## 4 Simulation Analysis of Car Crash Accidents in Circular Curved Road Sections
### Analysis of Results  
1. The driving speed before the collision was \(V_{10}=120\) km/h, and the superelevation \(i_{\text{h}}\) was 4%, 6%, 8%, and 10%, respectively, corresponding to the minimum radius of the circular curve of 718 m, 607 m, 520 m, and 451 m, respectively.
2. The driving speed before the collision was \(V_{10}=100\) km/h, the superelevation \(i_{\text{h}}\) was 4%, 6%, 8%, and 10%, respectively, and the corresponding minimum radius of the circular curve was 499 m, 422 m, 361 m, and 313 m, respectively.
3. The driving speed before the collision was \(V_{10}=80\) km/h, the superelevation \(i_{\text{h}}\) was 4%, 6%, 8%, and 10%, respectively, and the corresponding minimum radius of the circular curve was 319 m, 270 m, 232 m, and 200 m, respectively.  
In the PC-Crash platform, the car crash occurred along the circular curve road segment optimization scheme. The results of LTR and the yaw angular velocity after the vehicle collision are shown in Figures 6-11.  
Figure 8: Simulation results of LTR at a speed of 100 km/h before collision.  
Figure 7: Simulation results of the yaw angular velocity at a driving speed of 120 km/h.  
Figure 9: Simulation results of the yaw angular velocity at a driving speed of 100 km/h.  
As can be seen from Figures 7, 9 and 11, vehicles collided at speeds of 80 km/h, 100 km/h, and 120 km/h. In the collision stage, the yaw angular velocity of the vehicle changed abruptly, and there was a risk of sideslip and tail-flick drift. Lateral instability mainly occurred in the stage of two-vehicle collisions, when the yaw angular velocity of the vehicle changed sharply. The yaw angular velocity can be controlled by the operation stability control system. In the post-collision stage, the yaw angular velocity of the vehicle gradually approaches zero, but lateral instability can also occur. The driver needs to keep calm and take correct control measures to avoid secondary accidents and minimize injuries as much as possible.  
It can be seen from Figures 6-10 that when a vehicle crashes (about \(t=0.2\) s), the lateral load transfer rate of the vehicle changes sharply. The lateral load transfer rate is in an extreme state, and the possibility of vehicle rollover is in a relatively dangerous state and a dangerous state. After the collision, LTR will increase to a dangerous state when the vehicle continues to move, and the changes in LTR in the three groups of simulation experiments were similar. In the simulation results, LTR under the three working conditions was less than 1, so the accident vehicle would not rollover. However, at the same time, LTR was also close to 1, so the vehicle was in the dangerous state of rollover, which is consistent with the minimum radius under rollover criticality in the theoretical calculation.  
Therefore, when a vehicle crashes, the vehicle-road coupling safety dynamic model of the circular curve section can be established, and the proposed optimization scheme of the minimum radius and superelevation of the circular curve was shown to meet the safety requirements for vehicle rollover.  
Figure 11: Simulation results of the yaw angular velocity at 80 km/h before collision.  
Figure 10: Simulation results of LTR at 80 k m/h before collision.