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.
How was it only the Pat’s footballs were affected, and 11/12 at that?
The most obvious cause for different result conditions is different starting conditions. P is only one, V is pretty much fixed…so T would be different. Any balls which lost T, would HAVE to lose P. If they didn’t lose P, then they didn’t change T.
The rules are the rules. If they don’t specify the temperature at which the ball must be inflated, then any team that doesn’t take advantage of it is a fool. It’s not cheating. If other teams have a problem with it, lobby the league to tighten the rules. But that would be discriminatory against quarterbacks that prefer a softer ball.
Also, if this is a violation of the “spirit of the rules”, then I would also want to see a new rule to stop coaches that try to “ice” the field goal kicker by calling time-out at the last second before the opposing team hikes the ball for a game-winning field-goal attempt. THAT is “gaming the game” if I’ve ever seen it, and I HATE HATE HATE it when a coach pulls this crap. But not only do the referees permit it, there’s usually one standing right there beside the coach to blow the whistle on the coach’s command.
Then again, if every coach played within the “spirit of the rules”, then they would decline penalties they knew were wrongly called against the other team, and if a penalty was not called on his own team when it should have been, he would do something on the next play to make up for it. And in a potential replay situation, they wouldn’t line up so quickly for the next play, so the referees (and the opposing coach) would have a chance to call for a replay. And every receiver who got credited for a completion when he knew he dropped it would own up to it. Hell, for that matter, they wouldn’t burn as much time as they could off the clock between plays when leading late in the game, or even choose running plays over passing plays in that same situation.
These and many other tactics are examples of “gaming the game”. They are all perfectly legal, but are not in accord with the “spirit of the rules”. And they all have far more effect on the outcome than 2 pounds of pressure in a football.
There is evidence that the Patriots have possibly using deflated balls since the 2007 rule change that allows the offense to provide their own footballs. This is shown in fumble statistics. Players who have played for other teams see their “touch to fumble” ratio rise dramatically when the join the Patriots. Also, once they leave the Patriots, it drops back to normal. A softer football is easier to hold onto and results in fewer turnovers. If a team can greatly reduce the number of turnovers across an entire season’s worth of games, they will end up higher in the standings.
http://www.sharpfootballanalysis.com/blog/2015/new-england-patriots-fumble-more-often-when-playing-for-other-teams
Glad you got this indisputable evidence for us. It has allowed me to look through the stats and figure out who else was cheating. Hmm, in Adrian Peterson’s first 3 years in the league, he averaged a fumble every 49.9 touches, yet since then he’s gone 114.9 touches per fumble. Clearly this can’t be due to change in coaching focus, but must instead be due to the indisputable fact that he started using deflated footballs in 2010.
The tires of large commercial airliners are filled with nitrogen not air. One reason for this is that the water vapour in air will freeze out at altitudes. The ice inside the tire will unbalance the wheel and lower the tire pressure. This will cause difficulty on landing and may cause the tire to burst.
Thus the issue of loss of pressure caused by water condensation is recognized in the airline industry and prevention of this is the reason the for the regulation requiring the use of dry nitrogen
I bought a new set of tires last week for my Camry. They filled them with nitrogen without my asking them, so I assume this is going to become the norm. Does this prevent water vapor?
Sorry, what were we talking about? Inflation holding pretty steady… not enough for Janet to start yellin’ ; – )
Of course, _everybody_ knows the Patriots deserve to lose all games in perpetuity, since the refs handed them that snow-bowl game against the Raiders a few years back.
The rest is just details.
Interesting points from Dr. Roy about the source of the compressed air, though.
If you’ve ever pumped up a bicycle tire with those tiny cylindrical pumps that come with the bike you should know that the air “exhaled” by the pump can be quite hot. I’ve had pumps hot enough to be difficult to hold. Granted that the pressure in the football is less than a bike tire but the temperature of the air out of the pump is a function of how hard you compress it inside the pump. If it can’t escape rapidly into the football it can attain considerable pressure.
If the football was inflated with a compressor the same physics applies. If the compressor was run recently the temperature of the air in the tank will be higher than the ambient temperature in the room. They don’t have cooling fins on those compressors for nothing. The smaller the compressor (a little portable just for inflating footballs vs a big shop compressor with a tank the size of a refrigerator for instance) the more likely the air will be hotter than the room air.
It is, of course, possible that they used a big compressor that had enough pressure from being topped off days ago and the compressor never had to run and the air in the big tank was the same as room temperature. But I think it’s more likely that the team carries a small compressor just for this job and it has to be pressurized each time. And that means the ball was inflated with air that was hotter than room temperature.
Actually there are methods of starting fires which use that principle.
Don’t forget that compression of air increases the temperature, so the air actually inflating the ball is warmer than ambient. I have not done the calculation, but this would increase the effect. However I think you are right that the main difference is condensation.
Agree that the most important aspect of this silly debate is that by going on the record as a denier of one of the most basic laws of thermodynamics, Bill Nye has destroyed any credibility he may have had with other than conspiracy theorists.
In addition to whatever else they did, the Patriots have thus made a great contribution to humanity.
Once upon a time long years ago I was tasked with designing a relief valve for racing cars to be put in a secret location on the inside of the wheel. It was to relieve at 33 psi and reseal at 28 psi. Now normally racing tires heat up a good bit when running and this contributes to lack of grip and wear which is a disadvantage. This is why the NASCAR boys change all 4 tires every time they have a caution. They often put the same tires back on later in the race. This little valve was, of course, blatantly against the rules. The driver using this little device was quite successful for a good long time. Then he got caught. They had a huge wreck with many cars involved and the race track completely blocked so the red flag came out. Our guy was in second at the time so he was in a good position. When a race is stopped like that all the cars are lined up in their running order and no one is allowed to touch them until the race is restarted. After sitting stopped for about 45 minutes the tires cooled off and our guys tires were flat. Big OOPS. Gotcha! Black Flag, penalties, suspension, and fines. But it was good while it lasted then we were at the mercy of PV=NRT.
Brady did it. That’s how the balls lost 2 PSI. Tom Brady.
c’mon, nobody even looked at the picture
Gronk did it
and what about that Coefficient of Restitution thingy? I know that is temperature dependent . . . just sayin’ there’s science and then let the games begin.
Gronk should be incarcerated ’til Monday, too.
Really, who cares if the balls were off by 2psi, and technically in violation of the rule? Well, you should if it can be proven that an advantage can be had by doing this. Whether or not Tom likes the feel is inconsequential, and in my opinion a red herring. Rather, see if there is any correlation to important statistics on game performance and see if the Patriots have been significantly improved since the rule went into effect, which was 2007.
Well, in that regard, take a look at fumbles by each team in the league and you will see that the Patriots have significantly improved their ball handling skills as compared to the rest of the league, and it all started in 2007. Fumbles have a much larger impact on game outcomes, and the Patriot performance demonstrates a dramatic shift in performance since the rule was adopted. Somehow, the way Tom liked the feel of the ball doesn’t play much of a rule in that.
So where were the balls stored? Outside the shower area? (IE humid and warm, since people don’t like cold dressing rooms?
And this has what exactly to do with this page?
Maybe the headline was meant to be ironic, but it’s wrong.
Let’s not forget the cheating done by the NFL guru, the BIg Tuna, Bill Parcells. As the coach of the New York Giants and on a particularly windy day at Giants Stadium, he had the stadium service crew open the huge bay door at the end of the stadium allowing a howling wind to enter the stadium from that direction, but only when the opposing team was headed that way. When his Giants were headed that way, the bay door was closed. Most people, except the opposing team and their fans though it was clever. But then Bill Parells could do no wrong in peoples eyes.
There once was a mouse named Strauss.
They called him Deflatormouse.
The rodent did it.
Very funny, but most football fans are Americans, who won’t get it because they wouldn’t know that “Die Fledermaus” (“The Bat”) is an operetta written by Johann Strauss Jr.
Here is a very relevant ‘backgrounder’ from Wilson, the company that makes the NFL footballs.
Enjoy! And don’t challenge ‘Emmit’ to an arm wrestling contest!
http://youtu.be/K8kZP4dRe3w
Your equation T1 = P1 X T2/ P2, is the same as P2 = T2 x P1 / T1, and at extremely cold temperatures, say -200 F, P2 = (-200 +460) * (12.5 + 14.7) / (50 + 460) = 13.9 = 14.7 – 0.8 psi? So at -200 F the pressure in the ball is negative??? How can it be negative when there is a higher concentration of air inside the ball than outside the ball? If the temperature inside the ball is the same as the air outside the ball, there will always be some positive pressure measured on the ball, until you get to 0 Rankine. So since the ball will be at zero pressure at 0 Rankine, shouldn’t your equation leave out the 14.7 psi from your calculations? Sure 12.5 is a gauge pressure above atmospheric pressure, but that gauge pressure is what will vary linearly with the ideal gas law isn’t it? Assuming atmospheric pressure remains constant. On Venus atmospheric pressure is 1337 psi, if I had a 12.5 psi gauge pressure football on Venus, then according to your equation with atmospheric pressure included, a 20 F(or R) temperature drop from 50 F would result in a pressure of P2 = (30 +460) * ( 12.5 +1337) / (50 +460) = 1297 psi , or 1337 – 30 psi, so the ball would be reading a negative pressure of 30 psi with a 20 F temperature drop?? Even though there is a higher concentration of air inside the ball than outside the ball?
The pressure / temperature change calculation has to be done against gauge pressure, so the pressure is always positive in the ball until you get to 0 R. Which means a ball at 50 F that had a for a 2 psi temperature drop started at a temperature of T1 = 12.5 * ( 50 + 460 ) / 10.5 = 607 R = 147 F.
Pressure inside the ball relative to outside pressure can certainly go negative as temperatures continue to fall. Just remember the assumption that the ball stays the same size, as if it were a rigid container. As the air outside continues to drop in temperature it becomes very dense while the air in the ball remains of the same density. When the density outside exceeds the density inside then the outside air will be pushing to get in.
Above I posted the results of my calculation and actual football-inflation experiment.
To summarize: Like many others, I both calculated and measured experimentally using an actual football that a ball inflated at 70F would lose just over 1.5psi when cooled to 40F (under the conditions of my experiment). Cooling started after temperature and pressure had stabilized. The first cool football measurement was 1hour after the ball was placed in 40F temperature air.
In the original post, I forgot to add:
When the ball returned to room temperature, its pressure was restored exactly (less the 0.05 psi per measurement).
I also did not mention that my temperatures were taken with a digital thermometer with 0.1F resolution.
Thus, it partly depends on when the NFL measured the air pressure, how many times they checked it, and what measurement device they used. At room temperature, the balls should be at the former room temperature pressure (minus any loss due to measurements).
My data does not “clear” the Patriots of wrongdoing. It merely roughly confirms their finding regarding football pressure loss as the temperature drops. And, there are other physical considerations besides temperature that might alter football pressure measurably — as noted in other posts.
Yeah except humidity isn’t air. It’s moisture IN air. Condensation only collects that moisture together. The amount of air stays the same.
Humidity is water vapor, which is a gas, and is a component of air. When water vapor condenses to liquid water it is no longer a gas and the amount of air is lessened.
It’s only gridiron, who gives a stuff.
At least one ref handles the ball after each play. Why did the Colt player notice this and not the refs? Or were they not impressed? If each side provides 12 balls, why not mix all 24 at 5 minutes before kickoff and then distribute 12 to a side for use in the game?
Yawn.
Okay, I haven’t read the entire thread, above, but I searched it for some keywords. I didn’t find any mention of exactly how they inflate the balls or one obvious ploy: Have the QB or his stand-in SQUEEZE the ball while it’s being inflated at outdoor temperature. When he says ‘NUFF, stop the pump and store the ball in a warm room. They’ll test ok before the game and gradually return to the desired pressure over about 15 minutes.
Also, condensation of water vapor within the ball could produce an unstable ball, since more water collect on one side of the ball when thrown.
Funny seems like every time I mention temperature is not equal to energy and therefore humidity and pressure are needed with temperature other wise the measurements can’t really be compared I get jumped and everyone says I don’t understand the ideal gas law. Perhaps someone would like to explain to me how this is different than the earths atmosphere? Wouldn’t a high humidity air mass lose moisture as it passed a desert and vice versa changing the temperature but not the energy?
There’s more mixing in an air parcel passing a desert than between a football and atmosphere, for one.
I don’t understand what you mean with “Wouldn’t a high humidity air mass lose moisture.” Conservation of mass argues that moisture either falls out as precipitation or is diluted if the surrounding air is drier due to mixing. The former releases latent heat, the latter doesn’t.
How about absorbed by the arid ground and plants? We all know energy is never “lost”. The question is how much does the temperature change simply due items such as the latent release of heat as you describe. Currently everyone assumes it is balanced over the globe and sums to zero. What if it doesn’t?
This isn’t a science issue, it’s a rules issue
Basketball, soccer, and even baseball (pitchers’ quirks notwithstanding) leave the suitability of a given ball up to the officiating crew, and even baseball doesn’t generally use two dozen actual game balls to complete a single game. In order to maintain its credibility, look for the NFL to eventually move to using footballs prepared and approved by the officiating crew ONLY (rather than from either team) in every playoff game at least, if not in all games during the season.
Why does an NFL game need a dozen balls per team, anyway? 2 or 3 per quarter on a bad weather day seems like plenty to me (to allow for towel drying between uses, etc.). And why wouldn’t it be fair for both teams to use the same set of officially approved footballs in the first place?
[Note: this commenter is not the erstwhile WUWT Smokey. ~mod.]