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.     

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.     

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.     

A new device for evaluating distance and directional performance of golf putters

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.     

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.     

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.     

Acoustics of ping-pong: Vibroacoustic analysis of table tennis rackets and balls

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.     

高尔夫球员体能训练方法探析

运用文献资料法、实验法、访谈法和数理统计法等方法,对高尔夫球员的专项体能训练方法进行研究,根据高尔夫球员体能训练过程中所需遵循的基本训练原则和高尔夫运动特点,针对柔韧性、力量、身体核心稳定性制定课时训练计划,帮助球员提升专项素质和挥杆稳定性从而使球员创造优异成绩。运用此体能训练方法进行的实验结果表明,实验组球员的专项技能测评的平均成绩明显优于实验前的成绩,且该差异性具有高度显著性,表明此体能训练方法具有较高的应用与推广价值。     

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.     

高尔夫文化对大学生影响的调查——以江汉大学学生为例

通过对高尔夫文化内容和特征的分析,运用文批资料法．问誊调查法和访谈法等方法,对江汉大学高尔夫参与者进行高尔夫文化对大学生影响的调查,分析高尔夫文化对大学生的积极和消极的影响,并对高校发展高尔夫运动文化提出建议。     

Soccer ball modal analysis using a scanning laser doppler vibrometer (SLDV)

Soccer equipment manufacturers invest significant amounts of time and money researching and developing soccer balls, using advanced materials and constructions in an attempt to create a ball that has better flight and impact characteristics. An important consideration in any structure subject to dynamic or impact loading is its mechanical response. The recent development of non-contact optical vibration measurement tools such as the SLDV have made the accurate measurement of such responses possible. The technique of vibrometry utilises the Doppler principle to provide a measure of the surface velocity at the point at which a laser beam is incident. The SLDV benefits from its non-contact and non-marking method, and the speed and ease with which measurements can be recorded. This paper reports the method and results from a study aimed at determining the dynamic responses of two different soccer balls. The balls were excited using an acoustic source and the velocity of each ball’s surface at a series of points was recorded. The natural frequencies and vibration mode shapes were identified and a comparison made between the responses of each ball. Significant mode shapes were observed between 150 Hz and 1500 Hz. At the lower frequencies, the mode shapes were observed to be independent of the outer panels, based more on the structure of the ball as a whole. At higher frequencies, one of the balls tested showed mode shapes centred on individual panel oscillations. The soccer balls tested show some noticeable differences in mode shapes.     

高尔夫运动中的力学原理

为了更好的理解高尔夫球飞行路线的影响机制,以便为高尔夫球手更加自如的控制球路。文章从运动生物力学角度,结合空气动力学原理,分析高尔夫运动挥杆击球以及球在空中飞行和落地后的受力形式,围绕高尔夫球飞离地面、空中飞行、落地滚动及停止等主要环节,分析不同的击打方式对球飞行路线产生差别的受力情况,为高尔夫运动者进行练习提供科学的理论基础。     

Biomechanical risk factors and mechanisms of knee injury in golfers

Knee injuries in golf comprise approximately 8% of all injuries, and are considered to result from overuse, technical faults or a combination of those factors. This review examines factors involved in injury, including the structure of the knee joint, kinematics and kinetics of the golf swing, forces sustained by knee joint structures and the potential for joint injury as well as injury prevention strategies. The golf swing generates forces and torques which tend to cause internal or external rotation of the tibia on the femur, and these are resisted by the knee ligaments and menisci. Research has shown that both maximum muscle forces and the forces sustained during a golf swing are less than that required to cause damage to the ligaments. However, the complex motion of the golf swing, involving both substantial forces and ranges of rotational movement, demands good technique if the player is to avoid injuring their knee joint. Most knee injury in golf is likely related to joint laxity, previous injuries or arthritis, and such damage may be exacerbated by problems in technique or overuse. In addition to appropriate coaching, strategies to remedy discomfort include specific exercise programmes, external bracing, orthotics and equipment choices.     

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.     

Methodological considerations for the 3D measurement of the X-factor and lower trunk movement in golf

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.     

Acute effects of different warm-up protocols on highly skilled golfers’ drive performance

Previous research has highlighted the positive effect that different warm-up protocols have on golf performance (e.g. Sorbie et al., 2016; Tilley & Macfarlane, 2012) with the design of warm-ups and programmes targeting and improving golf performance through the activation and development of specific muscle groups. This study aimed to examine the acute effects of two warm-up protocols on golf drive performance in comparison to a control condition. Using a randomised counterbalanced design over three testing sessions, twenty-three highly skilled golfers completed the control, dynamic and resistance-band warm-up conditions. Following each condition, a GC2 launch monitor was used to record ball velocity and other launch parameters of ten shots hit with the participants’ own driver. A repeated-measures ANOVA found significant increases in ball velocity (η_p² = .217) between the control and both the dynamic and resistance-band warm-up conditions but no difference between these latter two, and a reduction in launch angle between control and dynamic conditions. The use of either a dynamic stretching or resistance-band warm-up can have acute benefits on ball velocity but golfers should liaise with a PGA Professional golf coach to effectively integrate this into their golf driving performance.     

A new device for evaluating distance and directional performance of golf putters

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.     

Golf-related injuries: A systematic review

Abstract

A review was undertaken to assess the prevalence of musculoskeletal injuries in golf and to stimulate the discussion on possible injury mechanisms. The main conclusion of most published studies is that although professional and amateur golfers show a similar anatomical distribution of injuries by body segment, differences tend to be seen in the ranking of injury occurrence by anatomical site. This could be due to many things, including the player's handicap, age, golf swing biomechanics, and training or playing habits. The impact of golf injuries deserves special attention due to the interaction of the nature of the injury, practice routines, amount of practice, handicap, and frequency of activity. Individual differences and clinical and coaching procedures deserve investigation. Other epidemiological information should be regarded as insufficient with respect to a full understanding of injury mechanisms, which can give us a better insight into the evolutionary nature of the injury. Also, a better understanding of golf swing mechanisms and individual neuromuscular aspects can help explain why some individuals are more injury-prone than others.     

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 alterations in foot centre of pressure on lower body kinematics during the five-iron golf swing

ABSTRACT

The research aimed to evaluate the effects of an intervention aimed at altering pressure towards the medial aspect of the foot relating to stability mechanisms associated with the golf swing. We hypothesised that by altering the position of the foot pressure, the lower body stabilisation would improve which in turn would enhance weight distribution and underpinning lower body joint kinematics. Eight professional golf association (PGA) golf coaches performed five golf swings, recorded using a nine-camera motion analysis system synchronised with two force platforms. Following verbal intervention, they performed further five swings. One participant returned following a one-year intervention programme and performed five additional golf swings to provide a longitudinal case study analysis. Golf performance was unchanged evidenced by the velocity and angle of the club at ball impact (BI), although the one-year intervention significantly changed the percentage of weight experienced at each foot in the final 9% of downswing, which provided an even weight distribution at BI. This is a highly relevant finding as it indicates that the foot centre of pressure was central to the base of support and in-line with the centre of mass (CoM), indicating significantly increased stability when the CoM is near maximal acceleration.