## 4 Discussion  
Collected racket parameters were approximated by the main principal components (PCA1). Head sizes and natural frequencies of tennis rackets have changed most significantly during their development and correlate best with PCA1. We suggest that these main changes were likely to be facilitated by the increased stiffness of composite materials. Wood was the common material for tennis rackets until the 1960s, when composites were used as reinforcement on a wooden frame. By the 1970s, engineers were experimenting with steel, aluminium and fibre-polymer composites, as they are stronger than wood and allowed for rackets with larger heads. Oversized rackets made tennis easier to play, but metal frames had lower natural frequencies than their composite counterparts and offered limited damping, so that vibrations from ball contact away from the node (the'sweet spot') lasted longer [40]. By the 1980s, composites had surpassed wood as the common racket material, providing engineers with more freedom over frame shape, stiffness, and mass distribution. Many racket properties, such as the frame cross section shape (Figure 6b), mass (Figure 7a), Polar MOI (Figure 7c) and natural frequency (Figure 8a) were more varied in modern designs, giving the player greater choice to suit their style, experience and preference. The analysis presented here did not reveal a lasting brand that departed radically from established principles of tennis racket design. All brands tended to follow the same fundamentals with regards to head size, stiffness and material. Differences revealed in the analysis appear to have been due to the longevity of particular brands and the era of their presence within the marketplace. Observed differences were due to restrictions in racket material for a brand prevalent in the wooden era compared to modern tennis racket brands. This study provides the first presentation of how string bed densities, damping and external cross section dimensions of tennis rackets have changed over time. While other racket parameters have been previously documented by [PERSON] et al. [3], over three times more rackets were characterised here with a wider variety of measurements, analysis methods and reporting of materials. Findings agreed with [PERSON] et al. [3] in terms of trends in properties since the 1870s, including overall length, grip and head length, head width, mass, CoM location, natural frequency and transverse MOI (reported as swingweight (Figure 1a) in [3]), but this study also shows how materials have driven the development of the tennis racket. [PERSON] et al. [3] only includes rackets up to 2007; data presented here indicates that the rate of change for some properties, such as head size (Figure 5a) and mass (Figure 6a), may have slowed recently, since 2007. [PERSON] et al. [3] showed scatter in their results for Polar MOI with no clear trend over time, while those reported here show little change until 1970 followed by a steady increase with the move to rackets with wider heads, as expected [29; 38]. [PERSON] et al. [3] estimated Polar MOI from measurements of transverse and lateral MOI (using a Babolat Racquet Diagnostic Centre) [3],  
Figure 9: Seven tennis rackets showing developments over time: (**a**) Early racket by [PERSON] (1870s); (**b**) wooden racket by [PERSON] (1886); (**c**) steel racket by Dayton Steel Racket Corporation (1922); (**d**) Dunlop “Maxply” (1955); (**e**) Prince “Classic” (1976); (**f**) Snauwaert Hi-Ten 50 (1986); (**g**) Head Graphene XT Prestige with the sensor (2017). and the assumption that a racket is planar, combined with uncertainty from two measures may have influenced their results [28]. Holding a racket by the handle can change modal frequencies and shapes and substantially increase damping [40; 41; 42], and future work could investigate the dynamic properties of rackets from different eras in more depth, if freely suspended, hand-held and with mass added at the handle to represent the hand.