Research on the inrun profile optimization of ski jumping based on dynamics
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INDUSTRIAL APPLICATION PAPER
Research on the inrun profile optimization of ski jumping based on dynamics Yazhen Sun 1 & Rui Guo 1 & Lin Gao 2 & Changyu Wu 1 & Huaizhi Zhang 1 Received: 13 March 2020 / Revised: 21 July 2020 / Accepted: 9 September 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The profile of the inrun is crucial in ski jumping. With the development of technology, a considerable number of geometric lines have been proposed from a mathematical perspective and applied to the inrun. The third power function is the latest standard design of the transition zone profile proposed by the International Ski Federation (FIS). Therefore, the transition zone profile (third power function) was studied. The research on athlete’s force states can help make the profile better meet the competition requirements. The dynamic differential equations of the athlete were first obtained by considering air resistance and skiing friction. Mathematica was used to solve the equations, and the skiing velocity of the athlete at each structural point was obtained. Meanwhile, the skiing velocity of the athlete at the arc and the third power function were compared with the force. The results show that, under the condition that the length and height of the inrun are the same, there is no difference in the athlete’s skiing velocity. By comparing the athlete-exerted forces under two types of profiles, it was found that the third power function will make the athlete-exerted forces slowly increase without instantaneously raising the point of the arc, which is conducive to the maintenance of the athlete’s movement. It was shown that the third power function has a great advantage in controlling the reaction force of the athlete. Therefore, the inrun with a third power function in the transition zone is more conducive to the athlete’s skiing, which further improves the level of competition and optimizes the original inrun system. It can provide theoretical support for the application of the geometric profile of the ski jumping inrun at the Beijing Winter Olympic Games. Keywords Ski jumping . Inrun . Arc . Third power function . Dynamic differential equation . Athlete-exerted force
1 Introduction Ski jumping has been an official Winter Olympic sport since the 1930s. The inrun is shown in Fig. 1. As shown in Fig. 1, the inrun is mainly divided into three sections: the straight section of the start zone, the curve section of the transition zone, and the straight section of the takeoff zone. According to the building rule,
Responsible Editor: Yoojeong Noh * Huaizhi Zhang [email protected] 1
School of Transportation Engineering, Shenyang Jianzhu University, Shenyang 110168, China
2
School of Civil Engineering, Chongqing University of Arts and Sciences, Chongqing 402160, China
most of the transition zones of the inruns have been constructed as arcs. If the arc is used as the transition area, the point of instantaneous increase in curvature will appear on the profile, which is not conducive to skiing. In the
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