Effect of materials and design on the bending stiffness of tennis rackets

Lawn tennis rackets have changed considerably since the origins of the game. Early rackets were wooden, making them heavier and more flexible than modern designs made from fibre-polymer composites. The fundamental frequency of a freely suspended tennis racket is often used as an analogue to stiffness, despite it being dependent on mass. We estimate the bending stiffness of 525 rackets, dating from 1874 to 2017, using a uniform beam model that accounts for mass. The model suggests composite rackets are typically about twice as stiff as their wooden predecessors. Applying typical values of Young's modulus, density and second moment of area, the model was used to demonstrate the benefits of fibre-polymer composites for making lightweight, stiff rackets. Undergraduate students could make use of our large dataset of tennis rackets to explore these patterns themselves. They could also go on to measure the dimensions, mass and fundamental frequency of tennis rackets and model them as a uniform beam. Students could also apply the theory to other implements, like badminton and squash rackets or baseball and cricket bats.