Research on the inrun profile optimization of ski jumping based on dynamics

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.