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.     

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.     

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.     

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.     

Modelling the flight of a soccer ball in a direct free kick

This study involved a theoretical and an experimental investigation of the direct free kick in soccer. Our aim was to develop a mathematical model of the ball's flight incorporating aerodynamic lift and drag forces to explore this important 'set-play'. Trajectories derived from the model have been compared with those obtained from detailed video analysis of experimental kicks. Representative values for the drag and lift coefficients have been obtained, together with the implied orientation of the ball's spin axis in flight. The drag coefficient varied from 0.25 to 0.30 and the lift coefficient from 0.23 to 0.29. These values, used with a simple model of a defensive wall, have enabled free kicks to be simulated under realistic conditions, typical of match-play. The results reveal how carefully attackers must engineer the dynamics of a successful kick. For a central free kick some 18.3 m (20 yards) from goal with a conventional wall, and initial speed of 25 m·s^?1, the ball's initial elevation must be constrained between 16.5° and 17.5° and the ball kicked with almost perfect sidespin.     

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.     

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.     

Fundamental aerodynamics of the soccer ball

When the boundary layer of a sports ball undergoes the transition from laminar to turbulent flow, a drag crisis occurs whereby the drag coefficient (C _d) rapidly decreases. However, the aerodynamic properties and boundary-layer dynamics of a soccer ball are not yet well understood. In this study we showed that the critical Reynolds number (Re _crit) of soccer balls ranged from 2.2 × 10⁵ to 3.0 × 10⁵. Wind-tunnel testing, along with visualisation of the dynamics of the boundary layer and the trailing vortex of a ball in flight, demonstrated that both non-spinning and spinning (curved) balls had lowC _d values in the super-critical region. In addition, theRe _crit values of the soccer balls were lower than those of smooth spheres, ranging from ∼ 3.5 × 10⁵ to 4.0 × 10⁵, due to the effects of their panels. This indicated that the aerodynamic properties of a soccer ball were intermediate between those of a smooth ball and a golf ball. In a flow visualisation experiment, the separation point retreated and theC _d decreased in a super-critical regime compared with those in a sub-critical regime, suggesting a phenomenon similar to that observed in other sports balls. With some non-spinning and spinning soccer balls, the wake varied over time. In general, the high-frequency component of an eddy dissipated, while the low-frequency component increased as the downstream vortex increased. The causes of the large-scale fluctuations in the vortex observed in the present study were unclear; however, it is possible that a ‘knuckle-ball effect’ of the non-rotating ball played a role in this phenomenon.     

Modelling the flight of a soccer ball in a direct free kick

This study involved a theoretical and an experimental investigation of the direct free kick in soccer. Our aim was to develop a mathematical model of the ball's flight incorporating aerodynamic lift and drag forces to explore this important 'set-play'. Trajectories derived from the model have been compared with those obtained from detailed video analysis of experimental kicks. Representative values for the drag and lift coefficients have been obtained, together with the implied orientation of the ball's spin axis in flight. The drag coefficient varied from 0.25 to 0.30 and the lift coefficient from 0.23 to 0.29. These values, used with a simple model of a defensive wall, have enabled free kicks to be simulated under realistic conditions, typical of match-play. The results reveal how carefully attackers must engineer the dynamics of a successful kick. For a central free kick some 18.3 m (20 yards) from goal with a conventional wall, and initial speed of 25 m x s(-1), the ball's initial elevation must be constrained between 16.5 degrees and 17.5 degrees and the ball kicked with almost perfect sidespin.     

Variability of impact kinematics and margin for error in the tennis forehand of advanced players

The kinematics of the racket and ball near impact in tennis forehands were studied to document typical variation in successful and unsuccessful shots, in order to determine biomechanically meaningful differences in advanced players and confirm models of groundstroke trajectories. Seven tennis players (six males and one female) were videoed from the side at 180 Hz as they performed 40 forehand drives on an indoor tennis court. Vertical plane kinematics of the racket and ball near impact were analysed for sub samples of successful and unsuccessful shots for each subject. Most racket kinematic variables were very consistent (mean CV< 6.3%) for successful shots, so bio mechanically meaningful differences in angles and velocities of the racket and ball (3° and 2 m s⁻¹) near impact could be detected between successful and unsuccessful shots. Four subjects tended to miss long and three subjects missed shots in the net that were reflected in initial ball trajectories. Mean (SD) initial trajectories for long shots were 9.8° (1.4°), while netted shots were 0.7° (1.1°) above the horizontal. The initial ball trajectories and margins for error for these subjects were smaller than those previously reported (Brody, 1987) because players tended to select mean ball trajectories close to one error than another, differing amounts of topspin, or incorrect lift and drag coefficients for tennis balls had not been published when this model was created. The present data can be used to confirm if recent models (Cookeet al., 2003; Dignallet al., 2004) more closely match actual performance by advanced players.     

Understanding the effect of finger–ball friction on the handling performance of rugby balls

Handling errors are often seen in professional rugby games and even more so in amateur rugby. This paper analyses the problem of ball mishandling using high-speed video footage of passes and a bespoke finger friction rig. The high-speed video analysis showed that when the ball is caught, often there is a fluctuating movement of the fingers over the surface of the ball. It also showed that the fingers move over the surface of the ball when the ball is thrown, confirming that the dynamic friction is a good measure of how easily a ball can be handled. Rugby ball surface samples were used, on a finger friction rig, to assess the coefficient of friction between the finger and the balls. The currently manufactured balls displaying the highest coefficients of friction in clean, dry conditions were the design with square, ‘sharp’ pimples and also the design with a mixture of small and large pimples. The most consistent ball across wet and dry conditions was the ball with round, large, densely populated pimples. It was also shown that when water is added to the surface of the ball or finger, there was little variation in performance between the ball varieties.     

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.     

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

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

Effects of contrasting colour patterns of the ball in the volleyball reception

The effects of three different colour patterns on the surface of volleyballs (versus that of a plain white ball) on the behaviour of a reception player were examined by presenting sidespin volleyball serves. Expert (n = 10) and novice (n = 10) volleyball players intercepted volleyballs projected straight at them or at an initial angle of 9.5° outwards but eventually curving towards the players' original position. In the latter trajectories, players generally took one or more steps laterally before returning to the landing position of the ball. These excursion patterns were significantly more pronounced with the white balls than the coloured balls. Differences between balls of different colour combinations were also observed. The first finding supports the thesis that next to a prospective type of control, such as on-line maintenance of a certain spatiotemporal relationship between the player and the ball, properties of the ball itself allow prediction of the future path of the ball. Differences between types of colour patterns are explained within the framework of the between-colours wavelength contrasts of each type of ball.     

Reliability and construct validity of soccer skills tests that measure passing, shooting, and dribbling

In this study, we examined the reliability and construct validity of new soccer skills tests. Twenty soccer players (10 professional and 10 recreational) repeated trials of passing, shooting, and dribbling skills on different days. Passing and shooting skills required players to kick a moving ball, delivered at constant speed, towards one of four randomly determined targets. Dribbling required players to negotiate seven cones over 20?m. Each trial consisted of 28 passes, 8 shots, and 10 dribbles. Ball speed, precision, and success were determined for all tests using video analysis. Systematic bias was small (<9% in all measures) and all outcome measures were similar between trials. Test-retest reliability statistics were as follows: ball speed (passing, shooting, dribbling; coefficient of variation [CV]: 6.5%, 6.9%, 2.4%; ratio limits of agreement [RLOA]: 0.958?×/÷ 1.091, 0.990?×/÷ 1.107, 0.993?×/÷ 1.039), precision (passing, shooting, dribbling; CV: 10.0%, 23.5%, 4.6%; RLOA: 0.956?×/÷ 1.147, 1.030?×/÷ 1.356, 1.000?×/÷ 1.068), and success (passing, shooting, dribbling; CV: 11.7%, 14.4%, 2.2%; RLOA: 1.017?×/÷ 1.191, 0.913?×/÷ 1.265, 0.996?×/÷ 1.035). Professional players performed better than recreational players in at least one outcome measure for all skills. These findings demonstrate the reliability and validity of new soccer skill protocols.     

Effects of contrasting colour patterns of the ball in the volleyball reception

The effects of three different colour patterns on the surface of volleyballs (versus that of a plain white ball) on the behaviour of a reception player were examined by presenting sidespin volleyball serves. Expert (n = 10) and novice (n = 10) volleyball players intercepted volleyballs projected straight at them or at an initial angle of 9.5 degrees outwards but eventually curving towards the players' original position. In the latter trajectories, players generally took one or more steps laterally before returning to the landing position of the ball. These excursion patterns were significantly more pronounced with the white balls than the coloured balls. Differences between balls of different colour combinations were also observed. The first finding supports the thesis that next to a prospective type of control, such as on-line maintenance of a certain spatiotemporal relationship between the player and the ball, properties of the ball itself allow prediction of the future path of the ball. Differences between types of colour patterns are explained within the framework of the between-colours wavelength contrasts of each type of ball.     

Reliability and construct validity of soccer skills tests that measure passing,shooting, and dribbling

Abstract

In this study, we examined the reliability and construct validity of new soccer skills tests. Twenty soccer players (10 professional and 10 recreational) repeated trials of passing, shooting, and dribbling skills on different days. Passing and shooting skills required players to kick a moving ball, delivered at constant speed, towards one of four randomly determined targets. Dribbling required players to negotiate seven cones over 20 m. Each trial consisted of 28 passes, 8 shots, and 10 dribbles. Ball speed, precision, and success were determined for all tests using video analysis. Systematic bias was small (<9% in all measures) and all outcome measures were similar between trials. Test–retest reliability statistics were as follows: ball speed (passing, shooting, dribbling; coefficient of variation [CV]: 6.5%, 6.9%, 2.4%; ratio limits of agreement [RLOA]: 0.958 ×/÷ 1.091, 0.990 ×/÷ 1.107, 0.993 ×/÷ 1.039), precision (passing, shooting, dribbling; CV: 10.0%, 23.5%, 4.6%; RLOA: 0.956 ×/÷ 1.147, 1.030 ×/÷ 1.356, 1.000 ×/÷ 1.068), and success (passing, shooting, dribbling; CV: 11.7%, 14.4%, 2.2%; RLOA: 1.017 ×/÷ 1.191, 0.913 ×/÷ 1.265, 0.996 ×/÷ 1.035). Professional players performed better than recreational players in at least one outcome measure for all skills. These findings demonstrate the reliability and validity of new soccer skill protocols.     

Elite tennis player sensitivity to changes in string tension and the effect on resulting ball dynamics

Eighteen elite male tennis players were tested to determine their ability to identify string tension differences between rackets strung from 210 N (47 lb) to 285 N (64 lb). Each player impacted four tennis balls projected from a ball machine before changing rackets and repeating the test. Eleven participants (61%) could not correctly detect a 75 N (17 lb) difference between rackets. Only two participants (11%) could correctly detect a 25 N (6 lb) difference. To establish whether varying string tensions affected ball rebound dynamics, the ball’s rebound speed and landing position were analysed. The mean rebound ball speed was 117 km h⁻¹, with only the trials from the 210 N racket producing significantly lower (P < 0.05) rebound speeds than the 235 N and 260 N rackets. This is contrary to previous laboratory-based tests where higher rebound speeds are typically associated with low-string tensions. The anomaly may be attributable to lower swing speeds from participants as they were not familiar with such a low string tension. Ball placement did not appear related to string tension, with the exception of more long errors for the 235 N racket and fewer long errors for the 285 N racket. It was concluded that elite male tennis players display limited ability to detect changes in string tension, impact the ball approximately 6% faster than advanced recreational tennis players during a typical rallying stroke, and that ball placement is predominantly unrelated to string tension for elite performers.