Shape Optimization of a Wooden Baseball Bat Using Parametric Modeling and Genetic Algorithms

Baseball is a popular and very lucrative bat-and-ball sport that uses a wooden bat to score runs. We hypothesize that new design features for baseball bats will emerge from their shape optimization using parametric modeling and genetic algorithms. We converge the location of two points on bats made from maple (Acer sp.) and ash (Fraxinus sp.) wood that are associated with increased velocity of a ball rebounding off a bat: vibrational nodal points and the center of percussion (COP). Our modeling and optimization approach was able to reduce the distance between the nodal points and COP from 166.0 mm to 52.1 mm. This change was similar in both wood species and resulted from changes to the geometry of the bat, specifically shifting of the mass of the bat toward the center of the barrel and removing mass from the very end of the barrel. We conclude that the combination of parametric finite element modeling and optimization using genetic algorithms is a powerful tool for exploring virtual designs for baseball bats that are based on performance criteria and suggest that our designs could be realized in practice using subtractive manufacturing technology.

Characterization of Maple and Ash Material Properties for the Finite Element Modeling of Wood Baseball Bats

To assist in developing a database of wood material properties for the finite element modeling of wood baseball bats, Charpy impact testing at strain rates comparable to those that a wood bat experiences during a bat/ball collision is completed to characterize the failure energy and strain-to-failure as a function of density and slope-of-grain (SoG) for northern white ash (Fraxinus americana) and sugar maple (Acer saccharum). Un-notched Charpy test specimens made from billets of ash and maple that span the range of densities and SoGs that are approved for making professional baseball bats are impacted on either the edge grain or face grain. High-speed video is used to capture each test event and image analysis techniques are used to determine the strain-to-failure for each test. Strain-to-failure as a function of density relations are derived and these relations are used to calculate inputs to the *MAT_WOOD (Material Model 143) and *MAT_EROSION material options in LS-DYNA for the subsequent finite element modeling of the ash and maple Charpy Impact tests and for a maple bat/ball impact. The Charpy test data show that the strain-to-failure increases with increasing density for maple but the strain-to-failure remains essentially constant over the range of densities considered in this study for ash. The flat response of the ash data suggests that ash-bat durability is less sensitive to wood density than maple-bat durability. The available SoG results suggest that density has a greater effect on the impact failure properties of the wood than SoG. However, once the wood begins to fracture, SoG plays a large role in the direction of crack propagation of the wood, thereby determining if the shape of the pieces breaking away from the bat are fairly blunt or spear-like. The finite element modeling results for the Charpy and bat/ball impacts show good correlation with the experimental data.

The Kinetics of Swinging a Baseball Bat

The purpose of this study was to compute the 3-dimensional kinetics required to swing 3 youth baseball bats of varying moments of inertia. The 306 swings by 22 male players (age 13–18 y) were analyzed. Inverse dynamics with respect to the batter’s hands were computed given the known kinematics and physical properties of the bats. Peak force increased with larger bat moments of inertia and was strongly correlated with bat tip speed. By contrast, peak moments were weakly correlated with bat moments of inertia and bat tip speed. Throughout the swing, the force applied to the bat was dominated by a component aligned with the long axis of the bat and directed away from the bat knob, whereas the moment applied to the bat was minimal until just prior to ball impact. These results indicate that players act to mostly “pull” the bat during their swing until just prior to ball impact, at which point they rapidly increase the moment on the bat. This kinetic analysis provides novel insight into the forces and moments used to swing baseball bats.