Minimal force to move the heavier opponent Investigation of sumo game

Abstract

In sports and daily life, we often experience situations where we should carry an object by pushing it. In this study, we analyse sumo, a Japanese traditional sport, in which one can be a winner by pushing the opponent to the outside of dohyo, the wrestling ring. The optimal strategy for the lighter wrestler to carry the heavier opponent by sliding on dohyo is explored in terms of physics. Although the lighter wrestler can never slide the opponent by pushing forward, this can be achieved by exerting the force diagonally upward. As a result of analysis, we obtain the magnitude and direction of the force that should be applied to initiate the sliding motion and ensure its fastest movement. The result reveals the existence of a critical weight ratio of the wrestlers; if the ratio is upper than a certain value, the lighter wrestler should push to a specific direction, while otherwise the optimal force direction depends on the weight. Due to the generality of physics and mathematics, the application is not limited to sumo; the result provides the most effective way to carry an object on a floor in all activities in sports, exercises, and daily life.