## 4 Discussion
### The Influence of Yaw Rotation  
It is observed that as the multi-body system undergoes yaw rotation, its initial symmetric configuration gradually transforms into an asymmetric shape, altering its flow configurations. The results of this study demonstrate that yaw rotation significantly generates a yaw force, yaw moment, and roll moment, while also exerting a significant influence on the lift, drag, lift-to-drag ratio, and pitch moment of the multi-body system. From Table 4 and Figure 5, it is evident that yaw rotation leads to a notable decrease in the total lift-to-drag ratio and complicates the force distribution on the multi-body system, thereby exerting unfavorable effects on the mechanical characteristics and impeding stable flight and the athlete's sport performance. It should be noted that the numerical values of aerodynamic characteristics in these influence relationships may vary depending on the flight postures of the multi-body system.  
Notably, the multi-body system in this study exhibits clockwise yaw rotation in the top view, rotating along the \(-\)Y axis, but consequently generates yaw moments in the \(+\)Y direction. According to the principles of rotational motion, the yaw moment induces an angular acceleration opposite to the yaw rotation direction of the multi-body system, thus causing the system to return to its initial symmetric configuration and exhibiting a suppressing effect on the yaw rotation. This phenomenon can be referred to as yaw self-stabilization or static equilibrium, which has been observed in previous studies conducted by [PERSON] et al. (2009) in the context of the two-dimensional numerical calculation of aerodynamic stability on the yaw direction in ski jumping [41].  
It is worth noting that when the yaw rotation angle is 2.5\({}^{\circ}\), the yaw force, yaw moment, and roll moment of the multi-body system are relatively small, measuring 8.78 N, 2.16 N\(\cdot\)m, and \(-\)1.67 N\(\cdot\)m, respectively. However, when the yaw rotation angle increases to 7.5\({}^{\circ}\), the yaw force reaches 24.89 N, the yaw moment becomes 6.78 N\(\cdot\)m, and the roll moment reaches \(-\)5.26 N\(\cdot\)m. Similarly, under lateral wind conditions, the multi-body system exhibits a significant yaw force, yaw moment, and roll moment. For instance, when the wind speed in the \(+\)Z direction is 4.5 m/s, the yaw force, yaw moment, and roll moment of the multi-body system are 9.48 N, 2.27 N\(\cdot\)m, and \(-\)2.80 N\(\cdot\)m, respectively. When the wind speed in the \(+\)Z direction increases to 7.5 m/s, the yaw force, yaw moment, and roll moment become 26.31 N, 6.32 N\(\cdot\)m, and \(-\)7.80 N\(\cdot\)m, respectively. It can be observed that the results of the yaw force, yaw moment, and roll moment are similar for the two scenarios: a yaw rotation angle of 2.5\({}^{\circ}\) and a lateral wind speed of 4.5 m/s, as well as a yaw rotation angle of 7.5\({}^{\circ}\) and a lateral wind speed of 7.5 m/s. This finding suggests that employing an appropriate yaw rotation angle may potentially counteract or even eliminate the adverse effects of lateral wind on the flight stability of ski jumping.  
Furthermore, the flow field results in Figure 8 demonstrate that with variations in the yaw rotation angle, the velocity values of the streamlines exhibit minimal changes, but the streamlines shift noticeably towards the right rear. Concurrently, the vortex patterns undergo significant transformations, transitioning from an initial symmetric configuration to an asymmetric one, with repeated fluctuations in vortex structure size. Specifically, the vortex structure size of the left ski gradually increases. These observations indicate that yaw rotation significantly alters the original mechanical characteristics of the multi-body system, giving rise to new lateral forces and corresponding moments that align with the previously obtained numerical statistics of the mechanical characteristics.