The National Football League is currently investigating the New England Patriots to determine why game balls used AFC Championship game were under-inflated. The "Deflategate" scandal continues to make national headlines in the lead up to the Super Bowl. According to the most recent reports, the NFL has requested the help of Columbia University's Physics Department. UMass Dartmouth Mechanical Engineering Professor Alex Fowler provides his thoughts on the science of Deflategate, Bill Nye, and what the NFL could do moving forward.
What is PSI and how does it affect footballs?
AF: PSI is an acronym for "pounds per square inch" and it is a unit of measure for pressure. Atmospheric pressure at sea level is about 14.7 psi, which means the air at sea level exerts a force of about 14.7 pounds on every square inch of any surface it contacts. You don't feel it because it pushes you equally in all directions, even inside your lungs, but it exerts a lot of force. The pressure in a football is measured as gauge pressure, which is a measure of how much the air pressure inside the ball exceeds atmospheric pressure. A football inflated to 12.5 psi is actually inflated to an absolute internal pressure of 27.2 psi if it is inflated at sea level. The higher the gauge pressure is inside the ball the more force it will take to compress the ball—i.e. it will be harder.
How does temperature affect pressure in a ball?
AF: In high school we all learned the ideal gas law– PV = mRT—where P is pressure, V is volume of a gas, m is the mass of the gas (you can replace m with n and use moles of gas instead if you want), R is a constant that depends on the gas and T is temperature. When you are inflating or deflating a ball you are changing m—the amount of air mass inside the ball—by adding or removing air. Once you stop inflating or deflating m will remain constant. R is always constant and for a football V is very close to constant if the ball is fully inflated—the volume of the ball changes very little as a function of pressure provided the internal bladder is being held tightly by the leather outer covering. Since m, R and V are all constant we can easily calculate the effect of T (temperature) on P (pressure). If a ball is inflated to a pressure P1 at temperature T1 then at a new temperature T2 the ball's pressure will simply be P2 = (T2/T1) * P1. A lower temperature will lead to a lower pressure inside the ball.
What pressure should the Patriot's footballs have been on a 50°F night if properly inflated?
AF: This is simple—we use the relationship above, but we need to use an absolute temperature scale and an absolute pressure scale. We talked about absolute pressure already. The Patriots said they asked the officials to inflate their balls to 12.5 psi which is about 27.2 psi in absolute pressure (14.7 + 12.5 because Foxboro is close to sea level): P1 = 27.2 psi. We need to assume we know the temperature at which the initial inflation occurred. We know this is done in the locker room so I will assume 75ºF, but that might be a bit on the cold side for a locker room where multi-millionaires are trying to stay loose for a game. We need to use an absolute temperature scale, which means a scale that goes to zero at absolute zero, where all molecular motion stops, not zero when sea water freezes (otherwise all gas pressures would go to zero on a really cold day). Rankine is an absolute temperature scale that is just like Fahrenheit, but goes to zero at absolute zero. To get a temperature in Rankine you simply add 460 to a Fahrenheit measurement, so 75°F is equal to 535oR.: T1 = 535°R. Similarly, 50°F = 510oR. Now we can calculate P2.
P2 = (510/535)*27.2 psi = 0.953*27.2 psi = 25.9 psi.
The gauge pressure would be 25.9-14.7 = 11.2 psi.
If the balls were properly inflated to 12.5 psi as the Patriots asked, then all the balls should have had an internal pressure of about 11.2 psi once they cooled to 50°F.
The latest news reports indicate that as many as 10 of the 12 Patriots balls were almost exactly at this expected pressure (CSSNE.com).
The league states that at least some of the balls were measured at 10.5 psi at half-time. Doesn't that mean the Patriots deflated some of the balls during the game to reduce the pressure from 11.2 psi to 10.5 psi?
AF: That seems unlikely for a lot of reasons. The most important reason is that the NFL's reported measurements indicate a high degree of variability in the inflation and testing results. They report that only 11 of the 12 balls the Patriots had were below 12.5 psi at half time. It is quite surprising that one ball was still above 12.5 psi after spending hours in the cold. Even a ball that was inflated to the allowable maximum of 13.5 psi should have been below 12.5 psi after being out on the field for hours (more on that later). The only explanation for this would appear to be that the whole process of inflating and testing ball pressure is deeply uncertain, so it is probably somewhat futile to try and explain a discrepancy of less than 1 psi between the expected pressure of 11.2 psi and the 10.5 that was measured in at least some of the balls, when another ball was inexplicably overpressure by at least 1.3 psi.
Basically the inflation and testing process is poorly defined and there are many variables involved in the process that aren't being measured or controlled. Among the many things that could have increased the measured drop in pressure below 11.2 psi are: poor initial inflation, a warmer locker room, an electric pump that slightly heated the air as it entered the ball, a ball that was actually colder than 50°F at half time due to cold rain and/or evaporation and possibly the ball preparation described by Coach Belichick which the Patriots say elevates the ball pressure by 1 psi due to intense rubbing prior to final inflation.
Experiments performed to simulate the effect of game conditions on footballs that were performed by HeadSmart Labs at Carnegie Mellon indicated pressure drops of as high as 1.95 psi in the cold and wet conditions that existed on the field.
Why did Bill Nye say that Coach Belichick's explanation for how the balls become deflated made no sense?
AF: I think what we have here is a failure to communicate. Coach Belichick described that the ball preparation they use to alter the texture of the football induces a 1 psi increase in ball pressure prior to final inflation. He didn't offer an explanation for why that occurs (he's no scientist), but it is possible that the intense rubbing actually heats the ball and thereby increases the internal pressure just as we discussed above. A 1 psi increase means a pretty significant increase in temperature for the ball—it would have to get up to about 90°F, but it is possible to heat something up significantly by rubbing it; and Bill Nye certainly knows that. You can start a fire by rubbing sticks together and you rub your arms when you get cold in order to generate frictional heat. I think Bill Nye is using the word deflate in its proper sense of letting air out of it—you can't deflate a ball by rubbing it; but you can heat a ball by rubbing it so that it has a higher initial temperature in the locker room and loses more pressure than expected when brought into a cold environment.
That said, the rubbing seems unlikely to have affected all the balls since I would expect they don't rub them all at once and then immediately hand them to the officials for inflation. More likely most of the balls would have time to cool down somewhat post-rubbing before inflation as other balls were rubbed.
So if the cold caused "deflation" why were the Colts balls not under pressure at half time?
AF: In the blogosphere this question seems to get asked by people who believe the Patriots cheated as if it is unanswerable and proves the Patriot's guilt; but this is actually a very interesting question. If the Colts asked to have their balls inflated to the maximum allowable pressure of 13.5 psi, you would expect every single Colts ball to be below 12.5 psi when equilibrated to 50°F at half time. They should all be at about 12.2 psi. It is at least as surprising that all 12 Colts balls exceeded 12.5 psi after spending hours outside in the cold as it is that some of the Patriots balls were at 10.5 instead of 11.2. Moreover, if it is such an advantage to have a ball with lower inflation pressure (something that seems questionable at the pressures involved but forms the basis of the Colts' accusation), why would the Colts choose the maximum allowable inflation pressure to start with? Did they want a disadvantage? On the other hand we really don't know much about the Colt's procedure. Their locker room may have been cooler, or they might have gone to some effort to keep their balls warm during the game, either because they prefer them that way or because, as we now know, they were planning to raise this issue of possible underinflation before they played and therefore wanted to make sure their balls were OK. The fact their balls were inexplicably over the pressure that simple physics would predict for a legal ball is somewhat surprising, but the questions that raises should be about what the Colts did or didn't do to prevent their balls from obeying the ideal gas law..
What effect might the rain have on ball pressure?
AF: The rain has a number of possible effects. The first is that it causes the ball to cool down much faster than it would when exposed to cold dry air. The rain water is a much better heat conductor than air and thus will remove heat from the ball more quickly than air can. In addition rain water is usually colder than the surrounding air at ground level -- and it can be quite a bit colder. This means the ball could actually be colder than the air around it. The water could affect the leather cover, allowing it to expand slightly when wet (thereby lowering internal pressure) or causing it to shrink when dry. Also a wet ball will not warm as fast as a dry ball, and when exposed to a dry and warm environment the ball could actually cool down rather than warm up initially due to evaporation. There is virtually no possibility that a wet football could be dried and warmed to ambient locker room conditions during a 15 minute half-time; and most likely any pressure measurements that were made at half time were made while the ball was still wet and experiencing evaporative cooling.
What should the NFL do?
AF: The NFL should recognize that the rule on ball inflation pressure is poorly conceived and terribly written. Every single ball that is legally inflated to 12.5 psi is immediately underinflated as soon as it enters a cooler environment and every ball legally inflated to 13.5 psi becomes immediately overinflated on a hot day. No specification of pressure makes any sense without temperature control; and no pressure measurement made during a game can have any validity due to the effects of uncontrolled temperature and precipitation during the game. It would take hours to dry off and equilibrate a ball back to a specified temperature so you could make a valid and controlled pressure measurement. Most of the Patriots' balls were at almost exactly the pressure expected in the given climactic conditions and even those that were not were less than 1 psi below the expected pressure. The Colts' balls were less than 1 psi over their expected pressure. Pressure discrepancies of less than 1 psi have been shown to be undetectable by touch in a number of studies. Possible explanations for both of these discrepancies exist that are far more plausible than someone cheating to alter ball pressure by a virtually undetectable amount. I think the NFL should probably just eliminate this rule and allow teams to use regulation balls inflated to a pressure of their own choosing so as to avoid the endless complications that would result from trying to establish and ensure standard conditions in which to make pressure measurements for balls; but if they do decide to regulate ball pressure they should hire an engineer to design the testing equipment and procedures so as to avoid a future mess like this.
About Alex Fowler
Dr. Alex Fowler (Duke University, PhD) has served in UMass Dartmouth's Mechanical Engineering Department since 1994. His areas of research interests include bio-active materials, bioengineering, cryopreservation, and thermal fluids. He has published more than 30 peer reviewed journal papers in the areas of heat and mass transfer. Professor Fowler has previously been awarded Fellowships at the Marine Biological Lab, Harvard Medical School's Department of Surgery, and Shriner's Hospitals for Children's Burns Institute. He also earned a Faculty Development Award from Harvard Medical School's Center for Engineering in Medicine.