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It kill me that most of the talking heads are not really addressing the science heads on. If the ball deflation is explained by the temperature drop, then the texts, phone calls, etc all become irrelevant. So, I've tried to simplify how the perfect gas law applies to this.
Perfect gas law says that absolute ball pressure is directly proportional to absolute temperature assuming ball volume is constant. If absolute temperature were to increase 50%, absolute ball pressure would go up by 50%.
Absolute ball pressure is measured ball pressure plus ambient atmospheric pressure.
Absolute temperature is measured temperature converted to Degrees Kelvin.
Locker room temperature of 72 Deg F converts to 295 Deg K
Playing field temperature of 45 Deg F converts to 280 Deg K, a 5% drop.
Now, given that ball pressure is directly proportional to temperature, let’s apply the 5% drop to the pressure. Remember that the measured ball pressure was 12.5 psi.
Ambient air pressure at sea level is 14.7 psi.
Absolute ball pressure measured in 72 Deg F locker room is 12.5 psi + 14.7 psi = 27.2 psi
Apply 5% drop to that and you get 25.8 psi at 45 Deg F.
Subtract the ambient air pressure (14.7) and you get 11.1 psi.
NOT THAT COMPLICATED!
Now, if you consider the ball got wet, it gets a bit more complicated. The wet ball would soften the leather, allowing it to expand a bit, thus increasing its volume, resulting in a somewhat even lower air pressure in game conditions.
Reference:
PV=nRT
P=Absolute Pressure (air gauge pressure plus ambient pressure)
V=Volume (volume of a dry football is constant across range of temperature)
n=number of molecules of air in the football (constant across the range of temperature)
R=Gas Constant. It's a constant, like pi.
T=Temperature in Deg K.
P=(nr/V)T
nr/V = K (constant)
P=KT
P directly proportional to T
EDIT 8/4/15
I've been called out because the temperature values I used above were not the ones reported in the Wells Report. That's a valid observation; the numbers I chose were to illustrate a point. So I recalculated using the Wells Report data: Locker Room Temp 71-74, Field Temp 48-50. I calculated the four permutations using the min and max for each reported range with the starting ball pressure set to 12.5 psi.
Locker Room-Field-Ball Pressure
71-----------48-----------11.32
74-----------50-----------11.28
71-----------50----------- 11.42
74---------- 48------------11.17
Calculated Average------11.30
Wells Report Average---11.49 (Logo), 11.11 (Non Logo)
Note that the Wells Report is based on several unsupported assumptions: the field temperature was not recorded, the initial ball pressures were not recorded, the locker room temperature was not recorded, which gauge was used was not recorded. It all makes for bogus science, recognized even by the NFL given their new ball handling procedures released just recently.
My point, though, is that even the bogus Wells numbers are consistent with the Natural Gas Law.
Perfect gas law says that absolute ball pressure is directly proportional to absolute temperature assuming ball volume is constant. If absolute temperature were to increase 50%, absolute ball pressure would go up by 50%.
Absolute ball pressure is measured ball pressure plus ambient atmospheric pressure.
Absolute temperature is measured temperature converted to Degrees Kelvin.
Locker room temperature of 72 Deg F converts to 295 Deg K
Playing field temperature of 45 Deg F converts to 280 Deg K, a 5% drop.
Now, given that ball pressure is directly proportional to temperature, let’s apply the 5% drop to the pressure. Remember that the measured ball pressure was 12.5 psi.
Ambient air pressure at sea level is 14.7 psi.
Absolute ball pressure measured in 72 Deg F locker room is 12.5 psi + 14.7 psi = 27.2 psi
Apply 5% drop to that and you get 25.8 psi at 45 Deg F.
Subtract the ambient air pressure (14.7) and you get 11.1 psi.
NOT THAT COMPLICATED!
Now, if you consider the ball got wet, it gets a bit more complicated. The wet ball would soften the leather, allowing it to expand a bit, thus increasing its volume, resulting in a somewhat even lower air pressure in game conditions.
Reference:
PV=nRT
P=Absolute Pressure (air gauge pressure plus ambient pressure)
V=Volume (volume of a dry football is constant across range of temperature)
n=number of molecules of air in the football (constant across the range of temperature)
R=Gas Constant. It's a constant, like pi.
T=Temperature in Deg K.
P=(nr/V)T
nr/V = K (constant)
P=KT
P directly proportional to T
EDIT 8/4/15
I've been called out because the temperature values I used above were not the ones reported in the Wells Report. That's a valid observation; the numbers I chose were to illustrate a point. So I recalculated using the Wells Report data: Locker Room Temp 71-74, Field Temp 48-50. I calculated the four permutations using the min and max for each reported range with the starting ball pressure set to 12.5 psi.
Locker Room-Field-Ball Pressure
71-----------48-----------11.32
74-----------50-----------11.28
71-----------50----------- 11.42
74---------- 48------------11.17
Calculated Average------11.30
Wells Report Average---11.49 (Logo), 11.11 (Non Logo)
Note that the Wells Report is based on several unsupported assumptions: the field temperature was not recorded, the initial ball pressures were not recorded, the locker room temperature was not recorded, which gauge was used was not recorded. It all makes for bogus science, recognized even by the NFL given their new ball handling procedures released just recently.
My point, though, is that even the bogus Wells numbers are consistent with the Natural Gas Law.
Last edited: