25 January 2015

A Note of Thanks to Blog Readers

Is everyone getting tired of hearing and reading about deflated footballs?  I certainly am.  Like many football fans, I would prefer having the two-week buildup to the Super Bowl filled with stories about matchups, strategies, and predictions.  Instead, we've had deflate-gate dominate the past week's NFL news.  I think most of us hope that nothing illicit took place with any of the footballs used in the Patriots win over the Colts.  We like to believe the games we watch are on the level.  But I also think most of us believe that if any person (or persons) did anything outside the bounds of the rule book, that person (or persons) should be held accountable.

I now wish to hold myself accountable for a lack of clarity when I first commented on deflate-gate.  When I was contacted by NPR early morning last Tuesday (20 January) to talk about deflated footballs, I had only heard about possible under-inflated balls used in the Patriots AFC title game win over the Colts.  I spoke to NPR's Geoffrey Brumfiel for at least 20 minutes on the phone that Tuesday morning, and then a couple of quotes made it to air and in a story.  I was talking about the science associated with footballs and pressure and noted that quarterback grip could improve with a little less air pressure in the ball.  I then spoke in general terms about how each quarterback could have performed with an under-inflated ball.  Brady outperformed Luck, so "if" both quarterbacks were using balls with the same pressure inside, it certainly didn't appear to help Luck.  Where I lacked clarity was not including and emphasizing "if" enough in that comment.  I further assumed the "if" when I wrote a blog post early morning this past Wednesday (21 January).

It was a couple hours later while I was teaching when Geoffrey Brumfiel e-mailed me about an ABC news story (click here for that story).  That story noted that 11 of the 12 Patriots footballs were found to be under-inflated.  That was the fist time I learned that there was alleged proof that balls used in the AFC title game were under-inflated, and that the balls that were alleged to be problematic were the ones provided by the Patriots.  I emphasize those last seven words because before I had seen any alleged proof, I was making general comments about under-inflated balls and the associated science.  Had I seen the ABC news story, which posted after 11:00 pm last Tuesday evening, before I wrote my blog post early morning last Wednesday, I wouldn't have ended on general terms about both quarterbacks using the same balls.

I was certainly aware of Rule 2, Section 2 on how teams supply balls for a game.  But a few readers contacted me about my general comments that concerned both teams.  They had heard and read news before I had that tests of balls supplied by the Patriots had revealed problems.  To those readers:  Thank you so much for you kind comments!  You reminded me how challenging communicating can sometimes be.  As much as I was focused on the science behind how pressure and temperature affect footballs, I wasn't as focused on being as clear as possible on my general game comments.

When I wrote another blog post last Thursday (22 January), I emphasized science and concluded that I certainly have no way of knowing the environments in which the balls were tested and retested.  When interviewed by Fox News last Friday (click here for the story), my focus was solely on the science.

My goal when talking to media is to communicate the science behind sports.  Honing my craft of communicating clearly is a never-ending process.  I apologize for a lack of clarity and, again, I thank readers for contacting me with kind comments that sought clarification.

22 January 2015

Footballs, Temperature, and Pressure

Have you ever gotten together with friends and family on Thanksgiving Day and gone outside for your annual Turkey Bowl?  You go into a shed and retrieve your football, only to find that it's not quite as robust as it was in the summer.  You may not have a leak in your football.  Air molecules don't bounce around as much in the cold as they do in warm weather.  Inside a football, air molecules bounce around and collide with the interior walls of the ball (bladder, really).  The air's pressure inside a football will go down with temperature.

The deflate-gate controversy has people asking how how a given drop in temperature affects pressure.  Unfortunately, I keep seeing the same mistake over and over again in the various analyses I've read.  Using the ideal gas law is just fine.  Assuming the ball's volume doesn't change is a great approximation.  If there are no leaks -- and no illegal removing of air -- the number of air molecules inside the ball remains constant.  The simple result predicted by the ideal gas law with those assumptions is that pressure is proportional to temperature.

Here is where the problem comes.  The pressure that must be used is the total pressure.  The pressure range that's stated for a legal NFL football is 12.5 psi - 13.5 psi, but those pressures are gauge pressures.  The gauge pressure is what we measure above the normal atmospheric pressure we experience all the time, and never notice.  Atmospheric pressure is about 14.7 psi.  That's right, we all have the weight of a bowling ball pushing on each square inch of our bodies.  Luckily, we evolved in Earth's atmosphere and our cells have interior pressures just above 14.7 psi, so we feel equal forces on each side of our skin.  The legal total pressure inside an NFL football is thus 27.2 psi - 28.2 psi.

Assume that an NFL football is at 13 psi when checked inside a locker room at 70 F (21 C or 294 K).  Now take the ball outside.  Using the ideal gas law, and remembering that temperature must be in Kelvin, the graph below shows what to expect for the ball's interior gauge pressure.  The horizontal axis shows possible outside temperatures and the vertical axis shows the gauge pressure (click on the graph for a larger view).
I put a red, dashed vertical line to find the temperature at which the interior gauge pressure hits 12.5 psi, the bottom of the legal range.  That temperature is 60.4 F (15.8 C or 289 K).  You can see in the above graph how a ball that's legal in the warm locker room can lose pressure in the colder outside.

Now, I wish to make it clear that I do not know how and where referees check balls before games.  I don't know if balls are checked in a warm environment or if they are checked in the outside environment where the game will be played.  I don't know the manner in which the balls were rechecked when 11 of 12 of the balls in the Pats win over the Colts were found to be under-inflated.  I do know, though, that if balls that were checked before the game were rechecked at the same temperature at some later date, and found to be at lower pressure, then air must be missing from the balls.

In what I calculated above, I did not account for changes in humidity or anything else.  If air does not leave the football, temperature change is likely to be the dominant factor in changing interior pressure.

21 January 2015

More on Deflate-Gate

I was invited by Geoff Brumfiel of NPR's All Things Considered to comment on the controversy surrounding under-inflated footballs used in the AFC title game between the New England Patriots and the Indianapolis Colts.  The Pats won in convincing fashion, 45-7, but a dark cloud now palls the game, so much so that the silly "gate" suffix has been used.  After something like 20 minutes conversation with Geoff Brumfiel, a few of my comments made it to air and into the accompanying story.  That story and an audio link may be obtained here.  What I wish to do in this space is elaborate on what appears in the story by repeating some of my comments to Geoff Brumfiel that did not make the final cut.

Bad weather, like the rain and wind in the Pats win over the Colts, will make a quarterback desire a better grip on the ball.  Water on the ball, after all, reduces friction between the ball's surface and the quarterback's hand.  Anyone who has ever tried to palm a basketball, but finds one's hand just a wee bit too small, has noticed that palming the ball becomes easier if the basketball is slightly deflated.  Deflating a football slightly allows for better grip, too.

Losing a little air reduces the ball's mass.  How much?  Well, a normal football has nearly 98% of its mass in the non-air material that comprises the ball.  Only a little more than 2% of the ball's mass is from the air.  Of course, the ball's volume displaces air, leading to a buoyant force that matches the weight of the air displaced.  NFL balls are supposed to be at a gauge pressure of 12.5 psi (pounds per square inch) to 13.5 psi.  Note that gauge pressure is the pressure above atmospheric pressure, which is about 14.7 psi.  An example I described that did not make it to air is to assume that a ball is under-inflated by 2 psi.  Accounting for atmospheric pressure, that amounts to about a 7% loss in pressure.  The ball's weight loss, however, is less than 0.2%.  A less massive ball decelerates faster than a normal ball, but the mass loss in my example is too small to have much effect.

Referees are supposed to inspect balls used in games.  A referee sets the ball on the field before the start of each play.  As I told Geoff Brumfiel, an under-inflated ball may not have been noticed by a referee hurrying to place a ball on a play or two, but should have been noticed if balls used for most plays were under-inflated.  Nobody wants to think conspiracy when trying to figure out what happened, just like nobody wants to think a referee is incompetent or that a team cheated.  Given that both quarterbacks used the game balls, both should have had the same advantage that would have come from better-to-grip balls that may have been under-inflated.  Andrew Luck, however, had such a terrible game for the Colts that any advantage would have gone to Tom Brady, the quarterback for the Pats.  Luck's game, however, does not excuse any possible cheating.

We will have to see what comes of all this silliness.

15 January 2015

Talk on Sunday, 18 January

The Holy Trinity Lutheran Church in Lynchburg has invited me to give a talk on my Tour de France and World Cup soccer research.  My general-audience talk will begin in the church at 6:30 pm on Sunday, 18 January 2015.  This will be my first talk inside a church.  I'm looking forward to it!