# Numerical Simulation Research on Aerodynamic Characteristics during Take-Off Phase in Ski Jumping
## 1 Introduction  
Ski jumping is an exhilarating winter sports activity where athletes slide down a sloping ramp on specially designed skis. With the help of speed and the ground reaction force, they launch themselves into the air and land on a designated slope after a period of flight. The entire technique of ski jumping can be divided into four different phases: irrun, take-off, flight, and landing. These phases involve two major aspects: ballistics and aerodynamics. Ballistics depends on the athlete's speed and take-off position, while aerodynamics encompasses the aerodynamic characteristics of the anti-body system ofthe athlete and skis (such as the speed, athlete/ski system posture, drag and lift, clothing design, ski length, etc.) [1; 2]. Both ballistics and aerodynamics pose specific requirements for ski jumpers, aiming to maximize vertical lift and minimize drag. Aerodynamics plays a crucial role in all four phases, although previous research has predominantly focused on the invn and flight phases [3; 4; 5; 6]. Computational fluid dynamics (CFD) is an important tool in the study of ski jumping aerodynamics as it allows for the direct and accurate calculation of an athlete's aerodynamic forces and moments. CFD can also provide visual or analytical representations of the surrounding flow field. However, the current CFD research on ski jumping is primarily focused on the invn and flight stages [7; 8; 9; 10; 11; 12]. The main reason for this is that, compared to the invn and flight stages, the take-off stage involves rapid and drastic changes in the athlete's posture within a very short period. The dynamic complexity of this stage far exceeds that of the invn and flight stages, making numerical simulation studies of the take-off process more challenging and less cost-effective. The take-off phase is the transition motion from the invn posture to the flight posture for ski jumpers. The take-off motion is considered to be the most important phase in the entire ski jumping performance because it plays a decisive role in the initial flight conditions [13]. During the take-off phase of ski jumping, the ballistic characteristics become more evident. Although some predictions have been made regarding its aerodynamic properties [14], the aerodynamic effects during the take-off phase have not been extensively studied. From an aerodynamic perspective, take-off is crucial because athletes need to strike a balance between maximizing vertical acceleration and minimizing aerodynamic drag. As the athlete extends their body to be fully exposed to the air during the take-off phase, the aerodynamic drag rapidly increases. However, the aerodynamic lift during the take-off phase is beneficial as it reduces the load on the athlete, leading to a shorter take-off time and a higher power development rate [15]. In actual ski jumping conditions, each jump training session is limited to a few seconds, and the take-off process itself lasts only about 0.3 s. However, a significant amount of time is required for preparation, and the number of training jumps completed per day is limited. Therefore, one effective way to improve an athlete's subjective perception of the aerodynamic forces and training duration is to conduct take-off training in a wind tunnel [16; 17; 18; 19]. Furthermore, based on a series of wind tunnel experiments, [PERSON] et al. (2001) and [PERSON] et al. (2023) obtained force measurements by using the force measuring balance, which represents the combined effect of the take-off force and aerodynamic forces [15; 20]. However, a direct measurement of the transient aerodynamic forces during take-off is still not possible. Additionally, by analyzing the kinematic parameters and take-off patterns of the top male ski jumpers in China, [PERSON] et al. (2022) investigated the main factors influencing the flight distance in men's ski jumping [21]. [PERSON] et al.