# Numerical Simulation Research on Aerodynamic Characteristics during Take-Off Phase in Ski Jumping
## 4 Discussion
### Aerodynamic Characteristics of Different Take-Off Postures  
It can be observed that the HDK mode exhibits a significantly higher total drag compared to the KPH mode. This is mainly due to the difference in hip joint angles, or the angle of attack of the torso. As shown in Figures 6 and 7, the angle of attack of the torso is noticeably higher in the HDK mode compared to the KPH mode. Figure 7e clearly shows a large area of a low-speed region behind the athlete in the HDK mode at \(-18\) ms. This low-speed region represents a decrease or even stagnation in the airflow velocity, and its size is an important factor influencing the pressure drag acting upon the athlete. The separation of airflow behind the athlete is caused by the excessive upright posture of the torso, resulting in the formation of this low-speed region and subsequently increasing the pressure drag acting upon the athlete. Although the HDK mode initially exhibits a higher total lift compared to the KPH mode, in the final take-off posture, the total lift in the HDK mode does not continue to increase but decreases. This results in a reversal of the lift values at the last time stage (Figure 3b). It can be considered that the HDK mode experiences a stall phenomenon at the last time stage, where an increase in the angle of attack leads to a decrease in the lift coefficient. [PERSON] et al. (2001) suggested that a good take-off helps the athlete achieve a favorable flight posture, specifically a forward-leaning position, during the early flight phase [15]. Additionally, [PERSON] and [PERSON] (2002) proposed that the aerodynamic lift should gradually increase during the early flight phase after the take-off phase [25]. Therefore, when a stall occurs in the HDK mode, it can put the athlete's aerodynamic characteristics in a disadvantageous state during the flight phase. In Figure 3a,c, it is evident that the moment trends over time are similar to the total drag trend. In this study, the moment refers to the pitch moment, with \"+\" representing a moment that causes the multi-body system, i.e., the athlete, to tilt backwards, and \"\(-\)\" representing a moment that causes the multi-body system to tilt forwards. [PERSON] (2008) suggested that one of the main objectives in the take-off phase is for the athlete to acquire angular momentum for forward rotation [26]. To achieve a favorable flight posture, for the HDK mode, the athlete must consume more physical energy to generate more forward rotational angular momentum compared to the KPH mode, as the aerodynamic forces generate a larger pitch moment, which causes the athlete to tilt backwards in the HDK mode compared to the KPH mode, as shown in Figure 3c. In Figure 3d, it is evident that the lift-to-drag ratio of the KPH mode is consistently higher than that of the HDK mode. From the aerodynamic perspective, this is because the body opening angle in the KPH mode is significantly smaller than that in the HDK mode. The KPH mode provides a noticeable aerodynamic advantage for the athlete in the flight phase after the take-off phase. During the take-off process, to create favorable aerodynamic conditions for the early flight phase, the athlete should increase the force generated by the knee joint extension and appropriately reduce the speed of the hip joint extension, control the using force order of the lower limb joints, and push the hip joint extension by the knee joint extension in order to avoid issues such as the hip joint angle being too large, the hip joint extension angle being too fast, the center of gravity being too far back, and other problems, and to avoid the adverse impact of aerodynamic drag on take-off. [PERSON] et al.