An investigation into the power point in tennis

This paper investigates the nature of the power point in tennis. A series of static racket impacts and a polynomial fit were used to simulate four different racket shots with increasing amounts of angular velocity—identifying the true ‘power point’ for each shot. A rigid body model was used to define the ‘ideal point’ for each shot—the impact point which theoretically yields maximum outbound ball velocity. Comparing theory with experiment revealed that the ‘ideal point’ is most accurate for impacts around the racket’s node point (the rigid body model does not account for frame vibration). Previous research has shown that tennis players aim to strike the node point of the racket. The concept of the ideal point has potential in tuning the weight distribution of a racket to a player’s shot type. If the ‘ideal point’ exists at the racket node point for a player’s typical forehand shot, then outbound ball velocities can be maximised.     

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.     

String vibration dampers do not reduce racket frame vibration transfer to the forearm

In this study, we examined the effect of string vibration damping devices on reducing racket frame vibration transfer to the forearm. Twenty participants volunteered to hold a tennis racket stationary in a forehand and backhand stroking position while tennis balls were fired at 20 m x s(-1) towards two impact locations, the node of vibration and the dead spot. A three-way analysis of variance with repeated measures on damping condition, impact location and stroke condition was performed on the data. The resonant frequency of the hand-held racket was found to be approximately 120 Hz. No significant differences in amplitude of vibration at the resonant frequency were found for the wrist or the elbow when damped and non-damped impacts were compared. Impacts at the dead spot produced greater amplitudes of vibration (P < 0.01) but no interaction between impact location and string dampers was evident. The string dampers had no effect on the grip force used or the muscle electrical activity in the forearm after impact. In conclusion, we found that string dampers do not reduce the amount of racket frame vibration received at the forearm. We suggest that string dampers remain a popular accessory among tennis players because of their acoustic effects and psychological support rather than any mechanical advantage.     

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.     

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.     

String vibration dampers do not reduce racket frame vibration transfer to the forearm

In this study, we examined the effect of string vibration damping devices on reducing racket frame vibration transfer to the forearm. Twenty participants volunteered to hold a tennis racket stationary in a forehand and backhand stroking position while tennis balls were fired at 20 m?·?s^?1 towards two impact locations, the node of vibration and the dead spot. A three-way analysis of variance with repeated measures on damping condition, impact location and stroke condition was performed on the data. The resonant frequency of the hand-held racket was found to be ～120 Hz. No significant differences in amplitude of vibration at the resonant frequency were found for the wrist or the elbow when damped and non-damped impacts were compared. Impacts at the dead spot produced greater amplitudes of vibration (P <?0.01) but no interaction between impact location and string dampers was evident. The string dampers had no effect on the grip force used or the muscle electrical activity in the forearm after impact. In conclusion, we found that string dampers do not reduce the amount of racket frame vibration received at the forearm. We suggest that string dampers remain a popular accessory among tennis players because of their acoustic effects and psychological support rather than any mechanical advantage.     

Acoustics of ping-pong: Vibroacoustic analysis of table tennis rackets and balls

ABSTRACT

The sound resulting from the impact of a table tennis racket and ball can influence a player’s perception of equipment quality in addition to providing clues to personal performance. This study explores the vibrational modes of both racket and ball and how those modes contribute to the impact sound. Experimental modal analysis reveals that the racket exhibits a large number of structural vibration modes typical of elliptical plates. Acoustic analysis reveals that two of those structural modes dominate the sound produced by the ball-paddle impact. The rubber padding provides some damping and a significant mass loading to the racket vibrations. The hollow cellulose nitrate balls exhibit vibrational modes typical of a hollow spherical shell, starting with frequencies around 5920 Hz. Experimental frequencies confirm theoretical and computational models. However, the contact time between racket and ball is long enough that the lowest acoustic modes of the ball do not contribute to the radiated sound. Instead, acoustic analysis suggests that the ball appears to radiate sound at a much higher frequency sound (8.5–12 kHz) most likely due to snap-through after buckling common to spherical shells undergoing deformation while impacting a rigid surface at high speeds.     

网球运动员目标定向与归因方式的研究

随着网球运动在中国飞速发展,网球运动的研究也成为体育领域中关注的论题。对网球运动员目标定向与归因方式的研究还比较缺乏。鉴于研究应用心理测量法对网球运动员的目标定向和归因方式进行探讨。了解中国网球运动员的目标定向及归因方式的现状,丰富运动员对目标定向和归因方式的认识。研究结果显示：网球运动员的目标定向在性别上存在显著性差异;网球运动员基本归因类型,在成功情境下为：内部的、稳定的、可控的;在失败情境下为：内部的、稳定的、不可控的;网球运动员在成功情境下的归因方式没有性别差异,在失败情境下内外源、稳定性存在性别差异;网球运动员的目标定向与归因方式的相关性不高,存在着低度相关。     

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.     

Mutual point-winning probabilities (MPW): a new performance measure for table tennis

ABSTRACT

We propose a new performance measure for table tennis players: the mutual point-winning probabilities (MPW) as server and receiver. The MPWs quantify a player’s chances to win a point against a given opponent, and hence nicely complement the classical match statistics history between two players. These new quantities are based on a Bradley-Terry-type statistical model taking into account the importance of individual points, since a rally at 8–2 in the first set is less crucial than a rally at the score of 9–9 in the final set. The MPWs hence reveal a player’s strength on his/her service against a given opponent as well as his/her capacity of scoring crucial points. We estimate the MPWs by means of maximum likelihood estimation and show via a Monte Carlo simulation study that our estimation procedure works well. In order to illustrate the MPWs’ versatile use, we have organized two round-robin tournaments of ten respectively eleven table tennis players from the Belgian table tennis federation. We compare the classical final ranking to the ranking based on MPWs, and we highlight how the MPWs shed new light on strengths and weaknesses of the players.     

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.     

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.     

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.     

Investigation of high-speed badminton racket kinematics by motion capture

The kinematics of a badminton racket during a smash stroke was observed in this study with the purpose of investigating stroke dynamics and racket behaviour. Motion capture measurements of the racket during several smash strokes performed by three players of different skill levels indicated a clear increase in racket velocity at impact with increasing skill level. Variations between translational and rotational contributions to the impact speed could also be seen between the players. The advanced player produced a much higher peak angular velocity and also relied much less on translation, with a translational velocity of only 8% of the total velocity versus the 20% for the recreational player. It is proposed that, as an alternative to shuttlecock speeds, racket head speed measurements can be used as an indicator of performance, and can also provide some insight into the interaction between the racket and player.     

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.     

网球肘的成因及诊疗进展

"网球肘",即肱骨外上髁炎,是一种以肘关节外侧疼痛为特征的肱骨外上髁部前臂伸肌总腱附着处的慢性损伤性肌筋膜炎,因网球运动员最易患此病而得名。"网球肘"的主要外在表现是肘部隐隐的酸痛感以及持拍击球时产生的强烈疼痛感。网球肘妨碍了运动员的日常生活、训练、比赛,严重者甚至影响运动员的职业生涯。本文从病理特征、致病原因、致病机理、诊疗标准、诊疗措施、预防等方面对"网球肘"这一职业病进行深入分析,以期对该病的治疗、网球运动员的正确训练起到指导作用。     

Quantitative assessment of the serve speed in tennis

A method is presented for assessing the serve speeds of tennis players based on their body height. The research involved a sample of top world players (221 males and 215 females) who participated in the Grand Slam tournaments in 2008 and 2012. The method is based on the linear regression analysis of the association between the player’s body height and the serve speed (fastest serve, average first-serve, and second-serve speed). The coefficient of serve speed (CSS) was calculated as the quotient of the measured and the theoretical value of the serve speed on a regression line relative to the player’s body height. The CSS of >1, 1 and <1 indicate above-average, average, and below-average serve speeds, respectively, relative to the top world tennis players with the same body height. The CSS adds a new element to the already existing statistics about a tennis match, and provides additional information about the performance of tennis players. The CSS can be utilised e.g. for setting the target serve speed of a given player to achieve based on his/her body height, choosing the most appropriate match strategy against a particular player, and a long-term monitoring of the effectiveness of training focused on the serve speed.     

中外优秀女子网球运动员竞技年龄特征比较分析

采用文献资料法、数理统计法、逻辑归纳法等研究方法对中外20名优秀女子网球运动员的竞技年龄特征进行比较分析,发现:中外优秀女子网球运动员在启蒙训练年龄上的差异并不显著;但是外国优秀女子网球运动员转为职业选手的年龄较早,所以其成为职业选手的年限也较长。中国优秀女子网球运动员之间的现役年龄的分布较为离散,中国十名优秀女子网球运动员的现役年龄差异大于国外十名优秀女子网球运动员的现役年龄差异;并且中国优秀女子网球运动员达到最高竞技水平的年龄比国外优秀女子网球运动员达到最高竞技水平的年龄晚。     

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.