# Numerical Simulation Research on Aerodynamic Characteristics during Take-Off Phase in Ski Jumping
## 5 Conclusions  
1. Through numerical simulations using CFD, the aerodynamic characteristics and differences in various postures in the take-off phase in ski jumping have been analyzed. This study focuses on comparing the effects of two take-off modes on aerodynamic characteristics. The aerodynamic characteristics change dramatically during the take-off phase, and the aerodynamic characteristics of the two take-off modes are quite different, and these changes and differences are difficult to observe during real training and at the competition site.
2. The aerodynamic forces on the athlete's torso and legs are significantly larger, while the contribution of the arms may be less pronounced. However, the position of the arms should not be ignored as it can still have a considerable impact on the overall aerodynamic characteristics of the athlete. The KPH mode demonstrates clear aerodynamic advantages. During the take-off process, 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 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 the aerodynamic drag on take-off. This creates favorable aerodynamic conditions for the early flight phase.
3. Numerical simulations of the aerodynamics in the take-off phase of ski jumping can accurately capture the aerodynamic characteristics. Numerical simulations combined with repeated training in a wind tunnel to simulate competition scenarios help athletes improve their subjective perceptions and adaptability to aerodynamic forces during the take-off phase. It also enables athletes to utilize aerodynamic forces to achieve favorable flight postures after the take-off phase. This research provides important scientific guidance for athletes to improve their take-off and flight technique training strategies and enhance their competitive performance.
4. Computational fluid dynamics (CFD) techniques can be employed to model and simulate the flow of air around athletes, sports equipment, or sports facilities. These simulations can provide valuable insights into aerodynamic forces, drag, lift, and other relevant parameters, aiding in the design and optimization of sports equipment, training techniques, and performance analysis. CFD simulations can also help increase understanding of the impact of wind conditions on sports performance, enabling athletes to make informed decisions and improve their strategies.  
Formal analysis, Q.H.; methodology, Q.H. and W.T.; writing--original draft, Q.H. and W.T.; writing--review and editing, Q.H., W.T., and Y.L.; funding acquisition, Q.H. and Y.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Plan Project of China, grant number 2018 YFF0300500, and the National Natural Science Foundation of China, grant numbers 11932013 and 11802068.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors would also like to express their gratitude to [PERSON] and [PERSON] from the Aerodynamics Research Institute in China for conducting the 3D scanning of the athletes' postures and providing the original scanned models of the athletes.  
The authors declare no conflicts of interest.