To: Pats Organization

From: Tom Kordis

I strongly believe that I have the solid PROOF, mathematical proof, that the Wells report is wrong. Just simply wrong.

We know it has to be wrong.

Here it is, in a nutshell:

1. We KNOW, from your experiments & mine, that the Pats balls deflated exactly the right amount, as demanded by physics & Mother Nature. There is NO way around this statement.

2. We KNOW, if we believe the referees measurements (and I do believe them!) that the Colts’ balls deflated by a lower amount. While their measurement technique was sloppy and the data may have been absolutely (i.e., measured against calibrated standards) inaccurate, the data is relatively (i.e., comparatively between the Pats’ balls & the Colts’ balls) accurate.

3. We KNOW that, in order for the Colts’ balls to have deflated less, the temperature difference that they experienced had to be less. There is no way around this.

4. We KNOW that both sets of balls equilibrated to very close to the same final temperature. This is simply because the outdoors, the grass, the rain, the balls being thrown, dropped etc. is a much better thermal reservoir than sitting anywhere in stagnant air at any temperature. Any differences in internal temperature between individual balls (due to non-use, different amount of use, etc) are going to be relatively small, and will not explain the gross, large difference in pressure loss.

5. The combination of 2., 3, & 4 leads to only one conclusion: The temperature of the air inside the Colts’ balls **must have been less**, significantly less, 11° to 13°F less, than the temperature of the Pats’ balls when they were gauged before the game.

So we’ve been looking at this backward.

The issue is not “Why was the pressure drop in the Pats’ balls so high?"

The real issue is, “Why was the pressure drop in the Colts’ balls so low?"

There’s only one answer: the temperature drop in the Colts balls was lower than expected.

The rest of this is:

1) Proof that the pressure drop in the Pats’ balls was correct.

2) A calculation of what was the temperature of the air inside the Pats’ balls.

3) A calculation of what was the real temperature of the air inside the Colts’ balls.

4) A solid proof that the Wells Reports assumptions, methods & results are simply wrong.

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Here is the mathematical proof, using the data taken from the Wells Report itself) that proves that (the temperature in the Colts balls was lower than Exponent Labs assumed):

As we all know:

P1 / T1 = P2 / T2

P2 = P1 * (T2/T2)

When we run the numbers, using the following starting P1 & T1, and the final temp T2:

P1 = (12.5 psig + 14.7) psia = 27.2 psia

T1 = (74°F + 460)°R = 534°R

T2 = (49°F + 460)°R = 509°R

we get, that the resultant pressure MUST BE:

P2 (theoretical) = 27.2 psia * (509°R / 534°R) = 25.9 psia = (25.9 psia - 14.7) psig = 11.2 psig.

This is right, according to theory.

When we run the experiment, we find a slighter greater pressure drop, and a slightly lower final pressure.

P2 (experimental) = 11.0 psig.

We’ve all tentatively concluded that the soaking of the leather causes the balls to swell slightly, thereby lowering the final pressure. That’s probably the main factor, certainly not the only factor, if one wants to create a PhD thesis out of it.

But it really doesn’t matter here what the exact reason is: "Experiment Trumps Theory."

And this is exactly how real engineering works: theory gets you close, experiment gets you home.

Everything about the theory & our experiments is correct.

And is exactly as a technically savvy person would expect.

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From the above numbers, we can calculate the Pressure Lapse Rate (PLR), which equals the change in pressure divided by the change in temperature: ∆P / ∆T = (P2 - P1) / (T2 - T1)

Theoretical PLR:

PLR = ∆P / ∆T = (11.2 - 12.5) psig / (49°F - 74°F) = 0.052 psi / °F

Experimental PLR:

PLR = ∆P / ∆T = (11.0 - 12.5) psig / (49°F - 74°F) = 0.052 psi / °F = 0.060 psi / °F.

Note that we used the theoretical P2 (11.2 psig) in the first calculation, and the experimental P2 (11.0 psig) in the second.

You’ve seen all of these numbers before, if you’ve managed to stay awake thru any of my previous epics.

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So, here is the cross check & validation of our numbers for the Pats balls:

We can do a little algebra on the Pressure / Temperature equation (2nd one from the top), and come up with:

P2 = P1+ (PLR * ∆T) = P1 + (PLR * (T2 - T1)).

P2 = P1 + (PLR * T2) - (PLR * T1)

T1 = ((P1 - P2) + (PLR * T2)) / PLR

T1 = T2 + (P1 - P2) / PLR

T1 = T2 + (∆P / PLR)

This last equation does exactly what we want. It allows us to calculation the starting temperature of the air inside the ball, knowing the pressure difference (which we get from the official’s records), the final Temperature (T2 = 49°F) and the Pressure Lapse Rate (which we know from experiment, and which does NOT change).

Let’s check the starting temperature of the **air inside** the Pats’ balls:

(* Note: in doing these calculations, since we are measuring differences instead of absolute values, we can use psig & °F, unlike before, where we had to use psia & °R. I encourage you to repeat these calculations using psia & °R. You’ll see that you get the same answers.)

T1 = 49°F + [(12.5 - 11.0) psig / 0.060 psi/°F] = 49°F + (1.5 / 0.06)°F = 49°F + 25°F = 74°F. Exactly as expected, the air inside the Pats’ balls had equilibrated to room temperature.

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Now let’s check the temperature of the air inside the Colts’ balls, when they were measured before the game:

Using The Numbers In The Wells Report:

T1 = T2 + (P1 - P2) / PLR

T1 = 49°F + (13.0 - 12.3 psig) / (0.06 psi/°F) = 49°F + 11.7°F = 60.7°F

This is INCONTROVERTIBLE.!

This is correct.

The Pressure Lapse Rate is NOT a variable.

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This is *prima facie* proof that the air inside the Colts’ balls, whose temperature nobody ever measured, was colder than room temperature. In fact, it was clearly in the low 60’s.

And I believe that I know exactly what caused it.

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But, we can take one step further:

The Wells Report also gives us values from which we can calculate a Pressure Lapse Rate:

According to the Wells Report, they have established - by legal edict - the Colts' balls to be the “gold standard”, the “control”.

Assuming that the air inside the colts balls had time to equilibrate to room temp, as the Report asserts, then the Colts balls Pressure / Temperature performance shows a Pressure Lapse Rate of:

[Corrected Locker Room Temperature:

The Exponent Labs portion of the Wells Report uses the following:

Pre-game locker room temp: 67 - 71°F.

Game temp: 48 - 50°F

Half time inspection: 71 - 74°F.

I have no idea why they use different temps for "before game" and "at half time", but we'll use their numbers.

I found out, just today, that the correct number, per the Pats organization, is 71 - 74°F.]

So let's re-do the calculation, using the Wells Report numbers.

PLR = ∆P / ∆T = (13.0 psi - 12.3 psi) / (69°F - 49°F) = 0.035 psi / °F.

While better, THIS PLR IS WRONG.!!!

[Note: Using the numbers that the Exponent Labs should have used, T1 = (71 + 74)/2 = 72.5°F, we get PLR = 0.030 psi/°F. Still wrong.]

Added for clarity: Remember, the correct number for wet footballs is PLR = 0.060 psi/°F.

There is no way that any footballs (or soccer ball, volley ball, basketball, etc) ever used in any game ever played, at any level of competition, ever exhibited the Pressure Lapse Rate claimed (indirectly) in the Wells Report.

There is no way in the engineering or scientific world to justify the Wells Report's Pressure Lapse Rate to anybody, for any reason.

This is junk science.

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(...)

All of the above is correct.

You can show it to anybody that you want.

You can call a press conference & announce it, as far as I am concerned.

And I will stand up in front of Mr. Well, Dr. Marlow & Exponent Labs, and try not to laugh as they try to defend this wrong number.

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The only thing left to this tale is to figure out why the temp in the Colts balls was so low.

I believe that I know why. But we’ve got to run an experiment to prove it.

(...)

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FINAL IMPORTANT NOTE:

The fact that the wells report is wrong **does not depend** on us being able to figure out why the temp of the air inside the Colts’ balls was so low.

The Pressure Lapse Rate that is inherent in the Wells Report’s numbers (but that they don’t mention) is alone sufficient to throw that report into the trash.

There is no scientifically valid defense for using that number.

And you’ll further note that, the instructions of Wells’ legal office to “use the Colts’ balls as a control” is, in essence, simply a verbose way of telling them to “use that scientifically unjustifiable PLR”.!

The Wells Report will **never** hold up to scrutiny.

[Edited, 5/8/15 8:35 pm PST, in deference to literary & personal sensitivities.]