01-24-2015, 11:51 PM
OK, let's do the math. Here are the known facts:
Temperature at Gameday was 51 degrees F, which is 283.7 K
The pressure minimum is 12.5 psi (86 kPA)
The pressure in 11 of the 12 balls was found to be 2 PSI below the minimum pressure, which would be 10.5 psi (72.4 kPA)
Assuming that the volume of a football is fixed*, then we know that P/T must be a constant, which we know from the halftime measurement is 72.4 KPa/283.7 K = 0.255 KPa/degK.
If those balls were inspected 2 hrs before the game, and barely passed with 12.5 pSI (86 kPA), then the internal temperature must have been at least 86 kPa/0.255/degK = 336.5 K, which is 63 degrees C, which is 146 degrees F.
No amount of handling the football, unless they put it in an oven, would have gotten the internal temperature up to 146 degrees.
BC
* Note, the volume of the football is probably slightly dependent on the pressure, so the volume would have been lower at the lower pressure. That means that the temperature would have had to be even higher than 146 F for the balls to pass the inspection. Basically, I can see only a few possible ways that the observed facts could have happened. The assumption of fixced volume, therefore, is conservative.
1) The balls were underpressured when they were inspected before the game, and the referees didn't really pay attention.
2) The balls were heated to 60+ degrees C right before the inspection so they could pass the inspection, and then naturally cooled and the pressure dropped. 60 degrees would have been noticeably hot, and this approach ran the risk that the balls cooled enough to drop below the minimum. But if this is what happened, the Pats found a way to legally get around the letter of the law, if not the spirit.
3) At some point between inspection and halftime, air was let out of the balls.
I'm willing to entertain other explanations, but gameday temperature alone cannot explain the results. Sorry.
BC
Temperature at Gameday was 51 degrees F, which is 283.7 K
The pressure minimum is 12.5 psi (86 kPA)
The pressure in 11 of the 12 balls was found to be 2 PSI below the minimum pressure, which would be 10.5 psi (72.4 kPA)
Assuming that the volume of a football is fixed*, then we know that P/T must be a constant, which we know from the halftime measurement is 72.4 KPa/283.7 K = 0.255 KPa/degK.
If those balls were inspected 2 hrs before the game, and barely passed with 12.5 pSI (86 kPA), then the internal temperature must have been at least 86 kPa/0.255/degK = 336.5 K, which is 63 degrees C, which is 146 degrees F.
No amount of handling the football, unless they put it in an oven, would have gotten the internal temperature up to 146 degrees.
BC
* Note, the volume of the football is probably slightly dependent on the pressure, so the volume would have been lower at the lower pressure. That means that the temperature would have had to be even higher than 146 F for the balls to pass the inspection. Basically, I can see only a few possible ways that the observed facts could have happened. The assumption of fixced volume, therefore, is conservative.
1) The balls were underpressured when they were inspected before the game, and the referees didn't really pay attention.
2) The balls were heated to 60+ degrees C right before the inspection so they could pass the inspection, and then naturally cooled and the pressure dropped. 60 degrees would have been noticeably hot, and this approach ran the risk that the balls cooled enough to drop below the minimum. But if this is what happened, the Pats found a way to legally get around the letter of the law, if not the spirit.
3) At some point between inspection and halftime, air was let out of the balls.
I'm willing to entertain other explanations, but gameday temperature alone cannot explain the results. Sorry.
BC