## 4 Discussion
### The Influence of Roll Rotation  
As the multi-body system undergoes roll rotation, its initial symmetric configuration gradually transforms into an asymmetric shape, altering its flow configurations. The findings of this study indicate that roll rotation significantly generates a yaw force, yaw moment, and roll moment, while also exerting a substantial influence on the lift, drag, lift-to-drag ratio, and pitch moment of the system. Table 5 and Figure 6 clearly demonstrate that roll rotation leads to a significant decrease in the total lift-to-drag ratio and complicates the force distribution on the system. These effects have unfavorable implications for the mechanical characteristics, hindering 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.  
It is noteworthy that the multi-body system in this study undergoes clockwise roll rotation in the top view, rotating along the \(-\)X axis, resulting in roll moments in the +X direction. According to the principles of rotational motion, the roll moment induces an angular acceleration opposite to the roll rotation direction, causing the system to return to its initial symmetric configuration and exhibiting a suppressing effect on roll rotation. This phenomenon is referred to as roll self-stabilization or static equilibrium, which has also been observed in previous studies conducted by [PERSON] et al. (2009) regarding the two-dimensional numerical calculation of aerodynamic stability on the roll direction in ski jumping [41].  
It is worth noting that when the roll rotation angle is 2.5\({}^{\circ}\), the yaw force, yaw moment, and roll moment of the system are relatively small, measuring \(-\)12.33 N, \(-\)2.91 N\(\cdot\)m, and 2.04 N\(\cdot\)m, respectively. However, when the roll rotation angle increases to 5\({}^{\circ}\), the yaw force becomes \(-\)28.72 N, the yaw moment is \(-\)6.47 N\(\cdot\)m, and the roll moment reaches 4.53 N\(\cdot\)m. Similarly, under lateral wind conditions, the system exhibits a significant yaw force, yaw moment, and roll moment. For example, when the wind speed in the +Z direction is 4.5 m/s, the yaw force, yaw moment, and roll moment of the 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 roll rotation angle of 2.5\({}^{\circ}\) and a lateral wind speed of 4.5 m/s, as well as a roll rotation angle of 5\({}^{\circ}\) and a lateral wind speed of 7.5 m/s. This finding suggests that employing an appropriate roll 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 9 demonstrate that with variations in the roll rotation angle, the velocity values of the streamlines exhibit minimal changes, but the streamlines noticeably shift towards the left rear. Simultaneously, the vortex patterns undergo significant transformations, transitioning from an initial symmetric configuration to an asymmetric one, with a gradual decrease in vortex structure size behind the athlete and skis. These observations indicate that roll rotation significantly alters the original mechanical characteristics of the system, giving rise to new lateral forces and corresponding moments that align with the previously obtained numerical statistics of the mechanical characteristics.