Hey ct.
I disagree that there are a bunch of unknowns.
I disagree because I ran some tests.
We don't actually know this.
That drop you cite assumes a certain drop in temperature. Without knowing the exact details of how the Patriots prep the balls, we don't know what the initial temperature of the balls was.
I disagree. I believe that there is sufficient information available to make valid ESTIMATES of the actual conditions. And the rest of the unknowns can be covered with a reasonable sensitivity analysis.
For example, I believe that the following assumptions are justifiable:
1. Room temp in locker room: 71 - 76°F.
2. Internal air temp of footballs in locker room: 71 - 80°F
3. Pressure in balls in locker room: 12.4 - 12.6 psig ("reasonably accurate pressure gauge")
4. Dry bulb temp for last 15 minutes before half time: 48 - 51°F
5. Rain temp: 46 - 50°F
Using best case & worst case THEORETICAL calculations yield:
10.7 psig < P2 < 11.6 psig
Using the same best & worst case temps, along with the experimentally determined pressure lapse rate (0.06 ± 0.02 psi/°F) yields:
10.3 psig < P2 < 11.4 psig
We also don't know how long it takes for the balls to reach thermal equilibrium with the ambient air. For all we know, it might take 12 hours.
Nope, I do know.
It was a component of the experiment I ran.
In mine, I exposed 3 official game balls 6to cold water (@ 48°F), then cold air (@ 50°F) for 70 minutes. I ran 3 duty cycles of water/air, just to look for a difference.
These cycles were intended to be a "reasonable simulation" of a ball's typical use. One play used, dried off,
i) 1 minute immersion in cold water, dry off with a towel, 9 minutes cold air. (7 cycles = 70 minutes)
ii) 1 minutes immersion, dry off, 4 minutes cold air. (14 cycles = 70 minutes)
iii) 7 minutes immersion, dry off, 3 minutes room temp (71°F) (7 cycles = 70 minutes)
The pressure drop over the course of the testing reached the same steady state level, which tells me that even the 1 minute water/9 minutes cold air had sufficient heat transfer to reach the steady state cold value (represented by the 7 minute immersion/3 minute room temp air).
The dousing exposure to cold rain & water guarantees a HIGH heat transfer between the balls & the cold water/air when the balls were cooling off.
Drying the balls off & sitting them in a warm room (with cold water soaked leather) and only convection as the heat transfer mechanism guarantees a LOW heat transfer when the balls were warming up.
A full 3 hours after concluding my tests, drying the balls off & sitting at room temp, the pressure in the balls was STILL in the low 11 psi range.
All the speculation that's happened here is to explain what might have happened. Physics can explain a drop of ~1 PSI, but we don't know that it needs to.
Theoretical physics can explain a drop of about 1.3 psi between 75°F & 49°F.
Experimental physics (at least in my tests) suggests a drop of 1.5 psi between those same temps.
In other words: it is possible that, as Rapoport reported, most of the balls were just under the limit.
I missed your explanation as to how this is possible.
The ONLY way that I see this to be possible is for someone to have been inflating the balls while they were cold.
Can you point me to where you described your explanations?
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In conclusion, having run the experiments, I am completely comfortable stating that I consider the issue settled within the likely extremes of initial & final values for temp & pressure.
