A heuristic model-based approach for compensating wind effects in ski jumping

Abstract

Wind influences the jump length in ski jumping, which raises questions about the fairness. To counteract the wind problem, the International Ski Federation has introduced a wind compensation system in 2009: time-averaged wind velocity components tangential to the landing slope are obtained from several sites along the landing slope, and these data are used in a linear statistical model for estimating the jump length effect of wind. This is considered in the total score of the ski jump. However, it has been shown that the jump length effect estimates can be inaccurate and misleading. The present manuscript introduces an alternative mathematical wind compensation approach that is based on an accurate mechanistic model of the flight phase. This estimates the jump length effect as difference between the jump length of the real ski jump at the given wind condition and the computed jump length of the simulated ski jump at calm wind. Inputs for the computer simulation are the initial flight velocity and aerodynamic coefficients of the real ski jump and can be obtained from kinematic and wind velocity data collected during the flight. The initial flight velocity is readily available from the kinematic data and inverse dynamics can be used to compute the aerodynamic coefficients. The accuracy of the estimated jump length effect of the mechanistic model-based approach depends only on the measurement errors in the kinematic and wind velocity data, but not on inaccuracies of an approach that is based on a linear statistical model.