Advanced modelling and design of a tennis ball

Modern tennis has been played for over a hundred years, but despite significant improvements in the design and manufacture of tennis balls to produce a long-lasting and consistent product, the design of a tennis ball has barely changed in the last century. While some work has been done to better understand the dynamic behaviour of a tennis ball, no structured analysis has been reported assessing how the typical constructions of the inner rubber core and cloth panels affect its behaviour and performance. This research describes the development of an advanced and validated finite element (FE) tennis ball model which illustrates the effects of the viscoelastic and anisotropic materials of a tennis ball on ball deformation and bounce during impacts with the ground and the racket,representative of real play conditions. The non-linear strain rate properties exhibited by the materials of a tennis ball during high velocity impacts were characterised using a series of experiments including tensile and compressive tests as well as low and high velocity impact tests. The impacts were recorded using a high speed video (HSV) camera to determine deformation, impact time, coefficient of restitution (COR) and spin rate. The ball material properties were tuned to match the HSV results, and the ball s model parameters were in good agreement with experimental data for both normal and oblique impacts at velocities up to 50 m/s and 35 m/s, respectively. A time sequenced comparison of HSV ball motion and FE model confirmed the accuracy of the model, and showed significant improvement on previous models. Although the existing construction of tennis ball cores was found to provide a sufficiently uniform internal structure to base competition standard tennis balls, the anisotropic nature of the cloth panels resulted in deviation angles as high as 1.5 degrees in ball bounce. Therefore, new cloth panel configurations were modelled which allowed the cloth fibre orientations around the ball to be adjusted resulting in better bounce consistency. The effect of cloth seam length on ball flight was explored through wind tunnel tests performed on solid balls made by additive manufacturing (AM) and on actual pressurised tennis ball prototypes. A reverse Magnus effect was observed on the AM balls, however, this phenomenon was overcome by the rough nature of the cloth cover on the real tennis ball prototypes. A ball trajectory simulation showed that there was no obvious dependence between seam length and shot length or ball velocity. Finally, a basic panel flattening method was used to determine the 2Dsize of the cloth panel patterns corresponding to the new configurations, and tiling methods were designed to estimate cloth wastage. The traditional dumbbell design appeared to result in the minimum amount of waste. The work reported in this thesis represents a significant improvement in the modelling of tennis ball core, cloth and seams, as well as the ball s interaction with the ground and racket strings. While this research focused on woven cloth, needle cloth is also widely used in the manufacture of balls in the US. The modelling of needle cloth could therefore be part of a future study. Additionally, details such as the depth and roughness of the cloth seam could be included in the model to study their effect on spin generation. Also, including cloth anisotropy in the flattening method would allow a better prediction of cloth wastage which could then have an influence on the configuration of the cloth panels.