Re: How does the temperature of a baseball affect it on contact with a bat ?

The temperature most definitely affects the physics of baseball. As always, I recommend The Physics of Baseball by Robert K. Adair. However, anyone who has played baseball or softball in cold and warm weather can tell you that the difference can be painful. I will speak about the measurements made on softballs because I am familiar with this information. The same information is available for hardballs (baseballs), yet I have not found a reasonable source other than a few statements in Adair's book. Adair briefly mentions how temperature affects the flight of a baseball. However, in general, there is not much available specific information on how temperature affects the bat-ball collision or the kinetic energy transferred to the ball. So, I will give you the information I have and could find.

There are two characteristics of the ball that are measured, at least with softballs, that have temperature dependence: coefficient of restitution (COR) and compression. These two quantities are now tested and printed on every new softball made for Amateur Softball Association (ASA) league play in the United States by the American National Standards Institute (ANSI) [http://www.softball.org/about/certified_equipment.asp].

The coefficient of restitution is a measure of speed lost at collision. Specifically, COR is defined as the ratio of the speed of the ball rebounding from a hard surface of an immovable object to the initial speed. It is equal to the square root of the proportion of energy dissipated in the collision. This is done at an assigned speed for testing. However, the ball is hit at different collision speeds during a game.

The compression number printed on the softball is how many pounds of force are required to compress the softball a quarter inch. Typical values are 375 to 525 pounds. The 525 compression softballs, from my experience, go a lot farther and come off the bat at dangerous speeds. The league I played in for the summer of 2003 was given an incorrectly marked batch of softballs. The first three weeks we played with 0.47 COR, 525 Compression softballs. A Few men were injured by line drives (broken fingers and a broken collar bone), and big fly balls were travelling 300 to 350 feet on a common basis. The league was alerted to the error, and switched to 0.47 COR, 375 Compression softballs made by the same manufacturer.

A COR of 1 is perfectly elastic and no kinetic energy is lost at collision. A COR of 0 is a perfectly inelastic collision in which the objects colliding stick together. A softball typically has a COR of 0.44 to 0.47. The difference between 0.44 and 0.47 does not look like much, but the difference translates into about a 10% to 20% (13% with observational margin of error) decrease in ball speed and distance based on the ratio of the COR squared (0.44 / 0.47)² = 0.876.

Adair cites a value of 0.563 for official major league baseballs (1985 - 1987 tests), and that the value of COR falls off considerably for increased collision speed. Unfortunately, I do not believe the temperature dependence is simple, and it probably needs to be measured by experiment.

In addition, the bat, especially aluminum bats have COR and compression that change with temperature. Some bats become so stiff below about 60 F that the manufacturers recommend not using them. A stiff bat will result in more sting in the hands for hits that are not at the sweet spot of the bat.

Softball makers have responded by making softer, lower COR and compression, balls for cold weather, and print graphs of COR versus percentage of bat damage. A lower compression of the ball means it takes the brunt of the damage at ball-bat impact.

From my own experience, the distance and speed of the ball is inversely related (not necessarily inverse linear) to temperature. Adair states that a 400-foot home run will go about 20 feet farther on a 95 F day in Atlanta versus a 45 F day in Chicago. It is implied that this difference in distance is due to the reduction in air drag with increasing temperature. Also mentioned is the increasing elasticity of the ball with increasing temperature which will allow the ball to bounce of the bat with more energy which is more related to your question.

Previous related answers (self referential)which speaks to humidity

Re: Does the temperature of a baseball affect it's rebound rating?