## 2 Experiment
### Results  
The process of the long-rod penetrating the concrete target is shown in Figure 4. Weak firelight was generated at the moment of the impact, then the long-rod projectile penetrated the target body. The concrete near the contact point shattered and splashed back. It is known that the tensile strength of concrete is much lower than its compressive strength. When the projectile impacted the concrete target, strong shock waves would be formed in the target, which can be several GPa or even several tens of GPa. The shock waves formed tensile waves after being reflected from the front of the concrete target, causing the concrete spallation. The damage of the concrete targets is shown in Figure 5 and the corresponding crater parameters are listed in Table 1. The data listed in Table 1 includes the length (\(L_{p}\)) and mass (\(m_{p}\)) of the long-rod projectile; impact velocities; yaw angles; DOPs (depth of penetrations); and crater dimensions, where \(D_{c}\) and \(H_{c}\) are the equivalent diameter and depth of the crater and \(V_{c}\) is the crater volume. The equivalent \(D_{c}\) was obtained by measuring the crater area with the help of image recognition and calculating the diameter of the circle with the same area. According to the contour of the impact crater, the shape of the crater can be approximated as a spherical cap shape, as shown in Figure 6.  
Figure 4: Typical photographs of the long-rod projectile penetrating a concrete target at 2117 m/s. Figure 3: Typical long-rod projectile photographs from the high-speed camera. Figure 7 presents the influence of the impact velocity on the crater dimensions. It is observed from Figure 7a that the non-dimensional equivalent crater diameter (\(D_{c}\)/\(D_{p}\), \(D_{p}\) is the original long-rod projectile diameter) increased with the increasing impact velocity within the parametric range covered by the present experiment. When the velocity of the long-rod projectile was 3086 m/s, the equivalent crater diameter was up to 56 times the diameter of the projectile. Figure 7b indicates that the non-dimensional \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Target No.**} & \multicolumn{3}{c}{**Long-Rod Dimensions**} & \multirow{2}{*}{\(V_{0}\) **(m/s)**} & \multirow{2}{*}{\(\dfrac{\text{{Yaw}}}{\text{{Angle (\textasciitiflation{{}^{\circ}})}}}\)} & \multirow{2}{*}{\(\dfrac{\text{{Crafter Dimensions}}}{\text{{D_{c}}}}\)} \\ \cline{2-2} \cline{5-10}  & \(m_{p}\) **(g)** & & & & & & \\ \hline \#4 & 24.26 & 6.98 & 69.83 & 2688 & 0.8 & 442.2 & 61 & 3959 \\ \#6 & 24.13 & 6.98 & 70.02 & 2117 & 1.2 & 321.1 & 49 & 1561 \\ \#7 & 23.79 & 7.00 & 70.46 & 2220 & 0.5 & 357.2 & 59 & 2316 \\ \#9 & 23.99 & 7.02 & 70.32 & 3086 & 0 & 395.4 & 80 & 4388 \\ \#17 & 24.26 & 6.99 & 70.00 & 2494 & 0 & 384.8 & 52 & 3611 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test results. Figure 5: Frontal damage of concrete targets. Figure 6: Sectional view of the typical crater for target #9 with a \(V_{0}\) = 3083 m/s. crater depth (\(H_{c}\)/\(D_{p}\)) generally increased with the increasing impact velocity, which was found similarly in flat-nose projectile penetration tests into mortar targets by [PERSON] et al., 1. Besides this, it is obtained from Figure 7c that the non-dimensional crater volume (\(V_{c}\)/\(V_{p}\), \(V_{p}\) is the original long-rod projectile volume) showed an increase with increasing impact velocity. To analyze the effect of projectiles with different length to diameter ratios (\(k_{p}\)) on impact craters, the test data of [PERSON] et al. 1 and [PERSON] et al. 2 are citied and compared with the present experimental results. The crater volume was related to the projectile volume \(V_{p}\), and hence it is dimensionless. The relation between the dimensionless crater volume and the projectile kinetic energy for different length to diameter ratio projectiles is shown in Figure 8 in which the dotted lines represent the linear fit (the correlation coefficient \(R^{2}\) from left to right are 0.98, 0.97, 0.98) to the test data.