Optimization of the flight style in ski jumping. Jung, A., Staat, M., & Müller, W. In Oñate, E., J. Oliver, J., & Huerta, A., editors, 11th World Congress on Computational Mechanics (WCCM XI), 5th European Conference on Computational Mechanics (ECCM V), 6th European Conference on Computational Fluid Dynamics (ECFD VI) July 20-25, 2014, Barcelona, Spain, pages 799-810, 2014.
Optimization of the flight style in ski jumping [pdf]Website  abstract   bibtex   
During the flight phase the athlete has to optimize the aerodynamic forces in order to maximize the jump length while keeping the flight stable, both with respect to his features and abilities. A system of first order nonlinear differential equations describes the motion of a ski jumper and provides the basis for solving this constrained optimization problem by means of an optimization algorithm and comprehensive wind tunnel measurements. An optimization algorithm was developed on the basis of Pontryagin´s minimum principle combined with a penalty function derived from flight position constraints. By varying the constraints, it has been recently shown that there are various possibilities to reach comparable jump lengths and individual athletes have to develop their individual optimum which is to be tuned with their personal features and abilities. In this study, the effect of the take-off velocity perpendicular to the ramp (v_p0) on the flight style is examined in order to deepen the understanding of the individual flight style optimization. It is shown that a reference value of v_p0=2.5 ms^-1 can be used for optimization studies in elite ski jumping. Optimization studies can be used advantageously for guiding the individual training. Since the optimization algorithm was developed for the flight phase starting at t=0.7 s, future work should be based on the extension concerning the initial flight and the landing preparation. Furthermore, the take-off phase can be added since it can be also described by a first order nonlinear differential equation. For this purpose new comprehensive wind tunnel measurements with athletes using the latest equipment and field studies are necessary. The presented optimization approach can be applied to any sports which can be described by ordinary differential equations. That provides a new basis for improving the performance.

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