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.     

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.     

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

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.     

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.     

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.     

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.     

直拍横打技术对广东高校乒乓球教学的启示

通过对第49届世界乒乓球锦标赛团体赛马琳对柳承敏的录像分析,发现双方均是直拍快攻型选手,而马琳反手是推挡加横打型,柳承敏反手是推挡加攻球型,马琳的直拍横打优于柳承敏的反手推挡,直拍横打解决了直拍运动员反手攻击力不强的问题,直拍近台快攻打法有强大的生命力。结合广东部分高校体育专业乒乓球班学生与普通系乒乓球班学生的现状进行分析,访谈了广东高校一些乒乓球教师,结果表明,广东高校乒乓球直拍横打的发展比较滞后,应该在乒乓球教学中采取措施开展直拍横打,方能使乒乓球的群众性运动进一步发展。     

Effects of neuromuscular function and split step on reaction speed in simulated tennis response

Abstract

The purpose of this study was to examine whether split step (small hop before step) would be more beneficial than no-split condition in simulated tennis response situation. In addition, it was studied if movement time of the response is related to separately measured force production capabilities and reflex sensitivity of the players. Nine skilled male tennis players participated in this study. Subjects stood on a force plate and reacted to a light signal and moved to appointed direction as fast as possible. With split step the participants were 13.1% faster (P <0.05) than without split step from the start to the distal end of the so called close range movement continuum (2.70 m). This was mainly explained by 43.6% faster time (P <0.05) from the signal to the onset of force production. Greater vertical forces were observed with split step: 15.7% greater F(z) mean force (P <0.05), 60.0% greater F(z) peak force (P<0.01). In split step both mean (r= ? 0.813, P <0.01) and peak (r=?0.765, P <0.05) vertical forces (Fz) correlated negatively with the time from the onset of the force production to the photocell. With split step higher EMGs were observed in muscles responsible for ankle joint movement indicating that different strategies were used. Due to the split step the players were able to start the movement faster which mostly explains the advantages over the no-split step condition. Split step condition may also benefit from stretch shortening type of muscle action.     

女子乒乓球运动员横拍反手生胶的接发球技术

对4名现役优秀女子横拍反手生胶打法运动员接发球技术进行统计分析,结果显示:4名运动员反手接发球的比例高达93.2%～100%,其命中率高达82.9%～98.0%,但其直接得失分率都很低,分别为0～7.3%和2.0%～17.1%.在处理台内球的技术应用中,弹击技术的使用率均为零,接发球落点位置50%以上都在对方反手位,落点在对方正手位的比例均为零.因此,这几名运动员反手接发球使用率高,侧身正手接发球使用率却很低.反手接发球失误少,但很难直接得分.     

A three-dimensional analysis of the contributions of upper limb joint movements to horizontal racket head velocity at ball impact during tennis serving

In this study, we examined the relationship between upper limb joint movements and horizontal racket head velocity to clarify joint movements for developing racket head speed during tennis serving. Sixty-six male tennis players were videotaped at 200 Hz using two high-speed video cameras while hitting high-speed serves. The contributions of each joint rotation to horizontal racket velocity were calculated using vector cross-products between the angular velocity vectors of each joint movement and relative position vectors from each joint to the racket head. Major contributors to horizontal racket head velocity at ball impact were shoulder internal rotation (41.1%) and wrist palmar flexion (31.7%). The contribution of internal rotation showed a significant positive correlation with horizontal racket head velocity at impact (r = 0.490, P < 0.001), while the contribution of palmar flexion showed a significant negative correlation (r = - 0.431, P < 0.001). The joint movement producing the difference in horizontal racket head velocity between fast and slow servers was shoulder internal rotation, and angular velocity of shoulder internal rotation must be developed to produce a high racket speed.     

Measurement of badminton racket deflection during a stroke

The compliance of a badminton racket is an important design consideration, which can be better understood by studying the deflection behaviour of the racket during a stroke. Deflection can be measured using direct methods, such as motion capture or high speed video, or by indirect methods, which then require a mathematical model in order to calculate the deflections from indirect measures. Indirect methods include strain gauges and accelerometers. Here, racket deflection is measured directly using motion capture and compared with deflections calculated from strain gauge data using a beam model. While the elastic behaviour is better calculated from strains than measured by motion capture, it is not possible to extract the whole motion of the racket from strain data. Motion capture is therefore also necessary to determine the rigid body velocity, in order to put the elastic velocity (as calculated from strains) in perspective.     

乒乓球正手快攻和弧圈球技术中球拍的运动学特征

对10名乒乓球运动员正手快攻、弧圈球技术(每种技术分中等力量和最大力量两种发力方式)进行测试与分析后发现,重打和重拉的引拍结束时刻的球拍速度分别大于轻打和轻拉.在击球时刻,轻打的速度小于重打,轻拉的速度小于重拉,重打的速度小于重拉;正手弧圈球技术的总时间长于正手快攻技术;拉的幅度大于打的幅度.     

系绳网球回弹器对网球初学者练习的影响

网球教学初期,学习者会选择不同的方法去掌握网球技能与技术.对于目前市场上出现的网球教学辅助器材来说,系绳网球回弹器是最常见的一种,仅对此类型的教辅器材进行分析与评价,提出合理化建议.