Simon Goodwill

Understanding the Effect of Seams on the Aerodynamics of an Association Football

Abstract The aerodynamic properties of an association football were measured using a wind tunnel arrangement. A third scale model of a generic football (with seams) was used in addition to a ‘mini-football’. As the wind speed was increased, the drag coefficient decreased from 0.5 to 0.2, suggesting a transition from laminar to turbulent behaviour in the boundary layer. For spinning footballs, the Magnus effect was observed and it was found that reverse Magnus effects were possible at low Reynolds numbers. Measurements on spinning smooth spheres found that laminar behaviour led to a high drag coefficient for a large range of Reynolds numbers, and Magnus effects were inconsistent, but generally showed reverse Magnus behaviour at high Reynolds number and spin parameter. Trajectory simulations of free kicks demonstrated that a football that is struck in the centre will follow a near straight trajectory, dipping slightly before reaching the goal, whereas a football that is struck off centre will bend before reaching the goal, but will have a significantly longer flight time. The curving kick simulation was repeated for a smooth ball, which resulted in a longer flight time, due to increased drag, and the ball curving in the opposite direction, due to reverse Magnus effects. The presence of seams was found to encourage turbulent behaviour, resulting in reduced drag and more predictable Magnus behaviour for a conventional football, compared with a smooth ball.

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.

Ball Spin Generation for Oblique Impacts with a Tennis Racket

In this paper, we describe an experimental investigation of the oblique impact between a tennis ball and head clamped tennis racket. It was found that the magnitude of the ball rebound spin was not a function of the material, gage or tension of the string used in the tennis racket. Furthermore, it was concluded that all strings exhibit a sufficiently large friction coefficient that the ball begins to roll during impact. There is anecdotal evidence from tennis players that suggests that a high string tension or a rough string surface enable them to impart more spin to the ball. For example, players have been quoted as saying that a high string tension makes the strings “bite” into the ball, giving more spin. The data reported in this study do not support these observations. Analysis of the experimental data has shown that the balls are rebounding from the surface with more spin than would typically be associated with rolling. A second experiment showed that the balls commenced rolling at the mid-point of the impact. This information was used in a theoretical model to show that the spin that acts on the ball during the impact can be higher than the value of the rolling spin at the end of the impact.

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.

Spring damper model of an impact between a tennis ball and racket

Abstract A model has been derived that determines the ball, stringbed and racket frame motion for an impact between a tennis ball and racket. This paper describes the model and methods used to verify it experimentally. The model incorporated parameters such as racket mass, moment of inertia and ball stiffness. The work was conducted to produce a tool that could be used to identify the importance of each of the parameters on the impact. The ball was modelled as simple spring and damper in parallel while the stringbed was modelled as a spring in series with the ball. The values of these spring and damper parameters were determined experimentally. It was assumed that the racket frame was a rigid body to simplify the analysis. Two different methods of supporting the racket were modelled, and the balls were always projected perpendicular to the string plane. Firstly, the racket was head-clamped and all the balls impacted at the geometric string centre of the racket. Good agreement was found between the experiment and model data for both ball rebound velocity and maximum stringbed deflection during impact. The second method of support involved freely suspending the racket at the tip on a small pin. Three different impact positions along the longitudinal axis of the racket were tested. Good agreement between the experiment and model data was found for the ball rebound velocity for impacts at the geometric string centre of the racket. The model over-predicted the experimental racket rebound velocity (generally by less than 5 per cent) for all impact positions. A qualitative analysis assigned this small difference to the assumption that the frame was a rigid body and therefore vibration losses were not accounted for.

Modelling of tennis ball impacts on a rigid surface

Abstract A viscoelastic model of a tennis ball impact at normal incidence on a rigid surface is presented in this study. The ball model has three discrete elements that account for the structural stiffness, material damping and momentum flux loading. Experiments using a force platform are performed to determine the force that acts on the ball during impact, for a range of ball inbound velocities. The inbound and rebound velocities of the ball are measured using speed gates. The contact time and coefficient of restitution for the impact are also determined in these experiments. The model parameters are determined such that the values of the coefficient of restitution and contact time that are calculated by the model are consistent with those values determined experimentally. The model can be used to calculate the force that acts on the ball during impact. Generally, the force-time plots calculated by the model were consistent with those determined experimentally. Furthermore, the model can be used to calculate the three components of the force that acts on the ball during impact. It is shown that the main component of the force during the first 0.6 ms of impact is that due to momentum flux loading. This is approximately equal in magnitude for each ball type and explains why the total force acting on each ball is very similar during this period.

Effect of friction on tennis ball impacts

There are currently no restrictions on the coefficient of friction of tennis courts or strings. The aim of this paper was to determine the effect of friction on tennis ball impacts. Finite element models were used to determine the effect of friction for oblique spinning impacts both between a tennis ball and a rigid surface and between a tennis ball and the string bed of a freely suspended racket. The results showed that during an oblique impact a tennis ball can behave in any of the following ways: first, it can slide, second, it can slide and then ‘overspin’, or, third, it can slide, overspin, and then converge towards rolling. The ball will slide throughout the majority of impacts on the court during play. Therefore, the rebound topspin of the ball will increase with increasing court friction and the horizontal rebound velocity will decrease. The ball will roll off the string bed for the majority of groundstrokes, and the rebound properties will effectively be independent of string bed friction.

A new measure of roughness for defining the aerodynamic performance of sports balls

Abstract A new analysis is presented of the major findings in sports ball aerodynamics over the last 20 years, leading to a new method for defining surface roughness and its effects on the aerodynamic performance of sports balls. It was shown that the performance of balls in soccer, tennis, and golf are characterized by the position of the separation points on the surface of the ball, and that these are directly influenced by the roughness of the surface at a given Reynolds number and spin rate. The traditional measure of roughness k/D (the ratio of surface asperity dimension to diameter) was unable to predict the transition from laminar to turbulent flow for different sports balls. However, statistical measures of roughness commonly used in tribology were found to correlate well with the Reynolds number at transition and the minimum Cd after transition. It was concluded that this new measure and a further one of dimension should allow the complete characterization of the aerodynamic performance of sports balls. The effects of surface roughness on spin rate decay were also considered, and it was found that tennis balls had spin decay over six times that of golf balls and was due to the increased skin friction of the nap.

Effect of tennis racket parameters on a simulated groundstroke

Abstract 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.

Oblique impact of thick walled pressurized spheres as used in tennis

Abstract A model is presented in which the normal impact of a thick walled pressurized sphere, such as a tennis ball, is modelled as a non-linear viscoelastic spring and damper, coupled with momentum-flux forces where the shell wall deforms with high stiffness and damping. These momentum-flux forces are only present in the impact phase and do not appear during restitution. Rotation set up during an oblique impact causes the momentum-flux forces at the front and rear of the sphere to be different such that the total vertical reaction force acts in front of the centre of mass when topspin is present. The sphere was allowed to deform and this caused both the torque and the effective moment of inertia of the sphere to decrease. The result of this is that the deformed sphere gains sufficient spin during impact for reverse slip to occur when the ball reforms towards the end of impact. Tennis balls were projected at two similarly constructed surfaces with a coefficient of friction of 0.51 and 0.62. It was found that displacements and rotations from the model compared well with experimental results recorded using a high-speed video running at 7100 frames per second. The model was able to predict these results with only the coefficient of friction as the varying parameter.