Mechanical Optimization of Skateboard Pumping

Skateboarders perform a reciprocating motion on a curved ramp, called pumping, by moving their bodies up and down perpendicular to the ramp's surface. We propose a simple mechanical model for this pumping motion and solve the equation of motion explicitly in angular coordinates. This allows us to derive an optimal control strategy to maximize amplitude by dynamically adjusting the center of mass of the skateboarder. This optimal strategy is compared to experimental results for the motion of a skilled and an unskilled skateboarder in a half-pipe, validating that a skilled skateboarder follows the optimal control strategy more closely.