The Application of the Variational Method to Optimize a Snowboard Course

In this paper, by using the variational method, we obtain the optimal design on the “halfpipe” shape for a skilled player to maximize the production of “vertical air”. The main idea is that we make the halfpipe shape such that the player can get maximal kinetic energy. Neglecting the air resistance, friction drag, and so on, we formulate the variation for the steepest descent curve so that the player gets a maximum velocity at the bottom of the halfpipe. Then, we consider the bottom plane of the halfpipe to continue optimization. Having the aid of the obtained maximum velocity together with the optimizations in the bottom plane, the player can obtain more kinetic energy to jump up and twist as higher and better as possible. We also make some numerical simulation to verify the theoretical analysis. Finally, according to above analysis, we design a better halfpipe for players to use in practice. Our conclusion is that, based on our design with the standard sizes, the maximum vertical air and the time for twist in the air can exceed the known best results obtained by the world class players.