# Low Speed Impact of an Elastic Ball with Tapes and Clay Court
## 4 Results and Discussion  
The general behavior of the coefficient of restitution is graphically investigated in the following section. Each data point in Figures 6-8 illustrates the mean of three experiments repeated at the same drop height, the same impact angle, and on the same surface. The coefficient of restitution (\(e\)) of a tennis ball on a granular surface is shown in Figure 6. Figure 6a shows the chance of \(e\) with respect to pre-impact velocity, \(V_{\rm C}(t_{0})\), and Figure 6b shows the chance of \(e\) with respect to impact angle, \(\beta\). Figure 6a reveals no trend in the change of \(e\) with normal pre-impact velocity; moreover, there is no apparent separation between angle groups. Mean \(e\)'s and standard deviations are \(\overline{e}=0.735\) and \(\sigma=0.0097\) for normal impact, \(\overline{e}=0.716\) and \(\sigma=0.0062\) for oblique angle \(\beta=7.5^{\circ}\), \(\overline{e}=0.718\) and \(\sigma=0.0219\) for oblique angle \(\beta=15^{\circ}\), \(\overline{e}=0.709\) and \(\sigma=0.0302\) for oblique angle \(\beta=22.5^{\circ}\). Figure 6b shows a slight decrease in \(e\) with increasing angle. The standard deviation in Figure 6b is \(\sigma=0.0112\). The coefficient of restitution (\(e\)) of tennis balls on tape 1 is shown in Figure 7. Figure 7a shows the chance of \(e\) concerning pre-impact velocity, \(V_{\rm C}(t_{0})\), and Figure 7b shows the chance of COR with respect to impact angle, \(\beta\). Figure 7a does not show any systematic behavior of COR with normal pre-impact velocity and impact angle. Mean \(e\)s and standard deviations are \(\overline{e}=0.777\) and \(\sigma=0.0219\) for normal impact, \(\overline{e}=0.754\) and \(\sigma=0.0204\) for oblique angle \(\beta=7.5^{\circ}\), \(\overline{e}=0.751\) and \(\sigma=0.0262\) for oblique angle \(\beta=15^{\circ}\), and \(\overline{e}=0.777\) and \(\sigma=0.0500\) for oblique angle \(\beta=22.5^{\circ}\). Figure 7b shows a slightly higher \(e\) for normal impact and \(\beta=22.5^{\circ}\) degrees compared to \(\beta=7.5^{\circ}\) and \(\beta=15^{\circ}\). The standard deviation in Figure 7b is \(\sigma=0.0317\). The coefficient of restitution (\(e\)) of tennis balls on tape 2 is shown in Figure 8. Figure 8a shows the chance of \(e\) with respect to pre-impact velocity, \(V_{\rm C}(t_{0})\), and Figure 8b shows the  
Figure 6: (a) \(e\) for different initial velocities from 1.6 to 2.5 m/s and different impact angles \(\beta\) for the granular surface; (b) Mean \(e\) for different impact angles for the granular surface. Figure 7: (a) \(e\) for different initial velocities from 1.6 to 2.5 m/s and different impact angles \(\beta\) for tape 1, (b) Mean \(e\) for different impact angles for tape 1.  
chance of \(e\) with respect to impact angle, \(\beta\). Figure 8a shows no trend or separation of \(e\) with normal pre-impact velocity and impact angle. Mean \(e\)s and standard deviations are \(\overline{e}=0.772\) and \(\sigma=0.0121\) for normal impact, \(\overline{e}=0.745\) and \(\sigma=0.0123\) for oblique angle \(\beta=7.5^{\circ}\), \(\overline{e}=0.761\) and \(\sigma=0.0313\) for oblique angle \(\beta=15^{\circ}\), and \(\overline{e}=0.755\) and \(\sigma=0.0084\) for oblique angle \(\beta=22.5^{\circ}\). The standard deviation in Figure 8b is \(\sigma=0.0116\). Figures 6-8 illustrate no apparent linear trend for the coefficient of restitution. However, the variation in the coefficient of restitution is small. Therefore, the coefficient of restitution can be almost constant in practical applications. Previous studies on tennis ball impact for different configurations [20,27] also show no linear trends with a small deviation. The stiffness (\(k\)) and damping (\(b\)) coefficients must be determined to verify the mathematical model with the oblique impact. To find \(k\) and \(b\), at least two independent experimental results are needed. The normal impact experimental data set consists of 12 experiments in three replications of four different initial drop heights.