Home Run Distance and Humidity

There has been some controversy about what conditions make a baseball "carry". The variables of wind speed, temperature, and humidity all have something to do with it ^[1]. The infamous case of Coors Field, the home of the Colorado Rockies, where the ball travels 9% farther at 5,280 feet than at sea level, leading to record numbers of home runs.

Table \(\PageIndex{1}\) Rockies Home Runs

Season Runs/game HR/game 2000 14.37 3.02 2001 13.40 3.31 2002 12.21 2.86 2003 11.94 2.84 2004 12.69 2.73 2005 11.09 2.10 2006 10.73 2.07 2007 10.58 2.23

Figure \(\PageIndex{1}\) Coors Field in Denver, CO

It is estimated that a home run hit 400 feet in sea-level Yankee Stadium would travel about 408 feet in Atlanta and as far as 440 feet in the Mile High City^[2].

Balls have been stored in humidors at Coors Field to reduce the number of home runs since the 2002 season, and he chart above shows that this is effective, but how does this work?

Several weather web sites have claimed that higher humidity leads to longer hits, because water is ligher than the other constituents of the atmosphere, so high humidity would lead to "thinner" air like that at high altitudes. ^[3].

Researchers who focused on the larger size or increased density of balls in high humidity conditions found that humidity would actually increase the distance a ball travels, if only these factors were involved ^[4]

But chemists and physicists have shown that the important factor is probably disruption of chemical bonding in baseball materials, by the water that the baseball absorbs when it comes to equilibrium with moist air ^[5][6][7]. Water molecules disrupt the hydrogen bonding in the wool windings inside the ball to make it less "lively", so it can't be hit as sharply with the bat. In physics this is called the "coefficient of restitution" of the ball ^[8]

To understand how this works, we need to see how a baseball is made. They have a cork nucleus of prescribed weight (0.5 oz) and diameter (2.86 to 2.94 inches) whichis encased in two thin rubber layers weighing a total of 7/8 oz. This is machine-wound under high, consistent tension with 121 yards of four-ply blue-gray wool yarn, 45 yards of three-ply white wool yarn, 53 more yards of three-ply wool yarn and 150 yards of fine white polyester-cotton blend yarn. This all is coated with rubber cement an covered with cowhide. before the cover is put on^[9].

Balls are shot from an air cannon at 85 feet per second at a wall made of northern white ash--the wood used to make bats, to test the coefficient of restitution. Each tested ball must bounce back at between 0.514 and 0.578 of its original speed to be suitably lively for MLB.

The balls become less lively under high humidity because water disrupts the hydrogen bonds in the wool windings^[10]. The hydrogen bonds between wool polyamide chains are similar to those between two polyamide chains shown in the Figure below:

Figure \(\PageIndex{2}\) Aramid (aromatic polyamide) structure

In high humidity, water molecules separate the two polyamide strands by hydrogen-bonding to the individual strands of polyamide, separating them, and loosening the packing, making the ball less lively.

Hydrogen bonds form between water molecules because they are very polar, with an electrostatic negative charge on the electronegative oxygen atom, and a positive charge on the hydrogen atoms. The small hydrogen atoms can approach very closely to the oppositely charged end of a second water molecule. A small degree of covalent-bond character arising from hydrogen accepting some lone pair electron density, which in addition to the electrostatic attraction, produces the abnormally strong intermolecular force called the hydrogen bond. The O-H bond length in H₂O is 99 pm, and they are clearly covalent bonds; The other two O--H bonds are at a distance of 177 pm, and are the hydrogen bonds.

Figure \(\PageIndex{3}\) Hydrogen bonds in water

In order for hydrogen bonding to occur, there must be a hydrogen atom connected to a small, highly electronegative atom (usually fluorine, oxygen, or nitrogen) in one molecule. A second molecule must have a very electronegative atom (again usually fluorine, oxygen, or nitrogen) which has one or more lone pairs of electrons. Separation of two molecules joined by a hydrogen bond requires 10 to 30 kJ mol^–1, roughly 10 times the energy needed to overcome dipole forces. Thus hydrogen bonding can account for the unusually high boiling points of NH₃, H₂O, and HF.

In the absence of water, the hydrogen bonds between the C=O and H-N groups of the wool in a baseball make the wool very dense and springy, so the ball is "lively." Inserting water molecules separates the strands and makes the ball less lively, or "spongy".

The kind of open structure that leads to increased volume and "sponginess" in baseballs also explains the increased volume of water as it freezes (although the ice isn't spongy, because the polymers are absent). Figure 1 shows two computer-drawn diagrams of the crystal lattice of ice. In the model we can clearly see that each O atom is surrounded by four H atoms arranged tetrahedrally.

 

Figure \(\PageIndex{4}\). Two computer images of the structure of ice. The water molecules have been arranged, so that each oxygen atom is surrounded by four hydrogen atoms in tetrahedral geometry. Two of these atoms are covalently bound to oxygen, while the other two are hydrogen bonding with the oxygen.

Ice thus is lower in density than water and floats on it. Due to hydrogen bondng, water at 0^oC is still less dense than water at 4^oC, but as it warms above 4^oC increased rapid movement of the molecules leads to the more normal expansion with increased temperature.

From ChemPRIME: 8.11: Ice and Water

References

1. ↑ http://www.exploratorium.edu/baseball/howfar3.html
2. ↑ USA Today Article http://www.usatoday.com/sports/baseball/nl/rockies/2007-10-09-humidor2-coors_N.htm
3. ↑ http://www.theweatherprediction.com/habyhints/285/
4. ↑ http://www.nature.com/news/2007/071207/full/news.2007.362.html
5. ↑ www.ultimatecapper.com/sports...rticles-42.htm
6. ↑ http://www.livestrong.com/article/155931-the-effects-of-humidity-on-baseballs/
7. ↑ R. Adair, The Physics of Baseball, Harper and Row, New York, 1990, p. 68.
8. ↑ The Physics Teacher, Vol. 42, September 2004 p 92; webusers.npl.illinois.edu/~a-...dity-kagan.pdf
9. ↑ What's that Stuff: Baseballs:http://pubs.acs.org/cen/whatstuff/stuff/7713scit3.html
10. ↑ CHEMTECH, March 1992, p. 170

Contributors and Attributions

• Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn.