‘Tis the spooky season, and what could be more seasonal than bats? This week we’re exploring a different kind of bats than the usual, though. So let’s take a swing at the physics of baseball and softball bats!
A baseball or softball bat is an irregularly shaped object that is swung as a lever and then experiences a large impact. This impact sets up vibrations in the bat; you can see several vibrational modes modeled on this webpage created by Dan Russell of Penn State University: https://www.acs.psu.edu/drussell/Demos/batvibes.html He illustrates here that wooden bats are solid, and bend lengthwise, like a tuning bar; aluminum and composite bats, however, are frequently hollow, and can flex across their diameters as well, like a hoop or bell.
One of the most widely recognized specialists in the field of baseball physics is Alan Nathan of the University of Illinois; you can check out his homepage here: http://baseball.physics.illinois.edu/ where he discusses many aspects of the physics of the sport, current and historical. Particularly interesting is his collection of slow-motion images of ball and bat collisions and their analysis: http://baseball.physics.illinois.edu/ball-bat.html .
You can experiment with this physics yourself with our demonstration D2-21 Center of Percussion: Bat and Mallet.
Many articles have been published over the years exploring the physics of bats, particularly with a view to classroom discussion. We’ve collected for you some highlights from the American Journal of Physics and The Physics Teacher, presented chronologically so you can explore the development of this topic over time.
H. Brody. “The sweet spot of a baseball bat”
American Journal of Physics 54, 640 (1986); https://doi.org/10.1119/1.14854
Explores the idea of a bat’s “sweet spot,” the point of impact at which maximum energy is imparted to the ball.
G. Watts & S. Baroni. “Baseball–bat collisions and the resulting trajectories of spinning balls”
American Journal of Physics 57, 40 (1989); https://doi.org/10.1119/1.15864
Examines collisions between bat and ball as rigid bodies.
H. Brody. “Models of baseball bats”
American Journal of Physics 58, 756 (1990); https://doi.org/10.1119/1.16378
Examines collisions between bat and ball and the bat’s vibrations, treating it as a free object in space.
L. L. Van Zandt. “The dynamical theory of the baseball bat”
American Journal of Physics 60, 172 (1992); https://doi.org/10.1119/1.16939
Models the bat as a vibrating elastic mass with a normal mode.
R. Cross. “The sweet spot of a baseball bat”
American Journal of Physics 66, 772 (1998); https://doi.org/10.1119/1.19030
Compares the calculation of a bat’s “sweet spot” as the center of percussion or as a vibrational node.
A. Nathan. “Dynamics of the baseball–bat collision”
American Journal of Physics 68, 979 (2000); https://doi.org/10.1119/1.1286119
Presents a way to model the physics of the collision between a bat and a ball.
A. Nathan. “Characterizing the performance of baseball bats”
American Journal of Physics 71, 134 (2003); https://doi.org/10.1119/1.1522699
Introduces ways of measuring and modeling baseball bats in the physics lab.
R. Cross. “A double pendulum swing experiment: In search of a better bat”
American Journal of Physics 73, 330 (2005); https://doi.org/10.1119/1.1842729
Looks at the motion of a double pendulum and how it can model the swing of a bat or racquet.
R. Cross & A. Nathan. “Scattering of a baseball by a bat”
American Journal of Physics 74, 896 (2006); https://doi.org/10.1119/1.2209246
Examines the relationship between distance, speed, and spin of a ball hit by a bat.
R. Cross & A. Nathan. “Experimental study of the gear effect in ball collisions”
American Journal of Physics 75, 658 (2007); https://doi.org/10.1119/1.2713788
Looks at the possibility of whether slippage between surfaces in a baseball impact can be modeled like meshing gears.
R. Cross. “Mechanics of swinging a bat”
American Journal of Physics 77, 36 (2009); https://doi.org/10.1119/1.2983146
Models the force pairs at work in swinging a bat.
D. Russell. “Swing Weights of Baseball and Softball Bats”
The Physics Teacher 48, 471 (2010); https://doi.org/10.1119/1.3488193
Explores the moment of inertia of bats, commonly called the “swing weight” in sports writing.
A. Nathan, L. Smith, & D. Russel. “Corked bats, juiced balls, and humidors: The physics of cheating in baseball”
American Journal of Physics 79, 575 (2011); https://doi.org/10.1119/1.3554642
Examines the physics underlying several baseball controversies.
D. Kagan. “The vibrations in a rubber baseball bat”
The Physics Teacher 49, 588 (2011); https://doi.org/10.1119/1.3661118
Discusses some experiments with a rubber bat.
I. Aguilar & D. Kagan. “Breaking Bat”
The Physics Teacher 51, 80 (2013); https://doi.org/10.1119/1.4775523
Describes experiments with the breaking points of different wooden bats.
J. Kensrud, A. Nathan, & L. Smith. “Oblique collisions of baseballs and softballs with a bat”
American Journal of Physics 85, 503 (2017); https://doi.org/10.1119/1.4982793
Examines ball and bat collisions with a high speed camera.
K. Wagoner & D. Flanagan. “Baseball Physics: A New Mechanics Lab”
The Physics Teacher 56, 290 (2018); https://doi.org/10.1119/1.5033871
Describes a series of student lab activities to explore the mechanics of baseball.
And one final note, on balls rather than bats: new work in materials science is studying how softer materials inside solid projectiles can affect how they launch. Read all about it in this new post at the American Physical Society website:
Springy Material Boosts Projectile Performance https://physics.aps.org/articles/v13/160
Update: And for those who read all the way to the end but are still upset about the lack of cute fuzzy bats: "What Bats Can Teach Humans About Coronavirus Immunity" at JSTOR Daily