Improving Punching "Power": Reconsidering the roles of initial strike velocity and effective mass

Abstract

We review the principal features of one-dimensional, elastic collisions pertinent to modeling strike-mediated impacts in martial arts and combat sports contexts. Arguing for the post-collision velocity of a stationary, target mass as a useful proxy for determining overall punch efficacy, we demonstrate that pre-collision velocities for real strikes are bounded, such that speed prior to impact has a more limited effect on the impulse experienced by said target than suggested by supporting literature. We find that the value of incoming, "effective" mass -- despite eluding uniform establishment criteria or measurement protocols across the same body of literature -- exerts an independent influence on the target velocity which can, in principle, match or exceed that of the strike speed. We perform explicit numerical analyses to supplement these theoretical considerations, in dynamical regimes relevant to real human combat, and then briefly discuss the potential for a given fighter to attain a fold-increase in effective mass (from a reasonable baseline value based on bodyweight, and supported by previous work) sufficient to realize limits for upper-limb strikes to the body, in practice, as a trainable goal.