Hoop frequency as a predictor of performance for softball bats

Hollow metal and composite baseball and softball bats exhibit two types of vibrational modes, bending modes and hoop modes. The hoop modes are unique to hollow bats and involve only a radial vibration of the barrel of the bat. The lowest frequency hoop mode is responsible for the both the "ping" sound of a metal bat and the so-called "trampoline effect." Modal analysis is used to determine the mode shapes and frequencies for a wide variety of softball bats. Hoop mode frequencies are shown to separate families of bats (ie., single-wall, multi-wall, and composite) according to barrel construction. A simple mass-spring model of the trampoline effect suggests that hoop frequency might be correlated to measured performance. A general trend is observed that higher performance bats, with respect to batted ball speed, tend to have lower hoop frequencies. This result suggests that hoop frequency might be one explanation for differences in performance between different types of hollow softball bats.