Guest post by Alec Rawls
Just fill the ball with warm humid indoor air, then when it temperature-equalizes with the 25°F cooler outdoor air on your AFC Championship playing field some of the water vapor in the ball will condense into water, leaving less air in the ball, solving the great mystery: how did the footballs used by the Championship winning New England Patriots show 12.5 psi of inflation pressure in the official pre-game check but only 10.5 psi when checked at halftime?
There is also a decrease in pressure due to the cooling of the molecules that remain gaseous. Those air molecules are not zipping around as fast as they were so they exert less outward pressure on the ball. But according to the ideal gas law, if there were no reduction in the number of gas molecules in the balls it would have taken a large drop in temperature, about 40°F, to cause the observed drop in air pressure. So says Boston College professor Martin Schmaltz:
In order for a ball to register a 10.5 PSI in a 50 degree environment [the temperature on the field at halftime] but register a 12.5 PSI in the testing environment, the ball would have to have been inflated, stored, and/or tested in a 91 degree environment.
I verify Schmaltz’s calculations at the end of this post, and while I’m no expert in the field, I get the same answer he does.
It wouldn’t be hard to deliver balls to the pre-game pressure check with 91° air inside. Just inflate them in a 100° sauna shortly before testing, but the Patriots are adamant that they do not know why the air pressure in their balls was low at halftime and if they had inflated their game balls in a sauna they would certainly know it.
The Carnegie Mellon experiment
An experiment performed by a team at Carnegie Mellon provides empirical support for the Patriots’ claim to have done nothing unusual. The Carnegie experimentalists inflated a batch of footballs to 12.5 psi at a room temperature of 75°F, then let the balls equalize to a new ambient temperature of 50°F, resulting in an average pressure drop of 1.8 psi. (They also wet the leather balls to simulate the rainy conditions of the game, surmising that this might allow stretching that would reduce air pressure in the ball, but this seems likely to be a minor factor.) The Carnegie experiment is video-documented here:
So how to account for the difference between the Carnegie findings and the ideal gas law, which predicts that a much larger decrease in temperature would be needed to create the observed pressure drop? Barring experimental error, it seems that the difference would have to be explained by condensation. Gas was removed from the ball, not via an inflation needle but by conversion to liquid water. What do our blog-reading experts say? Is this the likely explanation?
The Carnegie group was not monitoring humidity (at least in the short video above), but if this is the explanation for their greater-than-ideal pressure drop then it could easily have happened to the Patriots the same way without anyone intentionally manipulating the inflation temperature or humidity. Still…
It must be common knowledge around the league that indoor inflation yields a softer game ball
The fact that the Colts’ balls did not show a similar pressure drop suggests that teams do know how to make these manipulations. Just as Patriots’ quarterback Tom Brady prefers to throw a less inflated ball, other quarterbacks
are known to prefer harder footballs.
If Colts quarterback Andrew Luck prefers a harder ball then all the Colts had to do is fill their balls pre-game with cool outdoor air. Ambient outdoor temperatures actually rose from pre-game to halftime so the temperature effect would have made their balls firmer. Also, moisture beyond what the cooler air could hold would never have made its way into the ball in the first place so wouldn’t there be any pressure-reducing condensation inside the ball either.
Players and equipment managers would surely have noticed over the decades how the conditions in which balls are inflated to regulation pressures affect ball firmness on the field. The basics are hard to miss. In cold conditions, inflate outdoors to get a firm ball, indoors to get a softer ball.
The existing pressure-test regimen, intentionally or not, leaves this room for teams to manipulate ball pressure to suit their preferences. The rule just says that air cannot be put into or removed from the ball after the pre-game pressure check. It does not regulate the conditions in which the balls are inflated going into the pre-game pressure check.
“Belichick rules”
If Coach Belichick had exploited this loophole to the max by inflating balls in the sauna then there would be a legitimate question whether this rule-bending constitutes cheating and there is plenty of history, both recent and ancient, to indicate that Belichick is eager to wring every advantage out of a loophole that he can. Where others may see exploiting loopholes as cheating, Belichick sees it as part of the game.
By the time he is done the NFL rule-book will contain at least a few “Belichick rules,” closing the loopholes he has so nicely pointed out, most recently by confusing the Baltimore Ravens about which Patriots players were eligible to receive passes. “It’s not something that anybody has ever done before,” complained Ravens coach John Harbaugh, “I’m sure the league is going to look at it and make some adjustments.”
Belichicks’ reward (besides a trip to the AFC Championship): he is now tied with Tom Landry for the most post-season coaching wins in league history, to which I say GO PATRIOTS! (That’s what you call “full disclosure.”)
But the full explanation in the present case seems to be that the Patriots filled their game balls with indoor air. If that is manipulation at all it must be utterly commonplace and well within the rules.
The biggest loser: Bill Nye, the phony-science guy
While real scientists keep acknowledging that the move from inside to outside can cause a substantial drop in football psi, Nye went on national television to proclaim that air must have been taken out of the balls with a needle. So that’s good anyway. Half the Northeast now knows that Bill Nye is an idiot.
Addendum: Gas law calculations
I was looking up how to calculate the expected pressure drop in a ball for a given temperature drop when I came across the claim from Boston College physicist Martin Schmaltz that, following the ideal gas law, temperature inside the balls would have had to be 91°F during the pre-game pressure check to account for the 2 psi drop in air pressure by halftime. In the exercise below I come up with a similar answer but I have no background in this stuff and am just following readily available information so don’t take my explication on authority (and please do note any inaccuracies in the comments).
When the number of gas molecules in a container is fixed (no gas escaping out through the bladder and no gas converting to liquid via condensation) then the ideal gas law simplifies to the general gas law, also called the combined gas law. Like the ideal law, the general law is said to be close to accurate so long as extreme pressures or temperatures are not involved. Mathematically, the general law just says that gas temperature, volume and pressure all vary in direct proportion to each other:
(P1V1)/T1 = (P2V2)/T2, where P1 is pressure at time 1, V1 is volume at time 1, and T1 is temperature at time 1.
In plain language, for the gas pressure in the Patriots’ footballs to drop by 7% the general gas law says that the temperature of the air in the balls must drop by 7% or the volume inside the ball must increase by 7% or there must be a combination of percentage changes in temperature and volume that add to 7.
The problem can be simplified further by assuming (as Professor Schmaltz does) that the volume of the space inside the football remains constant. (This won’t be fully accurate. When pressure in a ball drops the volume inside the ball will drop a small amount. This shrinking of the ball will make pressures higher in the low pressure state than they would be if the ball didn’t shrink so the constant-volume estimate of the temperature change required to account for the observed pressure drop will be a bit on the low side, unless the Carnegie experimentalists are correct and there is an offsetting increase in volume when the balls get wet.)
With fixed volume the general gas law becomes: P1/T1 = P2/T2
All of these numbers are known except for T1, the temperature of the air in the ball when it was first tested 2 hours before game-time. The known numbers just have to be converted from relative to absolute form.
First, the inflation pressures measurements are in pounds per square inch above atmospheric pressure, thus to get the full pressure inside a ball it is necessary to add atmospheric pressure (about 14.7 psi) to the measured psi.
Also, the gas law is based on degrees above absolute zero, which for Fahrenheit-sized degrees are “degrees Rankine,” which are Fahrenheit + 460. Solving for T1 in degrees Rankine:
T1 = (P1 x T2)/P2 = ((12.5 + 14.7) (50 + 460))/(10.5 + 14.7) = (27.2 x 510)/25.2 = 550.5°R = 90.5°F
Which rounds up to Professor Schmaltz’s 91°F.
Calculations for the Carnegie-Mellon experiment
In the Carnegie-Mellon experiment the expected post-equalization ball pressure, calculated just using the general gas law (where no gas is lost to condensation), is:
P2 = (P1 x T2)/T1 = [(12.5 + 14.7) x (50 + 460)]/(75 +460) = 25.9 psi
Subtract atmospheric pressure (14.7 psi) to get an expected pressure test reading of 11.2 psi, vs. actual experimental readings of 10.7 psi. The suggestion here is that the additional pressure drop found in the Carnegie experiment is a result of water vapor condensation.
If the Carnegie experimentalists were careful they would have compensated for the pressure drop that comes from energizing their pressure tester but game officials (who measured halftime pressure as 10.5 psi) might well not have taken this source of pressure loss into account. If they had the then the difference between their measured pressure drop of 2 psi and Carnegie’s measured drop of 1.8 psi might disappear.
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Come on folks. It’s simple IPCC physics.
Assume a spherical football (football=globe). Man-made CO2 causes the globe to warm (‘global warming’).
Normally, warming would cause expansion and make the pressure higher. But this is man-made warming, so we know it has halted (temporally) and this global warming is now hiding in the oceans.
So the globe cools, due to man-made CO2, and the pressure drops by 2psi
Q.E.D.
/s
saw something yesterday (cannot find not) saying colts balls also had a drop pretty close to the patriots balls but they had started at max pressure while pats started at min pressure.
I think the balls should be filled with lead shot. American football is for people with attention spans of less than 5 seconds.
American football is for people who can take 5 seconds of time for other than work in every 40 seconds as they carry the burdens of the world.
Just like NHL hockey and MLB, the TV networks take advantage of natural gaps in the game to insert inflated ‘timeouts’.
Is FIFA next?
The ideal gas law explains of course why the kicking ball was not underinflated…
Face it, a softer ball is an advantage when it is cold and wet… just ask Jermaine Kearse of the Seahawks if the balls are hard to catch when they are wet, cold and fully inflated.
They wee that way for a reason, the mechanism is interesting but irrelevant. The current direction of the ‘probe’ to blame some low level functionary is fascinating but not exculpatory.
Brady and Belichick are responsible, they got caught.
Next.
http://www.businessinsider.com/patriots-ball-boy-bathroom-2015-1
According to ProFootballTalk’s Mike Florio, this locker-room assistant took the bag of game balls for the AFC Championship Game from the officials after they were measured, stopped in the bathroom for 90 seconds, and then went to the field.
number 1 or number2?
What could you do to the air pressure of 11 balls in in 90 seconds?
I use an interactive psychrometric program on Trane’s commercial web site to analyze industrial wet cooling towers. Suppose the balls are filled with 75 F 50% RH air. The dew point would be 55 F. Specific volume would be 13.67 cu ft/lb.
So if the balls cooled to/below 55F the water vapor would condense.
At 25 F and 100% humidity inside the ball specific volume drops to 12.27 cu ft/lb, 90% of the original specific volume. P1/V1=P2/V1. I get 12.5 psig falling to 9.7 psig and 13.5 psig falling to 10.6 psig.
So, yeah, it’s simply science.
Just conducted operator training for a new CCPP and hammered them on about psig, psia, and vacuum especially since the site is a mile high and not at sea level.
If the pressure gauges are as accurate as the thermometers contributing to our climate database, all we need to do is wait a couple of months so the readings can be homogenized and presto, no more deflategate.
You’d be more convincing with some numbers, so Let’s do some math
Going from 70F air to 45F (21C to 7C) air is a drop from 18.7 to 7.0 mmHg in water’s vapor pressure. That’s only a change of 0.226 psi.
http://usacetechnicalletters.tpub.com/ETL-1110-2-253/ETL-1110-2-2530017im.jpg
Starting with a 12.5 psi ball of saturated air at 70F and going to 45F.
(14.7+12.5)*(505/530) -0.226-14.7 = 10.99 psi when cooled
Now, There are several locations where it could easily be hotter, such as a croweded room or near a radiator, If the air started out staturated at 75F
(14.7+12.5)*(505/535)-0.273-14.7 = 10.70 psi when cooled
A quarter-psi is the most discrepancy you can expect due to measurement error even with a cheap gauge. However, 10.5 psi is hardly a suspicious difference. Any tiny stretching or leak could account for that difference.
[But the premise was a starting temperature of at least, if not more than, 95 F. .mod]
Moderator, you don’t need a 95F starting temperature. You can get to the expected pressure from fairly normal indoor temperatures in a locker room.
And I found a source saying that the temperature bottomed out at 41F in the game, so knock about 0.2 psi off my calcs above.
On the contrary, if they the balls in a locker room filled with sweaty men and hot showers, in which case the 100% humidity is practically guaranteed. Even before a game, the humidity is quite high due to warm ups and the sheer number of people moving about. Plus, it’s a logical setting to work the game balls and does not presume beforehand that there is ill will involved.
Also, if they used a compressor without a dryer, water accumulation happens naturally in the air tank while compressing air, so cheap air compressors are constantly putting out saturated or even condensate-filled air.
So assuming saturated is not only defensible, but it’s the most likely scenario.
NFL footballs right out to the box are rigid. For years kickers have worked the balls on the side lines to soften them up so they have a little more flexibility allowing a longer kick. They are no longer allowed to do so, That is why “kicking” balls are used only once right out of the box. However, this is not the case for game balls. Quarterbacks are allowed to “work” the game balls making them less rigid and more flexible. Did these experiments allow for that?
As an interesting note to all American football fans. Here is the reason for the “too many men in the huddle” rule. Back in the late 60’s Bud Grant was the head coach of the Minnesota Vikings. He would many times place 12-15 players in the huddle (for non Americans only 11 players are allowed to participate each play). As long as the extra players left the field prior to the play starting there was no infraction. And that’s what they would do. The extra players would run off the field, the quarterback would then immediately start the play leaving no time for the defense to figure out which players and formation to defend. Until they made the rule against this nobody thought Bud Grant was cheating, he was considered innovative.
In 1907, Glenn Scobey (Pop) Warner had returned to coach at the boarding school for Native Americans that he’d built into a football powerhouse beginning in 1899, largely through trick plays and deception. Over the years, he drew up end arounds, reverses, flea flickers and even one play that required deceptive jerseys. Warner had elasticized bands sewn into his players’ jerseys so that after taking the kickoff, they would huddle, hide the ball under a jersey and break in different directions, confounding the kicking team. Warner argued there was no prohibition against the play in the rules. The tricks were how the smaller, faster Native Americans could compete against players 30 or 40 pounds heavier.
Read more: http://www.smithsonianmag.com/history/the-early-history-of-footballs-forward-pass-78015237/#VcXRDYDG4ZxfPgyU.99
Was Pop Warner cheating?
In this context cheating is breaking a rule that has been agreed to or issued by a relevant authority. For those readers who ever played football outside a football league, did you ever measure the air pressure? Did you even own a gauge?
The same thing happened with the No Huddle offense. The offense team would start the play while the defense was making personnel substitutions, particularly on third and long, passing downs. The offense would snap the ball while the defense had more than eleven players on the field, resulting in a penalty and a free play for the offense.
Defenses eventually adjusted to this tactic, and the NFL modified the rule so that if the offense made player changes, they had to wait until the defense completed their substitutions before snapping the ball.
In a similar vein: In one of the Browns game this season the offense had two quarterbacks in the huddle (but still only 11 men on the field). Johnny Manziel pretended like he wasn’t supposed to be in the game and started walking off the field while coaches were screaming at him to get to the sidelines. The Browns snapped the ball and threw it to wide open Manziel for a touchdown, which was called back because of a penalty.
Alex Rawls says: “When the number of gas molecules in a container is fixed…”
======
A minor point, but if n in PV=nRT is fixed then the “amount of air in a football” is fixed.
Yes and no, n is the moles of gas in the container (football in this case). If water vapor condensed then the value of n went down because there is less gas in the football.
Thanks, Alec. Good catch.
Yes, for “ideal” gas.
Anyone who’s used a compressor extensively knows that compressors will build up a large amount of moisture if they’re not drained daily. Failure to drain this water will result in very humid air being pumped.
Also if the air was coming directly from a compressor it would certainly be warmer than ambient since compression raises the temperature.
Ergo: if you want a soft ball start up the compressor and fill the ball immediately. If you want a hard ball, run the compressor well in advance (preferably in a dry environment), and let the air cool in the storage tank before filling the ball.
However, when you let saturated air from a 60 or 80 PSI compressor tank down to 12 PSI, the relative humidity goes down. A lot.
If I wasn’t lazy, I could calculate the RH after taking that big pressure drop, but it’s going to be well below saturated.
I think the ideal gas law alone explains this. It had to be excessively hot air to begin with.
“Going from 70F air to 45F …” At 50% RH the dew point is 50F so at 45F the RH inside the ball would become 100%. Specific volume would go from 13.52 cu ft/lb to12.85 cu ft/lb, 95%, beginning 13.50 psia, ending 26.80 psia or 12.10 psig.
Vapor pressure is irrelevant. It’s why warm air holds more water vapor than cold, but so what.
“So that’s good anyway. Half the Northeast now knows that Bill Nye is an idiot.”
Thanks for the much needed chuckle.
Like many others, I did the calculations and ran the tests myself — using a Wilson “NFL” football, digital temperature gauge (0.05 psi resolution) and refrigerator in my house.
I checked equipment for consistent measurement. I pumped up the ball. I allowed ball to stabilize at room temperature (roughly 68F) for about 9 hours — psi fell off due to air being warmer when first pumped (due to compression — heck the pump even felt warm).
In my case, between pumping and stability, pressure fell approximately 0.4psi. I took the new lower pressure as the basis for the refrigerator cooling part of the experiment.
Put in refrigerator (about 30 degrees cooler) for 1 hour (may take a bit longer for ball to stabilize — but, game balls do not necessarily stabilize).
Merely measuring the air pressure removed 0.05 psi from the ball (due to air moving into the measurement device) — 10 measurements removes almost 0.5 psi. I took that into account.
My ideal gas law calculations resulted in roughly 1.5psi for 30F temperature change (starting at roughly 70F). The ball in the fridge dropped 1.6psi during the hour. An hour later (2hrs total), it had dropped 1.65psi. All in the “ballpark”.
So, the roughly 2 psi (+-??) reported for the “game day balls” (which may have been subjected to different conditions) seems reasonable.
That was a simple, one pass experiment with cheap equipment. Multiple runs could refine the numbers — but, the reported numbers themselves are only rough figures — given the sources of measurement error, differing conditions, and possible reporting errors.
I guess Bill Nye forgot the saying about folks wondering if he was an idiot—he opened his moth and removed all doubt.
Pardon my enthusiasm but – Go Patriots!!!
For a bit of perspective:
What? Bill Nye the “Science” guy is wrong on something? I don’t believe it.
So funny how everyone falls over themselves in order to correct the many statements made… Brilliant!
The solution to this is for NFL Officials to inflate each ball before the game with pure, dry CO2. When filled with the magic gas, the balls would be self-warming and offset any gas shrinkage due to temperature drops on the field.
Would hydrogen or helium gas leak thru the membrane?
And could they get there hands on some monatomic hydrogen?
Would hydrogen or helium gas leak thru the membrane?
Almost certainly yes.
Hmmm… Maybe you’re on to something! Maybe Brady had the footballs filled with helium? Everyone knows how helium seeps through just about anything, (picture those shrunken helium filled latex balloons laying on the floor the morning after the birthday party).
Please, all the information we have is provided by reporters from anonymous sources. There’s absolutely no chance for mischief is there? No siree Bob! The first report claimed that the player who intercepted the ball noticed it was deflated and gave the ball to the equipment coach to check it out. Nope, he just wanted to keep the ball as a souvenier because he’d intercepted Tom Brady in a championship game. The rest of the subsequent reports have all been anonymous too. (For you furriners, Brady is considered one of the top quarterbacks to ever play the game, if not the greatest.)
Compare and contrast science reporters and CAGW.
If 11 of the 12 balls “prepared” for the Patriots were done in a fashion different from that of the 12 balls “prepared” for the opposing team in every single Patriot home game, it doesn’t matter the methodology.
Rumor has it the refs knew in advance allegations of under inflated footballs for one team (and not the other) and, if true, would mean the Patriots were attempting to violate rules. If people who use science daily are interested in creating a scientific lesson, I’m all for it. It can be a teachable moment. Using that to speculate on whether cheating went on or not, using that same science, is a slippery slope. It would imply you can legally skirt the rules, in effect tricking the refs by presenting balls for inspection that have not been treated in the same manner – whether that’s inflating in a different environment or what have you. Measuring balls to make certain of their pressure is and should be a simple engineering event, and not a time to determine skullduggery.
Each team supplies it’s own balls. So the Patriots didn’t “prepare” the Colts balls, they take care of that themselves.
My misinterpretation of events, then. The ballboys would travel _with_ the team? That has to be a good gig. I missed my calling.
Folks, folks, folks. . .
A couple of overlooked items. . .
First of all, the PV = nRT equation is for an ideal gas in a rigid container. . . .a football is not an rigid container. It’s a elastic container with non-linear characteristic. Now it might be possible to regard it as a rigid container over the range of pressure that is being discussed. . .but I’m not sure about that.
Second. . . the ball manufacturer has stated that the footballs are inflated at the factory. . .and shipped inflated. In other words to wind up with 100% saturated air in the Patriots footballs at 91 degrees would require them to first deflate the balls. . .and then refill them with the completely saturated air, which would constitute tampering. Or. . . .they could inject just a couple of ccs of water into the football, which would result in complete water saturation of the air in the football, and then put them in the Sauna for a bit. Again. . . .that would constitute tampering. . . .under no circumstances could that be regarded as “normal ball preparation”. . . .
Third. . . no one has mentioned that one of the Patriots coaches, the defensive coordinator, is an expert on things like this. . . having a degree in Aeronautical Engineering from RPI.