## 3 Results and Analysis
### Overturning and Yawing during Underwater Penetration of Projectile at an Attack Angle
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Condition** \\ **No.** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Initial** \\ **Velocity V\({}_{0}\)** \\ **(m/s)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Attack** \\ **Angle (\({}^{\circ}\))** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Test** \\ **Method** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Condition** \\ **No.** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Initial** \\ **Velocity V\({}_{0}\)** \\ **(m/s)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Attack** \\ **Angle (\({}^{\circ}\))** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Test** \\ **Method** \\ \end{tabular} } \\ \hline No. 1 & 1016 & \(-\)50 & TEST/FEM & No. 18 & 1200 & 60 & FEM \\ No. 2 & 991 & 67 & TEST/FEM & No. 19 & 1600 & 0 & FEM \\ No. 3 & 1004 & 45 & TEST/FEM & No. 20 & 1600 & 15 & FEM \\ No. 4 & 400 & 0 & FEM & No. 21 & 1600 & 30 & FEM \\ No. 5 & 400 & 15 & FEM & No. 22 & 1600 & 45 & FEM \\ No. 6 & 400 & 30 & FEM & No. 23 & 1600 & 60 & FEM \\ No. 7 & 400 & 45 & FEM & No. 24 & 2000 & 0 & FEM \\ No. 8 & 400 & 60 & FEM & No. 25 & 2000 & 15 & FEM \\ No. 9 & 800 & 0 & FEM & No. 26 & 2000 & 30 & FEM \\ No. 10 & 800 & 15 & FEM & No. 27 & 2000 & 45 & FEM \\ No. 11 & 800 & 30 & FEM & No. 28 & 2000 & 60 & FEM \\ No. 12 & 800 & 45 & FEM & No. 29 & 2400 & 0 & FEM \\ No. 13 & 800 & 60 & FEM & No. 30 & 2400 & 15 & FEM \\ No. 14 & 1200 & 0 & FEM & No. 31 & 2400 & 30 & FEM \\ No. 15 & 1200 & 15 & FEM & No. 32 & 2400 & 45 & FEM \\ No. 16 & 1200 & 30 & FEM & No. 33 & 2400 & 60 & FEM \\ No. 17 & 1200 & 45 & FEM & No. 34 & 1200 & 8 & FEM \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Test conditions. to overturn anticlockwise due to inertia, the original \"tail\" of the projectile turns over to the \"nose\" position, and the direction of the resultant force on the projectile becomes downward. The Y-axis velocity of the projectile starts to decrease, and the resultant force is below the projectile's center of mass; thus, the projectile is subjected to a clockwise overturning moment, which generates an angular acceleration in the opposite direction to the overturning direction, and the anticlockwise overturning velocity decreases gradually. At t = 342 us, the angular velocity of the projectile declines to 0 rad/s, the projectile starts to overturn clockwise, and the Y-axis velocity of the projectile is increasing smaller. When the projectile overturns clockwise to the maximum incident flow area, the projectile starts to be subjected to an anticlockwise moment; thus, the angular velocity starts to decrease, the resultant force becomes upward, and the Y-axis velocity increases; finally, as the projectile contacts the back plate, the penetration ceases. Figure 8: Photographs of underwater penetration process. Figure 10: Y-axis velocity curve of projectile. (The red dash line is the dividing line of different stages). Figure 9: Attitude angle change of projectile in Test 3. (The red dash line is the dividing line of different stages). In summary, during projectile penetration into liquid at an attack angle, the projectile is always in the overturning state. Due to the change of the projectile position contacting with water, the projectile will undergo overturning many times. The yaw of the projectile is affected by the attack angle and attitude angle as the two angles determine the direction of the force on the projectile during penetration. As the initial velocity during water entry is large, greater dynamic pressure on the projectile leads to greater Y-direction component. Therefore, the yaw velocity of the projectile is fast at the initial stage of water entry; when the second overturn occurs, the projectile velocity becomes smaller, and the Y-direction component of the projectile is also smaller; thus, the trajectory tends to be stable with a relatively small yaw velocity at the later stage of water entry.