## 4 Results and Discussions
### Simulation Results of the Oblique Impact  
For the case of the oblique impact, the final position of the projectile tip was compared. If the position of the \(x\)-axis has a large value, it means that the projectile has moved a lot in the horizontal direction. Movement in the horizontal direction has an adverse effect on the penetration of the projectile. With the same kinetic energy, the ideal case is to penetrate in the travel direction. Figure 14 presents the coordinate of the projectile tip after impact with the velocity of 1208 m/s and the impact angle of 30\({}^{\circ}\). The dash-dotted line in Figure 8 presents the line with an angle of 30\({}^{\circ}\), which means the ideal result of the projectile movement. Additionally, the moving trajectories of the projectiles of various projectile geometries were presented in Figure 14.  
The simulation results of the oblique impact are summarized in Table 2. The final position of the projectile tip can be divided into two lengths. One is the length along the impact angle 30\({}^{\circ}\), which is shown as \(\rm{D_{L}}\) in Figure 14. Another is the perpendicular distance to the impact angle which is shown as \(\rm{D_{P}}\) in Figure 14. The ratio of the displacement in the normal direction (\(\rm{D_{P}}\)) to the displacement along the impact angle (\(\rm{D_{L}}\)) is selected as a measurement which indicates whether the projectile followed the impact angle. When \(\rm{D_{P}}\)/\(\rm{D_{L}}\) is small, the projectile follows the impact angle. When \(\rm{D_{P}}\)/\(\rm{D_{L}}\) is large, the projectile moved to the perpendicular direction.  
The cylinder geometry showed the smallest movement. The reaction forces due to the impact are very large. As a result, the plastic deformation of the projectile is also extensive. This is similar to the normal impact. For the blunt geometry, \(\rm{D_{P}}\)/\(\rm{D_{L}}\) showed the largest value among seven projectile geometries. It was shown that penetration depth is very low in the vertical direction and has moved in  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline  & **Cylinder** & **Blunt** & **Conical** & **Truncated** & **CRH = 1** & **CRH = 3** & **CRH = 5** \\ \hline \(\rm{D_{L}}\)/mass [m/kg] & 1.472 & 2.025 & 4.657 & 5.632 & 5.035 & 9.007 & 9.748 \\ \(\rm{D_{P}}\)/mass [m/kg] & 0.391 & 3.793 & 3.386 & 3.857 & 5.140 & 3.538 & 3.572 \\ Ratio (\(\rm{D_{P}}\)/\(\rm{D_{L}}\)) & 0.266 & 1.873 & 0.727 & 0.685 & 1.021 & 0.393 & 0.366 \\ \hline \end{tabular}
\end{table}
Table 2: Penetration depth concerning the projectile geometry in the oblique impact.  
Figure 14: Trajectories of the projectiles and the final coordinates of the projectile tip with respect to the projectiles.  
the horizontal direction. It means that the projectile cannot penetrate the target in the vertical direction. As the projectile moves, the projectile bends. Finally, the projectile moves along the bending direction.  
Conical and truncated geometries do not move along the angle of impact. The bending deformation of the projectile occurred for the aforementioned cases. The ratios of the two cases (D\({}_{\text{P}}\)/D\({}_{\text{L}}\)) are close. However, the projectile with the truncated geometry showed better penetration characteristics.  
The projectile with an ogive nose showed different results. For the projectile with an ogive nose with the CRH value of 1, the ratio is 1.021. The projectile moves similarly along the impact angle and the normal direction. Also, the bending deformation of the projectile occurred. However, if the CRH is 3 and 5, the projectile moves not far away from the impact angle. The ratio of the projectile (CRH = 3) is 0.393, and the projectile (CRH = 5) is 0.366. The blunt geometry is that the CRH value is 0.5. So, as the CRH value increases, the projectile moves more accurately along the impact angle. As the CRH value increases, the penetration depth of the projectile is increasing.