Baseball Papers of Alan Nathan
This page contains links to peer-reviewed physics of baseball papers I have written or co-authored for scientific journals, listed in chronological order with the earliest listed first. Conference proceedings are denoted by an asterisk. All papers linked to on this page are copyrighted but may be downloaded for personal use.
A. M. Nathan, Scientific American 277, 102-103 (1997).
Alan M. Nathan, American Journal of Physics 68, 979-990 (2000).
The moment of impact
Courtesy, Champaign News-Gazette
This paper develops a dynamic model for wooden bats, taking into account their vibrational properties. The model 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.
Alan M. Nathan, American Journal of Physics 71, 134-143 (2003).
schematic of the baseball-bat collision in the
(a) usual field frame and the (b) bat rest frame.
This article defines a set of laboratory measurements that can be performed on a bat and then used to predict performance in the field. Using a computational model, it is shown that bat performance depends on the interplay of the elasticity of the ball-bat collision, the inertial properties of the ball and bat, and the bat swing speed. This paper is the foundation for modern efforts to regulate the performance of non-wood bats.
Lloyd Smith, Jeff Broker, and Alan Nathan, Sports Dynamics Discovery and Applications, eds. A. Subic, P. Trivailo, and F. Alam, RMIT University, Melbourne Australia, pp. 12-17 (2003).
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).
Alan M. Nathan, Daniel A. Russell, and Lloyd V. Smith, The Engineering of Sport V, eds. M. Hubbard, R. Mehta, and J. Pallis, UC Davis, Davis CA, pp. 38-44 (2004).
Toy model for the trampoline effect.
This paper 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.
Rod Cross and Alan M. Nathan, American Journal of Physics 74, 896-904 (2006).
This paper 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.
Rod Cross and Alan M. Nathan, American Journal of Physics 75, 658-664 (2007).
Alan M. Nathan, American Journal of Physics 76, 199-224 (2008).
Forces on a baseball in flight.
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 movement of pitched baseballs as well as on the trajectory of a batted baseball.
Michael. K. McBeath, Alan M. Nathan, A. Terry Bahill, and David G. Baldwin, American Journal of Physics 76, 723-729 (2008).
Some trajectories of batted baseballs.
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.
Rod Cross and Alan M. Nathan, Sports Technology 2, 7-15 (2009).
by Rod Cross and myself (Sports Technology, vol. 2, pp 7-15, 2009). It is shown that for a given coefficient of restitution (COR), both the intrinsic power and the swing speed of a tennis racquet or baseball bat correlate strongly with the MOI about an axis through the handle and only weakly with the mass.
A. M. Nathan and L. V. Smith, 4th Asia-Pacific Congress on Sports Technology, Honolulu, Hawaii, The Impact of Technology on Sport, 257-262 (2009).
This paper 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 was published in the proceedings.
Lloyd V. Smith, Alan M. Nathan, and Joseph G. Duris, Sports Engineering 12, 163-169 (2010).
Alan M. Nathan, Lloyd V. Smith, Warren L. Faber, and Daniel A. Russell, American Journal of Physics 79, 575-580 (2011).
Three questions of relevance to Major League Baseball are
investigated from a physics perspective. Can a baseball be
hit farther with a corked bat? Is there evidence that the baseball is
more lively today than in earlier years? Can
storing baseballs in a temperature- or humidity-controlled environment significantly affect
home run production?
These questions are
subjected to a physics analysis, including an experiment and an
interpretation of the data. The answers to the three questions
are no, no, and yes.
A very nice popularized summary of the paper was written by Chris Solomon and appeared in Smithsonian Magazine in June, 2011.
Alan M. Nathan, J. J. Crisco, R. M. Greenwald, D. A. Russell, and Lloyd V. Smith, Sports Engineering 13, 153-162 (2011).
Alan M. Nathan, Lloyd V. Smith, and Warren L. Faber, Sports Technology (accepted for publication, April 2011).
A new technique is described to normalize the performance of a bat to the coefficient of restitution and stiffness of the baseball or softball used to measure the performance. The technique is developed theoretically and tested experimentally. It is shown to be vastly superior to a different normalization technique that has been popularly used.
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