# Measurement of Strain and Strain Rate during the Impact of Tennis Ball Cores
## 3 Results
### Impact Strain  
Figure 7 highlights that mean strain during impact increased with both impact angle and, to a greater degree, impact velocity. The exception being the mean strain for impacts at 90\({}^{\circ}\) with an impact velocity of 43.1 m\(\cdot\)s\({}^{-1}\) or greater which showed either no increase or a reduction in mean strain, a likely consequence of loss of surface computation at the largest deformations (e.g., Figure 6). The maximum mean strain occurred for impacts at 40\({}^{\circ}\) and 52.5 m\(\cdot\)s\({}^{-1}\) for both pressurised (0.06 strain) and pressureless ball cores (0.054 strain). Similarly, the minimum mean strain value occurred for impacts at 18.9\({}^{\circ}\) with in impact velocity of 13.7 m\(\cdot\)s\({}^{-1}\).  
Over 95% of strain measured was distributed between \(-\)0.1 and 0.1 strain for impacts at 18.9\({}^{\circ}\) with an impact velocity of 22.1 m\(\cdot\)s\({}^{-1}\) (Table 5). The remaining impact conditions at higher impact angles and faster impact speeds were more widely distributed (Figure 8). Table 5 also highlights a higher percentage of tensile (positive) strain is present than compressive (negative) strain, and was present to a greater degree at larger strains. For example, 8.4% of strain on average was distributed between 0.2 and 0.3 strain, compared to 2.1% for strains between \(-\)0.3 and \(-\)0.2, a trend present across all conditions except impacts at 18.9\({}^{\circ}\) and 22.1 m\(\cdot\)s\({}^{-1}\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Angle (\({}^{\circ}\))** & **Desired Ball Speed (m\(\cdot\)s\({}^{-1}\))** & **Pressurised** & **Pressureless** \\ \cline{3-4}  & & **Mean \(\pm\) SD** & **Mean \(\pm\) SD** \\ \hline
18.9 & 22.1 & 22.9 \(\pm\) 1.1 & 23.1 \(\pm\) 1.2 \\
40 & 52.5 & 54.8 \(\pm\) 0.4 & 53.0 \(\pm\) 0.6 \\
90 & 30.5 & 30.4 \(\pm\) 0.7 & 32.1 \(\pm\) 1.2 \\
90 & 52.5 & 52.1 \(\pm\) 0.6 & 51.5 \(\pm\) 1.7 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Mean pre-impact ball speed \(\pm\) one standard deviation (SD) for impact conditions of interest.  
Figure 6: Example impact frames with loss of surface tracking for impacts at 52.5 m\(\cdot\)s\({}^{-1}\) and 90\({}^{\circ}\).  
Figure 8: Strain distribution during impact for pressurised (**a**) and pressureless (**b**) ball cores.  
Figure 7: Mean strain during impact for pressurised (**a**) and pressureless (**b**) ball cores.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Strain Distribution** & \multicolumn{4}{c}{**Pressurised Core: Impact Angle \& Speed**} & \multicolumn{4}{c}{**Pressureless Core: Impact Angle \& Speed**} \\ \hline \multirow{2}{*}{**Bin Edges-Strain**} & **18.9\({}^{\circ}\)**, 22.1** & **40\({}^{\circ}\)**, 52.5** & **90\({}^{\circ}\)**, 30.5** & **90\({}^{\circ}\)**, 52.5** & **18.9\({}^{\circ}\)**, 22.1** & **40\({}^{\circ}\)**, 52.5** & **90\({}^{\circ}\)**, 30.5** & **90\({}^{\circ}\)**, 52.5** \\  & **m-s\({}^{-1}\)** & **m-s\({}^{-1}\)** & **m-s\({}^{-1}\)** & **m-s\({}^{-1}\)** & **m-s\({}^{-1}\)** & **m-s\({}^{-1}\)** & **m-s\({}^{-1}\)** & **m-s\({}^{-1}\)** \\ \hline \(-\)0.4 & \(-\)0.3 & 0.12 & 0.19 & 0.18 & 1.47 & 0.07 & 0.27 & 0.15 & 1.21 \\ \(-\)0.3 & \(-\)0.2 & 0.31 & 1.35 & 0.84 & 3.35 & 0.19 & 1.70 & 1.07 & 4.43 \\ \(-\)0.2 & \(-\)0.1 & 1.14 & 11.45 & 8.29 & 6.39 & 0.83 & 12.92 & 8.92 & 6.98 \\ \(-\)0.1 & 0 & 34.59 & 25.11 & 35.97 & 32.13 & 49.08 & 24.69 & 32.38 & 30.24 \\ 0 & 0.1 & 61.11 & 21.19 & 30.72 & 34.77 & 47.35 & 18.35 & 32.04 & 35.34 \\
0.1 & 0.2 & 2.02 & 25.35 & 13.98 & 11.10 & 2.06 & 27.80 & 14.55 & 12.92 \\
0.2 & 0.3 & 0.34 & 9.58 & 8.94 & 5.79 & 0.20 & 10.23 & 9.97 & 6.09 \\
0.3 & 0.4 & 0.10 & 5.27 & 0.84 & 4.04 & 0.09 & 3.66 & 0.72 & 2.47 \\
0.4 & 0.5 & 0.04 & 0.26 & 0.08 & 0.42 & 0.03 & 0.16 & 0.08 & 0.12 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Percentage distribution of strain during impact.