# Analyzing the Biomechanical Characteristics of Ski Jumping Take-Off Phase Based on CFD
## 4 Discussion
### Dominant Characteristics of Limbs during the Take-Off Phase
Previous research indicates that while the knee joint often plays a dominant role during take-off, an excessively large ankle joint angle at the start, combined with significant changes in this angle throughout take-off, increases overall air drag. To enhance the quality of take-off and achieve the best lift-to-drag ratio during the flight phase, it is crucial to minimize the ankle joint angle and maintain stability throughout take-off. This approach will help reduce air drag and ensure optimal aerodynamic performance. The CRP curve of the knee and hip joints illustrates the dominance characteristics between these two joints during the take-off phase in Chinese elite athletes. This curve shows that the hip joint remains dominant over the knee joint for a longer duration throughout the take-off process (Figure 4). [PERSON] et al. analyzed air drag on athletes' bodies in various take-off poses using wind-tunnel training. They concluded that a \"knee-driven hip\" approach minimizes air drag during the take-off process. Additionally, they suggested that the \"synchronous hip-knee variable speed\" approach results in the highest drag, likely due to the rapid opening of the hip joint while the lower limbs extend more slowly. This leads to uneven torso drag distribution and an early increase in the torso's force-bearing area, causing greater drag [25]. The study found that minimal variation in the CRP index values of the knee and hip joints during the initial 20% of the take-off phase indicates that Chinese elite athletes adopt a \"synchronous hip-knee variable speed\" approach. Throughout take-off, hip joint dominance accounts for 40% of the process, with the knee joint assisting. This movement pattern suggests that Chinese elite athletes might experience an excessively large hip joint angle during take-off, leading to an early and significant increase in torso air drag, thereby affecting their horizontal center-of-mass velocity. This finding highlights the need for optimizing the take-off technique to reduce aerodynamic drag and enhance performance. [PERSON] et al. argue that horizontal center-of-mass velocity is the most crucial factor affecting athletes during the take-off phase. Minimizing drag impact on horizontal center-of-mass velocity enables athletes to achieve greater flight  
Figure 9: CRP characteristics of Swiss elite athletes’ legs during takeoff. distances during the flight phase [3]. Previous studies indicate that hip joint kinematics during take-off significantly impact drag experienced during the jump [26]. Maintaining a smaller hip joint angle during take-off is suggested to improve performance [27]. Although Chinese elite athletes also use a knee-led hip take-off posture, the duration of this phase is relatively short. Based on the data from Tables 2 and 3, we found that Chinese athletes have smaller knee joint angles during take-off, resulting in lower thigh drag compared to Nordic athletes. This indicates that maintaining the knee joint at approximately 90 degrees during the take-off and sliding phases can more effectively reduce air drag. However, this also suggests that athletes complete the push-off action more quickly within the same time-frame. Data from Tables 2 and 4 also show that at the end of take-off, Chinese athletes have smaller knee joint angles, correlating with a higher total drag at that moment. Therefore, during the SMT and sliding phases, athletes should reduce the knee joint angle to lower air drag and enhance knee joint dominance during take-off. This approach will help the knee joint achieve the optimal angle by the end of take-off, thereby improving performance. Furthermore, frequent shifts in dominance between the knee and hip joints during this process may generate additional drag, affecting horizontal center-of-mass velocity.