The Physics of
Baseball 
The Physics of
Baseball
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How Much Does a Fly Ball "Carry"? (updated, August 16, 2009) Read a brief account on an analysis I did to quantify the term "carry". Included is an analysis of the home runs in the new Yankee Stadium to see if there is any measurable effect of wind. Effect of Ball Properties on the Ball-Bat Coefficient of Restitution (new, August 18, 2009) This paper, coauthored by Lloyd Smith and myself, presents a simple physical model relating the ball-bat coefficient of restitution (BBCOR) to the ball COR and stiffness. Using the model, a technique is developed to normalize the BBCOR to a standard ball. This paper will be presented at the 4th Asia-Pacific Congress on Sports Technology (APCST2009) in September 2009 and will appear in the proceedings.. Baseball and Physics: An Intersection of Passions (new, July 21, 2009) A 1-hour video of a lecture I gave in April 2009 as part of the lecture series Distinctive Voices@The Beckman Center: Insights on Science, Technology, and Medicine. The talk took place National Academies of Science and Engineering on the UC/Irvine campus. Talks. Powerpoint slides of talks I have given on the physics of baseball. Physics 199bb A freshman-level course on the physics of baseball given for non-scientists at the University of Illinois during the Fall 2007 semester. The Effect of Spin on the Flight of a Baseball: The following article appeared in the February 2008 issue of American Journal of Physics and may be found at Alan M. Nathan, Am J. Phys. 76, 119-124 (2008) (Copyright 2008 American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Association of Physics Teachers.) In this paper I report on an experiment to measure the quantitative effect of spin on the flight of a baseball. This topic has relevance for the break of a curveball, the hop of a fastball, and the flight of a long fly ball. A talk based on this work was presented at the IMAC XXIV Meeting of the Society of Experimental Mechanics, January 30, 2006. A presentation based on this work entitled "Baseball aerodynamics: What do we know and how do we know it?" was presented at the SABR36 convention in Seattle (June 2006). The effect of spin decay on the flight of a baseball.: A brief unpublished essay in which an estimate is made of the rate of spin decay of a baseball in flight and the effect of the spin decay on the flight of a baseball. Scattering of a Baseball by a Bat. The following article appeared in the October 2006 issue of American Journal of Physics and may be found at Rod Cross and Alan M. Nathan, Am. J. Phys. 74, 896 (2006) (Copyright 2006 American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Association of Physics Teachers.) This paper, coauthored by Rod Cross and myself, reports on an experiment to study the spin resulting from a low-speed ball-bat collision. The data are relevant for determining whether a hit curveball has more backspin than a hit fastball. Click here to see a short video clip of the experiment in action. That handsome fellow holding the bat is Rod. Video. As Yogi Berra once said, you can observe a lot by just watching. At this link you will find some pretty nifty high-speed videos and still photographs that demonstrate better than words alone some interesting physics related to the game of baseball. The Physics of the Trampoline Effect in Baseball and Softball Bats This paper, coauthored by Lloyd Smith, Dan Russell, and myself, presents a simple physical picture of the "trampoline effect" in hollow bats and demonstrates how the effect leads to a larger coefficient of restitution. A special section presents new data showing there is no measureable trampoline effect with a corked bat. This paper was presented at the September 2004 meeting of the International Sports Engineering Association in Davis CA. Watch a 50-minute video of my talk on the physics of baseball given March 2002 as part of the Jefferson Laboratory Science Series. The talk can be played on Windows Media Player. The video is the property of Jefferson Laboratory and is posted here with their permission. Corked Bats Click on the link for some remarks I prepared June 10, 2003 on the benefits or not of using a corked bat. Updated December 1, 2004. How to Hit Home Runs: Optimum Baseball Bat Swing Parameters for Maximum Range Trajectories. The following article appeared in the November 2003 issue of American Journal of Physics and may be found at Gregory S. Sawicki, Mont Hubbard, and William J. Stronge, Am. J. Phys. 71, 1152 (2003) (Copyright 2003 American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the the American Association of Physics Teachers. For other articles from the American Journal of Physics visit the AJP web site.) This paper uses improved models for the pitch, batting, and post-impact flight phases of a baseball in an optimal control context to find bat swing parameters that produce maximum range. One of the most interesting findings of the authors is that an optimally hit curve ball will travel farther than an optimally hit fastball or knuckleball due to increased lift during flight. This particular aspect is discussed at length in an NPR broadcast from November 20, 2003. This paper is one of many interesting projects undertaken by Professor Mont Hubbard and his talented students at the Sports Biomechanics Laboratory at UC/Davis. World Series Special. Is the World Series winner determined entirely from statistics? For an interesting article addressing that issue, see the American Institute of Physics web site for a statistical analysis of the probabilty the World Series will run for the full seven games. Vibrational Analysis of a baseball bat. This is a graphic I prepared showing how one does a "modal analysis" to determine the vibrational frequencies and shapes of a typical wood baseball bat. A Study of Softball Player Swing Speed, by Lloyd Smith, Jeff Broker, and Alan Nathan. This presents the results of a 2002 field study sponsored by the Amateur Softball Association. The data show that the swing speed of a typical player is inversely related to the bat moment of inertia about the handle (with a fixed bat weight) and nearly independent of the weight of the bat (at fixed moment of inertia). The offical citation is Smith, L, Broker, J, Nathan, A, 2003, "A Study of Softball Player Swing Speed," Sports Dynamics Discovery and Application, Edited by A. Subic, P. Trivailo, and F. Alam, RMIT University, Melbourne Australia, pp. 12-17. Dynamics of the Baseball-Bat Collision. The following article appeared in the November 2000 issue of American Journal of Physics and may be found at Alan M. Nathan, Am. J. Phys. 68, 979 (2000) (Copyright 2000 American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Association of Physics Teachers.) The paper describes a model for wooden bats which is then used to describe the collision between bat and ball. Based on the preliminary version of this paper, Jeremy Manier wrote an article Science has a Sweet Spot for Baseball that appeared in the April 3, 2000 issue of the Chicago Tribune (front page, above the fold!), which features an interview with me about the bat-ball collision. The Acoustics of Baseball An excellent and very readable report by Professor Bob Adair, based on a talk he gave in June 2001 before the Acoustical Society of America. Another account of this is in the excellent New York Times article by Jim Glanz. Click here for a nifty graphic based on this article. Professor Adair wrote the book entitled The Physics of Baseball, 3rd Edition, which every person serious about the science of the game should read. And speaking about books, you should also check out the book by Watts and Bahill entitled Keep Your Eye on the Ball. Although not as comprehensive as Adair's, it addresses some very interesting issues and give some good explanations based on simple physics principles. Research on Tennis Rackets. Despite the fact that this link is to a tennis site rather than baseball, some of the same considerations that apply to the baseball-bat collision also apply to the tennis ball-racket collision. This site will tell you all about the latter.
Rod Cross
The Evolution of the Baseball Bat, an interesting and highly readable article by former MLB pitcher Bernie Mussill. |
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Baseball Trajectory Calculator
(new, July 21, 2009) Click on the link to download an Excel spreadsheet that can be used to do baseball trajectory calculations, including the effects of air drag, spin and the Magnus force, wind, temperature, and altitude.
Field Equations: The Physics of Baseball (new, July 21, 2009) Link to a story appearing in the April 5, 2009 issue of Scientific American by John Matson. Newton in the Batter's Box Link to a story appearing in the April 28, 2008 issue of Newsweek by science writer Sharon Begley. PITCHf/x (updated, July 21, 2009) Learn about the PITCHf/x system for tracking pitched baseballs using video technology. This link will tell you about the system, some of the analysis that people have done using the system, and how you can do your own analysis. Hittracker: A web site due to Greg Rybarczyk that reports on home run distances, meaning how far the ball would have traveled had it made it back to ground level without hitting something first. Pay close attention to the section called "How Hit Tracker Works." Greg's algorithm is based on the precise location where the ball hit as well as the total flight time and takes into account atmospheric conditions. It is probably the best algorithm currently in use for determining home run distances. Wood Versus Non-Wood Bats. There has been a lot in the news recently about wood vs. non-wood bats. To find out the scientific facts on this subject, click on the link. Paradoxical popups: Why are they hard to catch? The following article appears in the August 2008 issue of American Journal of Physics and may be found at Michael K. McBeath, Alan M. Nathan, A. Terry Bahill, and David G. Baldwin, Am. J. Phys. 76, 723-729 (2008) (Copyright 2008 American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Association of Physics Teachers.) This paper examines the unusual trajectories of towering popups with lots of backspin. It is shown that the normal strategy used by outfielders to intercept fly balls leads to systematic vacillation in running paths for these popups. For a great example of a paradoxical popup, take a look at this video taken from a Red Sox vs. Tampa Bay game on September 15, 2008. Note the third baseman Kevin Cash (normally a catcher) overruns the ball, which initially was headed toward the seats along the third baseline but then veers back towards the field. This is the quintessential paradoxical popup, indicative of a lot of backspin on the ball. Note also what happens to the ball when it hits the ground. The backwards bounce is further indication of large amount of backspin on the ball. Baseball at High Altitude Click on this link to learn all about the effect of high altitude on the flight of a pitched or batted baseball. Chemical Bonds: What is the effect of steroid use on the rate of home run production? Professor Roger Tobin (Tufts University, Department of Physics) has written a paper recently published in American Journal of Physics (Copyright 2008 American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Association of Physics Teachers.) that directly addresses this question. Click here for my thumbnail summary and critique of Tobin's paper that was published in SABR's Baseball Research Journal in Summer 2009. In June 2006, a story appeared online at "ESPN Page 2" by Patrick Hruby that addressed the same issue. I wrote a short set of notes at that time (updated Feb. 17, 2009) in an attempt to quantify the effect of increased muscle mass on bat speed. Bonds 756th home run. The trajectory of Barry Bonds' record-breaking 756th home run. The Gyroball What's all this gyromania about? To find out, click on the link. Terry Bahill's Science of Baseball web site. Particularly take note of the very fine article entitled "Predicting a Baseball's Path", co-authored with former MLB pitcher Dr. Dave Baldwin and published in American Scientist (2005). Porter Johnson's Physics of Baseball web site. Dr. Johnson is a physics professor at Illinois Institute of Technology, in the shadow of U.S. Cellular Field, home of theWhite Sox. Listen to a very interesting presentation by Professor Bob Adair given at the Science of Baseball Symposium, part of the AAAS annual meeting in February 2000. His talk, entitled "Batting and Thinking", is a discussion of the process whereby a batter observes, process, decides, and swings the bat. As you listen, you should also look at this very nifty graphic , courtesy of the NYTimes. Listen to my own presentation at the Science of Baseball Symposium entitled "How Would a Physicist Design a Bat". If you like, you can observe the powerpoint slides as you listen. PBS - Scientific American Frontiers. On the Ball: Baseball Tech - watch online as Alan Alda explores the science of baseball. To see the video, click here and scroll down to the Baseball Tech video. Sites Geared Towards Younger People. The two most important of these sites are (1) Sport Science @ The Exploratorium, the superb site of The Exporatorium science museum in San Francisco, and (2) The K-8 Aerodynamics Textbook, an excellent site put together by Dr. Jani Macari Pallis. The former deals with the physics of baseball, hockey, and other sports. The latter is mostly about aerodynamics, but there is a special section on the physics of tennis. Both sites are well worth looking at.
Aerodynamics of the Baseball.
These are a series of web sites with information about the flight of
a hit or pitched baseball through the air. An excellent site is the NASA-sponsored site
Aerodynamics of Baseball, maintained by
Tom Benson. Other excellent sites are
aerodynamics
by the Glenn Learning Technologies Project and
Baseball Flight Simulator
to simulate the flight of a baseball.
Check our Brian Raue's site for a
study he did of
home run distances at Pro Player Stadium. A excellent article, The Mechanics of a Breaking Pitch
appeared in the April 1997 issue of Popular Mechanics. Take particular note of
the 4th page, which has a very nice description of the physics of a curveball by physicist Peter
Brancazio.
Finally, check out a nice description of a
knuckleball , then
watch a short mpeg video of Tim Wakefield in action.
The Juiced Baseball Issue.
Is the baseball
is "juiced." That is, is it more lively today than yesteryear?
Read the account by Rawlings on
their manufacturing procedures by clicking here
.
In 2000 MLB conducted a series of tests on baseballs. Click
here to download the
official report issued by Prof. Jim Sherwood of the Baseball Research
Center at the University of Massachusetts/Lowell, who performed the tests.
For a somewhat different take on this issue, see the nice
article written by
Bill Sloat in the Cleveland Plain Dealer.
Physics and Acoustics of Bats.
Hitting and Pitching Mechanics.
Three sites devoted to the mechanics of swinging a bat:
Batspeed.com , Coach Preston Peavy's VSI Baseball, and
Mike Epstein Hitting.
Three sites devoted to the mechanics of pitching a baseball:
Tom House,
Dr. Mike Marshall,
and American Sports Medicine Institute.
Both House and Marshall are former MLB pitchers. The ASMI is run by Dr. James Andrews, the surgeon who performs most of the shoulder operations on MLB pitchers.
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