The Science of Baseball

1. Front Matter

   Pages i-xxi

   PDF

2. Types of Bat-Ball Collisions

   • A. Terry Bahill

   Pages 1-8

3. Configurations of Bat-Ball Collisions

   • A. Terry Bahill

   Pages 9-17

4. Equations for Bat-Ball Collisions

   • A. Terry Bahill

   Pages 19-43

5. The BaConLaw Model for Bat-Ball Collisions

   • A. Terry Bahill

   Pages 45-103

6. Alternative Models

   • A. Terry Bahill

   Pages 105-143

7. Synopsis of Chapters 1 to 5

   • A. Terry Bahill

   Pages 145-151

8. The Ball in Flight Model

   • A. Terry Bahill

   Pages 153-202

9. Dénouement

   • A. Terry Bahill

   Pages 203-209

10. General Modeling Principles

    • A. Terry Bahill

    Pages 211-220

11. Back Matter

    Pages 221-222

    PDF

This book describes the dynamic collisions between baseballs, softballs, and bats, and the intricate modeling of these interactions, using only Newton’s basic principles and the conservation laws of physics. Veteran baseball science author Terry Bahill explains models for the speed and spin of balls and bats and equations for bat-ball collisions at a level accessible to high school and undergraduate physics students, engineering students, and, most importantly, students of the science of baseball. Unlike other, more technical accounts of these phenomena that exhibit similar rigor, the models presented in this volume use only basic physical principles to describe simple collision configurations. Elucidating the most important factors for understanding bat performance—bat weight, moment of inertia, the coefficient of restitution, and characteristics of humans swinging the bats, Dr. Bahill also explains physical aspects of the ideal bat and the sweet spot.

• Explains how to select or design an optimal baseball or softball bat and create models for bat-ball collisions using only fundamental principles of mechanics from high school physics;

• Describes the results of the collision between baseball and bat using basic mathematics such as equations for the speed of the ball after the collision, bat speed after the collision, and bat rotation after the collision;

•Accessible to high school and undergraduate students as well as non-technical aficionados of the science of baseball.

 “Dr. Bahill’s book is the perfect tool for teaching how to solve some of baseball’s basic science problems. Using only simple Newtonian principles and the conservation laws, Dr. Bahill explains how to model bat-ball collisions. Also, he derives equations governing the flight of the ball, and proceeds to show what factors affect air density and how this density affects the ball’s flight. And as a unique addition to his fine book, he provides advice for selecting the optimal bat—a surprising bonus!”

Dave Baldwin, PhD

Major League pitcher, 1966-1973, lifetime Major League ERA, 3.08

 “If I were the General Manger of a baseball team, I would tell my people to write a ten-page paper describing what this book contains that could improve our performance. I think the book provides the foundation for change.”

Bruce Gissing

Executive VP-Operations (retired)
Boeing Commercial Airplanes

“[I] had a chance to read your research, and I fully agree with your findings.”

Baseball Legend Ted Williams, in a 1984 letter to the author

• Science of Baseball
• Baseball Ball velocity after a collision
• Batted-ball speed
• Center of Percussion
• Coefficient of Restitution
• Collision at center of mass
• Collision at sweet spot
• Conservation of Angular Momentum
• Conservation of Linear Momentum
• Conservation of Momentum
• Equations for Bat-ball Collisions
• Models for swinging a bat
• Optimal bat
• Physics of baseball
• Pitch speed
• Sensitivity analysis
• Sensitivity functions
• Softball
• Spin of ball
• Sweet spot

• Systems and Industrial Engineering, University of Arizona, Tucson, USA

  A. Terry Bahill

Terry Bahill is an Emeritus Professor of Systems Engineering and of Biomedical Engineering at the University of Arizona in Tucson. He served as a Lieutenant in the United States Navy. He received his Ph.D. in electrical engineering and computer science from the University of California, Berkeley. He is the author of eight engineering books and over two hundred and fifty papers, over one hundred of them in peer-reviewed scientific journals. Bahill has worked with dozens of high-tech companies presenting seminars on Systems Engineering, working on system development teams and helping them to describe their Systems Engineering processes. He holds a U.S. patent for the Bat Chooser™, a system that computes the Ideal Bat Weight™ for individual baseball and softball batters. He was elected to the Omega Alpha Association, the systems engineering honor society. He received the Sandia National Laboratories Gold President's Quality Award. He is a Fellow of the Institute of Electrical and Electronics Engineers (IEEE), of Raytheon Missile Systems, of the International Council on Systems Engineering (INCOSE) and of the American Association for the Advancement of Science (AAAS). He is the Founding Chair Emeritus of the INCOSE Fellows Committee. His picture is in the Baseball Hall of Fame's exhibition "Baseball as America." 

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