# Analyzing the Biomechanical Characteristics of Ski Jumping Take-Off Phase Based on CFD
## 4 Discussion  
### Dominant Characteristics of Limbs during the Take-Off Phase  
This study utilizes the CRP method to examine the dominance characteristics of the ankle, knee, and hip joints during the take-off phase in athletes. By comparing these characteristics with those observed in NW elite athletes, the study seeks to offer a theoretical framework for improving athletes' take-off performance. Based on the ankle-knee CRP curve, it can be observed that during the take-off phase, the dominant relationship between the ankle and knee joints of Chinese athletes shows that for 40% of the total take-off time, the ankle leads the knee, while for 30% of the time, the knee leads the ankle. This pattern suggests that kinematic changes in the ankle of Chinese elite athletes are relatively more pronounced compared to those in the knee throughout the take-off process, and the knee's dominance over the ankle is less prominent. As shown in Figure 9[16], [PERSON] analyzed the dominant characteristics of elite athletes from the Swiss national ski-jumping team during the take-off phase using the CRP method. [PERSON] study assessed the coordination of the lower limbs by examining the angles between the limbs and the horizontal plane. Building on this research, we used the DLT method to develop a three-dimensional model and analyzed joint angle changes to explore lower-limb coordination during take-off. [PERSON] findings revealed a continuous decrease in CRP values for Swiss elite athletes during the first 75% of take-off, indicating that the thigh dominates the lower leg, with the knee joint leading the ankle joint. This suggests that high-level athletes exhibit significant dominance of the thigh over the lower leg during take-off, attributed to the stability of the lower leg and delayed rotation of the lower leg[16]. Maintaining maximum ankle stability, enhancing lower-limb extension, and increasing knee joint angular velocity during take-off are crucial for optimal intra-limb dominance and performance improvement. [PERSON] also found that, in the latter half of take-off, the lower-leg rotation dominates because the initial rapid extension brings the knee joint angle closer to its optimal position, enhancing forward angular momentum for an optimal flight posture. However, Chinese elite athletes show more frequent changes in ankle and knee joint dominance throughout the take-off phase. In the initial phase (first 20%), their knee and ankle joints move synchronously. During the middle phase,  
Figure 8: Static pressure diagram at the end moment of the take-off phase (EMT) for NW elite athletes. dominance changes frequently, indicating potential issues with ankle angle stability and lower-limb extension. This may prevent the knee joint from reaching its optimal angle, impacting the lift-to-drag ratio in the subsequent flight. Previous studies suggest that elite athletes maintain lower-leg stability and minimal ankle angle changes during take-off, facilitating greater angular momentum and optimal lower-limb extension, resulting in a better flight posture and lift-to-drag ratio after take-off [22; 23; 24]. Research by [PERSON] et al. found that professional ski jumpers have a smaller ankle angle and maintain high stability throughout the take-off phase compared to Nordic combined athletes [19]. Data from Tables 2 and 3 indicate that an excessive ankle joint angle during take-off may cause athletes to lean back excessively, increasing air drag and affecting acceleration and the horizontal center of mass velocity. Further analysis of the data in Table 4 reveals that a large ankle joint angle increases air drag on the lower leg and torso, negatively impacting the aerodynamic characteristics of the athlete-ski system. An excessive ankle joint angle impedes achieving the optimal lift-to-drag ratio at the end of the take-off phase, which, in turn, affects aerodynamic efficiency during the flight phase that follows. This suboptimal lift-to-drag ratio leads to shorter flight times and reduced jump distances.