OT-deflategate: Thought experiment--could the balls have been inflated at artificially hot temps?

Submitted by stephenrjking on
So this is the sports topic du jour, and this blog has a readership that tends to be well-educated. Let's try a thought experiment--gaming footballs with physics.

Let's say, hypothetically, that your football team likes footballs to be a bit under inflated. Now, you know that the balls will be in public view as soon as the refs release custody of them, and you don't want some ball boy caught doctoring the footballs on NFL Films.

It is 45 degrees outside. The balls are delivered to the referees 2.5 hours before kickoff. They are inspected at that time and must record an air pressure of between 12.5 and 13.5 PSI. They are measured in a 70 F room.

You're at home. You have your own rooms with thermostats, and possibly customized air delivery equipment.

Is it possible to deliberately inflate the balls at an artificially high temperature to measure the correct pressure (say, 15 minutes after inflation in a 70 degree room), knowing that the pressure will decrease once they spend time outside? Note that the balls are kept indoors with the refs for over two hours. By halftime they were 2lbs light, which suggests 10-10.5 PSI. Would it hold enough heat to work? How hot are we talking?

Cosmic Blue

January 26th, 2015 at 2:16 PM ^

from what i read it was 50° outdoors at game time, and the balls were inflated in a 75°F room. by my calculations that would account for a 1.3 psi drop which differs slightly from what someone posted above

 

the maths:

assuming ideal gas law, PV=nRT and V, n, and R remain the same, therefore, P/T= a constant. or writtten another way, P1/T1=k=P2/T2 or P2=(P1/T1)*T2

T1=75°F (or 534.67 Rankine since absolute temps are required)

P1=12.5 psig assuming the low end of legal range (equals 27.2 psia)

T2=50°F (or 509.67 Rankine)

Pluging in:  P2 = (27.2/534.67)*509.67= 25.93 psia (or 11.23 psig)

Thats a difference of 1.27 psi from the start. 

Air is pretty close to ideal, especially under this low of pressure and normal temps, but i also checked this against density tables i have at work. the difference i calculated that way was 1.28 psi so it checks out

 

And since we must now speculate on explanations to account for the other 0.7 psi,, i estimate all of these to be more likely than foul play: the balls leaking slightly, the calibration for the gauges used is not exact, or the temperaturesreported not accurate

 

harbaugh!

 

 

bluebrow

January 21st, 2015 at 11:22 AM ^

But, all of your theories that I have read have been assuming "real air".  Is it possible to inflate the balls with a gas different than "real air" that would react differently to a lower temp than the Colts balls did?

Just wondering if you intilectual types could help me out?

 

Ivan Karamazov

January 21st, 2015 at 12:07 PM ^

because it would destroy the rubber in the football, as well as other unknown reactions.... but think the pure phase change consequences of inflating the football with diatomic bromine gas.  

Its boiling point is 332 K (137.8F), which is a very very hot sauna, but doable assuming it only takes a few minute to fully inflate the ball.  Take it outside to STP, doesn't even have to be cold out, and watch it instantly start shrinking as all the gas condenses to liquid.  Of course you wouldn't want to do it without protective gear as bromine is a strong oxidizer and very toxic. 

EDIT: Just realized you would need to be much hotter if you wanted to actually pump the bromine into the football and have it above atomspheric pressure inside the football.

wolfman81

January 21st, 2015 at 12:33 PM ^

On a tangentially related note, the Mythbusters show did an episode where they filled footballs with helium to see if they would fly farther.

http://www.discovery.com/tv-shows/mythbusters/mythbusters-database/foot…

The article there says that regular air-filled footballs fly farther, though my recollection was there was no significant difference between the two (I watched the episode a couple of years ago).  Either way, there was no measurable advantage to having a helium-filled football.

BlueMan80

January 21st, 2015 at 1:36 PM ^

Helium atoms are smaller than the mixture Oxygen, Nitrogen, and CO2 found in air.  Could those little Helium atoms escape the rubber bladder in the ball more quickly than the larger atoms found in air?  Could enough leak out over the hours before the game to make a difference?  As I recall, Goodyear blimps have special bladders to reduce the loss of helium.

707oxford

January 21st, 2015 at 10:36 AM ^

Refs would still be spotting/handling the balls between downs, so assuming the OP plan works, the refs should presumably notice any significant difference on the field.

 

Accordingly, all of this focus of deflated balls should be focused on the refs.  Either it was significant enough to notice and the refs are at fault for not doing anything about it during the game, or it was not significant enough to notice and this whole "scandal" is nonsense.

creelymonk10

January 21st, 2015 at 10:37 AM ^

P1/T1 = P2/T2 

P1 = 12.5 psi (minimum allowed) + 14.7 psi (atmospheric pressure) = 27.2

T1 = ?

P2 = 10.5 psi (2 psi drop)  + 14.7 psi (atmospheric pressure) = 25.2

T2 = About 40 degrees Fahrenheit = 278 Kelvin

Solve for T1: 

T1 = P1/(P2/T2) = 27.2/(25.2/278) = 300 Kelvin

300 K = 80 degrees Fahrenheit 

It makes sense, but can argue why the Colt's balls weren't deflated as well (if they have checked that as well).

CompleteLunacy

January 21st, 2015 at 11:02 AM ^

There's no assumption on either end of WHERE the balls were inflated. The difference could simply be from the Colts inflating them outside and the Pats doing it in a very warm room and bringing them outside.



This doesn't explain the Pats' 12th ball. Perhaps they intentionally overinflated it inside or inflated it outside knowing they wanted it to be a fuller pressure for kicks.



The Pats certainly looked to bend the rules here. But it's still so much of a nonissue that frankly I'm surprised it's gotten this much discussion.

gbdub

January 21st, 2015 at 11:22 AM ^

Relating to the 12th ball, kicks use a different set of balls. Also, do we actually know that all 11 under inflated balls were exactly 2psi low? I think "11 balls were under inflated, by as much as 2psi" is much more likely.




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Everyone Murders

January 21st, 2015 at 11:07 AM ^

Doesn't your math assume that volume remains constant here?  If so, that's a faulty assumption.

The point of underinflation is to make the volume of the ball decrease slightly - making it easier to grip and (according to some) easier to put a spiral on.  The football is not a rigid system, and its volume varies with pressure and temperature changes.

/Charles's Law'd/

 

OccaM

January 21st, 2015 at 11:12 AM ^

The volume here wouldn't change b/c it's a gas no? Any change would be negligible I believe b/c the air would conform to the ball's volume. 

The first report suggested that there was a change in Mass in the football. This would suggest that someone removed/added more air sometime between the refs checking the balls prior to the game. 

The OP's thought experiment just changes Temperature which would only change the pressure keeping everything else constant..

I Like Burgers

January 21st, 2015 at 11:50 AM ^

Plus, those balls take a beating during the game getting crushed and squished constantly by very large men.  I highly doubt that a ball that's filled at 12.5 psi will still be 12.5 psi after going through a game.  I mean, they have to lose some air during the course of the game, which would also alter the final pressure.

saveferris

January 21st, 2015 at 12:22 PM ^

Actually, I think the point of underinflation is to make the ball "squishier" and easier to grip, not necessarily smaller.

Your premise is correct though, volume in this case is not truly a constant, but for the pressure differentials we're talking about in comparison to the overall volume of the football coupled with the membrane strength of the leather itself, the change in volume is so small it can be considered negligible.

zebbielm12

January 21st, 2015 at 10:47 AM ^

EDIT - first attempt was wrong, didn't account for gauge pressure vs actual pressure.

 

Actually, this is most likely what happened. Assume the balls measured 10.5 PSI at 45 F, they would measure 12.5 PSI at 85 F. The balls would be a little warm.

Yo_Blue

January 21st, 2015 at 11:03 AM ^

Deflategate --> Bill Gates --> Microsoft --> Redmond, WA --> Seattle, WA --> Seattle Seahawks --> Fu%k the Patriots

Boom!  Conspiracy theory linkage.

stephenrjking

January 21st, 2015 at 10:43 AM ^

Just to be clear, since several have brought up the Colts footballs: I'm not suggesting that this is incidental. I'm wondering if the Pats deliberately used hot temperatures to gain the desired effect without doctoring post-inspection, thus technically not breaking the rules. It would fit Belicheck's profile.

kylewds18

January 21st, 2015 at 10:44 AM ^

Don't mind me, just stopping by to say how much I love this thread. Who else but Michigan fans? (Possibly Stanford, Vanderbilt, Northwestern... but the point stands.)  :)

kehnonymous

January 21st, 2015 at 10:48 AM ^

Aside from the interesting question regarding the actual physics (which I'm too ignorant to comment on), this is such a non-issue.  And I say this as someone who wants Seattle to beat New England.

Generally ESPN reports what the NFL wants it to report. The information may be largely accurate but its dispersal is controlled. It's certainly in ESPN's best interest to maintain that symbiotic relationship and its access to league sources so it certainly isn't going to be doing any thorough investigation that isn't explicitly or implicitly countenanced by The Shield.



There may very well be fire behind that all smoke. But it's important to remember that as far the NFL is concerned the ultimate point of all this isn't the *fire* so much as it is the *smoke*. As the Deadspin article about the 11 deflated balls rightly remarks: 'Every year it seems a ridiculous story rushes in to fill the empty air of the two-week gap before the Super Bowl, but this one might top them all.' And it's certainly working - as a quick glance at your Facebook sidebar will confirm.

Erik_in_Dayton

January 21st, 2015 at 10:52 AM ^

...Sam Webb this morning: His understanding is that the Colts noticed the underinflation of the balls at halftime but didn't raise the issue until after the game.  If that's true, did the Colts really think this was a big deal? 

If I'm a baseball manager and I notice that an opposing pitcher is putting a foreign substance on the ball, I'm running out to the field and not leaving until the situation is sorted out. 

maiznblue

January 21st, 2015 at 10:51 AM ^

Lots of teams overinflate or underinflate balls in football.. at least college football it happens ALL THE TIME. Rules are more strict in NFL but I'd guess a lot of players are probably thinking, "Yeah, it's illegal but everyone does it." 

For the record, I am not a Pats fan. I am not even an NFL fan.

LSAClassOf2000

January 21st, 2015 at 12:23 PM ^

Even Aaron Rodgers has been out there before saying that he's played with footballs that were intentionally overinflated, which by rule is supposedly OK from what I understand, or at least it isn't looked upon as unfavorably as underinflation. 

What's funny about this now - sort of - is that the Ravens now suspect that some of the kicking balls used in their divisional game may have been underinflated as well, so I suppose we might have that to look forward to in the coming days. 

MoJo Rising

January 21st, 2015 at 10:57 AM ^

inflate them in your nice 72 degree home and then take them out in the cold and let them sit for an hour or so in the nice cold weathe to see the delta in PSI if any. MGOBLOG could really show the nfl up on this. 

bluebyyou

January 21st, 2015 at 11:03 AM ^

I mentioned PV=nRT in the earlier thread on this topic.

The NFL has found ways to avoid the ideal gas law.

If you want constant pressure, you would need to keep the balls in an environment where they did not get cooler or warmer during the game.

Add a wet night, evaporative cooling, etc.

If you allow the balls to adjust to ambient temperatures, you would have a huge variance in pressure considering some games are played when the temps are in the upper 90's and others when the temps are close to zero.

michelin

January 21st, 2015 at 11:08 AM ^

Did the team then violate any rules by allowing the balls to later cool down to the ambient temperature?  If the balls conformed to regulations when checked intially by the refs and the Pats did nothing further to them during the game, did they satisfy the letter of the law (if not the spirit of it)?