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.     

The dynamic impact characteristics of tennis balls with tennis rackets

The dynamic properties of six types of tennis balls were measured using a force platform and high-speed digital video images of ball impacts on rigidly clamped tennis rackets. It was found that the coefficient of restitution reduced with velocity for impacts on a rigid surface or with a rigidly clamped tennis racket. Pressurized balls had the highest coefficient of restitution, which decreased by 20% when punctured. Pressureless balls had a coefficient of restitution approaching that of a punctured ball at high speeds. The dynamic stiffness of the ball or the ball-racket system increased with velocity and pressurized balls had the highest stiffness, which decreased by 35% when punctured. The characteristics of pressureless balls were shown to be similar to those of punctured balls at high velocity and it was found that lowering the string tension produced a smaller range of stiffness or coefficient of restitution. It was hypothesized that players might consider high ball stiffness to imply a high coefficient of restitution. Plots of coefficient of restitution versus stiffness confirmed the relationship and it was found that, generally, pressurized balls had a higher coefficient of restitution and stiffness than pressureless balls. The players might perceive these parameters through a combination of sound, vibration and perception of ball speed off the racket.     

The dynamic impact characteristics of tennis balls with tennis rackets

Abstract

The dynamic properties of six types of tennis balls were measured using a force platform and high-speed digital video images of ball impacts on rigidly clamped tennis rackets. It was found that the coefficient of restitution reduced with velocity for impacts on a rigid surface or with a rigidly clamped tennis racket. Pressurized balls had the highest coefficient of restitution, which decreased by 20% when punctured. Pressureless balls had a coefficient of restitution approaching that of a punctured ball at high speeds. The dynamic stiffness of the ball or the ball-racket system increased with velocity and pressurized balls had the highest stiffness, which decreased by 35% when punctured. The characteristics of pressureless balls were shown to be similar to those of punctured balls at high velocity and it was found that lowering the string tension produced a smaller range of stiffness or coefficient of restitution. It was hypothesized that players might consider high ball stiffness to imply a high coefficient of restitution. Plots of coefficient of restitution versus stiffness confirmed the relationship and it was found that, generally, pressurized balls had a higher coefficient of restitution and stiffness than pressureless balls. The players might perceive these parameters through a combination of sound, vibration and perception of ball speed off the racket.     

A 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.     

A comparison of the ball rebound characteristics of wooden and composite cricket bats at three approach speeds

The primary aim of this study was to compare the rebound characteristics of wooden and composite cricket bats. The rebound characteristics of two 'experimental' bats manufactured from composite material were compared with three English willow bats and one Kashmir willow bat. The bats were tested using a specially designed testing rig, which propelled a 156 g Kookaburra cricket ball at three impact speeds: fast-medium, 67 km x h(-1); fast, 101 km x h(-1); and express, 131 km x h(-1) on to the bats mounted in position so that the ball impacts occurred at the position where the blade of the bats was the thickest. The rebound characteristics of the bats were calculated by measuring the approach and rebound speeds of the ball as it passed through a light beam positioned a short distance away from the point of impact. The statistical software package SAS was used to test for significant differences (p < 0.05) between the average rebound characteristics of the bats. Further, Scheffé's method was used as a post hoc comparison to determine whether differences existed between the composite and willow bats. When the composite and traditional willow bats were compared, the results showed no significant differences between the three average approach speeds, while the composite bats showed significantly smaller rebound speeds and coefficient of restitution at all three approach speeds. Thus, the rebound characteristics of the composite bats were significantly less than the traditionally designed English willow wooden bats and would not enhance performance by allowing the batsman to hit the ball harder, assuming all other factors, such as bat speed, mass distribution and the impact point, were the same for the bats. Further study is required to determine the physical properties of composite and wooden bats to enhance their impact characteristics.     

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.     

An examination of the Clegg impact hammer test with regard to the playing performance of synthetic sports surfaces

One of the tests used to evaluate the performance of sports surfaces measures the peak deceleration of a rigid mass during contact with the surface, after being dropped from a set height. It is widely used and is included in a number of international standards. The test was carried out using two drop heights on four different designs of artificial cricket pitch, with a full set of acceleration data being collected over the duration of impact. These data were then integrated twice with respect to time to produce velocity and displacement information. Oblique impacts of cricket balls were also carried out and analysed using a high-speed video system to evaluate the playing performance of each pitch design. It was found that, although the pitches gave quite different readings of peak deceleration, they produced similar values for coefficient of restitution and were therefore considered to ‘play’ in a very similar way. This was due to a high peak deceleration reading being accompanied by a short contact time and low peak deceleration being accompanied by a long contact time, meaning that the change in momentum was similar in both cases. It was concluded that for accelerometer tests to be useful, all the acceleration-time data should be analysed, rather than the peak value alone.     

Understanding the role of shaft stiffness in the golf swing

Theoretically, shaft stiffness can alter shot distance by increasing clubhead speed or altering clubhead orientation at impact. A 3D forward dynamics model of a golfer and flexible club simulated the downswing. A genetic algorithm optimized the coordination of the model’s muscles (four torque generators) to maximize clubhead speed. The maximum torque output and maximum rate of torque development from the torque generators were varied to simulate the swing of golfers that generate different clubhead speeds. Four shafts of varying stiffness (flexible, regular, stiff, and completely rigid) were entered into these simulations to examine the role that shaft flexibility had on clubhead speed and orientation at impact. Shaft stiffness was found to have a meaningful effect only on clubhead orientation (dynamic loft and dynamic close) at impact. There was no evidence to support the premise that matching the stiffness properties of the shaft with the golfer would improve clubhead speed.     

Biomechanical differences in soccer kicking with the preferred and the non-preferred leg

The aims of this study were to examine the release speed of the ball in maximal instep kicking with the preferred and the non-preferred leg and to relate ball speed to biomechanical differences observed during the kicking action. Seven skilled soccer players performed maximal speed place kicks with the preferred and the non-preferred leg; their movements were filmed at 400 Hz. The inter-segmental kinematics and kinetics were derived. A coefficient of restitution between the foot and the ball was calculated and rate of force development in the hip flexors and the knee extensors was measured using a Kin-Com dynamometer. Higher ball speeds were achieved with the preferred leg as a result of the higher foot speed and coefficient of restitution at the time of impact compared with the non-preferred leg. These higher foot speeds were caused by a greater amount of work on the shank originating from the angular velocity of the thigh. No differences were found in muscle moments or rate of force development. We conclude that the difference in maximal ball speed between the preferred and the non-preferred leg is caused by a better inter-segmental motion pattern and a transfer of velocity from the foot to the ball when kicking with the preferred leg.     

Biomechanical differences in soccer kicking with the preferred and the non-preferred leg

The aims of this study were to examine the release speed of the ball in maximal instep kicking with the preferred and the non-preferred leg and to relate ball speed to biomechanical differences observed during the kicking action. Seven skilled soccer players performed maximal speed place kicks with the preferred and the nonpreferred leg; their movements were filmed at 400 Hz. The inter-segmental kinematics and kinetics were derived. A coefficient of restitution between the foot and the ball was calculated and rate of force development in the hip flexors and the knee extensors was measured using a Kin-Com dynamometer. Higher ball speeds were achieved with the preferred leg as a result of the higher foot speed and coefficient of restitution at the time of impact compared with the non-preferred leg. These higher foot speeds were caused by a greater amount of work on the shank originating from the angular velocity of the thigh. No differences were found in muscle moments or rate of force development. We conclude that the difference in maximal ball speed between the preferred and the non-preferred leg is caused by a better inter-segmental motion pattern and a transfer of velocity from the foot to the ball when kicking with the preferred leg.     

A determination of the dynamic response of softballs

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

多元合作模式下高校高尔夫专业办学研究

我国高尔夫发展面临人才数量供需不足、人才素养参差不齐两个重要瓶颈,其核心在于传统“体教结合”、“课内外一体化”、“校企结合”办学模式固化、培养途径单一、培养目标模糊,所培养的人才无法满足社会需求。本文通过对我国高校高尔夫专业办学现状调查分析,融合多种办学思想,探究出“校-企”、“校-校”、“校-中高协-体育赛事方”多元合作模式下的办学新思路,通过多元化联合培养,针对性的塑造高尔夫需求人才,提升学校培养质量,为我国高尔夫运动的健康发展提供支持和帮助。     

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.     

Experimental and finite element analysis of a tennis ball impact on a rigid surface

An explicit finite-element (FE) model of a pressurised tennis ball is presented. The FE model was used to model an oblique impact between a tennis ball and a rigid tennis surface, to further the understanding of this impact. Impacts were also conducted in the laboratory and the results from the FE model were in good agreement with this experimental data. The FE model was used to illustrate why a tennis ball rebounds with a higher vertical coefficient of restitution in an oblique impact compared to an equivalent impact perpendicular to the surface; this equivalent perpendicular impact has the same inbound velocity as the vertical component of the oblique impact. The FE model was also used to illustrate that the structural compliance of the felt covering on a tennis ball was a contributing factor to the ball attaining more spin in the impact than would have been calculated using a conventional analytical model. Also, the spin values calculated in the FE simulation were in good agreement with experimental data.     

Technique analysis of the kuda and sila serves in sepaktakraw

The aims of this study were to gain insights on sepaktakraw serves, identify technique differences, and establish factors influencing ball speeds. The best successful kuda and sila serves of nine elite male national sepaktakraw players were captured using seven ProReflex 1000 optical cameras operating at 240 Hz. The kuda and sila serves are non-planar kicking techniques exhibiting a non proximal-to-distal sequence. Differences in kicking kinematics (P < 0.05) signify differences between techniques. Compared with the sila, the kuda kicking limb is a longer rigid segment that moves over a greater range of motion. Together with a greater increase in foot and shank angular accelerations approaching ball contact, this leads to marginally higher kuda foot impact speeds. Since foot speeds were not at their peak during impact, a longer rigid kuda kicking limb was the primary determinant of kuda ball release speeds. Greater range of motion enables the longer rigid kuda lever to generate greater kicking angular momentum, resulting in greater impact impulse. This immediately translated to the significantly higher ball release speeds based on the impulse-momentum relationship. Coaching implications include improving hip joint flexibility and working on a fluid movement of a longer rigid segment kicking technique.     

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.     

A three-dimensional forward dynamics model of the golf swing

Previously, forward dynamic models of the golf swing have been planar, two-dimensional (2D) representations. Research on live golfers has consistently demonstrated that the downswing is not planar. This paper introduces and evaluates the validity of a 3D six-segment forward dynamics model of a golfer. The model incorporates a flexible club shaft and a variable swing plane. A genetic algorithm was developed to optimise the coordination of the model’s mathematically represented muscles (torque generators) in order to maximise clubhead speed at impact. The kinematic and kinetic results confirmed previous findings on the proximal to distal sequencing of joints and the muscles powering those joints. The validity of the mathematical model was supported through comparisons of the model’s swing kinematics and kinetics with those of a live golfer.     

Technique analysis of the kuda and sila serves in sepaktakraw

The aims of this study were to gain insights on sepaktakraw serves, identify technique differences, and establish factors influencing ball speeds. The best successful kuda and sila serves of nine elite male national sepaktakraw players were captured using seven ProReflex 1000 optical cameras operating at 240 Hz. The kuda and sila serves are non-planar kicking techniques exhibiting a non proximal-to-distal sequence. Differences in kicking kinematics (P < 0.05) signify differences between techniques. Compared with the sila, the kuda kicking limb is a longer rigid segment that moves over a greater range of motion. Together with a greater increase in foot and shank angular accelerations approaching ball contact, this leads to marginally higher kuda foot impact speeds. Since foot speeds were not at their peak during impact, a longer rigid kuda kicking limb was the primary determinant of kuda ball release speeds. Greater range of motion enables the longer rigid kuda lever to generate greater kicking angular momentum, resulting in greater impact impulse. This immediately translated to the significantly higher ball release speeds based on the impulse–momentum relationship. Coaching implications include improving hip joint flexibility and working on a fluid movement of a longer rigid segment kicking technique.     

The influence of equipment variations on sliotar–hurley impact in the Irish game of hurling

The game of hurling is ranked as one of the fastest and most skilful field games in the world. It is played by a stick, hurley, made of ash wood and a ball, sliotar, made of a cork core or similar viscoelastic materials. Better standardisation of the game equipment requires analysing impacts to quantify precisely the effect of variations in equipment design on the resultant impact force at low and high striking speeds. Therefore, the purpose of the present study was to use a high-speed camera to (1) characterise the impact dynamics in term of impact force magnitude and duration, and (2) investigate whether a relationship exists between the game equipment and the magnitude of the impact force. An air cannon unit (ACU) test rig was set up to cause the sliotar to strike the hurley at predetermined speeds. A high-speed camera operating at 12,500 frames per second (fps) was used to capture 32 experimental impacts covering a range of sliotar and hurley brands, impact locations and impact speeds. The factor ??sliotar brand?? was identified as the most significant factor for the impact force among other main factors and two-factor interactions at a constant speed and it had a significant effect with up to 27?% difference between sliotar brands. It was demonstrated that, at higher impact speeds, the force?Cdeformation curves of the sliotar brands varied significantly, even though similar force?Cdeformation curves have been reported at quasi-static compression and similar COR values at low impact speeds using the standard free-drop test. This is the first known study to characterise the unique, highly non-linear and anisotropic sliotar?Churley impact using high-speed camera technology. It highlights the need for a tighter standard for sliotar materials and manufacturing to increase uniformity between different brands and strongly suggests that the standard free-drop test is not sufficient to characterise and compare game equipment.     

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.