Deflategate Science Simplified

raduray · Aug 4, 2015

I was called out for not using the Wells temperature numbers, so I've updated the original post to reflect what was in the report. The original point stands: observed ball deflation is consistent with the Natural Gas Law.

Ring 6 · Aug 4, 2015

raduray said:
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.

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 were not the ones reported in the Wells Report. That's a valid observation; the number 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)

It is much simpler than that.
They never recorded the temperature in the locker room before the game, at halftime, or on the field (although that is somewhat public record).

Didn't exponent also use a lower inside temperature at halftime (thus negating some of the rising effect?)

If you do not know what the initial temp was in the lockerroom, you don't even have science.
You are doing an experiment of what would happen to footballs under conditions, that are almost totally unlikely to have been the ones that existed, because it is simply a guess.

Ring 6 · Aug 4, 2015

raduray said:
I was called out for not using the Wells temperature numbers, so I've updated the original post to reflect what was in the report. The original point stands: observed ball deflation is consistent with the Natural Gas Law.

so you were called out by not using the temperature number that was MADE UP in order to produce the result?
How bizarre is that.

Shouldn't the investigation be what unknowns would have to happen for their to be no tampering rather than what can we assume happened in order to 'get a guilty'?

raduray · Aug 4, 2015

AndyJohnson said:
so you were called out by not using the temperature number that was MADE UP in order to produce the result?
How bizarre is that.

Shouldn't the investigation be what unknowns would have to happen for their to be no tampering rather than what can we assume happened in order to 'get a guilty'?

There are so many unsupported assumptions in the Wells report: the temperatures were 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.

patriot1136 · Aug 4, 2015

Goodell was probably using the common core to do the math, that's why he got it wrong.

MagicMarker · Aug 4, 2015

Can you imagine if this was in a court? The NFL was warned to look for deflated balls. The NFL is responsible for getting accurate readings and recording them. They failed to do so. If they chose to rely on the memory of the referee, even that doesn't show any deflation. They had garbage data and ignored the memory of the lead official.

That would get laughed out of court.

RobertWeathers · Aug 4, 2015

patriot1136 said:
Goodell was probably using the common core to do the math, that's why he got it wrong.

With children under the age of 13, if they decided to get rid of common core math my household would be a helluva lot calmer....

Big Bucks · Aug 4, 2015

There are plenty of videos on youtube showing the experiment using a football, a gauge, a warm indoors and a cold outdoors. It really isn't that hard to get people to understand, its just they just don't wish to understand

RobertWeathers · Aug 4, 2015

Anyone else think the NFL ref supervisor saying that balls are sometimes defective was impromptu or is there something more devious the league is trying to accomplish?

Maybe I'm paranoid but IMO there is nothing that comes out of a NFL mouthpiece without it being approved and with a specific motivation.

borg · Aug 4, 2015

Palm Beach Pats Fan said:
8) The 4 Colts footballs tested indeed dropped less in pressure, simply because of when they were tested, at the very end of halftime, after they sat in a warm room for probably at least 12 minutes.

The 71-74 degree locker room temperature??? Did the Wells Report specify how these temperature numbers were determined? Cold wet day....refs returning to a low 70's locker room? If I'm cold and drenched and likely to change wardrobe for the 2nd half, I would have cranked that locker room temperature up.
Then there is the reality that the body temperatures of ...7 referees, 3 NFL officials, at least one Patriots employee, and who knows who else was in that room ...would have also increased room temperature....likely peaking about the time the Colts balls were measured.
And lets not forget two more external factors that likely affected the PSI...wind chill on NE's exposed, wet game day balls vs INDY game day balls that were sheltered from the elements in bags.
It is a tragedy that real evidence will never be judged in an impartial setting.

Patstopia · Aug 4, 2015

Wait, what does ball pressure have to do with Tom's cell phone? Your just confusing the NFL with this stuff.

borg · Aug 4, 2015

"Shrinkage for Dummies"

BSR · Aug 4, 2015

raduray said:
There are so many unsupported assumptions in the Wells report: the temperatures were 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.

You are missing one big one: they don't know when they measured the Colts balls for certain. If the balls were measured a few minutes later then the Wells Team suggested they were then the results on the logo gauge also make sense for the Colts balls.

patsfan13 · Aug 4, 2015

One of the big problems with the Exponent experiment was the way they dealt with the balls being used in the rain. They simulated the conditions by spraying the balls with water then drying them. That is a joke, the balls were soaked the rate of warming by Exponent was way off.

Since it Sumer do this experiment, jump in the ocean, dry yourself of when you exit, note how quickly you warm up, then put on a shirt jump in the ocean, when you exit leave on the tee shirt, don't towel off and note how long it takes you to warm up.

The balls would warm up at a lower rate than the assumption Exponent used.

As noted then also used a reading for the internal temp that was off by 5F a significant difference.

NashuaPats · Aug 4, 2015

BSR said:
You are missing one big one: they don't know when they measured the Colts balls for certain. If the balls were measured a few minutes later then the Wells Team suggested they were then the results on the logo gauge also make sense for the Colts balls.

The time Exponent used for when the Colts balls were measure contadicted satements by the refs that they ran out of time because half time was coming to and end. It was a devious trick by Exponent. An honest estimate of the time would have lined the Colts balls up with the Patriots.

This whole thing is such a sham. I suspect the NFL did initially think the Patriots tampered with the balls, but then they learned of the IGL and have been framing them ever since.

Ring 6 · Aug 4, 2015

BSR said:
You are missing one big one: they don't know when they measured the Colts balls for certain. If the balls were measured a few minutes later then the Wells Team suggested they were then the results on the logo gauge also make sense for the Colts balls.

But none of that matters because you do not have data to reach a scientific conclusion.
The experiment is just an exercise in guessing at conditions.
I am sure that there could have been temperatures that could have existed that would mean that the decrease in air pressure could not be explained by the IGL.
I also know no one can tell if those conditions were present or not.

Tony2046 · Aug 4, 2015

Palm Beach Pats Fan said:
simplest possible thing to do is ask"explain this"

Do not no understand Quantum Physicals.

Sincerely,

Felger

Palm Beach Pats Fan · Aug 4, 2015

My condensed-down version is:

Footballs drop in pressure when you cool them by playing outside after they were inflated inside. Based upon game conditions, the Patriots footballs should have lost 1.0-1.2 psi based on the temperature drop.

The Patriots footballs dropped on average 1.0 psi, if you trust the ref's memory on the gauge he used. That indicates that nobody took any air out of the footballs, they just cooled down and lost pressure normally.

If you decide that you DON'T trust the ref's memory on what gauge he used, the Patriots footballs dropped on average 1.4 psi, or about 0.2 psi more than you'd expect by the temperature effect alone. So did someone take 0.2 psi out of the footballs? That's a silly conclusion, even if you (for no reason) distrust the ref's memory. Why? Because the 1.0-1.2 expected drop relies on many assumptions, such as temperatures that were not recorded. The football measurements (1.0 or 1.4 psi drop) also have some inherent error. For example, the same person testing the same ball (the intercepted one) with the same gauge three times got psi readings that varied by over 0.4 psi, so the 0.2 psi difference seen even with the "low gauge" in one reading is well within the normal variability (error bars, if you will) that comes with testing footballs for their pressure.

Patsfanin Philly · Aug 4, 2015

Palm Beach Pats Fan said:
simplest possible thing to do is ask"explain this"

Your balloon has a hole in it?
I've dumbed it down for the people around here. I ask them if their car reads "low tire pressure" in winter and if someone let the air own or was it nature? Most get it or at least they nod their head.....like they do.

PatsFanSince74 · Aug 4, 2015

raduray said:
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.

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 number 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.

First of all, thanks for all that work.

You're right. Conceptually it's not that complicated, but doing the calculations for a specific ball on a specific day under different wetness conditions is tough for most of us to follow.

It would be great if there were one big table that provides every practically conceivable outcome under various scenarios (locker room temp, field temp, altitude, wetness, etc), but that's probably too much to ask.

Deflategate Science Simplified

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