## 5 Aerodynamic Loads and Safety Analysis
### Safety Analysis  
#### 5.2.1 Derailment Coefficient  
The rollover accident occurred when the side contact force exceeded the vertical contact force to a certain extent. The rollover accident was discerned with DCs, which is defined as follows [38]:  
\[\text{DC}=Q/P \tag{28}\]  
where \(Q\) and \(P\) are the side and vertical contact forces, respectively. Figure 16: Evolution of five aerodynamic loads with respect to time during the train entering the tunnel (train speed = 250 km/h, crosswind velocity = 25 m/s): (**a**)side force; (**b**)lift force; (**c**) rolling moment; (**d**) pitching moment; (**e**) yawing moment. Figure 17 demonstrates the evolution of DCs with respect to the time of the head carriage wheelsets during the train entering tunnel under conditions of train speed = 250 km/h and crosswind velocity = 15 m/s. The value of DCs was removed when the value of the vertical contact force was zero. In this moment, the wheel tread was detached from the rail top and the DCs were meaningless. Section 5.2.3 discusses the safety assessment of the sudden separation of the wheel and rail. Figure 17: Time-history of head carriage derailment coefficient (DC) conditioned train speed 250 km/h, crosswind velocity 15 m/s, (**a**) 1 st wheelset, (**b**) 2 nd wheelset, (**c**) 3 rd wheelset, (**d**) 4 th wheelset (open air (OA); entering entrance (E); tunnel (T)). Figure 17a shows that the global maximum of the DCs is likely to happen when the train arrives at the tunnel entrance. When the time was less than approximately 0.5 s, the entire carriage ran in the open air, the train withstood the side force from the crosswind, and the rail in the leeward side was pressed by the edge of the wheel. This phenomenon is the reason why the DCs on the leeward side were larger and easier to fluctuate than those on the other side. Therefore, the maximum DC on the leeward and windward sides was 0.56 and 0.15, respectively. When the carriage had completely entered the tunnel, the side force in the windward suddenly revoked at this moment (approximately 1.1 s), thereby causing the sudden reverse rotation of the carriage around the longitudinal axis. The vertical contact force of the wheel in the windward side suddenly increased, thereby shocking the DCs in the windward side upwards. The shielding effects of the aerodynamic loads induced by the tunnel was intensely sudden, such that the global maximum of the DCs was presented (e.g., approximately 1.04 for the first wheelset, nearly 2 times than the maximum DCs in the open air). Finally, the DCs at both sides decreased to less than 0.2 when the carriage entered the tunnel (after 1.1 s). Notably, the sudden variation of the DCs due to the shielding effect of the tunnel in the lateral direction mainly occurred in the first and third wheels of windward side when the train was entering the tunnel (Figure 17a,c). Furthermore, the DC of the second and fourth wheels in the windward side remained relatively stable (Figure 17b,d), respectively). The coupling effect of the aerodynamic loads shielded in the first wheel was probably larger than those of the others, and the suspension system of the train automatically adjusted the influence of aerodynamic unloading. For example, the safety risk of the third wheel in the windward side increased with the wind speed. Figure 18 presents the evolution of DCs with respect to the time of the head carriage wheelsets under the conditions of train speed = 250 km/h and crosswind velocity = 25 m/s. It can be seen that the position where the maximum DC occurred shifted from the first wheel to the third wheel. This phenomenon may have been caused by the pitching movement of the leading carriage. The pitching moment increased with the wind speed in open air. When the pitching moment of the carriage increased, the contact between the wheel tread of the rear bogie and rail top became closer. Thus, the position where the maximum DC occurred moved backward as the wind speed increased.