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.     

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.     

Effect of string bed pattern on ball spin generation from a tennis racket

Topspin has become a vital component of modern day tennis. Ball-to-string bed and inter-string friction coefficients can affect topspin generation from a racket. The aim of this research was to determine the effect of string bed pattern on topspin generation. Tennis balls were projected onto nine head-clamped rackets with different string bed patterns. The balls were fired at 24 m/s, at an angle of 26° to the string bed normal with a backspin rate of 218 rad/s and outbound velocity, spin and angle were measured. Outbound velocity was shown to be independent of string bed pattern. Outbound angle increased with the number of cross strings, while outbound topspin decreased. In the most extreme case, decreasing the number of cross strings from 19 to 13 increased rebound topspin from 117 to 170 rad/s.     

乒乓球与球拍之间的摩擦

现代乒乓球运动中几乎所有技术都要借助于摩擦。制造旋转时，球拍与球之间的摩擦主要是静摩擦和滚动摩擦，它们的作用效果互不相同。静摩擦不但使乒乓球产生旋转，也使乒乓球产生平动；滚动摩擦则不利于乒乓球运动中制造旋转。静摩擦与滚动摩擦都是随时间变化的量，且两者的大小与多种因素有关。     

The effects of player grip on the dynamic behaviour of a tennis racket

The aim of this article is to characterise the extent to which the dynamic behaviour of a tennis racket is dependent on its mechanical characteristics and the modulation of the player’s grip force. This problem is addressed through steps involving both experiment and modelling. The first step was a free boundary condition modal analysis on five commercial rackets. Operational modal analyses were carried out under “slight”, “medium” and “strong” grip force conditions. Modal frequencies and damping factors were then obtained using a high-resolution method. Results indicated that the dynamic behaviour of a racket is not only determined by its mechanical characteristics, but is also highly dependent on the player’s grip force. Depending on the grip force intensity, the first two bending modes and the first torsional mode frequencies respectively decreased and increased while damping factors increased. The second step considered the design of a phenomenological hand-gripped racket model. This model is fruitful in that it easily predicts the potential variations in a racket’s dynamic behaviour according to the player’s grip force. These results provide a new perspective on the player/racket interaction optimisation by revealing how grip force can drive racket dynamic behaviour, and hence underlining the necessity of taking the player into account in the racket design process.     

Effect of skill decomposition on racket and ball kinematics of the elite junior tennis serve

Whole body kinematics of the tennis serve have been reported extensively in the literature, yet comparatively less information exists regarding the kinematic characteristics of the swing and toss. In attempting to develop consistency in placement of the toss and racket trajectory, coaches will often decompose the serve and practice it in separate parts. A 22-camera VICON MX motion analysis system, operating at 250 Hz, captured racket, ball and hand kinematics of the serves of five elite junior players under three conditions. The conditions were flat first serves (FS) directed to a 1 x 1 m target bordering the 'T' of the deuce service box, a ball toss (BT) in isolation and a free swing (SW) in isolation. Players were instructed to perform BT and SW as in the FS. Paired t-tests assessed within-group differences in hand, racket and ball kinematics between the discrete skill and the two decomposed conditions. Vertical displacement of the ball at its zenith increased significantly during BT compared with the FS and temporal associations between racket and ball motion during the FS (r = 0.861) were affected during task decomposition. This study questions the pervasive use of task decomposition in the development of the tennis serve.     

The effect of tennis racket string vibration dampers on racket handle vibrations and discomfort following impacts.

In this study, we evaluated the effect of the use of tennis racket string vibration dampers on racket handle vibrations, and perceptions of hand and arm discomfort experienced by tennis players owing to stationary racket impacts. Twenty tennis players (10 males, 10 females) aged 18-29 years volunteered for the study. Two different racket models were impacted at the geometric centre of the racket face and 100 mm distal to the centre both with and without string vibration dampers in place. The participants could neither see nor hear the impacts, and they indicated their discomfort immediately after each impact using a visual analogue scale. An analysis of variance (2 x 2 x 2 factorial) was performed on the scaled discomfort ratings with the factors damping condition, racket type and impact location. No significant differences in discomfort ratings between damped and undamped impacts or between the two racket types were found. Also, central impacts were found to be more comfortable than impacts 100 mm distal to the centre (P< 0.05). There were no significant interaction effects. Vibration traces from an accelerometer mounted on the racket handle revealed that string vibration dampers quickly absorbed high-frequency string vibration without attenuating the lower-frequency frame vibration. In conclusion, we found no evidence to support the contention that string vibration dampers reduce hand and arm impact discomfort.     

Effect of skill decomposition on racket and ball kinematics of the elite junior tennis serve

Whole body kinematics of the tennis serve have been reported extensively in the literature, yet comparatively less information exists regarding the kinematic characteristics of the swing and toss. In attempting to develop consistency in placement of the toss and racket trajectory, coaches will often decompose the serve and practice it in separate parts. A 22-camera VICON MX motion analysis system, operating at 250 Hz, captured racket, ball and hand kinematics of the serves of five elite junior players under three conditions. The conditions were flat first serves (FS) directed to a 1 × 1 m target bordering the ‘T’ of the deuce service box, a ball toss (BT) in isolation and a free swing (SW) in isolation. Players were instructed to perform BT and SW as in the FS. Paired t-tests assessed within-group differences in hand, racket and ball kinematics between the discrete skill and the two decomposed conditions. Vertical displacement of the ball at its zenith increased significantly during BT compared with the FS and temporal associations between racket and ball motion during the FS (r = 0.861) were affected during task decomposition. This study questions the pervasive use of task decomposition in the development of the tennis serve.     

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 computer simulation model of tennis racket/ball impacts

A forward dynamics computer simulation for replicating tennis racket/ball impacts is described consisting of two rigid segments coupled with two degrees of rotational freedom for the racket frame, nine equally spaced point masses connected by 24 visco-elastic springs for the string-bed and a point mass visco-elastic ball model. The first and second modal responses both in and perpendicular to the racket string-bed plane have been reproduced for two contrasting racket frames, each strung at a high and a low tension. Ball/string-bed normal impact simulations of real impacts at nine locations on each string-bed and six different initial ball velocities resulted in <3% RMS error in rebound velocity (over the 16–27 m/s range observed). The RMS difference between simulated and measured oblique impact rebound angles across nine impact locations was 1°. Thus, careful measurement of ball and racket characteristics to configure the model parameters enables researchers to accurately introduce ball impact at different locations and subsequent modal response of the tennis racket to rigid body simulations of tennis strokes without punitive computational cost.     

Single view silhouette fitting techniques for estimating tennis racket position

Stereo camera systems have been used to track markers attached to a racket, allowing its position to be obtained in three-dimensional (3D) space. Typically, markers are manually selected on the image plane, but this can be time-consuming. A markerless system based on one stationary camera estimating 3D racket position data is desirable for research and play. The markerless method presented in this paper relies on a set of racket silhouette views in a common reference frame captured with a calibrated camera and a silhouette of a racket captured with a camera whose relative pose is outside the common reference frame. The aim of this paper is to provide validation of these single view fitting techniques to estimate the pose of a tennis racket. This includes the development of a calibration method to provide the relative pose of a stationary camera with respect to a racket. Mean static racket position was reconstructed to within ±2 mm. Computer generated camera poses and silhouette views of a full size racket model were used to demonstrate the potential of the method to estimate 3D racket position during a simplified serve scenario. From a camera distance of 14 m, 3D racket position was estimated providing a spatial accuracy of 1.9 ± 0.14 mm, similar to recent 3D video marker tracking studies of tennis.     

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.     

乒乓球击球瞬间球拍形变力的实验研究

在击球时,乒乓球拍会产生一定的形变,其形变的大小反映了球拍受力的大小.运用动态应变测试系统测量了不同技术击球时球拍拍柄根部应变力的大小,结果表明:采用摩擦击球的方式击球,球拍形变幅度较大,获得的形变力也较大;撞击球的方式击球,球拍形变幅度小,震动较大,球拍击球瞬间所受的作用力时间相对较短.     

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

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.     

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.     

Hip joint kinetics in the table tennis topspin forehand: relationship to racket velocity

The purpose of this study was to determine hip joint kinetics during a table tennis topspin forehand, and to investigate the relationship between the relevant kinematic and kinetic variables and the racket horizontal and vertical velocities at ball impact. Eighteen male advanced table tennis players hit cross-court topspin forehands against backspin balls. The hip joint torque and force components around the pelvis coordinate system were determined using inverse dynamics. Furthermore, the work done on the pelvis by these components was also determined. The peak pelvis axial rotation velocity and the work done by the playing side hip pelvis axial rotation torque were positively related to the racket horizontal velocity at impact. The sum of the work done on the pelvis by the backward tilt torques and the upward joint forces was positively related to the racket vertical velocity at impact. The results suggest that the playing side hip pelvis axial rotation torque exertion is important for acquiring a high racket horizontal velocity at impact. The pelvis backward tilt torques and upward joint forces at both hip joints collectively contribute to the generation of the racket vertical velocity, and the mechanism for acquiring the vertical velocity may vary among players.     

Mechanical energy generation and transfer in the racket arm during table tennis topspin backhands

The ability to generate a high racket speed and a large amount of racket kinetic energy on impact is important for table tennis players. The purpose of this study was to understand how mechanical energy is generated and transferred in the racket arm during table tennis backhands. Ten male advanced right-handed table tennis players hit topspin backhands against pre-impact topspin and backspin balls. The joint kinetics at the shoulder, elbow and wrist of the racket arm was determined using inverse dynamics. A majority of the mechanical energy of the racket arm acquired during forward swing (65 and 77% against topspin and backspin, respectively) was due to energy transfer from the trunk. Energy transfer by the shoulder joint force in the vertical direction was the largest contributor to the mechanical energy of the racket arm against both spins and was greater against backspin than against topspin (34 and 28%, respectively). The shoulder joint force directed to the right, which peaked just before impact, transferred additional energy to the racket. Our results suggest that the upward thrust of the shoulder and the late timing of the axial rotation of the upper trunk are important for an effective topspin backhand.     

Contributions of upper limb rotations to racket velocity in table tennis backhands against topspin and backspin

The purpose of this study was to assess the contributions of racket arm joint rotations to the racket tip velocity at ball impact in table tennis topspin backhands against topspin and backspin using the method of Sprigings et al. (1994). Two cine cameras were used to determine three-dimensional motions of the racket arm and racket, and the contributions of the rotations for 11 male advanced table tennis players. The racket upward velocity at impact was significantly higher in the backhand against backspin than against topspin, while the forward velocity was not significantly different between the two types of backhands. The negative contribution of elbow extension to the upward velocity was significantly less against backspin than against topspin. The contribution of wrist dorsiflexion to the upward velocity was significantly greater against backspin than against topspin. The magnitudes of the angular velocities of elbow extension and wrist dorsiflexion at impact were both similar between the two types of backhands. Our results suggest that the differences in contributions of elbow extension and wrist dorsiflexion to the upward velocity were associated with the difference in upper limb configuration rather than in magnitudes of their angular velocities.     

The effect of ball impact location on racket and forearm joint angle changes for one-handed tennis backhand groundstrokes

Recreational tennis players tend to have higher incidence of tennis elbow, and this has been hypothesised to be related to one-handed backhand technique and off-centre ball impacts on the racket face. This study aimed to investigate for a range of participants the effect of off-longitudinal axis and off-lateral axis ball–racket impact locations on racket and forearm joint angle changes immediately following impact in one-handed tennis backhand groundstrokes. Three-dimensional racket and wrist angular kinematic data were recorded for 14 university tennis players each performing 30 “flat” one-handed backhand groundstrokes. Off-longitudinal axis ball–racket impact locations explained over 70% of the variation in racket rotation about the longitudinal axis and wrist flexion/extension angles during the 30 ms immediately following impact. Off-lateral axis ball–racket impact locations had a less clear cut influence on racket and forearm rotations. Specifically off-longitudinal impacts below the longitudinal axis forced the wrist into flexion for all participants with there being between 11° and 32° of forced wrist flexion for an off-longitudinal axis impact that was 1 ball diameter away from the midline. This study has confirmed that off-longitudinal impacts below the longitudinal axis contribute to forced wrist flexion and eccentric stretch of the wrist extensors and there can be large differences in the amount of forced wrist flexion from individual to individual and between strokes with different impact locations.     

Serving to different locations: set-up, toss, and racket kinematics of the professional tennis serve

The serve, as the most important stroke in tennis, has attracted considerable biomechanical interest. Of its component parts, the swing has received disproportionate research attention and consequently, little is known regarding toss kinematics. Indeed, the age-old question of whether players serve to different parts of the court from the same toss remains unanswered. Six right-handed professionally ranked players hit first serves (FSs) and second serves (SSs) to three 2 x 1 m target areas reflecting the landing locations of T, body and wide serves, respectively, on the deuce court. A 22 camera, 250 Hz VICON MX motion analysis system captured racket, ball, foot, and h and kinematics. Repeated measures ANOVAs assessed within-player differences in foot, racket, and ball kinematics within the FS and SS as a function of landing location. The positions of the front foot, ball zenith, and ball impact were significantly different in the FS, while kinematics across all SS were consistent. Front foot position was closer to the centre mark in the T FS and players impacted the ball further left in the wide FS compared to the T FS. This study discusses the findings in the context of the development of the serve as well as potential implications for the return.