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Influence of a Humidor on the Aerodynamics of Baseballs

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Influence of a Humidor on the Aerodynamics of Baseballs Influence of a humidor on the aerodynamics of baseballs ͒ Edmund R. Meyera and John L. Bohn JILA, NIST, and Department of Physics, University of Colorado, Boulder, Colorado 80309 ͑Received 26 November 2007; accepted 16 June 2008͒ We investigate whether storing baseballs in a controlled humidity environment significantly affects their aerodynamic properties. We measure the change in diameter and weight of baseballs as a function of relative humidity in which the balls are stored. The trajectories of pitched and batted baseballs are modeled to assess the difference between those stored at 30% relative humidity versus 50% relative humidity. We find that a drier baseball will curve slightly more than a humidified one for a given pitch velocity and rotation rate. We also find that aerodynamics alone would add 2 ft to the distance a wetter baseball ball is hit. This increased distance is compensated by a 6 ft reduction in the batted distance due to the change in the coefficient of restitution of the ball. We discuss consequences of these results for baseball played at Coors Field in Denver, where baseballs have been stored in a humidor at 50% relative humidity since 2002. © 2008 American Association of Physics Teachers. ͓DOI: 10.1119/1.2955796͔ I. INTRODUCTION Coors Field toward lower earned run averages and fewer runs ͑indicating more successful pitching͒ by more than two The game of baseball is strongly influenced by the aero- standard deviations. In a game as complex as baseball, it is dynamics of its central object, the ball. A typical home run difficult to attribute a cause-and-effect relation between these ball hit at sea level will travel 400 ft rather than the ϳ750 ft results and the humidor. For example, Rockies pitchers may it would travel in vacuum.1 And the same batted ball might have been more talented since 2002; they may also have be expected to go 420 ft in the thin air of Denver, 1 mile benefited from a larger called strike zone implemented in 7 above sea level. This increase is less than might be expected 2001; the consequences of these changes are difficult to from aerodynamic considerations alone due to the prevailing quantify by means other than the performance statistics we northeast winds in Denver.2 Because the ball is expected to use to check the humidor’s effect. travel farther, the idea of introducing a major league team Nevertheless, one may wonder what effects the humidor ͑The Colorado Rockies͒ to the Denver area was met with might possibly have on the game. In the late 1980s, the then opposition in the early 1990s. Hitters counted on the “Coors president of the National League, A. Bartlett Giamatti, asked Field advantage” to help boost their hitting numbers, such as Robert Adair, a Yale physicist, to test the effect of a humidor home runs, runs batted in, and batting average. Pitchers on baseballs. Adair found that under the most extreme con- dreaded throwing in Denver because the thin air was blamed ditions the humidified balls gained weight and were less 1 8 for the lack of break of a curveball or slider. elastic. Kagan has carefully measured the dependence of In 2002 the Rockies organization attempted to mitigate the ball’s coefficient of restitution on the relative humidity these effects by storing the balls in a humidity-controlled and converted this dependence into batted ball distance, find- environment. The conventional wisdom held that a light and ing that storing balls in an increased relative humidity envi- dry ball travels farther than a heavy and moist ball. Coors ronment reduces the distance a well-hit ball travels by 3 ft Field engineer Tony Cowell reported that baseballs stored in for every 10% change in relative humidity.8 This effect the dry atmosphere of Denver were both lighter and smaller would account for a 6 ft reduction in fly-ball distances at than the weight and circumference specified by the rules of Coors Field after the humidor was installed. Another possible Major League Baseball.3 Since the 2002 season the Rockies effect of the humidor is to make the surface of the balls more have stored their baseballs in a humidor maintained at a tem- supple, enabling the pitchers to maintain a better grip and perature of 70 °F and 50% relative humidity, consistent with therefore pitch as they would with balls stored in higher rela- the specifications of baseball manufacturer Rawlings. tive humidity elsewhere. This effect has been reported by The use of the humidor remains a matter of controversy pitchers but remains unexplored quantitatively. and fascination. It is widely believed that Coors Field has Kagan’s work focused on the influence of relative humid- yielded fewer home runs and fewer runs in the humidor era. ity on the bat-ball collision.8,9 In this article we expand this The statistics for various offensive and defensive bench- work to investigate how storing a ball in a humidor affects marks at Coors Field support a small but measurable corre- the aerodynamics of the ball in flight. To do so, we perform lation with the presence of the humidor as shown in Table I, measurements of the change in diameter and weight of base- which shows some statistics for games played at Coors Field balls as a function of the relative humidity. We find that this in the seven seasons before the humidor was installed com- variation is less than the variation already allowed by the pared to the same statistics from the first five seasons after- rules of Major League Baseball.7 Nevertheless, the lightest, ward. For comparison, the same numbers for the entire Na- smallest allowed balls, if dried out, will exceed the limits in tional League are presented in the same two time frames. the rulebook. To assess the effect of these changes on the In all the categories there has not been a significant change ball’s flight, we numerically solve the equations of motion for the National League as a whole. This fact presumably for pitched and batted balls, including lift and drag forces, represents an average over a host of other changes that might and the dependence of these forces on the speed and spin rate have taken place over this time. In contrast, there is a trend at of the ball. We find that, on average, curveballs break slightly 1015 Am. J. Phys. 76 ͑11͒, November 2008 http://aapt.org/ajp © 2008 American Association of Physics Teachers 1015 Table I. Examples of various statistics at Coors Field before and after the inception of the humidor in 2002. These are compared to the NL averages in the same two periods. There is a noticeable drop in ERAs, HR per team per game, and runs scored. The uncertainties are calculated using the year-to- year variance of the mean. These data were obtained from Refs. 4 and 5 except average fly-ball distances. These were obtained from Ref. 6, which reports only the years 2000 and 2001 and 2002–2007. Before After Difference Rockies ERA at Coors 6.14͑21͒ 5.34͑26͒ 0.80͑33͒ NL ERA at Coors 6.50͑19͒ 5.46͑24͒ 1.04͑31͒ NL average ERA 4.37͑7͒ 4.28͑6͒ 0.09͑9͒ (a) HR/team-game at Coors 1.59͑9͒ 1.26͑8͒ 0.33͑12͒ NL average HR/team-game 1.06͑4͒ 1.05͑2͒ 0.01͑5͒ Runs/team-game at Coors 6.94͑20͒ 5.87͑18͒ 1.07͑27͒ NL average runs/team-game 4.7͑8͒ 4.58͑6͒ 0.18͑10͒ Average fly ball distance 323͑4͒ 318͑1.5͒ 5͑4͒ more for dried baseballs than for humidified baseballs, and that batted balls travel slightly less far when they are dry than when they are humidified for a given initial trajectory. The combined effect of relative humidity on the elasticity and aerodynamics of the ball suggests that posthumidor bat- (b) ted balls travel approximately 4 ft less than dry baseballs. Fig. 1. ͑a͒ Relative diameter and ͑b͒ relative weight as a function of relative The rest of the paper is outlined as follows. Section II humidity ͑RH͒. provides the results of an experiment on the effect of the relative humidity on the size and weight of the ball. Section III discusses models of aerodynamic forces acting on a base- ball in flight. Section IV evaluates the effects of relative hu- between the diameters of dry and wet baseballs do not show midity on the aerodynamics for curveballs and well-hit base- the effect of relative humidity. We therefore report the data balls. In Sec. V we summarize our results and discuss / as the fractional change in the diameter d ddry from that of a possibilities for future work. dry ball held at 32% relative humidity. Based on this mea- surement, we are unable to distinguish a difference in the II. EXPERIMENT expansion of the ball’s diameter measured on the leather as opposed to on the seams. We therefore averaged all five mea- / To assess the effect of relative humidity on the baseballs surements of d ddry for each ball and all 25 measurements we measured the weight and diameter of a collection of balls for the five balls in each container. stored at various relative humidities. We stored five Major The experiment began with all balls held in a dry environ- League baseballs in each of three airtight containers in which ment for a time exceeding 2 months. Two sets of balls were the relative humidities were held at the constant values 32%, then moved into the 56% relative humidity and 74% relative / 56%, and 74%. These relative humidities were maintained by humidity containers.
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