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.     

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.     

Hip joint kinetics in the table tennis topspin forehand: relationship to racket velocity

The purpose of this study was to determine hip joint kinetics during a table tennis topspin forehand, and to investigate the relationship between the relevant kinematic and kinetic variables and the racket horizontal and vertical velocities at ball impact. Eighteen male advanced table tennis players hit cross-court topspin forehands against backspin balls. The hip joint torque and force components around the pelvis coordinate system were determined using inverse dynamics. Furthermore, the work done on the pelvis by these components was also determined. The peak pelvis axial rotation velocity and the work done by the playing side hip pelvis axial rotation torque were positively related to the racket horizontal velocity at impact. The sum of the work done on the pelvis by the backward tilt torques and the upward joint forces was positively related to the racket vertical velocity at impact. The results suggest that the playing side hip pelvis axial rotation torque exertion is important for acquiring a high racket horizontal velocity at impact. The pelvis backward tilt torques and upward joint forces at both hip joints collectively contribute to the generation of the racket vertical velocity, and the mechanism for acquiring the vertical velocity may vary among players.     

A biomechanical comparison of the topspin and backspin forehand approach shots in tennis

Three-dimensional (3-D) high-speed cinematographic techniques were used to record topspin and backspin forehand approach shots hit down-the-line by high-performance players. The direct linear transformation (DLT) technique was used in the 3-D space reconstruction from 2-D images recorded via laterally placed phase-locked cameras operating at 200 Hz. A Mann-Whitney U-test was calculated for the different aspects of the topspin and backspin shots to test for significance (P less than 0.05). A significant difference was recorded between topspin and backspin shots in the angle of the racket at the completion of the backswing. The racket was taken 0.48 rad past a line drawn perpendicular to the back fence for topspin trials, but only rotated 0.86 rad from a line parallel to the net in the backspin shot. Maximum racket velocities occurred prior to impact and were significantly higher in topspin (26.5 m s-1) compared to backspin (16.6 m s-1) trials. This resulted in the topspin trials recording a significantly higher ball velocity compared to backspin trials (27.6 m s-1 vs 21.7 m s-1). Pre-impact racket trajectories revealed that in topspin shots the racket moved on an upward path of 0.48 rad while in backspin shots it moved down at an angle of 0.34 rad. In the topspin trials impact occurred significantly further forward of the front foot than in backspin shots (0.26 m vs 0.05 m) while the angle of the racket was the same for both strokes (0.14 rad behind a line parallel to the net). The mean angle of the racket-face at impact was inclined backwards by 0.11 rad for backspin strokes and rotated forward by 0.13 rad for topspin strokes. Angles of incidence and reflection of the impact between the ball and the court showed that backspin trials had larger angles of incidence and reflection than topspin strokes.     

A biomechanical comparison of the topspin and backspin forehand approach shots in tennis

Three‐dimensional (3‐D) high‐speed cinematographic techniques were used to record topspin and backspin forehand approach shots hit down‐the‐line by high‐performance players. The direct linear transformation (DLT) technique was used in the 3‐D space reconstruction from 2‐D images recorded via laterally placed phase‐locked cameras operating at 200 Hz. A Mann‐Whitney U‐test was calculated for the different aspects of the topspin and backspin shots to test for significance (P<0.05).

A significant difference was recorded between topspin and backspin shots in the angle of the racket at the completion of the backswing. The racket was taken 0.48 rad past a line drawn perpendicular to the back fence for topspin trials, but only rotated 0.86 rad from a line parallel to the net in the backspin shot. Maximum racket velocities occurred prior to impact and were significantly higher in topspin (26.5 m s‐¹) compared to backspin (16.6 m s^‐1) trials. This resulted in the topspin trials recording a significantly higher ball velocity compared to backspin trials (27.6 m s^‐1 vs 21.7 m s^‐1). Pre‐impact racket trajectories revealed that in topspin shots the racket moved on an upward path of 0.48 rad while in backspin shots it moved down at an angle of 0.34 rad. In the topspin trials impact occurred significantly further forward of the front foot than in backspin shots (0.26 m vs 0.05 m) while the angle of the racket was the same for both strokes (0.14 rad behind a line parallel to the net). The mean angle of the racket‐face at impact was inclined backwards by 0.11 rad for backspin strokes and rotated forward by 0.13 rad for topspin strokes. Angles of incidence and reflection of the impact between the ball and the court showed that backspin trials had larger angles of incidence and reflection than topspin strokes.     

Contributions of upper limb rotations to racket velocity in table tennis backhands against topspin and backspin

The purpose of this study was to assess the contributions of racket arm joint rotations to the racket tip velocity at ball impact in table tennis topspin backhands against topspin and backspin using the method of Sprigings et al. (1994). Two cine cameras were used to determine three-dimensional motions of the racket arm and racket, and the contributions of the rotations for 11 male advanced table tennis players. The racket upward velocity at impact was significantly higher in the backhand against backspin than against topspin, while the forward velocity was not significantly different between the two types of backhands. The negative contribution of elbow extension to the upward velocity was significantly less against backspin than against topspin. The contribution of wrist dorsiflexion to the upward velocity was significantly greater against backspin than against topspin. The magnitudes of the angular velocities of elbow extension and wrist dorsiflexion at impact were both similar between the two types of backhands. Our results suggest that the differences in contributions of elbow extension and wrist dorsiflexion to the upward velocity were associated with the difference in upper limb configuration rather than in magnitudes of their angular velocities.     

The effects of stride technique and pitch location on slo-pitch batting

In slo-pitch softball, the ball is delivered in an arc trajectory with a moderate velocity; hence, batters have time to adjust their stride technique based on the pitched ball location. The purpose of this study was to examine the influence of stride technique and pitched ball location on the mechanics of slo-pitch batting. A two-way ANOVA of two locations of pitch (inside and outside) x three strides (open, parallel, and closed) repeated measure study was conducted in this study. The results showed that the stride technique and pitched ball location did not have a consistent impact on the participants across different batting conditions, so the study recommends slo-pitch batters to explore different stride techniques when striking the ball. Further, to better understand the generalizability of the findings, the results indicated that participants were quite homogeneous as a group. Hence, coaches and educators may apply the findings from this study to other players with similar skill level.     

Topspin in putters — a study of vertical gear-effect and its dependence on shaft coupling

Imparting topspin on a golf ball from putter impact can be achieved either by oblique impact from negative-lofted putter faces or by vertical eccentric impact (commonly referred to as ‘vertical gear-effect’). Negative loft gives a small amount of topspin but should preferably be combined with positive putter-head trajectory to give the ball lift at impact. Vertical gear-effect can provide high spin rates for impacts above the sweet spot and desirably gives the ball a small upward lift at impact. This paper outlines the theory of spin generation in putter impact, discusses how high vertical gear-effect can be implemented and considers the effect that such designs have on putt length control, directional accuracy and impact vibration. Ballistic measurement techniques to validate putter designs are described and an unexpected experimental result dependent on shaft coupling is analysed.     

Effect of string bed pattern on ball spin generation from a tennis racket

Topspin has become a vital component of modern day tennis. Ball-to-string bed and inter-string friction coefficients can affect topspin generation from a racket. The aim of this research was to determine the effect of string bed pattern on topspin generation. Tennis balls were projected onto nine head-clamped rackets with different string bed patterns. The balls were fired at 24 m/s, at an angle of 26° to the string bed normal with a backspin rate of 218 rad/s and outbound velocity, spin and angle were measured. Outbound velocity was shown to be independent of string bed pattern. Outbound angle increased with the number of cross strings, while outbound topspin decreased. In the most extreme case, decreasing the number of cross strings from 19 to 13 increased rebound topspin from 117 to 170 rad/s.     

Kinematics of table tennis topspin forehands: effects of performance level and ball spin

Abstract

The purpose of this study was to investigate whether performance level and ball spin affect arm and racket kinematics of the table tennis topspin forehand. Nine advanced and eight intermediate male table tennis players hit topspin forehands against light and heavy backspins. Five high-speed video cameras were used to record their strokes at 200 fps. Contributions of joint rotations to the racket speed, the racket kinematics at ball impact, the time required for racket acceleration and the maximum slope of the racket speed-time curve (s _max) were determined. The advanced players showed a significantly larger contribution of lower trunk axial rotation to the racket speed at impact and a significantly larger value of s_max, and tended to require a less time for racket acceleration than the intermediate players. The racket speed at impact was not significantly different between the two player groups. The players adjusted the racket face angle rather than the inclination of the racket path at impact to the different ball spins. The results suggest that the ability to accelerate the racket in less time in the topspin forehand against backspin balls may be an important factor that affects the performance level.     

Aerodynamic effects on the accuracy of an end-over-end kick of an American football

The effects of initial conditions on the flight of an American football kicked in an end-over-end manner were investigated using a dynamic simulation employing the quaternion method. The effects of initial tilt and spin about the longitudinal axis of the ball were considered. For the most accurate kick, our simulations show that the ball should be vertical leaving the kicker’s foot, and have no angular velocity about the longitudinal axis of the ball. A case study was performed for which experimental data were available, showing the trends of the flight of the ball captured in our simulations in actual game situations.     

Mechanical energy generation and transfer in the racket arm during table tennis topspin backhands

The ability to generate a high racket speed and a large amount of racket kinetic energy on impact is important for table tennis players. The purpose of this study was to understand how mechanical energy is generated and transferred in the racket arm during table tennis backhands. Ten male advanced right-handed table tennis players hit topspin backhands against pre-impact topspin and backspin balls. The joint kinetics at the shoulder, elbow and wrist of the racket arm was determined using inverse dynamics. A majority of the mechanical energy of the racket arm acquired during forward swing (65 and 77% against topspin and backspin, respectively) was due to energy transfer from the trunk. Energy transfer by the shoulder joint force in the vertical direction was the largest contributor to the mechanical energy of the racket arm against both spins and was greater against backspin than against topspin (34 and 28%, respectively). The shoulder joint force directed to the right, which peaked just before impact, transferred additional energy to the racket. Our results suggest that the upward thrust of the shoulder and the late timing of the axial rotation of the upper trunk are important for an effective topspin backhand.     

Experimental determination of baseball spin and lift

The aim of this study was to develop a new method for the determination of lift on spinning baseballs. Inertial trajectories of (a) ball surface markers during the first metre of flight and (b) the centre of mass trajectory near home-plate were measured in a pitch using high-speed video. A theoretical model was developed, incorporating aerodynamic Magnus-Robins lift, drag and cross forces, which predicts the centre of mass and marker trajectories. Parameters including initial conditions and aerodynamic coefficients were estimated iteratively by minimizing the error between predicted and measured trajectories. We compare the resulting lift coefficients and spin parameter values with those of previous studies. Lift on four-seam pitches can be as much as three times that of two-seam pitches, although this disparity is reduced for spin parameters greater than 0.4.     

Experimental determination of baseball spin and lift

The aim of this study was to develop a new method for the determination of lift on spinning baseballs. Inertial trajectories of (a) ball surface markers during the first metre of flight and (b) the centre of mass trajectory near home-plate were measured in a pitch using high-speed video. A theoretical model was developed, incorporating aerodynamic Magnus-Robins lift, drag and cross forces, which predicts the centre of mass and marker trajectories. Parameters including initial conditions and aerodynamic coefficients were estimated iteratively by minimizing the error between predicted and measured trajectories. We compare the resulting lift coefficients and spin parameter values with those of previous studies. Lift on four-seam pitches can be as much as three times that of two-seam pitches, although this disparity is reduced for spin parameters greater than 0.4.     

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.     

Dynamics of basketball-rim interactions

A dynamic model for motion of a basketball on the rim is derived. The model is used to investigate shot success sensitivity to initial conditions and to search for initial conditions that lead to long rim contact times. Nonlinear ordinary differential equations describe three components of ball angular velocity and contact point position on the toroidal rim. The model includes radial ball compliance and dissipation and contains three sub-models describing slipping contact, nonslipping contact and purely gravitational flight. Switching between the three sub-models depends on contact point velocity and friction forces. Equivalent radial stiffness and damping constants are estimated using experimental ball force-deflection hysteresis data. General initial conditions almost always involve slip of the ball on the rim. Bouncing on the rim can also occur. After contact it is possible for the ball to enter the rim with its centre passing significantly below the rim plane before rising and ultimately escaping. Exotic quasi-equilibrium periodic circular trajectories exist inside but below the rim plane, relying for their existence on a combination of centripetal force, friction and gyroscopic precession of radial spin about the contact point. Trajectories, and consequent ball capture or escape, are extremely sensitive to initial conditions, especially rim contact position and backspin angular velocity. Backspin aids capture on longrolling trajectories.     

Gymnastics

The 16 highest‐scored Roche vaults (G1) performed during the 2000 Olympic Games were compared with those receiving the 16 lowest‐scores (G2). A 16‐mm motion picture camera operating at 100 Hz recorded the vaults during the competition. The results of t tests (p < .05) indicated G1, compared to G2, had (a) shorter time of board support, greater normalised average upward vertical force and backward horizontal force exerted by the board, greater change in the vertical velocity while on the board, and greater vertical velocity at board take‐off, (b) comparable linear and angular motions in pre‐flight, (c) smaller backward horizontal impulse exerted by the horse, smaller loss of the horizontal velocity while on the horse, and greater horizontal and vertical velocities at horse take‐off, (d) greater height and larger horizontal distance of post‐flight, (e) higher body mass centre at knee release, and (f) higher mass centre, greater normalised moment of inertia, and smaller vertical velocity at mat touchdown. Therefore, gymnasts and coaches should focus on sprinting the approach; blocking and pushing‐off the take‐off board rapidly and vigorously; departing the board with a large vertical velocity; exerting large downward vertical force and small forward horizontal force from the handstand position while on the horse; departing the horse with large horizontal and vertical velocities; and completing the majority of the double salto forward near the peak of trajectory and releasing the knees above the top of the horse to prepare for a controlled landing.     

Comparison of a finite element model of a tennis racket to experimental data

Modern tennis rackets are manufactured from composite materials with high stiffness-to-weight ratios. In this paper, a finite element (FE) model was constructed to simulate an impact of a tennis ball on a freely suspended racket. The FE model was in good agreement with experimental data collected in a laboratory. The model showed racket stiffness to have no influence on the rebound characteristics of the ball, when simulating oblique spinning impacts at the geometric stringbed centre. The rebound velocity and topspin of the ball increased with the resultant impact velocity. It is likely that the maximum speed at which a player can swing a racket will increase as the moment of inertia (swingweight) decreases. Therefore, a player has the capacity to hit the ball faster, and with more topspin, when using a racket with a low swingweight.     

Direction of spin axis and spin rate of the pitched baseball

In this study, we aimed to determine the direction of the spin axis and the spin rate of pitched baseballs and to estimate the associated aerodynamic forces. In addition, the effects of the spin axis direction and spin rate on the trajectory of a pitched baseball were evaluated. The trajectories of baseballs pitched by both a pitcher and a pitching machine were recorded using four synchronized video cameras (60 Hz) and were analyzed using direct linear transform (DLT) procedures. A polynomial function using the least squares method was used to derive the time-displacement relationship of the ball coordinates during flight for each pitch. The baseball was filmed immediately after ball release using a high-speed video camera (250 Hz), and the direction of the spin axis and the spin rate (omega) were calculated based on the positional changes of the marks on the ball. The lift coefficient was correlated closely with omegasinalpha (r = 0.860), where alpha is the angle between the spin axis and the pitching direction. The term omegasinalpha represents the vertical component of the velocity vector. The lift force, which is a result of the Magnus effect occurring because of the rotation of the ball, acts perpendicularly to the axis of rotation. The Magnus effect was found to be greatest when the angular and translational velocity vectors were perpendicular to each other, and the break of the pitched baseball became smaller as the angle between these vectors approached 0 degrees. Balls delivered from a pitching machine broke more than actual pitcher's balls. It is necessary to consider the differences when we use pitching machines in batting practice.     

Effect of tennis racket parameters on a simulated groundstroke

Composite materials have given manufacturers the freedom to develop a broad range of tennis rackets, allowing them to change key parameters such as the structural stiffness, mass, and position of the balance point. The aim of this research was to determine how changing these parameters could affect ball resultant rebound velocity and spin for a simulated groundstroke. A finite element model of a freely suspended racket and strings was used to determine the effect of racket parameters for oblique spinning impacts at a range of locations on the stringbed. The finite element simulations were conducted in the laboratory frame of reference, where the ball is projected onto an initially stationary racket. The mean rebound velocity of the ball was 9% higher for a structurally stiff racket, 37% higher for a heavy racket, and 32% higher for a head-heavy racket. In addition, the mean rebound topspin of the ball was 23% higher for a heavy racket and 21% higher for a head-heavy racket. Therefore, in relation to a groundstroke with an impact location away from the node, the rebound velocity of the ball is likely to increase with the structural stiffness of a racket. The effect of changing the mass and position of the balance point is more complex, as it is dependent on the relationship between the transverse moment of inertia and maximum pre-impact swing velocity.