COMPUTER MODELLING OF A SKI JUMP

Abstract

INTRODUCTION: Ski-jumping was qualified as a sporting event 100 years ago in Scandinavia and northern regions of Russia, and from the first years scientists helped athletes to sharpen their techniques. The first of them was R. Shtrauman, who created the "Norway" style of jump in 1924. There have been several studies about ski-jumping published in the last two decades. Grozin (1971) made an integrated study of jump styles of the 1950s and 1960s. Aerodynamic coefficients are obtained from his experiment with figurines of ski-jumpers in an aerodynamic tube. Remizov (1973,1984) used these coefficients in the optimization problem solved by Pontryagin's maximum principle. Numerical methods were used for similar problems by Komi et al. (1974) and Tani et al. (1971). They all considered old techniques of jumping and, surprisingly, none considered the wind or used constraint on the landing velocity in the case of optimization problems. The most recent paper of Bagin et al. (1997) employs an original mathematical method based on the theory of complex variables and tries to add wind speed to movement equations, but they were written with an error. The overview of the works above allows us to come to the conclusion that none of the following issues have been sufficiently studied: landing velocity, the effect of wind on a jump and the influence of the exact individual parameters of a fully-equipped skier. The main purpose of this study is to construct a mathematical model involving these parameters.