Morphometrics for sports mechanics: Showcasing tennis racket shape diversity

Abstract

Tennis racket design has changed from its conception in 1874. While we know that modern tennis rackets are lighter and have larger heads than their wooden predecessors, it is unknown how their gross shape has changed specifically. It is also unknown how racket shape is related to factors that influence performance, like the Transverse and Polar moments of inertia. The aim of this study was to quantify how tennis racket shape has changed over time, with a view to furthering our understanding of how such developments have influenced the game. Two-dimensional morphometric analysis was applied to silhouettes extracted from photographs of 514 rackets dating from 1874 to 2017. A principal component analysis was conducted on silhouette outlines, to allow racket shape to be summarised. The rackets were grouped by age and material for further analysis. Principal Component 1 accounted for 87% of the variation in racket shape. A pairwise Pearson’s correlation test indicated that head width and length were both strongly correlated to Principal Component 1 (r = 0.916 & r = 0.801, p-values<0.001). Principal Component 1 was also correlated to the Polar (r = 0.862, p<0.001) and Transverse (r = -0.506, p<0.001) moments of inertia. Racket age and material had a medium (p<0.001, η2p = 0.074) and small (p = 0.015, η2p = 0.017) effect on Principal Component 1, respectively. Mean racket shapes were also generated from the morphometric analyses for the material and age groupings, and we consider how these shape changes may have influenced performance and injury risk. These mean shape groupings could support the development of models, such as finite element analysis, for predicting how historical developments in tennis equipment have affected performance and injury risk.