Last week, I looked at deflate-gate (the Patriots ball inflation “scandal”), and ran some numbers.
I used °F, and figured that if the balls were filled up to 12.7 psi at 70°F, and they cooled to 20°F, you would get a pressure drop of 1.38°F.
Boyle’s law is PV=nRT, where P=pressure, V=Volume, n=the amount of the gas in moles, R=the ideal gas constant, at T=temperature.
Since in the football, volume, amount of gas, and the ideal gas constant remains the same, so we can reduce this to:
P1/T1=P2/T2
Then we can solve for P2: P2=(P1/T1)T2
So, the math looks good, where is the “Jive Ass Newbie Mistake?
Because the pressure in the football isn’t 12.5 psi it’s 27.2 (12.5+14.7) psi.
Boyle’s law is based on absolute pressure, not gauge pressure. Gauge pressure is the difference between the absolute pressure of what you are measuring and the atmospheric pressure.
I am a complete tool for screwing this up.
It turns out that using absolute pressure, a 31 degree ball will be 2.076 psi under-inflated.
So, “Ball-Gate” is largely just an effort by Roger Goodell to make people forget that he is an incompetent and corrupt liar. (Ray Rice and Chronic Traumatic Encephalopathy, two name just 2)
Full disclosure: My wife is a Patriots fan, though I’m not.
I’ll be watching the Superbowl for the ads.
(On edit)
There also might be water vapor in the air used to inflate the ball that would further exacerbate the pressure drop as it condenses.
(2nd edit)
I just realized that I had not posted this on my blog before, the screw up was on a comment I made on Facebook.
Still, I will apologize here.