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Finite element modelling of tennis racket impacts to predict spin generation

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posted on 2013-05-24, 08:54 authored by David Weir
Over the last 20-30 years the subject of spin in tennis has become increasingly important. A great deal of work has been done to establish the effects which, increased levels of spin have, on shots. The most prominent effect of increased spin in a tennis shot is the resulting deviation in flight which allows players to, amongst other things, strike the ball harder with top-spin in the knowledge that it will still fall inside the court due to the extra aerodynamic downward force. With such significant advantages available racket manufacturers are naturally keen to maximise spin generation. That being said, very little research has been performed into the subject of spin generation in tennis and the affecting factors. This thesis details the development of a finite element model which is to be used to allow a greater understanding of spin generation and how varying properties such as string density (the number of strings in a string-bed), gauge and orientation affect its magnitude. The primary aim, or goal, of this research is to create an FE model which can be used to model oblique impacts and measure the resulting spin. Whilst considerable focus was placed on developing novel, modelling techniques to create the FE model, a great deal of emphasis was also placed on its validation. The validity of the model was examined under static loading conditions, such as that experienced during stringing. The dynamic performance was also validated using a combination of modal analysis and high speed video of dynamic impacts. Each of the validation methods provided assurance of the models performance, with all error margins less than 5%. The two areas of the FE model which required the most attention were the interaction properties (specifically coefficient of friction (COF)) and material properties. Previous studies have sought to obtain a single value for the COF of a tennis racket/ball system but this study examines how the COF varies as the strings interact first, with themselves and secondly with the ball. Each of the validation methods (dynamic and static) were deemed successful as they provided concise data which could be readily compared with the results produced by the FE model. Having validated the model s performance, with respect to predicting outbound spin, a number of oblique impact angles were modelled to allow a greater understanding of how the mechanisms of spin generation change with the inbound trajectory of the ball. This analysis showed that for the impact conditions studied the contact time of the impact was reduced from 6.2 milliseconds to 5.7 milliseconds when the angle was increased from 32 degrees to 40 degrees. Furthermore, a number of novel string-beds were modelled, with varying string orientations (between 30 degrees and 60 degrees relative to the rackets frame) and subjected to a similar analysis procedure, with their results providing the concluding section of the thesis.





  • Mechanical, Electrical and Manufacturing Engineering


© David Weir

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A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.

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