Apparent mass is a function of the striking technique. In the case of a punch, someone could punch with only the mass their arm, or they could put their entire body mass behind the punch by snapping the shoulder and hip into the strike. Striking speed is defined as the instantaneous velocity of the fist at the point of contact with the board.
The standard case is a fresh pine board with a volume of 0.0017 m3. With Mr=0.061 GN/m2 and E=8.81 GN/m2, the breaking energy is 359 J. The energy required to break the board is shown as a horizontal plane with z=359. Any combination of striking speed and apparent mass above this plane will result in fractured board, any combination below the plane will result in a fractured hand.
Several recognized limitations exist with this analysis. First, the breaking stress energy is defined as the average energy per unit volume. During a strike, the stress energy is highly localized, and therefore neither shape nor geometric variations are adequately addressed. Secondly, at least some energy from the strike is used to displace the board, and some is dissipated as heat and sound.
Overall, the predictions of the model are consistent with experiential evidence and provide a meaningful estimate of parameters that can determine whether a given board will break or not break.