Fig 1.
Tennis racket morphospaces based on the two main principal components (PC1 and PC2).
Panel a) shows the input shape data of 514 rackets, and panel b) shows the theoretical morphospace, both around the input data (within the dashed line box) and over an extended theoretical range of ± 2 standard deviations. Dashed line box identifies the actual data space in panel a) and b). Panel c) shows the PC contributions of PC1 and PC2 individually, when all other principal components are held at their mean values.
Fig 2.
Identifying racket shape patterns from the theoretical morphospace based on the two main principal components (PC1 and PC2).
Panel a) shows the theoretical morphospace, both around the input data (within the dashed line box) and over an extended theoretical range of ± 2 standard deviations. Dashed line box identifies the actual data space. Inset panels show main shape features identified by-eye, including embellished handles (orange area and inset panel b), narrow-angled throats (red area and inset c), wide-angled throats (purple area and inset d and f), and angled or straight sides (blue area and inset panels e and f). The dashed blue box indicates an overlap of the two features wide-angled throats and angled or straight sides. The red annotations on the inset panels show how the features are defined, by handle compartmentalisation (*), throat angle (θ) and orientation of the head sides.
Fig 3.
Tennis racket morphospaces based on the two main principal components (PC1 and PC2) of modern rackets (post-1990).
Panel a) shows the input shape data of 84 rackets, and panel b) shows the theoretical morphospace, both around the input data (within the dashed line box) and over an extended theoretical range of ± 2 standard deviations. Inset photographs show the two representative racket shapes over the morphospace—a symmetric, oval head (e.g., Wilson, Triad 2.0 Hammer 2003, top) and asymmetric head (e.g., Neoxx, ST 285 2008, bottom). Panels c) and d) show existing, older example rackets that are similar to the theoretical outlines. c) is a Keubler Plus 60 racket from the 1980s and d) is a Lambert racket from 1874.
Fig 4.
Example rackets with features from the theoretical morphospace in Fig 1B.
Including a) Embellished handles: Slazenger Phantom 1974; Defiance 1900; b) Narrow-angled throats: Keubler Plus 60 1980; Silver Arrow 1983; c) Angled or straight sides: Bonny Bergelin Long String 1986; d) Wide-angled throats with straight sides: Inter Business AG, Myrac, 1980; Reproduction racket from 1885; e) wide-angled throats: Table tennis bat; a Padel racket (Head Gravity Motion 2022). A mean composite racket outline is overlaid on each concept racket, taken from Fig 3D of Grant et al. (19). The center of area of each concept image is approximated by a red asterisk (*), as a basic indication of the centre of mass location for that shape.