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1.
Tennis courts are normally classified as fast or slow depending on whether the coefficient of sliding friction (COF) between
the ball and the surface is respectively small or large. This classification is based on the fact that the change in horizontal
ball speed is directly proportional to the COF if the ball is incident at a small angle to the horizontal. At angles of incidence
greater than about 16° it is commonly assumed that the ball will roll during the bounce, in which case one can show that the
ratio of the horizontal speed after the bounce to that before the bounce will be 0.645 regardless of the angle of incidence
or the speed of the court. Measurements are presented showing that (a) at high angles of incidence, tennis balls grip or ‘bite’
the court but they do not roll during the bounce, (b) the bounce:speed ratio can be as low as 0.4 on some courts and (c) the
normal reaction force acts through a point ahead of the centre of mass. An interesting consequence is that, if court A is
faster than court B at low angles of incidence, then A is not necessarily faster than B at high angles of incidence. An exception
is a clay court which remains slow at all angles of incidence. The measurements also show that the coefficient of restitution
for a tennis ball can be as high as 0.9 for an oblique bounce on a slow court, meaning that the ball bounces like a superball
in the vertical direction and that slow courts are fast in the vertical direction. 相似文献
2.
Alexander Nicolaides Nathan Elliott John Kelley Mauro Pinaffo Tom Allen 《Sports Engineering》2013,16(3):181-188
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. 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 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
5.
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
6.
Effect of tennis racket parameters on a simulated groundstroke 总被引：1，自引：0，他引：1
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. 相似文献
7.
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
8.
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
9.
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
10.
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
11.
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
12.
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
13.
Ivan Malagoli Lanzoni Sandro Bartolomei Rocco Di Michele Silvia Fantozzi 《Journal of sports sciences》2018,36(23):2637-2643
ABSTRACTThe 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. 相似文献
14.
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
15.
Abstract This study compared the amount of spin imparted to a tennis ball during impact with conventionally and diagonally strung tennis rackets. Balls were projected at the rackets at an angle of approximately 45°. The head of each racket was oriented vertically and clamped to eliminate any influence that deformations of the frame would have on the forces transmitted to the ball during impact. Ten multiple-image photographs (five using a relatively slow ball velocity and five using a relatively fast ball velocity) were taken of a ball approaching, striking, and leaving the rackets. For similar pre-impact conditions, it was found that the angular impulse of the contact force applied to the ball (and hence the amount of spin) was almost identical for the two string configurations. Possible explanations of this finding are discussed. 相似文献
16.
Variability of impact kinematics and margin for error in the tennis forehand of advanced players 总被引：1，自引：1，他引：0
The kinematics of the racket and ball near impact in tennis forehands were studied to document typical variation in successful
and unsuccessful shots, in order to determine biomechanically meaningful differences in advanced players and confirm models
of groundstroke trajectories. Seven tennis players (six males and one female) were videoed from the side at 180 Hz as they
performed 40 forehand drives on an indoor tennis court. Vertical plane kinematics of the racket and ball near impact were
analysed for sub samples of successful and unsuccessful shots for each subject. Most racket kinematic variables were very
consistent (mean CV< 6.3%) for successful shots, so bio mechanically meaningful differences in angles and velocities of the
racket and ball (3° and 2 m s−1) near impact could be detected between successful and unsuccessful shots. Four subjects tended to miss long and three subjects
missed shots in the net that were reflected in initial ball trajectories. Mean (SD) initial trajectories for long shots were
9.8° (1.4°), while netted shots were 0.7° (1.1°) above the horizontal. The initial ball trajectories and margins for error
for these subjects were smaller than those previously reported (Brody, 1987) because players tended to select mean ball trajectories
close to one error than another, differing amounts of topspin, or incorrect lift and drag coefficients for tennis balls had
not been published when this model was created. The present data can be used to confirm if recent models (Cookeet al., 2003; Dignallet al., 2004) more closely match actual performance by advanced players. 相似文献
17.
18.
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. 相似文献
19.
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. 相似文献
20.
Three‐dimensional (3‐D) high‐speed cinematographic techniques were used to record topspin and backspin forehand approach shots hit down‐the‐line by high‐performance players. The direct linear transformation (DLT) technique was used in the 3‐D space reconstruction from 2‐D images recorded via laterally placed phase‐locked cameras operating at 200 Hz. A Mann‐Whitney U‐test was calculated for the different aspects of the topspin and backspin shots to test for significance (P<0.05). A significant difference was recorded between topspin and backspin shots in the angle of the racket at the completion of the backswing. The racket was taken 0.48 rad past a line drawn perpendicular to the back fence for topspin trials, but only rotated 0.86 rad from a line parallel to the net in the backspin shot. Maximum racket velocities occurred prior to impact and were significantly higher in topspin (26.5 m s‐1) compared to backspin (16.6 m s‐1) trials. This resulted in the topspin trials recording a significantly higher ball velocity compared to backspin trials (27.6 m s‐1 vs 21.7 m s‐1). Pre‐impact racket trajectories revealed that in topspin shots the racket moved on an upward path of 0.48 rad while in backspin shots it moved down at an angle of 0.34 rad. In the topspin trials impact occurred significantly further forward of the front foot than in backspin shots (0.26 m vs 0.05 m) while the angle of the racket was the same for both strokes (0.14 rad behind a line parallel to the net). The mean angle of the racket‐face at impact was inclined backwards by 0.11 rad for backspin strokes and rotated forward by 0.13 rad for topspin strokes. Angles of incidence and reflection of the impact between the ball and the court showed that backspin trials had larger angles of incidence and reflection than topspin strokes. 相似文献