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1.
In this paper, we present results on the measurement and analysis of the sound that is produced by the sharp impact loading of a golf ball by a flat massive object (e.g. the face of a golf club). We discuss: (a) the motivation for such a study; (b) some necessary background information on how golf balls vibrate; (c) the techniques used to acquire and analyse the data; and (d) an analysis of the sound made by dropping balls on a smooth, massive concrete target surface. These results establish a simple method for rapid and non-destructive measurement of the effective high-frequency elastic shear moduli of balls and ball cores.  相似文献   

2.
In this paper, we report the discrete frequencies at which golf balls can vibrate, the mode patterns of these vibrations and how these modes can be excited. There are two broad classes of modes: those that radiate sound waves and those that do not. Both silent and acoustic modes are excited by tangential (i.e. spin-producing) impact forces; only acoustic modes are excited by radial impact forces. Exact analytical results for a homogeneous ball core are compared with finite element numerical results for both a core and a model two-piece ball. Correspondences are readily established for the important low-frequency modes, and the good agreement suggests the validity of these results for real golf balls. The results potentially provide the basis for a rapid, simple and non-destructive method of measuring the effective high-frequency elastic shear modulae of balls (and ball cores) as well as a method for 'tuning' the performance of balls for specific clubs. Some of these aspects are explored further in our companion paper in this issue.  相似文献   

3.
In this paper, we report the discrete frequencies at which golf balls can vibrate, the mode patterns of these vibrations and how these modes can be excited. There are two broad classes of modes: those that radiate sound waves and those that do not. Both silent and acoustic modes are excited by tangential (i.e. spin-producing) impact forces; only acoustic modes are excited by radial impact forces. Exact analytical results for a homogeneous ball core are compared with finite element numerical results for both a core and a model two-piece ball. Correspondences are readily established for the important low-frequency modes, and the good agreement suggests the validity of these results for real golf balls. The results potentially provide the basis for a rapid, simple and non-destructive method of measuring the effective high-frequency elastic shear modulae of balls (and ball cores) as well as a method for 'tuning' the performance of balls for specific clubs. Some of these aspects are explored further in our companion paper in this issue.  相似文献   

4.
Backspin rate and friction coefficients have been studied for a range of commercially available wedges and multi-piece golf balls using a mechanical golfer and a modified pin-on-disc tester. Analysis of shot characteristics for wedges with three different surface roughness values and two golf ball types (two-piece ionomer covered and three-piece polyurethane covered) was carried out using the mechanical golfer, whilst pin-on-disc testing was performed to determine the friction coefficient between the different golf ball covers (with a range of hardness values) and steel discs with a range of surface roughness values seen for different wedges. It was found that the polyurethane covered balls (lower hardness) showed greater backspin than the ionomer covered balls (higher hardness), and showed higher friction values during the pin-ondisc testing. During the mechanical golfer tests, however, it was observed that the ionomer covered balls showed an increase in friction coefficient for increasing surface roughness, although the effect of differences in cover material types was greater than that of surface roughness variation for the same cover material within the range of commercially available wedge face surface roughnesses.  相似文献   

5.
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.  相似文献   

6.
The role of shaft stiffness on the golf swing is not well understood. Studies in which golfers hit balls with clubs of varying shaft flex have reported changes in ball distance. The results of mathematical models suggest that shaft stiffness affects only the orientation of the clubhead at impact, not the speed of the clubhead, but there are no experimental results validating these findings. The purpose of this study was therefore to experimentally examine the influence of shaft stiffness on clubhead kinematics at ball impact. Forty golfers hit 10 balls with each of five drivers varying in shaft stiffness from 'Ladies' to 'Extra-Stiff', in a double-blind study design. The motions of three reflective markers attached to the clubhead were captured with a high-speed motion analysis system. At ball impact, shaft stiffness had a statistically significant influence on clubhead speed for 27 subjects, on loft angle for 11 subjects, and on lie angle for all 40 subjects. No effect was observed on face angle, in to out path angle, or attack angle. These results show that shaft stiffness can affect ball launch conditions by altering clubhead speed and/or loft angle.  相似文献   

7.
The purpose of this study was to construct and evaluate the reliability of an apparatus for testing golf putters with respect to distance and direction deviation at different impact points on the clubface. An apparatus was constructed based on the pendulum principle that allowed putter golf clubs to swing at different speeds. The mean speed of the club head before ball impact, and of the ball after impact, was calculated from time measurements with photocells. A pin profile rig was used to determine the directional deviation of the golf ball. Three different putters were used in the study, two that are commercially available (toe-heel weighted and mallet types) and one specially made (wing-type) putter. The points of impact were the sweet spot (as indicated by the manufacturer's aim line), and 1, 2 and 3 cm to the left and right of the sweet spot. Calculation of club head speed before impact, and of ball speed after impact (proportional to distance), showed errors < or = 0.5% of interval duration. The variability in ball impacts was tested by measuring time and direction deviations during 50 impacts on the same ball. The mean duration (+/- s) after ball impact in the test interval (1.16 m long) was 206 (0.8) ms and the standard deviation in the perpendicular spreading of the balls in relation to the direction of the test interval was 0.005 m. A test-retest of one putter on two consecutive days after remounting of the putter on the test apparatus showed less than 1% difference in distance deviation. We conclude that the test apparatus enables a precise recording of distance and direction deviation in golf putters as well as comparisons between different putters. The apparatus and set-up can be used in the laboratory as well as outdoors on the putting green.  相似文献   

8.
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.  相似文献   

9.
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.  相似文献   

10.
Abstract

The purpose of this study was to construct and evaluate the reliability of an apparatus for testing golf putters with respect to distance and direction deviation at different impact points on the clubface. An apparatus was constructed based on the pendulum principle that allowed putter golf clubs to swing at different speeds. The mean speed of the club head before ball impact, and of the ball after impact, was calculated from time measurements with photocells. A pin profile rig was used to determine the directional deviation of the golf ball. Three different putters were used in the study, two that are commercially available (toe-heel weighted and mallet types) and one specially made (wing-type) putter. The points of impact were the sweet spot (as indicated by the manufacturer's aim line), and 1, 2 and 3 cm to the left and right of the sweet spot. Calculation of club head speed before impact, and of ball speed after impact (proportional to distance), showed errors ≤ 0.5% of interval duration. The variability in ball impacts was tested by measuring time and direction deviations during 50 impacts on the same ball. The mean duration (± s) after ball impact in the test interval (1.16 m long) was 206 (0.8) ms and the standard deviation in the perpendicular spreading of the balls in relation to the direction of the test interval was 0.005 m. A test – retest of one putter on two consecutive days after remounting of the putter on the test apparatus showed less than 1% difference in distance deviation. We conclude that the test apparatus enables a precise recording of distance and direction deviation in golf putters as well as comparisons between different putters. The apparatus and set-up can be used in the laboratory as well as outdoors on the putting green.  相似文献   

11.
Experiment 1 examined whether it is more advantageous to direct learners' attention to the external effects of their movements relative to other external cues. Two groups of participants hit tennis balls at a target, with one group focusing on the ball coming toward them (antecedent) and the other group focusing on the ball leaving the racket (effect). The effect group demonstrated more effective learning. Experiment 2 examined whether it is more beneficial if the movement effect is related to the movement technique, relative to other movement effects (e.g., outcome). Two groups of participants hit golf balls at a target. The attention of these groups was directed to the club or the ball trajectory, respectively. The club group showed more effective learning than the target group, suggesting that focusing on technique-related effects is more effective.  相似文献   

12.
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.  相似文献   

13.
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   

14.
The dynamic impact characteristics of tennis balls with tennis rackets   总被引：1，自引：0，他引：1  
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   

15.
While the role of the upper torso and pelvis in driving performance is anecdotally appreciated by golf instructors, their actual biomechanical role is unclear. The aims of this study were to describe upper torso and pelvis rotation and velocity during the golf swing and determine their role in ball velocity. One hundred recreational golfers underwent a biomechanical golf swing analysis using their own driver. Upper torso and pelvic rotation and velocity, and torso-pelvic separation and velocity, were measured for each swing. Ball velocity was assessed with a golf launch monitor. Group differences (groups based on ball velocity) and moderate relationships (r > or = 0.50; P < 0.001) were observed between an increase in ball velocity and the following variables: increased torso-pelvic separation at the top of the swing, maximum torso-pelvic separation, maximum upper torso rotation velocity, upper torso rotational velocity at lead arm parallel and last 40 ms before impact, maximum torso-pelvic separation velocity and torso-pelvic separation velocity at both lead arm parallel and at the last 40 ms before impact. Torso-pelvic separation contributes to greater upper torso rotation velocity and torso-pelvic separation velocity during the downswing, ultimately contributing to greater ball velocity. Golf instructors can consider increasing ball velocity by maximizing separation between the upper torso and pelvis at the top of and initiation of the downswing.  相似文献   

16.
When the boundary layer of a sports ball undergoes the transition from laminar to turbulent flow, a drag crisis occurs whereby the drag coefficient (C d) rapidly decreases. However, the aerodynamic properties and boundary-layer dynamics of a soccer ball are not yet well understood. In this study we showed that the critical Reynolds number (Re crit) of soccer balls ranged from 2.2 × 105 to 3.0 × 105. Wind-tunnel testing, along with visualisation of the dynamics of the boundary layer and the trailing vortex of a ball in flight, demonstrated that both non-spinning and spinning (curved) balls had lowC d values in the super-critical region. In addition, theRe crit values of the soccer balls were lower than those of smooth spheres, ranging from ∼ 3.5 × 105 to 4.0 × 105, due to the effects of their panels. This indicated that the aerodynamic properties of a soccer ball were intermediate between those of a smooth ball and a golf ball. In a flow visualisation experiment, the separation point retreated and theC d decreased in a super-critical regime compared with those in a sub-critical regime, suggesting a phenomenon similar to that observed in other sports balls. With some non-spinning and spinning soccer balls, the wake varied over time. In general, the high-frequency component of an eddy dissipated, while the low-frequency component increased as the downstream vortex increased. The causes of the large-scale fluctuations in the vortex observed in the present study were unclear; however, it is possible that a ‘knuckle-ball effect’ of the non-rotating ball played a role in this phenomenon.  相似文献   

17.
Two different measurement techniques are used to examine the effect of surface geometry on soccer ball trajectories. Five professional players are observed using high-speed video when taking curling free kicks with four different soccer balls. The input conditions are measured and the average launch velocity and spin are found to be approximately 24 m/s and 106 rad/s. It is found that the players can apply more spin (~50%) on average to one ball, which has a slightly rougher surface than the other balls. The trajectories for the same four balls fired at various velocities and spin rates across a sports hall using a bespoke firing device are captured using high-speed video cameras, and their drag and lift coefficients estimated. Balls with more panels are found to experience a higher lift coefficient. The drag coefficient results show a large amount of scatter, and it is difficult to distinguish between the balls. Using the results in a trajectory prediction programme it is found that increasing the number of panels from 14 to 32 can significantly alter the final position of a 20 m-curling free kick by up to 1 m.  相似文献   

18.
Large-eddy simulation of atmospheric flow is combined with golf ball trajectory modeling that incorporates local plant canopy information to predict the trajectory of a golf shot at any hole on a golf course in a variety of wind conditions. The model is applied to examine golf shots on hole 12 of the Augusta National Golf Club, which is particularly well known for its wind-induced difficulty. The results indicate that the tree canopies around this hole play a significant role in golf ball trajectories and also induce a strong directional sensitivity on the landing spot of the ball for this hole.  相似文献   

19.
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.  相似文献   

20.
It is believed that increasing the X-factor (movement of the shoulders relative to the hips) during the golf swing can increase ball velocity at impact. Increasing the X-factor may also increase the risk of low back pain. The aim of this study was to provide recommendations for the three-dimensional (3D) measurement of the X-factor and lower trunk movement during the golf swing. This three-part validation study involved; (1) developing and validating models and related algorithms (2) comparing 3D data obtained during static positions representative of the golf swing to visual estimates and (3) comparing 3D data obtained during dynamic golf swings to images gained from high-speed video. Of particular interest were issues related to sequence dependency. After models and algorithms were validated, results from parts two and three of the study supported the conclusion that a lateral bending/flexion-extension/axial rotation (ZYX) order of rotation was deemed to be the most suitable Cardanic sequence to use in the assessment of the X-factor and lower trunk movement in the golf swing. The findings of this study have relevance for further research examining the X-factor its relationship to club head speed and lower trunk movement and low back pain in golf.  相似文献   

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