Evaluation of a simple ski jumping model

(Bewertung eines einfachen Skisprung-Modells)

INTRODUCT1ON: The influences of in-run and take-off velocities, lift and drag forces during take-off and flight phase as well as weight of the ski jumper and his equipment on the Jump distance were analysed in several Computer simulations (e.g. Ward-Smith, A.J., Clements, D., 1983). These simulations require input Parameters, which are usually not available for world class ski jumpers, e.g. weight or lift and drag as function of the stream direction. Thus in this study a simple model was evaluated without consideration of individual weight and individual lift and drag areas. METHOD: During the Bergisel jumping competition 2007 15 ski jumpers were recorded during the two competition Jumps, using two high speed cameras (230 Hz) during take-off and 4 cameras during the flight phase (60 Hz). 30 Jumps were digitized two times by two different persons. From the image coordinates the 2-d coordinates of the body points were determined by a DLT-method. An eight body segment model was used to compute the centre of mass and its velocity from the 2-d coordinates. The wind velocity was measured at 4 positions on the jumping hill using 2-d wind gauges with an accuracy of +/- 0.1 m s-1. To calculate the flight trajectory a simple 2-d model was developed, in which the jumper was represented as a mass point and the coefficients for drag and lift as function of the stream direction were taken from Rersenberger et al. (2002). He replaced the ski jumper by a rectangular plate. The numeric calculations of the equation of motion for the flight phase were carried out with a Runge-Kutta method with constant time Integration steps of 0.001 s. RESULTS: The mean take-off velocity of the 30 jumps was 2.35 m s"1. Repeated digitization of the 30 trials resulted in a maximum range of 0.18 m s"1 for a Singular trial. The difference between measured and simulated lengths of the jumps was less than 3 m for 26 jumps and between 4 and 10 m for 4 jumps. The difference between measurement and Simulation increased from 3 m up to 12 m when the wind velocity was varied about 1.0 m s-1. DISCUSSION: Although in our model the individual weight and the individual lift and drag forces of the jumpers were not considered, the jump lengths measured and calculated from the model agree surprisingly. One reason may be the limitation of the ski length by the FIS using body height and weight, through which all jumpers have approximately the same ratio between lift, drag and weight forces. Another reason is that world class elite jumpers optimize their flight Position in wind tunnels and therefore differences between the jumpers may be small. The study also proves the extreme importance of the flight angle for the jumping length. The wind velocity turned out to play an important role, consequently at least 4 wind gauges are necessary for an meaningful prediction of the jump length. CONCLUSION: It is demonstrated that using in-run and take-off velocities, flight angle course and wind velocity, jumping length was mostly predicted in a reasonable accuracy. In future the Computer model will be used to calculate the optimized flight angle course and pointing out the difference to the measured flight angles.
© Copyright 2007 4th International Congress on Science and Skiing. Veröffentlicht von University of Salzburg. Alle Rechte vorbehalten.

Bibliographische Detailangaben
Schlagworte:
Notationen:Kraft-Schnellkraft-Sportarten
Veröffentlicht in:4th International Congress on Science and Skiing
Sprache:Englisch
Veröffentlicht: Salzburg University of Salzburg 2007
Seiten:105
Dokumentenarten:Buch
Level:hoch