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1.
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. 相似文献
2.
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. 相似文献
3.
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. 相似文献
4.
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. 相似文献
5.
Bruce Elliott 《Research quarterly for exercise and sport》2013,84(4):277-281
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). 相似文献
6.
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. 相似文献
7.
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. 相似文献
8.
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. 相似文献
9.
Roger J. Missavage John A. W. Baker Carol A. Putnam 《Research quarterly for exercise and sport》2013,84(3):254-260
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. 相似文献
10.
11.
Simon Choppin 《Sports Engineering》2013,16(3):173-180
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. 相似文献
12.
Satoru Tanabe Akira Ito 《Sports biomechanics / International Society of Biomechanics in Sports》2013,12(3):418-433
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. 相似文献
13.
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. 相似文献
14.
Benjamin K. Williams Ross H. Sanders Joong Hyun Ryu Philip Graham-Smith Peter J. Sinclair 《Journal of sports sciences》2020,38(10):1115-1123
ABSTRACT To maintain the accuracy of squash shots under varying conditions, such as the oncoming ball’s velocity and trajectory, players must adjust their technique. Although differences in technique between skilled and less-skilled players have been studied, it is not yet understood how players vary their technique in a functional manner to maintain accuracy under varying conditions. This study compared 3-dimensional joint and racket kinematics and their variability between accurate and inaccurate squash forehand drives of 9 highly skilled and 9 less-skilled male athletes. During inaccurate shots, less-skilled players hit the ball with a more open racket, demonstrating a difference in this task-relevant parameter. No joint kinematic differences were found for accuracy for either group. Coordinated joint rotations at the elbow and wrist both displayed a “zeroing-in” effect, whereby movement variability was reduced from the initiation of propulsive joint rotation to a higher consistency at ball-impact; potentially highlighting the “functionality” of the variability prior to the impact that enabled consistent task-relevant parameters (racket orientation and velocity) under varying conditions. Further, highly skilled players demonstrated greater consistency of task-relevant parameters at impact than less-skilled players. These findings highlight the superior ability of highly skilled players to adjust their technique to achieve consistent task-relevant parameters and a successful shot. 相似文献
15.
Tanabe S Ito A 《Sports biomechanics / International Society of Biomechanics in Sports》2007,6(3):418-433
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. 相似文献
16.
Daniel A. Russell 《Journal of sports sciences》2018,36(23):2644-2652
ABSTRACTThe 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. 相似文献
17.
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. 相似文献
18.
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 smax, 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. 相似文献
19.
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. 相似文献
20.
The sweet spot of a cricket bat for low speed impacts 总被引：2，自引：1，他引：1
Rob Bower 《Sports Engineering》2012,15(2):53-60
The impact location of a cricket ball on a cricket bat has a large influence on the resulting rebound velocity of the ball. To measure this, a cricket bat was swung in a pendulum motion towards a cricket ball suspended in space. The position of the ball was modified so that it impacted the bat at 24 different positions on the face of the bat. This included six positions longitudinally and four positions laterally. The speed of the bat and each rebound were measured by a radar gun so that the apparent coefficient of restitution (ACOR) could be calculated. Impacts occurring centrally and 1?cm either side of the midline produced significantly higher rebound speeds and ACOR??s than impacts occurring 2 and 3cm off centre (p?<?0.01). Impacts occurring 15?C20?cm from the base of the bat produced the highest rebound speeds (p?<?0.01) and impacts occurring 20?C30?cm from the base of the bat produced the highest ACOR values. Implications for higher speed impacts and game scenarios are discussed. 相似文献