## 3 Results and Discussion
### Water Entry of 3D Torpedo
#### 3.2.2 Effect of Entry Angle
When the torpedo continues to enter water more deeply in the later stage, the impact loads of the \(x\)-component at entry angles of \(\beta=60^{\circ}\) and \(75^{\circ}\) gradually approach zero, as shown in Figure 14a; then, they increase toward the direction of the positive \(x\)-axis owing to the momentum introduced by the backflow of the fluid, as observed in Figure 13. Thus, the velocities of the \(x\)-component at those two entry angles slightly increase in the later stage of the water entry of the torpedo, as shown in Figure 14c. The torpedo is initially subjected to fluctuating vertical impact loads along the positive direction of the \(y\)-axis at all three entry angles and the larger entry angle yields a higher vertical impact load, as shown in Figure 14b. Correspondingly, the torpedo achieves higher downward velocity for a larger entry angle, as shown in Figure 14d. All those vertical impact loads increase slowly after the fluctuations. Considering the gravity force, the vertical resultant forces at those three entry angles are mostly along the opposite direction with the direction of the vertical velocity during the fluctuation period. Therefore, the absolute values of the velocities decrease first. In the later stage after \(t=0.02\) s, the variation trends of the vertical velocities at those three entry angles are slightly different, as shown in Figure 14b. The absolute value of the vertical velocity of the torpedo entering the water at \(\beta=90^{\circ}\) slowly decreases after \(t=0.02\) s as the induced vertical impact load is always slightly larger than the gravity force of the torpedo during this period. However, for entry angles of \(\beta=60^{\circ}\) and \(75^{\circ}\), the corresponding vertical impact loads increase from the loads being smaller than the gravity force to the loads being larger than the gravity force. Thus, the resultant forces at those two entry angles in the later stages first exhibit the same direction with the vertical velocities and then vary to the opposite direction. Correspondingly, the absolute values of the velocities at entry angles of \(\beta=60^{\circ}\) and \(75^{\circ}\) first increase and thereafter decrease in the later stages, as shown in Figure 14d. Variations in the horizontal displacement \(x\)-\(x_{0}\) and the vertical displacement \(y-y_{0}\) of the center of mass of the torpedo with time are shown in Figure 14e,f, respectively. In general, the displacements along the different dimensions are mainly determined by the corresponding initial velocities as the velocities at different dimensions and different entry angles fluctuate within relatively small ranges during such a short period from \(0\) s to \(0.2\) s. At the same entry velocity, the smaller entry angle results in a larger absolute value of the horizontal velocity and a smaller absolute value of the vertical velocity according to the principle of velocity orthogonal projection. Therefore, the smaller entry angle ultimately induces a larger absolute value of the horizontal displacement and, simultaneously, a smaller absolute value of the vertical displacement. Figure 15 shows the variations in the moment about the \(z\)-axis \(m_{z}\), the angular velocity \(\omega_{z}\), and the variation in the attitude angle of the torpedo \(\theta-\theta_{0}\) with time when the torpedo enters the water at different entry angles of \(60^{\circ}\), \(75^{\circ}\), and \(90^{\circ}\) under the same entry velocity of \(10\) m/s. When the torpedo vertically enters water at \(\beta=90^{\circ}\), there is no rotating movement of the torpedo observed, owing to the relatively uniform force acting around the torpedo body. Therefore, the angular velocity and the variation in the attitude angle at \(\beta=90^{\circ}\) are always maintained at zero. However, for the torpedo entering the water at the other two entry angles, similar and remarkable fluctuations in different parameters of the torpedo are observed.