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.     

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.     

A determination of the dynamic response of softballs

An apparatus is described for measuring the stiffness and coefficient of restitution (COR) of balls with application to softballs. While standardized test methods currently exist to measure these properties, they do not represent the displacement rate and magnitude that occur in play. The apparatus described herein involves impacting a fixed, solid cylindrical surface (matched to the diameter of the bat) with a ball and measuring the impact force during impact and speed of the ball before and after impact. The ratio of the ball speeds determines the COR, while the impact force is used to derive a ball stiffness. For an example of the contribution of the new ball test, the performance of hollow bats, which is sensitive to ball stiffness, was compared. Bat performance showed a much stronger dependence on the proposed ball stiffness than the traditional measure. Finally, it was shown that to achieve similar conditions between impacts with fixed and recoiling objects, the impact speed should be chosen so that the centre of mass energy was the same in the two cases. The method has application to associations wishing an improved method to regulate ball and bat performance.     

Measurements of drag and lift on tennis balls in flight

Measurements are presented of drag and lift on new tennis balls in flight. Two video cameras were used to measure the velocity and height of the balls at two positions separated horizontally by 6.4 m. The balls were fired from a ball launcher at speeds between 15 and 30 m/s and with topspin or backspin at rates up to 2,500 rpm. Significant shot-to-shot variations were found in both the drag and lift coefficients. The average drag coefficient was 0.507 ± 0.024, independent of ball speed or spin, and lower than the value usually observed in wind tunnel experiments. The lift coefficient increased with ball spin, on average, but significant lift was observed even at very low spin. The latter effect can be attributed to a side force arising from asymmetries in the ball surface, analogous to the side force responsible for the erratic path of a knuckleball in baseball.     

Viscoelastic impact characterisation of solid sports balls used in the Irish sport of Hurling

In recent years, variability in behaviour of the sliotar, a small leather-bound ball used in the Irish sport of hurling, has become evident in championship matches. The inconsistency in performance was attributed to the range of constructions and material compositions of currently approved ball types. With a view to adopting a standard core, a new methodology has been commissioned to assess the dynamic impact behaviour of approved sliotar cores. In this paper, the relationship between the dynamic stiffness and the coefficient of restitution is presented with regard to material properties, ball construction and viscoelastic strain and strain-rate dependencies. The modern polymer ball types were shown to exhibit strain-rate sensitivity, while the performance of the traditional multi-compositional ball types exhibited lesser strain-rate dependence. The traditional balls types were shown to be up to 2.5 times stiffer than the modern ball types, with this finding having implications for ball energy dissipation.     

Bat speed, trajectory, and timing for collegiate baseball batters hitting a stationary ball

The aims of this study were to examine whether batters hit stationary balls at the time of peak speed of the bat head and whether the impact occurs at the lowest point of the bat trajectory. Eight university baseball players hit three balls, each hung with a string; each ball was made of a different material and was different in weight. Bat movement was captured by four 240-Hz infrared cameras and analysed three-dimensionally. Time for peak speed of the bat head varied according to the conditions. When stationary balls of standard weight were used, the bat head was at maximum speed at impact with the ball; then, it decelerated drastically owing to the impact. In contrast, maximum speed was obtained after impact when lightweight stationary balls were used. The time-speed profile of the bat head before impact in the lightweight ball condition was identical with that in the standard weight ball condition. Regardless of conditions, the timing of the lowest point of the bat head was nearly identical for each batter and most participants hit the stationary balls at about the lowest point of the bat trajectory.     

Bat speed,trajectory, and timing for collegiate baseball batters hitting a stationary ball

The aims of this study were to examine whether batters hit stationary balls at the time of peak speed of the bat head and whether the impact occurs at the lowest point of the bat trajectory. Eight university baseball players hit three balls, each hung with a string; each ball was made of a different material and was different in weight. Bat movement was captured by four 240-Hz infrared cameras and analysed three-dimensionally. Time for peak speed of the bat head varied according to the conditions. When stationary balls of standard weight were used, the bat head was at maximum speed at impact with the ball; then, it decelerated drastically owing to the impact. In contrast, maximum speed was obtained after impact when lightweight stationary balls were used. The time–speed profile of the bat head before impact in the lightweight ball condition was identical with that in the standard weight ball condition. Regardless of conditions, the timing of the lowest point of the bat head was nearly identical for each batter and most participants hit the stationary balls at about the lowest point of the bat trajectory     

Strategies to improve impact efficiency in football kicking

In football, kicking with high ball velocity can increase scoring opportunities and reduce the likelihood of interception. Efficient energy transfer from foot to ball during impact is important to attain a high ball velocity. It is considered impact efficiency can be increased by reducing the change in ankle plantarflexion during foot–ball impact. However, conflicting evidence exists, questioning its effectiveness as a coaching cue. The aim of the present study was to systematically analyse joint stiffness, foot velocity and impact location with a mechanical kicking machine to determine if change in ankle plantarflexion during foot–ball impact and ball velocity are influenced. Sagittal plane data of the shank, foot and ball were measured using high-speed video (4,000 Hz). Increasing joint stiffness reduced change in ankle plantarflexion and increased ball velocity from a greater effective mass. Increasing foot velocity increased change in ankle plantarflexion and increased ball velocity. Distal impact locations increased change in ankle plantarflexion and reduced ball velocity as coefficient of restitution decreased. These results identify that change in ankle plantarflexion is a dependent variable during foot–ball impact and does not directly influence ball velocity. Coaches can assess ankle motion during impact to provide feedback to athletes on their impact efficiency.     

Acquiring an Attacking Forehand Drive: The Effects of Static and Dynamic Environmental Conditions

Abstract

Two groups of 10 novice subjects each were trained to perform attacking forehand drives in table tennis and land the balls as fast and as accurately as possible onto a target on the opposite side of the net under two different training conditions. Under the static training condition, the balls were to be struck from a constant position, and under the dynamic training condition, balls approached the subjects in a normal way. Both groups were tested under dynamic conditions prior to and after four days of training, during which they received 1,600 practice trials. Both groups of subjects were shown to increase the number of balls that landed on the target, and learning was also evident from an increased consistency of the direction of travel of the bat at the moment of ball/bat contact. However, no increase in consistency was found for the location of the bat at the moment of ball/bat contact and for the movement times. Thus, learning can occur in the absence of externally generated time-to-contact information, but this is not due to the establishment of a consistent movement form. Learning appears to progress from control at the moment of ball/bat contact backward, toward the moment of initiation.     

On generalized rolling of golf balls considering an offset center of mass and rolling resistance: a study of putting

This paper seeks to address the implications on putting a golf ball with an off-center mass by analyzing the effect of unbalanced mass of ball on its impact and subsequent rolling. We present the general formulation of a rigid golf ball rolling with slip that is able to transition to rolling friction on an arbitrary surface. Particular attention is given to the effects of the offset center of mass on the golf ball’s path. An experimental setup based on a USGA Stimpmeter is used to calibrate the position of contact point as the ball rolls on the green. The trajectories of the ball due to the mass imbalance were studied by numerically solving the equations of motion during putting. Theoretical predictions show that a mass imbalance has little effect on the launch conditions of the ball. However, on a level green a mass offset center of 0.2 % of the ball’s radius can impact the path of the ball with the consequences of missing the hole in a 5.8 m putt. Changing golf ball trajectories with mass offset center has implications on the development of balls and putting.     

The effect of ball compression on the match-play characteristics of elite junior tennis players

The purpose of this article was to examine the effect of equipment scaling, through the modification of tennis ball compression, on elite junior tennis players (aged 10 years) within a match-play context. The two types of ball compressions that were compared were the standard compression (the normal ball) and 75% compression (termed the modified ball). Ten boys and 10 girls participated in the study. Participants were stratified into pairs based on their Australian Age Ranking and gender. Each pair played two two-set matches: one match with standard compression balls and one match with modified balls. The characteristics of each match were analysed and compared. The results showed that the use of the modified ball increased rally speed, allowed players to strike the ball at a lower (more comfortable) height on their groundstrokes and increased the number of balls played at the net. Ball compression had no effect on the relative number of winners, forehands, backhands, first serves in and double faults. The results are discussed in relation to skill acquisition for skilled junior tennis players.     

Development and use of one-dimensional models of a golf ball

One-dimensional models of a golf ball are useful in modelling near-normal (90°) impact. The model described here has two masses connected by a non-linear spring in parallel with a non-linear damper. The behaviour of this system in collision with an infinite rigid mass is compared with the results of tests involving real golf balls. Values of the four unknown constants are found by fitting the model results, over a range of impact speeds from zero to 50 m· s -1 , to the coefficient of restitution and duration of contact found in the tests. The simplest model (Model 1) was a good fit for duration of contact over the whole range of impact speeds, but for the coefficient of restitution only at high speed (above 20 m· s -1 ). However, when used with a similar model of a flexible faced club, the simple model predicted the coefficient of restitution of the club-ball combination, determined by direct testing, quite well and as such is a useful screening tool. More complicated Models 2 and 3 fitted the rigid target coefficients of restitution better at low speed than Model 1. However, Models 2 and 3 have other disadvantages and are no better than Model 1 for high-speed impact with flexible faced clubs.     

Acquiring an attacking forehand drive: the effects of static and dynamic environmental conditions

Two groups of 10 novice subjects each were trained to perform attacking forehand drives in table tennis and land the balls as fast and as accurately as possible onto a target on the opposite side of the net under two different training conditions. Under the static training condition, the balls were to be struck from a constant position, and under the dynamic training condition, balls approached the subjects in a normal way. Both groups were tested under dynamic conditions prior to and after four days of training, during which they received 1,600 practice trials. Both groups of subjects were shown to increase the number of balls that landed on the target, and learning was also evident from an increased consistency of the direction of travel of the bat at the moment of ball/bat contact. However, no increase in consistency was found for the location of the bat at the moment of ball/bat contact and for the movement times. Thus, learning can occur in the absence of externally generated time-to-contact information, but this is not due to the establishment of a consistent movement form. Learning appears to progress from control at the moment of ball/bat contact backward, toward the moment of initiation.     

Assessment of the impact sound in golf putting

Abstract

The influence of impact sound in putting on players' perceptions of “feel” is explored in this paper. Tests were conducted to investigate the impact sound characteristics of five different ball types using two different putter types. The first test studied the impact sound of purely the ball, while the second test investigated the influence of putter construction and impact location on impact sound for the different ball types. Trends were found between sound spectra peaks in the 2 – 4 kHz range and the compression values of the balls. In addition, frequency content was more dependent on putter type and impact location than on ball construction in the 0 – 2 kHz range. The final test employed a paired comparison technique to investigate players' perceptions of sharpness and loudness of impact sound, ball speed from the clubface and ball hardness. Relationships between the subjective data and the sound characteristics of the balls were then examined. It was found that the ball the players' perceived to have the sharpest and loudest sound, to feel the hardest and to come off the clubface the quickest also had the largest calculated values of loudness and sharpness and had a spectral peak at a higher frequency than the other balls.     

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.     

The Influence of Tennis Racket Flexibility and String Tension on Rebound Velocity Following a Dynamic Impact

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).     

The influence of moment of inertia on baseball/softball bat swing speed

The speed at which a player can swing a bat is central to the games of baseball and softball, determining, to a large extent, the hit speed of the ball. Experimental and analytical studies of bat swing speed were conducted with particular emphasis on the influence of bat moment of inertia on swing speed. Two distinct sets of experiments measured the swing speed of colege baseball and fast-pitch softball players using weighted rods and modified bats. The swing targets included flexible targets, balls on a tee and machine pitched balls. Internal mass alterations provided a range of inertial properties. The average measured speeds, from 22 to 31 m s⁻¹, are consistent with previous studies. Bat speed approximately correlates with the moment of inertia of the bat about a vertical axis of rotation through the batter's body, the speed generally decreasing as this moment of inertia increases. The analytical model assumes pure rotation of the batter/bat system about a vertical axis through the batter's body. Aerodynamic drag of the batter's arms and the bat is included in the model. The independent variable is bat moment of inertia about the rotation axis. There is reasonable agreement between the model and the measured speeds. Detailed differences between the two suggest the importance of additional degrees of freedom in determining swing speed.     

Measurements of the horizontal and vertical speeds of tennis courts

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.     

The sweet spot of a cricket bat for low speed impacts

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.