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.     

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.     

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.     

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.     

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。     

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.     

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。     

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.     

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.     

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.     

Ball launch conditions for skilled golfers using drivers of different lengths in an indoor testing facility

Abstract

The displacement of the golf ball struck by a driving club is affected by several player characteristics and equipment parameters and their interrelationships. Some modelling and simulation studies have shown a relationship between shaft length and clubhead speed, supported by a few experimental studies. The aim of the present study was to examine the relationship between driver length and ball launch conditions in an indoor test facility using a ball launch monitor. Nine males considered to be skilled golfers participated in the study. Four driving clubs of total length 117, 119, 124, and 132 cm were assembled from commercially available components and were used to strike golf shots while initial ball velocity, backspin rate, and launch angles were measured. Statistical analysis identified a significant difference in initial launch speed due to club length, a significant difference between participants, but no difference between the trials for a given golfer. A positive trend was noted between backspin and launch angle for all four clubs, and significant inverse associations between initial launch speed and backspin rate and launch angle. However, the combined launch conditions associated with increasing length were not considered optimal, with uncontrolled swingweight and moment of inertia effects considered to be limiting factors.     

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.     

Three-dimensional trunk kinematics in golf: between-club differences and relationships to clubhead speed

The aims of this study were (i) to determine whether significant three-dimensional (3D) trunk kinematic differences existed between a driver and a five-iron during a golf swing; and (ii) to determine the anthropometric, physiological, and trunk kinematic variables associated with clubhead speed. Trunk range of motion and golf swing kinematic data were collected from 15 low-handicap male golfers (handicap = 2.5 ± 1.9). Data were collected using a 10-camera motion capture system operating at 250 Hz. Data on clubhead speed and ball velocity were collected using a real-time launch monitor. Paired t-tests revealed nine significant (p ≤ 0.0019) between-club differences for golf swing kinematics, namely trunk and lower trunk flexion/extension and lower trunk axial rotation. Multiple regression analyses explained 33.7–66.7% of the variance in clubhead speed for the driver and five-iron, respectively, with both trunk and lower trunk variables showing associations with clubhead speed. Future studies should consider the role of the upper limbs and modifiable features of the golf club in developing clubhead speed for the driver in particular.     

Influence of shaft length on golf driving performance

The aim of this study was to determine how shaft length affects golf driving performance. A range of drivers with lengths between 1.168 m and 1.270 m, representing lengths close to the 1.219 m limit imposed by R&;A Rules Limited (2008 R&;A Rules Limited. 2008. Rules of golf, St. Andrews: R&;A Rules Limited, The Royal and Ancient Golf Club of St. Andrews.  [Google Scholar]), were assembled and evaluated. Clubhead and ball launch conditions and drive distance and accuracy were determined for seven category 1 golfers (handicaps 0.21 ± 2.41) who performed shots on a purpose-built practice hole. As shaft length increased from 1.168 m to 1.270 m, initial ball velocity increased (+1.8 m/s, P < 0.01). Ball carry (+4.3 m, P = 0.152) also increased, although not significantly so. Furthermore, as shaft length increased, for all club comparisons there was no decrease in accuracy. Ball launch conditions of spin components and launch angle remained unaffected by shaft length. Launch angle increased (0.8°, F = 1.074, P = 0.362) as driver shaft length increased. Our results show that clubhead and ball velocity together with ball carry tended to increase with no loss of accuracy.     

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.     

Multi-segment trunk models used to investigate the crunch factor in golf and their relationship with selected swing and launch parameters

The use of multi-segment trunk models to investigate the crunch factor in golf may be warranted. The first aim of the study was to investigate the relationship between the trunk and lower trunk for crunch factor-related variables (trunk lateral bending and trunk axial rotation velocity). The second aim was to determine the level of association between crunch factor-related variables with swing (clubhead velocity) and launch (launch angle). Thirty-five high-level amateur male golfers (Mean ± SD: age = 23.8 ± 2.1 years, registered golfing handicap = 5 ± 1.9) without low back pain had kinematic data collected from their golf swing using a 10-camera motion analysis system operating at 500 Hz. Clubhead velocity and launch angle were collected using a validated real-time launch monitor. A positive relationship was found between the trunk and lower trunk for axial rotation velocity (r(35) = .47, P < .01). Cross-correlation analysis revealed a strong coupling relationship for the crunch factor (R² = 0.98) between the trunk and lower trunk. Using generalised linear model analysis, it was evident that faster clubhead velocities and lower launch angles of the golf ball were related to reduced lateral bending of the lower trunk.     

高尔夫运动传承的人类文化教育价值研究

高尔夫运动文化是现代物质文明与精神文明高度发展的产物,也是现代文化的一种高级形式,高尔夫不仅带给人类以运动锻炼,也能带来深厚的文化及教育价值。文章从高尔夫运动的起源、运动特点着手,以高尔夫文化的发展与教育相辅相成,分析高尔夫运动传承给现代人类文化及教育的价值。从而得出：文化促进了高尔夫运动的发展,高尔夫运动又带给当代社会新的文化价值;高尔夫运动要发展,依赖于教育与文化,文化教育的发展促使高尔夫人才的辈出,人才又反作用于教育,最终更加促进了高尔夫运动的发展,传承给人类文化教育价值源远流长、生生不息。     

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.