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Deflategate

Page history last edited by Ben Dreyfus 8 years, 11 months ago

7.1.P8

 

On Sunday, January 18, 2015, the New England Patriots and the Indianapolis Colts played a game to decide the American Football Conference championship and the right to play in Superbowl XLIX. The Patriots soundly defeated the Colts by a score of 45-7. Besides the standard physics relevant for every football game (projectile motion, collisions of heavy objects), a new bit of physics became relevant for that game -- the Ideal Gas Law.

 

In American professional football  there are strict regulations on the size, weight, and inflation of the football. The ball must be inflated to a (gauge) pressure of between 12.5 and 13.5 psi. [NOTE: "Gauge pressure" is a measurement of how much the air pressure inside the ball (or tire, etc.) is greater than atmospheric pressure. A ball that isn't inflated at all, where the pressure inside is equal to atmospheric pressure, would have a gauge pressure of 0. Atmospheric pressure is 14.7 psi.] This makes the ball quite firm. Each team uses their own footballs on offense and is responsible for their inflation. At halftime, it was discovered that 10 out of 11 of the Patriots footballs had a pressure of only 10.3 psi. A slightly softer ball makes it easier to grip and, while taking some distance off a long pass, makes it a bit easier to complete short passes. Since Tom Brady, the New England quarterback, uses a game plan that involves mostly short passes underinflation could be seen as an advantage. (An underinflated ball was detected by a Colt player who intercepted a Patriot's pass.)

 

The Patriots said that it was unintentional and was because the balls were inflated inside, where it was warm, and used outside, where it was colder, since gas pressure in a closed vessel drops when the temperature does. Although this was reported in many articles, it didn't seem as if anyone was actually able to do the calculation. Some scientists brushed this off as being "too small to matter".  Is this right? Do the following calculations to decide.

 

Source, New York Times, 1/21/15.

 

(a) Consider an extreme case where a ball is inflated to a pressure of 12.5 psi in a locker room at 80°F. Football is played in fall and winter. If the temperature on the field is 20°F, what would the pressure be in the ball outside? What assumptions do you have to make to do the calculation?

 

(b) Now consider the actual case. Suppose the footballs had been inflated to the proper minimum (gauge) pressure of 12.5 psi in a warm locker room. What temperature would the locker room have to have been at in order for the pressure in a ball on the field to have been 10.3 psi? Is this a reasonable temperature for a locker room?

 

(c) Another fact that might be involved is humidity. In a warm locker room -- especially if some people had been taking showers -- the humidity could be very high. When the ball cools, some of the water vapor inside the ball would condense into liquid, reducing the contribution to the pressure from water vapor. Is this a significant effect? Do a quantitative estimate.

 

(d) What is your conclusion as a scientist? Was there explicit cheating involved? Or was it simply that all the footballs were inflated in a warm place and used in a colder one? Explain your decision as if you were a scientist explaining to ESPN in an on-air interview. 

 

 

Joe Redish 1/25/15

 

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