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.

Baseball Pitches,

A. M. Nathan, Scientific American 277, 102-103 (1997).

Dynamics of the Baseball-Bat Collision,

Alan M. Nathan, American Journal of Physics 68, 979-990 (2000).

Baseball batter at moment of impact
The moment of impact

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.

Characterizing the Performance of Baseball Bats,

Alan M. Nathan, American Journal of Physics 71, 134-143 (2003).

Schematic of the baseball-bat collision
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.

A Study of Softball Player Swing Speed*,

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).

The Physics of the Trampoline Effect in Baseball and Softball Bats*,

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).

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.

Scattering of a Baseball by a Bat,

Rod Cross and Alan M. Nathan, American Journal of Physics 74, 896-904 (2006).

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.

Experimental Study of the Gear Effect in Ball Collisions,

Rod Cross and Alan M. Nathan, American Journal of Physics 75, 658-664 (2007).

Effect of Spin on the Flight of a Baseball,

Alan M. Nathan, American Journal of Physics 76, 199-224 (2008).

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).

Paradoxical Pop-ups: Why are They Difficult to Catch?,

Michael. K. McBeath, Alan M. Nathan, A. Terry Bahill, and David G. Baldwin, American Journal of Physics 76, 723-729 (2008).

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.

Performance Versus Moment of Inertia of Sporting Instruments,

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.

Effect of Ball Properties on the Ball-Bat Coefficient of Restitution*,

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 will appear in the proceedings.

A Determination of the Dynamic Response of Softballs,

Lloyd V. Smith, Alan M. Nathan, and Joseph G. Duris, Sports Engineering 12, 163-169 (2010).

Corked Bats, Juiced Balls, and Humidors: The Physics of Cheating in Baseball,

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.

A Comparative Study of Baseball Bat Performance,

Alan M. Nathan, J. J. Crisco, R. M. Greenwald, D. A. Russell, and Lloyd V. Smith, Sports Engineering 13, 153-162 (2011).

Reducing the Effect of the Ball on Bat Performance Measurements,

Alan M. Nathan, Lloyd V. Smith, and Warren L. Faber, Sports Technology (accepted for publication, June 2011).