# Analyzing the Biomechanical Characteristics of Ski Jumping Take-Off Phase Based on CFD
## 1 Introduction  
Ski jumping, a critical component of Nordic combined, influences the starting order for the subsequent cross-country skiing event. This sport is divided into four distinct phases: the in-run stage, take-off, flight, and landing [1]. The final score in ski jumping is primarily determined by the athlete's flight distance. During the take-off phase, athletes must rapidly extend their legs and torso to achieve an optimal body posture within a short timeframe, setting the stage for the flight phase. The take-off phase typically lasts around 300 milliseconds [2], necessitating high coordination and muscular strength in the lower limbs. At take-off, athletes reach horizontal speeds of approximately 25 m/s, and rapid changes in joint angles at such high speeds create significant physical drag. Previous research has demonstrated that kinematic parameters during the take-off phase are crucial for determining the final flight distance [2; 3]. Errors during the take-off phase cannot be corrected in the flight phase [4], highlighting the importance of take-off for overall performance. The effectiveness of the take-off phase directly influences the athlete's final score [5]. To analyze an athlete's coordination, quantitative methods can be used to measure the relationships among various joints during movement. This approach facilitates direct observation and comparison, offering valuable insights for athletic training [6]. Quantifying limb coordination provides a numerical representation of these relationships [7]. For example, continuous relative phase (CRP) analysis is employed to assess limb coordination. CRP analysis is widely used in sports to evaluate athletes' performance [8; 9; 10]. By applying CRP analysis to joint coordination, we gain a clear understanding of how different joints interact throughout a movement. This information is crucial for improving athletic techniques and training methods. [PERSON] et al. found that different take-off techniques used by ski jumpers significantly affect the drag experienced during the take-off phase [11]. Although ski jumping is closely linked to aerodynamic characteristics, computational fluid dynamics (CFD) methods are primarily applied to the flight phase [12; 13; 14; 15; 1]. Research on the take-off phase is relatively limited. This study investigates the kinematic and aerodynamic characteristics of Chinese athletes (CAs) in comparison to Nordic World athletes (NWAs) during the take-off phase using various analytical methods. We specifically analyzed the drag of the left and right lower legs (L/RLDs), left and right thighs (L/RTDs), drag of the torso (TOD), total drag (TD), and total lift (TL) at the start moment of the take-off phase (SMT) and the end moment of the take-off phase (EMT). We also calculated the lift-to-drag ratio (L/D) based on the total lift and total drag. We employed Direct Linear Transformation (DLT) to process images and develop a three-dimensional motion model, which provided the kinematic data of the athletes. Additionally, Continuous Relative Phase (CRP) analysis was used to quantify intra-limb coordination during the take-off phase. Combined with Computational Fluid Dynamics (CFD) analysis, we performed a comprehensive examination of the aerodynamic features of athletes in various postures. By integrating these complementary methods, we created a robust research framework to elucidate the mechanical mechanisms of the take-off phase. This study offers new insights into ski-jumping biomechanics and provides scientific evidence to enhance training and performance. This study investigates the impact of different joint motion characteristics on aerodynamic properties during the take-off phase using CFD and CRP methods. The findings provide a theoretical foundation for future sports training and research, enhance understanding of the aerodynamic effects of joint movements, and contribute valuable insights to the field of sports biomechanics.