Mathematical modelling of bat-ball impact in baseball

Rochelle Nicholls

Research output: ThesisDoctoral Thesis

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[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] Ball-impact injuries in baseball, while relatively rare, have the potential to be catastrophic. These injuries are primarily attributed to impact by the ball after it has been hit, pitched or thrown. As the closest infielder to the hitter, the pitcher is at greatest risk of being struck by the batted ball. This thesis investigated the influence of bat and ball design on ball exit velocity (BEV) and the potential for impact injury to pitchers. Finite element analysis (FEA) was used to quantify the dynamics of bat-ball impact for bats of various moment of inertia and baseballs with different mechanical properties. The analysis was conducted using ANSYS/LSDYNA explicit dynamics software. To replicate a typical bat-ball impact in the field, the model required input of bat linear and angular velocity and orientation in three-dimensional (3-D) space, at the instant prior to impact. This data was obtained from 3-D kinematic analysis using two high-speed video cameras operating at 200 Hz. Seventeen high-performance batters used a wood bat and a metal bat of equal length and mass to hit baseballs thrown by a pitcher. Hitters developed significantly higher resultant linear velocity for both the proximal (38.3 ± 1.8 ms-1;) and distal (8.1 ± 1.8 ms-1) ends of the metal bat (compared with 36.4 ± 1.7 ms-1 and 6.9 ± 2.1 ms-1 respectively for the wood bat). They also achieved a significantly more “square” bat position just prior to impact with the ball (264.3 ± 9.1 deg compared with 251.5 ± 10.4 deg). These factors are important in transferring momentum to the batted ball. Mathematical description of the large-deformation material behaviour of the baseball was also required for this analysis. Previous research is limited to compression tests to 10 % of ball diameter, despite conjecture that during impact with the bat, the ball might deform to 50 % of its original diameter. Uniaxial quasi-static compression tests on seven models of baseballs investigated baseball behaviour during deformation to 50 % of ball diameter. The resulting force-displacement relationship was highly non-linear. Hence FEA was used to derive and verify a relationship to describe the time-dependent and elastic behaviour of the ball during the 1 ms period typical of bat-ball impact.
Original languageEnglish
QualificationDoctor of Philosophy
Publication statusUnpublished - 2003


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