Deflategate, the Guy-Lussac law, Boyle, and scientific method

Factual Questions
1

GQ, not Games forum.

According to science, as announced by HeadSmart Labs, and its lead investigator, presumably, Thomas Healy., the relationship between temperature and pressure is direct; as temperature decreases, pressure decreases. They used “a simplified version” of the Ideal Gas Law, Gay-Lussac’s Law," to see what the initial temperature would need to be in order to see the measured pressure change of the supposed and much disputes deflated footballs found on the field relative to NFL standards.

To them, the deflation required no unseen nefarious hand.

The lab had two “control” rooms: a “hot room” simulating the “locker room” at 75°F–chosen arbitrarily–and a “cold room” set at 50°F, an average game day temperature taken at various times from nearby weather stations.

On average the footballs dropped 1.07 psi, ie, the measured 1.82 psi of the deflated balls from NFL standard 195 psi. Using the game-day temperatures and disputed lower psi, they came up with 70.93°F as the “locker room” temp, “relatively similar” to their given simulated “locker room” temperature of 75°F.

Moreover “it was also discovered that when a football was exposed to water, the pressure dropped an additional 0.75 psi.” [Italics added.] This they found using Boyle’s law, given that the pressure loss due to the “affects [sic] of water,” which “tend to expand” materials such as the leather and lining of the ball. (The field was wet.) Given their derived psi drop they announce that the deflated balls’ volume dropped by 3%.

  1. Any comments in general on the paper?

  2. My question is on scientific method. (I’m already on a roll for publishing, here and now, my first correction of a scientific paper: the devastating “sic” at the incorrect English.)

Personally I don’t see the necessity–the creativity and significance–of publishing the volume section and derived results at all. The volumes of the balls were not measured. I don’t know if NFL rules prescribe them, but that’s not the point. Because the input pressure data were derived and no empirical volume metric as a base point are given, the author could have said “yup, by Boyle’s law the ball’s deflated.” Otherwise, the entire section on the wet-volume decrease seems like the author is doing a student exercise of “showing the work” that he understands Boyle’s law analytically; I don’t think that is under dispute any more.

[Thomas Healy, a graduate student in mechanical engineering at Carnegie Mellon University in Pittsburgh, on the left, illustrates the scientific method in the photo at the jumping off cite for the paper, undoubtedly uncomfortable and under duress from a public reactions office.]

But since the input data were derived to begin with, the application of Boyle without pertinent empirical data is kind of useless as science in anything but pedagogy. I don’t see what “the discovery” is in this section of the paper. Am I wrong?

2

The NFL standard pressure is 12.5-13.5 psi from everything I’ve seen. Not sure where you got 195 psi. I think that might pop the ball.

3

<snip>

I see a few “sic” opportunities here:

<snip>

4

Nevermind. I’ve now looked at the paper and see what you did. What I quoted from you was written poorly and had a typo. They estimate that the balls could have lost up to 1.95 psi due to temperature and field conditions.

5

Can’t their use of “affect” be correct in the sense of what the water accomplished or created? You’re just assuming they meant something more like “the influence of the water”, right?

6

I’m not a big follower of football so I don’t have a dog in this fight. I do have a question though. Assuming the OP’s argument/statement is correct and the physics of temperature and pressure caused the underinflation, were the balls of the opposing team measured and also found underinflated? Since both teams played under the same conditions it would seem logical that both teams balls would have lost pressure equally.

7

This is the first time I’ve seen anyone address the effects on ball pressure from it getting wet.

Since it has been shown that temperature change alone would not likely account for the full pressure drop, they calculated what change in volume would be necessary to make up the difference. They found that only a relatively small increase in volume would be necessary.

Had they found that the ball would need to double in size, it would be safe to rule out volume change accounting for the additional pressure drop. But since the ball volume only needs to increase 3% to yield the additional pressure drop, it becomes a plausible explanation.

They didn’t apparently try to prove that a ball actually gets 3% bigger when it gets wet - they just showed that it would be enough.

If someone else wants to show theoretically or experimentally that footballs don’t stretch that much when they get wet, the claim could be refuted. Until then, it seems like useful information to be included in the discussion.

BTW - I only skimmed the paper so apologies if I’ve gotten it all wrong.

8

The test the OP cited didn’t have access to the balls from the game. You’ll probably get a better answer to your query in the game room thread that’s discussing the actual events.

9

I see that the paper correctly uses absolute pressure instead of gauge pressure, which many of the quoted scientists in the media did not initially account for, including Neil Degrasse Tyson. This is referenced in the linked article. When you correctly use gauge pressure, the predicted drop in pressure roughly doubles over the temperature range in question.

Since then, Mr. Tyson conceded his error.

I brought the same error to the attention of two news reporters and their sources. Both sources, university physics professors, wrote back to me and acknowledged their error.
By the way, in your OP, you wrote:

You do realize that you have seriously misquoted the paper such that it says something completely different? Not sure what happened here, but what you wrote here is essentially gibberish.

The correct quote is:

10

There’s a thread in the Game Room discussing this extensively, but in summary:

Yes, the Colts balls were tested and found to still be compliant. However, there is very little information available about the circumstances of the testing. We don’t know when the Colts balls were tested in comparison to the Patriots, nor do we have a baseline as to what the original pressures were.

Of course, we also don’t know the exact circumstances that the Patriots balls were tested in either. It’s possible that they were dried off and allowed to warm up before being tested as well.

In short, there is a lot more that we don’t know than there is that we do know.

11

Pointless scientific research about footballs in artificial conditions. The subject can be accurately studied later this year when the football season resumes using actual conditions.

12

If I recall my high school physics…

Boyle’s law is pretty simple - PV=nRT
P- pressure, V-Volume, n and R fixed for general purposes (Ideal gas constant, etc.), and T - temperature in absolute
(i.e. 0K = -273C)

So if a ball is inflated at room temperate - say 20C - to 13PSI, then allowed to cool to freezing (0C, 273K) I’ll cheat here and mix units, since in limited circumstances it won’t matter.
Volume stays the same so cancels out, assuming the ball does not swell too much…

PV/T = PV/T
(13)/(293) = P/(273) => P= 12.11

Which makes sense; one factor varies by about 20 in 300 or 7%, the other will too.

Note the main assumption - the volume does not change. Not sure how resilient a football is, how the size changes when it is deflated a bit; but if it does, that would suggest the ball volume shrinks, which would mean the pressure *drop *would be less than calculated, the resulting pressure higher.

13

Sorry, wrong answer.

As I indicated in the other thread here, you’re making the same mistake as many physicists who were quoted in the media (including Neil Degrasse Tyson).

While you accounted for absolute temperature in your calculation, you neglected the fact that footballs are measured using gauge pressure (psig), which is the pressure above atmospheric pressure. To use the ideal gas law, not only do you have to convert temperatures measured in degrees Fahrenheit or Celsius to absolute temperatures, but you have to convert gauge pressures to absolute pressures.

To convert from psig (gauge pressure) to psia (absolute pressure), you need to add 14.7 psi to account for atmospheric pressure: 0 psig = 14.7 psia; and 12.5 psig = 27.2 psia.

Redoing the erroneous calculation above indicates that the same football that measures 13 psig (27.7 psia) at 20 deg C (293 K), would actually drop to 11.1 psig (25.8 psia) in 0 deg C (273 K) weather.

This is a full psi below what you calculated, and since the whole controversy hinges on just a 2 psi difference, it would seem important to get this part right.

The volume of the football is constrained by the leather cover. If anything, as noted in the OP, some experiments that have been reported in the media indicate that the leather may stretch slightly when wetted, causing the pressure to drop *more * than calculated.

All of this has been hashed (and rehashed) to death in the other thread, BTW.

P.S. To get more exact, you would have to determine if the atmospheric pressure was exactly 14.7 psi, and of course, the ideal gas law itself assumes ideal gas behavior, which only approximates the behavior of air. This would likely not significantly change the answer, however.