## 4 Numerical Simulation
### Influence of Ice Thickness
#### 4.1.1 Influence on the Motion Characteristics of the Vehicle  
As illustrated in Figures 22 and 23, the velocity of the vehicle keeps decreasing in the process of breaking ice, and the ice thickness plays a significant role in the variation of the vehicle's velocity. When the ice thickness increases from 10 mm to 50 mm, the residual velocity of the vehicle after breaking ice is 35.9 m/s, 31.6 m/s, 28.0 m/s, 25.6 m/s, and 21.6 m/s, respectively, with the velocity loss rate of 10.3%, 21.0%, 30.0%, 36.0%, and 46.0%. With the increase in the ice thickness, the residual velocity of the vehicle after breaking ice decreases and the velocity loss rate becomes larger, which is attributed to the continuous conversion of the vehicle's kinetic energy into the internal energy of the ice during the ice-breaking process of the vehicle. With the identical initial velocity of the vehicle, the thicker the ice, the longer the time for the kinetic energy to convert into internal energy. Meanwhile, the residual kinetic energy of the vehicle after breaking ice becomes lower, so the residual velocity is smaller.  
As shown in Figure 24, after the flow field of the vehicle moving in the water is stabilized, the acceleration of the vehicle is approximately 5000-20,000 m/s\({}^{2}\). When the vehicle passes through the ice, its acceleration reaches a peak and then gradually decreases to 0. The acceleration peak of the vehicle is little affected by the ice thickness. When the acceleration of the vehicle is 0, it could be regarded that the vehicle has completely passed through the ice. When the ice thickness is 10 mm, 20 mm, 30 mm, 40 mm, and 50 mm, it  
Figure 23: The variation in the vehicle’s residual velocity and velocity loss rate with ice thickness.  
Figure 22: Curves of the vehicle’s velocity over time at different ice thicknesses.  
takes the vehicle 0.61 ms, 0.99 ms, 1.20 ms, 1.69 ms, and 2.02 ms, respectively, to completely pass through the ice. The time taken by the vehicle to pass through the ice increases with the ice thickness.  
Figure 25 shows the dynamic characteristic curves of the vehicle breaking ice with thicknesses of 10 mm and 50 mm. It can be seen that the process of the vehicle breaking through the ice is divided into three stages: (1) Movement in water: At this time, the vehicle has not come into contact with the ice, the speed decreases relatively slowly, and the acceleration value is small, corresponding to 0 ms to 0.1 ms in (a) and 0 ms to 0.1 ms in (b). (2) Ice-breaking: At this stage, the vehicle collides with the ice and is subjected to the impact load of the ice, causing the acceleration to increase rapidly and the speed to decrease significantly, corresponding to 0.1 ms to 0.4 ms in (a) and 0.1 ms to 1.75 ms in (b); (3) Separation of vehicle and ice: At this point, the head of the vehicle has broken through the ice, and the force between the vehicle and the ice is mainly friction. The speed change is small, and the acceleration gradually approaches 0, corresponding to 0.4 ms to 1.0 ms in (a) and 1.75 ms to 2.0 ms in (b).  
Figure 24: Curves of the vehicle’s acceleration over time at different ice thicknesses.  
Figure 25: _Cont._