ABSTRACT
CONTENTS 16.1 Pitch........................................................................................................... 446
16.1.1 Right-Hand Rules and the Cross Product ............................ 447 16.1.2 Right-Hand Rules Applied to a Spinning Ball .................... 447 16.1.3 Deflection of Specific Kinds of Pitches ................................. 448 16.1.4 Forces Acting on a Ball in Flight ............................................ 451 16.1.5 Comparison of the Slider and Curveball.............................. 454 16.1.6 Vertical Deflection .................................................................... 455 16.1.7 Modeling Philosophy ............................................................... 457 16.1.8 Somatic Metaphors of Pitchers ............................................... 458 16.1.9 Summary .................................................................................... 459
16.2 Bat-Ball Collisions .................................................................................. 459 16.2.1 Sweet Spot of the Bat ............................................................... 459 16.2.2 Coefficient of Restitution......................................................... 464 16.2.3 Performance Criterion.............................................................. 465 16.2.4 Vertical Size of the Sweet Spot ............................................... 466
16.3 Model for Bat-Ball Collisions ............................................................... 467 16.3.1 Ball’s Launch Velocity, Angle, and Spin Rate ..................... 470 16.3.2 Range, Hang Time, and Ground Time.................................. 473 16.3.3 Batting Success Probability Function .................................... 473 16.3.4 Example of Varying Offsets .................................................... 475 16.3.5 Results......................................................................................... 476 16.3.6 Discussion .................................................................................. 476
16.4 Swing of the Bat ...................................................................................... 478 16.4.1 Ideal Bat Weight and the Bat Chooser .................................. 478 16.4.2 Principles of Physics Applied to Bat Weight Selection ...... 479 16.4.3 Coupling Physics to Physiology............................................. 480 16.4.4 Ideal Bat Weight........................................................................ 480 16.4.5 Ideal Moment of Inertia........................................................... 482
16.5 Summary .................................................................................................. 484 List of Variables ................................................................................................. 485 References ........................................................................................................... 485
This chapter discusses the pitch, the bat-ball collision, and the swing of the bat. Section 16.1, based on Bahill and Baldwin [1], describes the pitch in terms of the forces on the ball and the ball’s movement. Section 16.2, based on Bahill [2] and Bahill and Baldwin [3], discusses bat-ball collisions in terms of the sweet spot of the bat and the coefficient of restitution (CoR). Section 16.3 based on Bahill and Baldwin [3], presents a model for bat-ball collisions, a new performance criterion, and the resulting vertical sweet spot of the bat. Section 16.4, based on Bahill [2] and Bahill and Karnavas [4], presents experimental data describing the swing of a bat and suggests ways of choosing the best bat for individual batters. This chapter is about the mechanics of baseball. To understand the whole
baseball enterprise, read Bahill et al. [5]. They populate a Zachman framework with nearly 100 models of nearly all aspects of baseball.
