On the acoustic signature of golf ball impact

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.     

The influence of golf club shaft stiffness on clubhead kinematics at ball impact

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.     

The relationship between the golf swing plane and ball impact characteristics using trajectory ellipse fitting

The trajectory of the clubhead close to ball impact during the golf swing has previously been shown to be planar. However, the relationship between the plane orientation and the orientation characteristics of the clubhead at ball impact has yet to be defined. Fifty-two male golfers (27 high skilled, 25 intermediate skilled) hit 40 drives each in an indoor biomechanics laboratory. This study successfully fitted the trajectory of the clubhead near impact to an ellipse for each swing for players of different skill levels to help better explain this relationship. Additionally, the eccentricities of the ellipses were investigated for links to skill level. The trajectory of the clubhead was found to fit to an ellipse with RMSE of 1.2 mm. The eccentricity of the ellipse was found to be greater in the high-skilled golfers. The club path and angle of attack generated from the ellipse fitted clubhead trajectory were found to have a normalised bias-corrected RMSE of 2% and 3%, respectively. A set of “rule of thumb” values for the relationship between the club path, angle of attack and delivery plane angle was generated for use by coaches.     

论木球与高尔夫

从术球与高尔夫的起源、技术特征、运动特点、心理特点等方面进行比较分析,旨在为术球在国内乃至世界各地进一步推广和发辰提供参考。     

The vibrational mode structure of a golf ball

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.     

The vibrational mode structure of a golf ball

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.     

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.     

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 degrees) 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 x 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 x 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.     

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.     

Assessment of the impact sound in golf putting

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.     

The influence of club-head kinematics on early ball flight characteristics in the golf drive

Despite many coaching and biomechanical texts describing how the kinematics of the club-head at impact lead to distance and accuracy of the ball flight, there is limited quantitative evidence supporting these assertions. The purpose of this study was to quantify the relationships between club-head kinematics and subsequent early ball flight characteristics during the golf drive. An opto-reflective system operating at 400 Hz was used to capture the swings of 21 male golfers using their own drivers. The 3D displacement data permitted the calculation of club-head kinematics at impact, as well as subsequent early ball flight characteristics. Using regression analyses, club-head kinematics at impact (velocity, orientation, path, and centeredness) were used to explain the variability in five dependent variables of early ball flight characteristics (resultant velocity, launch angle, side angle, back spin, and side spin). The results of the study indicated that club-head kinematics at impact explained a significant proportion of early ball flight characteristics (adjusted r ² = 0.71–0.82), even when generalized across individual clubs.     

The influence of golf shaft torque on clubhead kinematics and ball flight

ABSTRACT

The purpose of this study was to investigate the influence of shaft torque (torsional rigidity) on clubhead kinematics and the resulting flight of the ball. Two driver shafts with disparate levels of torque, but otherwise very similar properties, were tested by 40 right-handed golfers representing a range of abilities. Shaft deflection data as well as grip and clubhead kinematics were collected from 14 swings, with each shaft, for each golfer using an optical motion capture system. Ball flight and additional clubhead kinematics were collected using a Doppler radar launch monitor. At impact, the high torque shaft (HT) was associated with increased delivered loft (P = .028) and a more open face (P < .001) relative to the low torque shaft (LT). This resulted in the HT shaft being associated with a ball finishing position that was further right (P = .002). At the individual level, the change in face angle due solely to shaft deformation was significantly higher for the HT shaft for 25/40 participants. Although shaft twist was not directly measured, it was logically deduced using the collected data that these outcomes were the result of the HT being twisted more open relative to the LT shaft at impact.     

A three-dimensional forward dynamic model of the golf swing optimized for ball carry distance

A 3D predictive golfer model can be a valuable tool for investigating the golf swing and designing new clubs. A forward dynamic model, which includes a four degree of freedom golfer model, a flexible shaft based on Rayleigh beam theory, an impulse-momentum impact model and a spin rate dependent aerodynamic ball model, is presented. The input torques for the golfer model are provided by parameterized joint torque generators that have been designed to mimic muscle torque production. These joint torques are optimized to create swings and launch conditions that maximize carry distance. The flexible shaft model allows for continuous bending in the transverse directions, axial twisting of the club and variable shaft stiffness as a function of the length. The completed four-part model with the default parameters is used to estimate the ball carry of a golf swing using a particular club. This model will be useful for experimenting with club design parameters to predict their effect on the ball trajectory and carry distance.     

Shape optimization of golf clubface using finite element impact models

To model the impact dynamics of a golf drive, finite element (FE) models of the ball and the clubhead are created and combined to simulate the collision of the two bodies. A three-piece golf ball is modelled using only solid elements, while the clubhead is modelled using solid elements for the crucial area of the impact, i.e. the clubface, and using shell elements for the rest of the clubhead to improve the computational efficiency of the simulation. The correct transfer of forces and moments in the transition area between the shell and solid elements is assured by introducing kinematic nodal constraints using rigid elements. The FE model is used to optimize the shape of the clubface in three steps to maximize the launch velocity of the golf ball for central impacts. A final clubface shape is reached and a total improvement of 4.8 m/s over the initial design is obtained. This is a 7% gain in launch velocity, which results in a driving length advantage of approximately 20 m (or 22 yards) until the first contact with the ground. During the optimization process, the mechanical impedances of the two colliding bodies were recorded and compared. It is shown that the optimal clubhead geometry does not agree with the impedance matching theory by comparing the optimization results to those obtained from a simple lumped parameter model.     

The effect of dimple error on the horizontal launch angle and side spin of the golf ball during putting

This study aimed to examine the effect of the impact point on the golf ball on the horizontal launch angle and side spin during putting with a mechanical putting arm and human participants. Putts of 3.2 m were completed with a mechanical putting arm (four putter-ball combinations, total of 160 trials) and human participants (two putter-ball combinations, total of 337 trials). The centre of the dimple pattern (centroid) was located and the following variables were measured: distance and angle of the impact point from the centroid and surface area of the impact zone. Multiple regression analysis was conducted to identify whether impact variables had significant associations with ball roll variables, horizontal launch angle and side spin. Significant associations were identified between impact variables and horizontal launch angle with the mechanical putting arm but this was not replicated with human participants. The variability caused by “dimple error” was minimal with the mechanical putting arm and not evident with human participants. Differences between the mechanical putting arm and human participants may be due to the way impulse is imparted on the ball. Therefore it is concluded that variability of impact point on the golf ball has a minimal effect on putting performance.     

Material and surface effects on the spin and launch angle generated from a wedge/ball interaction in golf

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.     

高尔夫运动的符号消费

从消费社会学的视角,对高尔夫运动在我国发展遭遇的困境进行分析.研究结果表明,我国的高尔夫运动符号消费象征意义超出了其运动本身的价值和意义,并引发人们对它的抵触和不认同;高尔夫运动项目的异化发展导致国家出台政策对其进行控制;大众传播媒介对高尔夫运动符号消费意义的传播起到直接导向作用.     

高尔夫球起源考辨

在介绍几种流行说法的基础上,对高尔夫球起源问题进行探究.认为,苏格兰起源说和荷兰起源说均缺乏有力的资料证据,中国的捶丸文献丰富、记载明确,规则也与高尔夫球十分类似,可以认为与高尔夫球运动有着密切的血缘关系.同时认为,高尔夫球起源与现代高尔夫球运动的产生需要区别对待,必须尊重现代高尔夫球运动产生于苏格兰这一事实;捶丸西传资料和研究的欠缺是其成为高尔夫球统一起源的最大障碍,也是今后此研究的重点领域;各种与高尔夫球类似的游戏都脱胎于生产劳动.     

Oblique impact of a tennis ball on the strings of a tennis racket

Measurements are presented of the friction force acting on a tennis ball incident obliquely on the strings of a tennis racket. This information, when combined with measurements of ball speed and spin, reveals details of the bounce process that have not previously been observed and also provides the first measurements of the coefficient of sliding friction between a tennis ball and the strings of a tennis racket. At angles of incidence less than about 40° to the string plane, the ball slides across the strings during the whole bounce period. More commonly, the ball is incident at larger angles in which case the ball slides across the string plane for a short distance before gripping the strings. While the bottom of the ball remains at rest on the strings, the remainder of the ball continues to rotate for a short period, after which the ball suddenly releases its grip and the bottom of the ball slides backwards on the string plane. The bounce angle depends mainly on the angle of incidence and the rotation speed of the incident ball. Differences in bounce angle and spin off head-clamped and hand-held rackets are also described.     

Novel mathematical model to estimate ball impact force in soccer

To assess ball impact force during soccer kicking is important to quantify from both performance and chronic injury prevention perspectives. We aimed to verify the appropriateness of previous models used to estimate ball impact force and to propose an improved model to better capture the time history of ball impact force. A soccer ball was fired directly onto a force platform (10 kHz) at five realistic kicking ball velocities and ball behaviour was captured by a high-speed camera (5,000 Hz). The time history of ball impact force was estimated using three existing models and two new models. A new mathematical model that took into account a rapid change in ball surface area and heterogeneous ball deformation showed a distinctive advantage to estimate the peak forces and its occurrence times and to reproduce time history of ball impact forces more precisely, thereby reinforcing the possible mechanics of ‘footballer’s ankle’. Ball impact time was also systematically shortened when ball velocity increases in contrast to practical understanding for producing faster ball velocity, however, the aspect of ball contact time must be considered carefully from practical point of view.