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.     

Flow analysis and aerodynamic characteristics of a badminton shuttlecock with spin at high Reynolds numbers

A badminton shuttlecock flies in a high-drag, and thus, the sport has been a subject of research from the point of view of aerodynamics. A badminton shuttlecock generates significant aerodynamic drag and has a complex flight trajectory. It also has the smallest ballistic coefficient and exhibits the largest in-flight deceleration of any airborne sporting projectile. The ballistic coefficient of a projectile is a measure of its ability to overcome air resistance in flight and is inversely proportional to deceleration. The primary objectives of this study were to measure the aerodynamic properties of feather shuttlecocks under a range of the wind speed (10–60 m/s) and pitch angle (0°–25°). In particular, measurements of aerodynamic forces were performed at high Reynolds numbers (more than Re = 210,000), and the effect of shuttlecock deformation on aerodynamic properties was also investigated, because it is presumed that the flight dynamics is affected by the deformation of the shuttlecock skirt. A shuttlecock skirt is composed of an array of diverging stems, the ends of which are at the convergent end of the skirt, joined together in an end ring. The shuttlecock rotates about its major axis in actual flight, and thus, the experiments were performed on shuttlecocks with and without rotation (spin). Furthermore, the effect of the flow passing through the gaps between the slots (stiffeners) located at the leg portion of the shuttlecock skirt on aerodynamic characteristics is demonstrated by means of a shuttlecock model without gaps, which was completely covered with cellophane tape. The free rotation rate of a shuttlecock increased with an increase in the Reynolds number, and the drag coefficient gradually decreased above Re = 86,000 for a non-rotating shuttlecock. The reduction of drag can be explained by the deformation of the skirt observed in wind tunnel experiments at high speed. In this study, for a rotating shuttlecock, a reduction of drag was not observed over a whole range of Reynolds numbers, because deformation of the skirt for a rotating shuttlecock becomes smaller than that for a non-rotating shuttlecock. However, there was no significant difference in drag coefficient between rotating and non-rotating shuttlecocks, in contrast to the difference in drag coefficient between shuttlecocks with and without gaps. The drag coefficient for a shuttlecock without gaps was significantly smaller than that for a standard shuttlecock (with gaps). For a standard shuttlecock, the air flowed through the gaps into the shuttlecock skirt, and this flow was related to high aerodynamic drag.     

Optimal release conditions for the free throw in men's basketball

Abstract

The purpose of this study was to determine the optimum release conditions for the free throw in men's basketball. The study used hundreds of thousands of three-dimensional simulations of basketball trajectories. Five release variables were studied: release height, release speed, launch angle, side angle, and back spin. The free throw shooter was assumed to shoot at 70% and to release the ball 2.134 m (7 ft) above the ground. We found that the shooter should place up to 3 Hz of back spin on the ball, should aim the ball towards the back of the ring, and should launch the ball at 52° to the horizontal. We also found that it is desirable to release the ball as high above the ground as possible, as long as this does not adversely affect the player's launch consistency.     

Is there a sweet spot on the foot in Australian football drop punt kicking?

In the collision between a striking implement and ball, the term “sweet spot” represents the impact location producing best results. In football kicking, it is not known if a sweet spot exists on the foot because no method to measure impact location in three-dimensional space exists. Therefore, the aims were: (1) develop a method to measure impact location on the foot in three-dimensional space; (2) determine if players impacted the ball with a particular location; (3) determine the relationship between impact location with kick performance; (4) discuss if a sweet spot exists on the foot. An intra-individual analysis was performed on foot-ball impact characteristics of ten players performing 30 Australian football drop punt kicks toward a target. (1) A method to measure impact location was developed and validated. (2) The impact locations were normally distributed, evidenced by non-significant results of the Shapiro-Wilk test (p > 0.05) and inspection of histograms, meaning players targeted a location on their foot. (3) Impact location influenced foot-ball energy transfer, ball flight trajectory and ankle plantar/dorsal flexion. (4) These results indicate a sweet spot exists on the foot for the Australian football drop punt kick. In conclusion, the impact location is an important impact characteristic.     

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.     

Experimental validation of dynamic stability analysis applied to dart flight

The game of darts attracts a large international following and can be fiercely competitive. Despite its popularity, and the large equipment market, no previous peer-reviewed studies have examined the trajectory of a dart in flight. This study used high-speed video techniques to measure the trajectories of 225 dart throws from 19 amateur players. The dart’s pitch and angle of attack were found to oscillate during flight in a manner that is analogous to damped harmonic motion. It was also found that the dart’s oscillation frequency was strongly correlated to launch speed, whilst its characteristic wavelength and damping ratio were independent of launch speed. The measured wavelength of oscillation (2.16 m) was found to be similar to the regulation throwing distance (2.37 m). It is proposed that the dart is ‘tuned’ to the throwing distance such that it undergoes one full oscillation before striking the board. The dart flight was modelled using a classical dynamic stability analysis and good agreement was found between the experimental observations and the theoretical predictions. The success of the model confirms that the approach can be used to explore the dynamics of different dart designs through parametric sensitivity analyses.     

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.     

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.     

Flight dynamics of the screw kick in rugby

This paper describes the aerodynamic forces and the flight trajectory for the screw (spiral) kick in rugby. The screw kick is defined as that which causes the ball to spin on its longitudinal axis. The aerodynamic forces acting on a rugby ball spinning on its longitudinal axis were measured in a wind tunnel using a six-component strut type balance. It was found that the drag, the lift and the pitching moment depend on the angle of attack, while the side force (Magnus force) depends on both the spin rate and the angle of attack in the range where the wind speed lies between 15 and 30 m s^-1 and the spin rate is between 1 and 10 revolutions per second. Moreover, the flight trajectory was obtained by integrating the full nonlinear six degrees of freedom equations of motion on the basis of aerodynamic data. In a simulation, a ball spinning on its longitudinal axis tended to hook toward or away from the touchline even if the velocity and angular velocity vectors were parallel to the touchline. The direction of the hook depends on the direction of the angular velocity vector. The initial direction of the hook depends on the relationship between the flight path angle and the pitch angle as well as the direction of the angular velocity vector.     

Mechanical factors associated with the development of high ball velocity during an instep soccer kick

The purpose of this study was to determine whether joint velocities and segmental angular velocities are significantly correlated with ball velocity during an instep soccer kick. We developed a deterministic model that related ball velocity to kicking leg and pelvis motion from the initiation of downswing until impact. Three-dimensional videography was used to collect data from 16 experienced male soccer players (age = 24.8 ± 5.5 years; height = 1.80 ± 0.07 m; mass = 76.73 ± 8.31 kg) while kicking a stationary soccer ball into a goal 12 m away with their right foot with maximal effort. We found that impact velocities of the foot center of mass (CM), the impact velocity of the foot CM relative to the knee, peak velocity of the knee relative to the hip, and the peak angular thigh velocity were significantly correlated with ball velocity. These data suggest that linear and angular velocities at and prior to impact are critical to developing high ball velocity. Since events prior to impact are critical for kick success, coordination and summation of speeds throughout the kicking motion are important factors. Segmental coordination that occurs during a maximal effort kick is critical for completing a successful kick.     

Calculating football drag profiles from simulated trajectories

As a bluff object, a football experiences high aerodynamic drag when flow is laminar due to early boundary layer separation and a large low-pressure region. The length and depth of a football’s seams can influence the separation point by triggering a turbulent boundary layer at lower Reynolds numbers. Football manufacturers can control a football’s behaviour through careful design and material choice. However, assessing the aerodynamic performance of a football can be a lengthy and expensive process, traditionally requiring the use of a suitable wind tunnel. Measuring the drag force at varying Reynolds numbers gives a full aerodynamic profile which determines how the ball will behave during flight. Some studies have attempted to establish the aerodynamic properties of footballs using recorded trajectories, but these only ascertained average properties rather than a full aerodynamic profile. This paper describes a method which uses a series of recorded trajectories to calculate the full aerodynamic properties of a football. To assess the accuracy and robustness of this method, simulated trajectory data were used to which varying degrees of noise and aerodynamic lift were added. The assessment found that random noise does not affect the accuracy of the methodology significantly. At larger magnitudes, random aerodynamic lift makes the methodology ineffective (equivalent to ball spin >100 rpm). Future work will concentrate on assessing the effectiveness of the methodology using ball trajectories recorded using 3D high-speed video techniques.     

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.     

Measurements of drag and lift on tennis balls in flight

Measurements are presented of drag and lift on new tennis balls in flight. Two video cameras were used to measure the velocity and height of the balls at two positions separated horizontally by 6.4 m. The balls were fired from a ball launcher at speeds between 15 and 30 m/s and with topspin or backspin at rates up to 2,500 rpm. Significant shot-to-shot variations were found in both the drag and lift coefficients. The average drag coefficient was 0.507 ± 0.024, independent of ball speed or spin, and lower than the value usually observed in wind tunnel experiments. The lift coefficient increased with ball spin, on average, but significant lift was observed even at very low spin. The latter effect can be attributed to a side force arising from asymmetries in the ball surface, analogous to the side force responsible for the erratic path of a knuckleball in baseball.     

Assessing rugby place kick performance from initial ball flight kinematics: development,validation and application of a new measure

The appropriate determination of performance outcome is critical when appraising a performer’s technique. Previous studies of rugby place kicking technique have typically assessed performance based on ball velocity, but this is not the sole requirement. Therefore, a mathematical model of rugby place kick ball flight was developed to yield a single measure more representative of true performance. The model, which requires only initial ball flight kinematics, was calibrated and validated using empirical place kick data, and found to predict ball position with a mean error of 4.0% after 22 m of ball flight. The model was then applied to the performances of 33 place kickers. The predicted maximum distance, a single performance measure which accounted for initial ball velocity magnitude and direction, and spin, was determined using the model and was compared against ball velocity magnitude. A moderate association in the rank-order of the kicks between these two measures (ρ = 0.52) revealed that the relative success of the kicks would be assessed differently with each measure. The developed model provides a representative measure of place kick performance that is understandable for coaches, and can be used to predict changes in performance outcome under different ball launch or environmental conditions.     

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.     

Perception of spin and the interception of curved football trajectories

Using plain white and chequered footballs, we evaluated observers’ sensitivity to rotation direction and the effects of ball texture on interceptive behaviour. Experiment 1 demonstrated that the maximal distance at which observers (n = 8) could perceive the direction of ball rotation decreased when rotation frequency increased from 5 to 11 Hz. Detection threshold distances were nevertheless always larger for the chequered (decreasing from 47 to 28 m) than for the white (decreasing from 15 to 11 m) ball. In Experiment 2, participants (n = 7) moved laterally along a goal line to intercept the two balls launched with or without ±4.3 Hz sidespin from a 30-m distance. The chequered ball gave rise to shorter movement initiation times when trajectories curved outward (±6 m arrival positions) or did not curve (±2 m arrival positions). Inward curving trajectories, arriving at the same ±2 m distances from the participants as the non-curving trajectories, evoked initial movements in the wrong direction for both ball types, but the amplitude and duration of these reversal movements were attenuated for the chequered ball. We conclude that the early detection of rotation permitted by the chequered ball allowed modulation of interception behaviour without changing its qualitative characteristics.     

An examination of slo-pitch pitching trajectories

Many slo-pitch coaches and players believe that generating spin on a ball can affect its trajectory. The influence of air resistance on a ball that is thrown at a moderate speed and spin is unclear. The aim of this study was to examine the influence of spin on the ball's trajectory in slo-pitch pitching using both experimental results and ball flight simulations. Fourteen pitchers participated in the study, each of whom threw five backspin and topspin pitches each. Data were collected using standard three-dimensional videography. The horizontal velocity, vertical velocity, angular velocity, release height, and horizontal displacement of the backspin pitches were significantly higher than those of the topspin pitches. The ball flight simulations were developed to examine the influence of the ball spin, and it was concluded that the spin of the ball had a significant effect on the ball's vertical and horizontal displacements. Furthermore, our results suggest that a backspin pitch that reaches the maximum height allowable and lands in the front edge of the strike zone has the steepest slope. The present results add to our understanding of projectile motion and aerodynamics.     

The effect of foil on paddling efficiency in a short surfboard

Surfboard volume and shape affect human performance while riding waves, but little is known regarding the impact of these variables on paddling, where surfers spend a majority of their time. The purpose of this study was to determine whether changing the foil (fore/aft thickness profile) of a short surfboard will alter paddling mechanics and efficiency if surfers are allowed to self-select their prone position. Twenty recreational surfers paddled three different surfboards in a freshwater swim flume while measurements of drag force, board motion, body position, heart rate, and oxygen use were acquired. All boards shared the same volume (31 L) and gross dimensions (172.7 cm long × 50.8 cm wide × 6 cm thick), but the geometric center was placed in a different location along the fore/aft axis of each board. Surfers were blinded to the volume and shape of each board. Results indicated that surfers positioned their center of mass further forward in response to a more nose-heavy board and further aft in response to a more tail-heavy board (22.04 ± 6.34 mm difference in position between boards, p = 0.008). This self-selected positioning yielded no statistical difference in drag force, board angle and accelerations, heart rate, or oxygen use across the three boards. These data suggest that when surfboard volume and gross dimensions are fixed, foil has little effect on the efficiency of paddling a short surfboard in recreational athletes.     

The effect of surface geometry on soccer ball trajectories

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

Optimal release conditions for the free throw in men's basketball

The purpose of this study was to determine the optimum release conditions for the free throw in men's basketball. The study used hundreds of thousands of three-dimensional simulations of basketball trajectories. Five release variables were studied: release height, release speed, launch angle, side angle, and back spin. The free throw shooter was assumed to shoot at 70% and to release the ball 2.134 m (7 ft) above the ground. We found that the shooter should place up to 3 Hz of back spin on the ball, should aim the ball towards the back of the ring, and should launch the ball at 52 degrees to the horizontal. We also found that it is desirable to release the ball as high above the ground as possible, as long as this does not adversely affect the player's launch consistency.