I wish to thank the NFL and the New England Patriots for giving all of us STEM teachers an opportunity to help teach some science. During the AFC championship game, the New England Patriots were found to have been using balls during the game that were under inflated. I’m not going into the football or controversy behind this, the press is all over this. Go and run an internet search for these kind of details.
I’m interested in the Physics here and the opportunity to teach students some relevant classroom curriculum. Much of the media and fan rantings is that when the ball is inflated in a warm area and then brought out to the cold field it will decrease in pressure. OK this makes sense. Let’s check out the Math(eek, not Math!!)
According to the Ideal Gas Law. Gas (like air) has a relationship spelled out as PV=nRT.
P is the pressure of the gas
V is the volume of the gas
n is the number moles of gas there are (how much air)
R is a constant for used for the gas
T is the temperature of the gas.
The balls weighed before and after the game have things that will not change such as Volume of the ball, number of moles of air in the ball, and the constant of the air. So the only variables are the pressure and temperature.
First, this law is used with SI units. So we need to do some converting. According to NFL rules all balls to be used in the game are to be inflated to between 12.5 and 13.5 PSI of pressure. Using Google to convert the units that’s 86,184.4662 to 93079.2235 Pascals of pressure in each ball at game start. For argument’s sake, let’s say the room temperature the ball’s were checked pre-game was at 72 degrees Fahrenheit. Again, using the wizardry of the internet, this converts to 295.372 degrees Kelvin. Game start temperature was reported to be about 51 degrees Fahrenheit. But, the ball issue didn’t become apparent until the third quarter, it had gotten colder out. Let’s say it got to about 40 degrees Fahrenheit (the temperature it was on my way home after the game.) This converts to 277.594 Kelvin. Much of the conversation I have found on the internet has failed to convert the numbers to SI units making some pretty odd results.
Going back to the formula, we will be looking at the on field pressure at 40 degrees Fahrenheit. The balls would drop to between 87997.2 and 87476.9 Pascals of pressure or 11.7 to 12.7 PSI.
So, yes, the cold weather would make a difference in the pressure of the balls used in the AFC game. But, the NFL reported the balls used by the Patriots were under inflated by over 2 pounds per square inch. The cold could not have accounted for this much pressure drop. I’m not claiming the Patriots knowingly cheated, there are too many people involved in the handling of those balls. But, I do claim that the under inflation was not due to weather alone.