order of deliveries at a grid-based target. Ball speed, accuracy and full and final 5-m run-up speed were measured on each ball. Nude mass, heart rate, core temperature, capillary blood lactate, pH and glucose, perceptual measures of RPE and muscle soreness (MS) and repeated vertical jump efforts were measured prior to, during and following each spell. Results indicated no decrement (P=0.41) and small effect sizes (d<0.2) in bowling speed (125.7+/-5.1 and 125.4+/-4.5 km.h(-1)) or accuracy (40.4+/-16.1 and 41.6+/-18.0 AU) between spells 1 and 2. No differences (P=0.6-0.8) were present between spells for heart rate, core temperature, lactate, pH, glucose, RPE, MS or vertical jump. Only final 5-m run-up speed showed a large correlation with ball speed (r=0.70), while accuracy and speed were not correlated (r=0.05). In conclusion, repeated 6-over spells in well-trained bowlers results in minimal performance decrement in mild conditions (22 degrees C). As faster bowlers had faster final 5-m run-up speeds, the maintenance of high final 5-m run-up speeds might be important to maintaining bowling speed. Future research should also include a third bowling spell and warmer environmental conditions.     

Measurements of drag and lift on tennis balls in flight

Measurements are presented of drag and lift on new tennis balls in flight. Two video cameras were used to measure the velocity and height of the balls at two positions separated horizontally by 6.4 m. The balls were fired from a ball launcher at speeds between 15 and 30 m/s and with topspin or backspin at rates up to 2,500 rpm. Significant shot-to-shot variations were found in both the drag and lift coefficients. The average drag coefficient was 0.507 ± 0.024, independent of ball speed or spin, and lower than the value usually observed in wind tunnel experiments. The lift coefficient increased with ball spin, on average, but significant lift was observed even at very low spin. The latter effect can be attributed to a side force arising from asymmetries in the ball surface, analogous to the side force responsible for the erratic path of a knuckleball in baseball.     

Fatigue decreases skilled tennis performance

The aim of this study was to examine the effect of fatigue from maximal tennis hitting on skilled tennis performance. Eighteen senior county tennis players (9 males, 9 females) volunteered to participate in the study. Their mean (+/- s(mean)) age and body mass were as follows: males 20.7 +/- 0.9 years and 60.6 +/- 2.7 kg respectively, females 21.7 +/- 0.6 years and 71.5 +/- 1.8 kg respectively. The players undertook two performance tests, both against a tennis ball serving machine, on an indoor tennis surface: (1) a pre- and post-skill test of groundstrokes and service; (2) the Loughborough Intermittent Tennis Test (4 min work plus 40 s recovery) to volitional fatigue. Body mass decreased by 1.5% (P < 0.0001). Mean heart rates differed between rest, post-warm-up and all intermittent test values (P < 0.01), between the pre- and post-skill tests (P < 0.0001) and between bouts and recoveries (P < 0.01). Peak blood glucose and lactate concentrations were 5.9 mmol l(-1) (50% into the intermittent tennis test) and 9.6 +/- 0.9 mmol x l(-1) (25% into the test) respectively. Mean time to volitional fatigue was 35.4 +/- 4.6 min. Groundstroke hitting accuracy decreased by 69% from start to volitional fatigue in the intermittent test (P < 0.01). Service accuracy to the right court declined by 30% after the intermittent tennis test. The results of this study suggest that fatigue was accompanied by a decline in some but not all tennis skills.