With another Super Bowl right around the corner, and another year of Tom Brady and the Patriots breezing through the AFC, we thought that now would be a great time to remind everyone about Deflate-Gate, and that the Patriots are a bunch of dirty cheaters! But do the numbers actually prove the accusations? Let’s take a look.
To start, let’s be clear that the Colts accused the Pats of deflating the footballs they were using, which is apparently how Tom Brady prefers it. What’s it matter? Well, each team uses their own set of footballs for each game, so in theory this could give the Patriots an advantage of catching a softer ball in the cold temperatures, as well as giving Tom a leg up by getting to throw balls the way he likes.
CHEATS!! Fortunately for the other 31 law abiding teams of the NFL, there are rules about these things! Before the game, balls are to be measured and have a guage pressure between 12.5 and 13.5 psi. And our trusty referee, Walt Anderson, did his job to measure these. Let’s not get bogged down in the details of “did he use the right gauge” or “did he accurately note the temperature of the locker room” because we have engineering on our side! Enter Gay-Lussac’s law:
P1*T2 = P2*T1 or in this case Ppregame / Tpregame = Phalftime / Thalftime
Anyone who took a thermodynamics course in college remembers this one, as it was basically the answer to any question asked. When using this law, we have to use absolute pressure and temperature values. For this, let’s use Rankine (just add ~460 to degrees F) and then add 14.7 to the gauge pressure to get absolute pressure. Now, what do we know about these values?
Ppregame = 12.5 (assumed gauge pressure of balls since Tom likes ‘em soft)
Tpregame = 71F (temperature of the locker room)
Thalftime = 48F (temperature on the field)
Perfect! That means we just have 1 unknown to solve for. Adjusting some things around we get:
OK, so the balls will likely be under the (assumed) starting value of 12.5 psig because of mother nature, but the Patriots, and specifically Tom Brady (who probably personally significantly under-inflated the balls himself) were playing with footballs well under even the 11.32 psig value, right? Here were the 12 pressure values for the Patriots balls:
So the average value is higher than the calculated 11.32 psig, likely due to the balls warming up. It doesn’t matter because the Colts were playing with properly inflated balls! Vindication! Wait… these same equations applied to balls inflated to the highest legal limit also drop, to 12.2 psig. For those of you bad at math, 12.2 < 12.5. Bad news for you, Andrew Luck. It looks like you have a suspension headed your way!
To me, it looks like even a Sophomore in Mechanical Engineering could show that the Patriots were playing within the rules for once, and that the Colts should have just accepted their beat down with a little more grace. Does that mean you shouldn’t hate Brady and the Patriots? No way! Go Falcons! #SB51