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).     

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.     

Theoretical Modeling of Grip Firmness during Ball-Racket Impact

Abstract

This study was undertaken to establish theoretical bases for the experimental results reported by Baker and Putnam (1979), and Walanabe, Ikegami and Miyashita (1979), concerning grip firmness on a tennis racket and its effect on the ratio of post- to pre-impact ball velocity. The model predicted that, for central impacts, there was no change in the ball velocity ratio when a regular tennis racket was tightly clamped at the grip or allowed to freely stand on its butt. To validate the model further, alterations were made to two parameters of the racket—a tennis racket was modified to increase the stiffness, and a racketball racket was used to simulate a shortened tennis racket. Multiple exposure photographs were taken of balls striking the center of the rackets under the two extremes of grip firmness. Measurements were taken from enlargements of these photographs in order to calculate the horizontal component of post- to pre-impact ball velocity. It was found that shortening the length and greatly increasing the stiffness was required before the effect of grip firmness was noticeable.     

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.     

Comparison of a finite element model of a tennis racket to experimental data

Modern tennis rackets are manufactured from composite materials with high stiffness-to-weight ratios. In this paper, a finite element (FE) model was constructed to simulate an impact of a tennis ball on a freely suspended racket. The FE model was in good agreement with experimental data collected in a laboratory. The model showed racket stiffness to have no influence on the rebound characteristics of the ball, when simulating oblique spinning impacts at the geometric stringbed centre. The rebound velocity and topspin of the ball increased with the resultant impact velocity. It is likely that the maximum speed at which a player can swing a racket will increase as the moment of inertia (swingweight) decreases. Therefore, a player has the capacity to hit the ball faster, and with more topspin, when using a racket with a low swingweight.     

A Determination of Velocities and Angles of Projection for the Tennis Serve

Abstract

The purpose of this study was to determine the minimum and maximum velocity of the tennis ball for selected heights of contact and angles of projection and wall impact points during the tennis serve. By use of a ballistics formula, a number of variables which determine the trajectory of the tennis ball were programed for the computer. Tables were tabulated and are available for all data gathered. Angles of projection from the horizontal were selected to range from ?5° to 15° in increments of 1°. Velocity of the serve ranged from a low of 30 ft. per second to a high of 176 ft. per second. Finally, the height of the contact point ranged from a low of 6.0 ft. to a high of 9.0 ft. in increments of .5 ft. Height of the ball when crossing the net (impact point on the practice court) ranged from a low of 3.01 ft. to a high of 8.47 ft. The minimum height at crossing was achieved at 6.5 ft. service height, a ?3° angle of projection and time from baseline of .30 sec. This is a relatively high velocity serve. In contrast, the maximum height over the net of 8.47 ft. was achieved at an 8.5 ft. service height, a 15° angle of projection, and time of .79 sec. to point of impact. These data indicate that at higher service heights and slower velocities, a ball can hit the impact area as much as 8.47 ft. from the floor, 4.47 ft. above the net and still remain in the service court.     

Vibration and Rebound Velocity Characteristics of Conventional and Oversized Tennis Rackets

Abstract

Stroboscope photography and accelerometry techniques were used to measure rebound velocities of tennis balls from impact locations on the strings and vibration levels at the rotation point on the racket handle for both conventional and oversized tennis rackets. The oversized rackets demonstrated lower vibration levels and higher rebound velocities than their conventional counterparts when balls struck by the racket were compared along a transverse axis drawn perpendicular to the racket shaft and through the geometric center of the strings. These differences were, however, only significantly different (p < .01) at the impact location 6 cm along this axis toward the top edge of the racket. Higher rebound velocities were recorded at all impact points from the oversized rackets along the axis in line with the racket shaft. Significantly lower vibration levels were apparent at locations 4 cm, 6 cm, and 8 cm from the string center away from the racket handle. The lower vibration levels, particularly at the extremes of the racket face, in conjunction with higher rebound velocities, support the concept that this new racket design is of practical benefit to users.     

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.     

Oblique impact of a tennis ball on the strings of a tennis racket

Measurements are presented of the friction force acting on a tennis ball incident obliquely on the strings of a tennis racket. This information, when combined with measurements of ball speed and spin, reveals details of the bounce process that have not previously been observed and also provides the first measurements of the coefficient of sliding friction between a tennis ball and the strings of a tennis racket. At angles of incidence less than about 40° to the string plane, the ball slides across the strings during the whole bounce period. More commonly, the ball is incident at larger angles in which case the ball slides across the string plane for a short distance before gripping the strings. While the bottom of the ball remains at rest on the strings, the remainder of the ball continues to rotate for a short period, after which the ball suddenly releases its grip and the bottom of the ball slides backwards on the string plane. The bounce angle depends mainly on the angle of incidence and the rotation speed of the incident ball. Differences in bounce angle and spin off head-clamped and hand-held rackets are also described.     

Experimental and finite element analysis of a tennis ball impact on a rigid surface

An explicit finite-element (FE) model of a pressurised tennis ball is presented. The FE model was used to model an oblique impact between a tennis ball and a rigid tennis surface, to further the understanding of this impact. Impacts were also conducted in the laboratory and the results from the FE model were in good agreement with this experimental data. The FE model was used to illustrate why a tennis ball rebounds with a higher vertical coefficient of restitution in an oblique impact compared to an equivalent impact perpendicular to the surface; this equivalent perpendicular impact has the same inbound velocity as the vertical component of the oblique impact. The FE model was also used to illustrate that the structural compliance of the felt covering on a tennis ball was a contributing factor to the ball attaining more spin in the impact than would have been calculated using a conventional analytical model. Also, the spin values calculated in the FE simulation were in good agreement with experimental data.     

Kinematics of table tennis topspin forehands: effects of performance level and ball spin

Abstract

The purpose of this study was to investigate whether performance level and ball spin affect arm and racket kinematics of the table tennis topspin forehand. Nine advanced and eight intermediate male table tennis players hit topspin forehands against light and heavy backspins. Five high-speed video cameras were used to record their strokes at 200 fps. Contributions of joint rotations to the racket speed, the racket kinematics at ball impact, the time required for racket acceleration and the maximum slope of the racket speed-time curve (s _max) were determined. The advanced players showed a significantly larger contribution of lower trunk axial rotation to the racket speed at impact and a significantly larger value of s_max, and tended to require a less time for racket acceleration than the intermediate players. The racket speed at impact was not significantly different between the two player groups. The players adjusted the racket face angle rather than the inclination of the racket path at impact to the different ball spins. The results suggest that the ability to accelerate the racket in less time in the topspin forehand against backspin balls may be an important factor that affects the performance level.     

A kinematic comparison between long-line and cross-court top spin forehand in competitive table tennis players

ABSTRACT

The aim of the present study was to compare the biomechanical characteristics of the table tennis top spin shot when played cross-court (CC) or long-line (LL) in competitive table tennis players. Seven national level players respectively completed 10 long-line and 10 cross-court top spin shots responding to a standard ball machine. A stereophotogrammetric system was used to track body segments while executing the motion. Significantly more flexed right knee and elbow angles were measured at the moment of maximum velocity of the racket (MMV) in LL. In addition, significantly greater angles between the feet and the table and between the shoulders and the table at the MMV, indicated more pronounced rotation angles of the lower upper and upper-body in LL compared to CC with respect to the table. A higher inclination of the racket at the MMV was found in LL. The elbow flexion and the racket inclination may be associated to the direction of the shot. The present findings show that kinematic differences exist between the LL and the CC topspin forehand in competitive table tennis players. Coaches should be aware of these differences to adopt the optimal teaching strategies and to reproduce proper joint angles during training.     

The influence of club-head kinematics on early ball flight characteristics in the golf drive

Despite many coaching and biomechanical texts describing how the kinematics of the club-head at impact lead to distance and accuracy of the ball flight, there is limited quantitative evidence supporting these assertions. The purpose of this study was to quantify the relationships between club-head kinematics and subsequent early ball flight characteristics during the golf drive. An opto-reflective system operating at 400 Hz was used to capture the swings of 21 male golfers using their own drivers. The 3D displacement data permitted the calculation of club-head kinematics at impact, as well as subsequent early ball flight characteristics. Using regression analyses, club-head kinematics at impact (velocity, orientation, path, and centeredness) were used to explain the variability in five dependent variables of early ball flight characteristics (resultant velocity, launch angle, side angle, back spin, and side spin). The results of the study indicated that club-head kinematics at impact explained a significant proportion of early ball flight characteristics (adjusted r ² = 0.71–0.82), even when generalized across individual clubs.     

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.     

Effect of tennis racket parameters on a simulated groundstroke

Composite materials have given manufacturers the freedom to develop a broad range of tennis rackets, allowing them to change key parameters such as the structural stiffness, mass, and position of the balance point. The aim of this research was to determine how changing these parameters could affect ball resultant rebound velocity and spin for a simulated groundstroke. A finite element model of a freely suspended racket and strings was used to determine the effect of racket parameters for oblique spinning impacts at a range of locations on the stringbed. The finite element simulations were conducted in the laboratory frame of reference, where the ball is projected onto an initially stationary racket. The mean rebound velocity of the ball was 9% higher for a structurally stiff racket, 37% higher for a heavy racket, and 32% higher for a head-heavy racket. In addition, the mean rebound topspin of the ball was 23% higher for a heavy racket and 21% higher for a head-heavy racket. Therefore, in relation to a groundstroke with an impact location away from the node, the rebound velocity of the ball is likely to increase with the structural stiffness of a racket. The effect of changing the mass and position of the balance point is more complex, as it is dependent on the relationship between the transverse moment of inertia and maximum pre-impact swing velocity.     

Visual Search and Biological Motion Perception in Tennis

Purpose

The purposes of this study were to: (a) examine the effect of experience and goal constraints (speed, accuracy) on kicking patterns; (b) determine if effective striking mass was independent of ankle velocity at impact; and (c) determine the accuracy of kicks relative to independent factors.

Method

Twenty participants were recruited to kick at 3 different velocities with and without an accuracy requirement. Multivariate analysis of variance determined if relative timing of joint angular velocities changed during the kick. Chi-square analysis determined if calculated effective mass was independent of ankle velocity at impact. Analysis of variance (ANOVA) was used to examine differences in absolute constant error and variable error according to independent factors.

Results

Results indicated that experience and speed affect absolute timing of joint velocities with no changes in the relative timing of peak joint velocity across independent factors. Chi-square analysis indicated that calculated effective mass is not independent of ankle velocity. ANOVA indicated that experienced performers displayed less variability error than did inexperienced performers.

Conclusion

It was concluded that: (a) Experience, velocity, and accuracy do not affect the relative timing of kicks; (b) kickers trade ankle velocity at impact for greater effective striking mass and ball velocity; and (c) variability in ball placement is affected by experience.     

Carbon outclasses wood in racket paddles: Ratings of expert and intermediate tennis players

Abstract

Wooden racket paddles were modified with rubber and carbon fibre laminates and their differences tested in terms of flexural, damping, and coefficient of restitution properties. Four rackets types were designed: a wood reference, wood with rubber, carbon fibre 0°, and carbon fibre 90°. Seven expert and eight intermediate tennis players tested the rackets. To determine which of the four rackets suited the players best, we asked the players to compare the rackets two by two. After each pair tested, participants had to fill out a 4-item questionnaire in which different aspects of the rackets' performance were judged. The most preferred racket was the 0° carbon fibre racket, followed by the 90° carbon fibre racket, the wood racket and, finally, the 1-mm rubber racket. Thus, rackets with the highest stiffness, least damping, and highest coefficient of restitution were the most preferred. Interestingly, although experts and intermediate players overall judged the rackets in very similar ways according to force, vibration, and control, they were sensitive to quite different physical characteristics of the rackets.     

Effect of the racket mass and the rate of strokes on kinematics and kinetics in the table tennis topspin backhand

The purpose of this study was to investigate the effect of the racket mass and the rate of strokes on the kinematics and kinetics of the trunk and the racket arm in the table tennis topspin backhand. Eight male Division I collegiate table tennis players hit topspin backhands against topspin balls projected at 75 balls · min^?1 and 35 balls · min^?1 using three rackets varying in mass of 153.5, 176 and 201.5 g. A motion capture system was used to obtain trunk and racket arm motion data. The joint torques of the racket arm were determined using inverse dynamics. The racket mass did not significantly affect all the trunk and racket arm kinematics and kinetics examined except for the wrist dorsiflexion torque, which was significantly larger for the large mass racket than for the small mass racket. The racket speed at impact was significantly lower for the high ball frequency than for the low ball frequency. This was probably because pelvis and upper trunk axial rotations tended to be more restricted for the high ball frequency. The result highlights one of the advantages of playing close to the table and making the rally speed fast.     

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.