Flight style optimization in ski jumping on normal, large, and ski flying hills

In V-style ski jumping, aerodynamic forces are predominant performance factors and athletes have to solve difficult optimization problems in parts of a second in order to obtain their jump length maximum and to keep the flight stable. Here, a comprehensive set of wind tunnel data was used for optimization studies based on Pontryagin′s minimum principle with both the angle of attack α and the body-ski angle β as controls. Various combinations of the constraints αmax and βmin(t) were analyzed in order to compare different optimization strategies. For the computer simulation studies, the Olympic hill profiles in Esto-Sadok, Russia (HS 106 m, HS 140 m), and in Harrachov, Czech Republic, host of the Ski Flying World Championships 2014 (HS 205 m) were used. It is of high importance for ski jumping practice that various aerodynamic strategies, i.e. combinations of α- and β-time courses, can lead to similar jump lengths which enables athletes to win competitions using individual aerodynamic strategies. Optimization results also show that aerodynamic behavior has to be different at different hill sizes (HS). Optimized time courses of α and β using reduced drag and lift areas in order to mimic recent equipment regulations differed only in a negligible way. This indicates that optimization results presented here are not very sensitive to minor changes of the aerodynamic equipment features when similar jump length are obtained by using adequately higher in-run velocities. However, wind tunnel measurements with athletes including take-off and transition to stabilized flight, flight, and landing behavior would enable a more detailed understanding of individual flight style optimization.