## 3 Results  
### Geometric Properties  
Figure 3 summarises how the frame materials (Figure 3b) and lengths (Figure 3a) of the racket, grip, throat region and head (ext. ), and CoM location, changed over time. Wood was the common material until the 1960s, although there were also twenty metal rackets in our sample from this time (2 steel, 2 aluminium, 16 wood + steel). The first example of a steel racket was from 1887 (Metallic Racquet Corporation, Aberdeen), with an aluminium example from the 1920s (Birmal, Birmingham Aluminium Casting Limited). Following a small increase over the first few decades, the length of the rackets barely changed (mean (\(\mu\)) \(\pm\) standard deviation (\(\sigma\)), 0.69 \(\pm\) 0.01 m), possibly due to the limit introduced by the ITF in 1981. The CoM of the rackets moved towards the handle from the 1870s to the 1980s, and then back towards the tip with the move to composites (\(\mu\) \(\pm\)\(\sigma\), 0.34 \(\pm\) 0.02 m). The COM moved from the throat region into the head during the 1990s as a response to the introduction of oversize rackets (one of the key claims of [PERSON]'s racket patent [6]). The rackets predating 1890 had long grips, limited throat regions and short heads. The head length of the rackets barely changed from the 1890s to the 1970s, as throat regions lengthened and grips shortened. Composites first occurred in the rackets from the 1960s (wood + comp. ), mainly as reinforcement on a wooden frame (e.g., \"Fibre Armoured\" on 1961 Challenge Power, Slazenger; \"Fibre Face\" on 1966 Kramer Cup, Wilson), with wood remaining as the common material. The first examples of entirely composite rackets were from the 1970s (Phantom, Slazenger, 1974; TR10, Rossignol, 1977; make and model unknown, WTM 1995/136, 1970s). Two rackets from the 1970s had a composite core sandwiched between aluminium plates (Arthur Ashe and Drive, Head). Wooden rackets made up around a third of those from the 1970s, and there were still examples of composite reinforced wooden frames. The number of composite (64%) rackets increased in the 1980s, as the proportion of wooden (13%) and metal (11%) rackets declined. Rackets from the 1980s had longer heads and shorter throat regions than those from the 1970s. Head and grip lengths increased further in the rackets from the 1990s, with little change over the last three decades, with all but two being composite. Only one racket from 2011 had a wooden \"spine\" in a composite frame (Core 1 Number 20, Pro-Kennex), with claims that it benefitted from the damping properties of wood. Figure 4a shows the oldest rackets typically had lopsided or other unconventionally-shaped heads, with most samples postdating 1890 having'regular' elliptical heads. Figure 4b shows that the rackets predating 1920 typically had convex wedge-shaped throats, those dating from 1920 to 1980 typically had closed throats and those postdating 1980, which were mainly composite, typically had'regular' open throats. Figure 4c shows that most of the rackets had a'regular' shaped handle, although some of the older samples had more ornate handle shapes and a small portion from 1910 to 1980 had a handle made from a different material to the rest of the frame. Figure 4d shows that the vast majority of the rackets had'regular' stringing patterns, with some examples of less conventional patterns. Figure 5 summarises how the head area, the string bed density and the depth to thickness ratio of the rackets changed over time. Figure 5a shows head area increased in the 1970s with material experimentation. The aluminium racket with a large head area (0.0702 m\({}^{2}\)) from 1976 was [PERSON]'s 'oversize' design (Classic, Prince), following which there was an increase in the head area of the rackets (\(\sim\)0.045 to \(\sim\)0.07 m\({}^{2}\)) coinciding with the move to composites.