DeflateGate and the Temperature of the Playing Field

Question:    Can a cold artificial turf field explain the lower pressure in the Patriots footballs?
Answer:    It was January in New England.  The cooling from the turf due to the ball sitting at the line of scrimmage in between each play, and the fact that the Patriots had a sustained drive just before half-time totally explains the wide variety of pressures in the Patriots balls, and the difference between the Colts balls and the Patriots as measured at halftime.

Overview

Artificial turf fields can get very hot on sunny summer days. Field temperatures of 150oF to 200oF have been reported. To compensate, manufacturers put in high heat capacity sand to retain cool temperatures, and utilize the grass fibers to conduct cooling from that sand to the surface.

But what happened on the cold cloudy day of January 18th, 2015, when the Colts played the Patriots in the AFC Championship game that is now known as the DeflateGate game. It was not a hot day, and the sun was not shining.  But it was a hot day for January! The air temperature rose dramatically from a night time temperature of 20oF to 50oF, with most of that rise occurring in the last 7 hours before game time. In addition, the temperatures of the prior week had averaged less than 25oF, with the day before the game falling close to single digits. Indeed, all of January up to that point had only two or three days that rose above the freezing point.

That same high heat capacity sand which attempts to keep the field cooler on hot summer days, would have been cold as well, and would have kept the field cooler than the ambient air temperature on this warmer than normal winter day. And the ground underneath would have been frozen.

So during the Patriots – Colts game on January 18, 2015, the temperature of the turf field is expected to have been colder than the ambient air temperature.

The colder temperature would have an impact on the balls that came in contact with the field, lowering the temperature and pressure of the balls.

Using reasonable assumptions, the distribution in the pressures and the lower absolute pressure of the Patriots footballs measured at halftime is consistent with a lower field temperature.

Inclusion of this effect removes the requirement of a person removing air from the Patriots footballs.  The lower pressures and the scatter in the pressures can be  explained simply by the weather, and the play on the field.

This effect was not discussed in the NFL Official Wells Report .

Description

Before the game 13 Patriots footballs were measured by a referee to have a pressure of 12.5psi at a temperature of 70oF.

They were put into a ball bag, and carried out to the ball field with an air temperature of 50oF which dropped to 48oF by halftime.

Using the Ideal Gas Law, and knowing that a dry football in open air exponentially will go from a warmer temperature to a colder temperature with a time constant of 15 minutes  (see Appendix A, and the Wells report), we expect the footballs exponentially approached 11.4psi, dropping  63% in the first 15 minutes, and were 98% of the way there in 1 hour.  [Note: this assumes there is no ball bag effect – i.e. balls in a ball bag might take longer to begin changing in temperature.   The bag and the air inside the bag may insulate the balls from the outside air].

The ball game started approximately 2 hours after the balls were brought to the field.

After the start of the game, with the teams on the field, a ball for the team on offense was placed on the field at the line of scrimmage in between plays.  These balls were regularly exchanged as needed by ball boys in between some plays.

The air was damp, misting, and rain was expected in a couple of hours.  The temperature had risen from 30oF to 50oF in the last 6 hours.  It was 6pm.  The temperature for the last week had been in the teens and 20’s.

Artificial Turf

So what temperature was the field?  The field is artificial turf.  An ad for it shows a side on view of small rubber pellets mixed with sand, with most of the sand sitting under the pellets, with grass like plastic feathers coming up from under.

FieldTurf
FieldTurf is the brand of Artificial Turf used at Gillette Stadium

 

Undoubtedly, under the turf field was frozen earth, probably matching the average temperature of the last week, maybe 25oF or below (see Appendix B below).  The grass blades would be damp from the mist.  They are not frozen – the composite substance provides some level of thermal insulation.  In the literature the artificial turf is described as being of high heat capacity, with a heavy total system weight providing that heat capacity.  Physically, that heat capacity is probably provided by the sand.  We might expect the sand is still in a sub-freezing state, since it has been cloudy.  The rubber particles provide the springy earth like feeling and are probably insulating.  The blades of artificial grass pass up through the sand and rubber pellets.  They are designed to bring some of the cooling power of the sand to the surface, keeping it cool on high temperature days.

So what is the temperature of the field?  It is probably a gradation of temperatures, starting near the temperature of the surrounding air near the top of the grass, but quickly falling to match the temperatures of the substrate underneath.

Water collected on the grass, and would have been cooled by the presence of the cooled substrate below.

Painting the Football with Cold Dampness

Would the damp grass have painted cold water on the ball as the ball hit the ground or the center spun it into position?  Did contact with the ground bring the temperature down faster than the exponential law for the open air?  It seems easy to answer yes to these questions.  We just don’t know what the temperature was, because we do not have a temperature analysis of the field, or that of a football sitting on a cold, damp artificial turf field.

Is it possible the field had completely warmed up in the surprisingly warm( 50oF) afternoon of an otherwise frigid January in Boston?  I could not find a detailed analysis of modern artificial turf thermal characteristics in the literature that might give that answer.   There are descriptions of early turf fields being unbearably hot in the sun.  The modern fields talk about their high heat capacity which keeps them cool.  That is about as much as I could find.  But given the timing of the atmospheric temperature changes that day, it may be enough to assume (given the literature) that the turf is colder than the air temperature, and its high heat capacity is what keeps it cool, and the artificial grass which transmits that coolness to the surface.

The Final Patriots Drive of the First Half

The first half was played over a time period of about 2 hours.  The first half wound up with a sustained drive by the home team, with multiple balls used as they got replaced by the ball boys.  Every ball that was used became wet with the cold dampness of the field.  They sat on the field at the line of scrimmage in between each play.  The center leaned on them and spun them in the grass.

Each time a ball gets replaced, it gets brought back to the bag, where it starts to warm back up to the air temperature of 48oF.  The time constant for warming of a dry ball is 15 minutes like before, but experimental measurements done later (see an analysis of Fig 21 of the Wells report below) show the time constant of a wet ball is more like 20 minutes — probably due to the layer of water on its surface needing to heat up as well.  And those first 20-25 minutes only bring it to 63% of the way to the ambient temperature in the ball bag.

At the end of the half, all the balls were put in the bag, and are brought back inside to a 70oF locker room.  The ball bags were then unzipped, and the pressure was measured in all the balls within 3-8 minutes.

The Pressures in the Balls

So how do we model the pressure in the balls?

Shouldn’t we expect to see a distribution of ball pressures?  Shouldn’t we find that the ball most recently used in the game will have the lowest pressure, a set of balls which have had more time to warm up, but are still slightly damp having a range of pressures, and winding up with a set of balls that are still dry because they were not used at the pressure suggested by the Ideal Gas Law as applied to the ambient air temperature?

Here is the distribution of Patriots football pressures reported in the Wells report represented graphically:

pressures2

Figure 1. Pressure in the Patriot footballs, Gauge 1.   This figure was created using the pressure gauge the Referee recalled as the one he used for the initial measurement prior to the game.

pressures

Figure 2. Pressure in the Partriot footballs, Gauge 2.

This top figure was created using the ball measurements using the Pressure gauge Referee Walt Anderson recalled was the one he used.  Since he had two gauges and there was some uncertainty in which gauge was used, the measurements are shown for both gauges.  The Wells report noted a .3-.45psi difference in the measurements of the balls by the different gauges.   The uncertainty in the actual measurement (using the same gauge) seems to be between .1psi and .2 psi.

Based on this distribution, we might expect that the 3 balls at the high end of the range were dry, and not used in the game.  The balls used in the game were slightly damp, and would be at the lower end of the range.  Additionally, the Wells report displayed an empirical difference of .1psi to .2psi difference between balls that were damp, and those that remained dry as they settled to the lower pressure (see Appendix A.)

What was the Field Temperature?

Predicting the absolute pressures require that we know the effective temperature that the grass will reduce the football down to (we don’t have this data, so here is a guess).  Remember that the ball sits on the grass at the line of scrimmage in between plays which sometimes can be several minutes.  The direct contact will allow for quickly reaching equilibrium faster than might be expected if it is just air.  If we assume a temperature of between 25oF and 30oF for the substrate, is it reasonable to assign a value of 38oF to the football that rests on the grass for some time?  This is 10oF lower than the ambient temperature.

An Explanation that Works!

A ball temperature 10oF lower than the ambient air temperature would bring the expected pressure to 10.75psi (see Appendix A).  This is well below all the pressures measured with the first gauge, and all but two of the balls with the other gauge.  From there, the measured pressure is entirely dependent upon the amount of warm-up time before the half-time measurement.  The amount of time, which would vary from 5-20 minutes based on the play of the game and the amount of time exposed to the locker room air would have created a wide variance in pressures, at values less than what would be expected from just the ambient air. This explains the distribution of pressures we see in the Patriots balls, and their lower pressures as well.

Four of the Colts balls were measured as well.  However, we don’t have measurements for all their balls, and we don’t know anything about whether those 4 balls were used in game conditions or not.  The 4 balls all measured at the high end of the range, to the right, and lie within measurement uncertainty at the same value.  If the above theory is correct, we might find that those balls had not been used in the game, or used very early in the game.  In any case, without having all the balls measured, we find that given the timing of the measurements, they are consistent with having been dry balls or relatively unused balls, and directly follow the conclusions of the Wells report.

Conclusion

There is strong reason to believe that the turf field was at a lower temperature than the surrounding air.  If so, we would expect to see a distribution of ball pressures in the Patriots ball bag at halftime due to the Patriots sustained drive leading up to halftime.  In fact, a distribution of pressures was measured at half-time. With reasonable assumptions, the actual ball pressures are consistent with the Patriot ball pressures measured in the locker room at the beginning of the game.  However, an investigation modelling this scenario must be done before making a final determination.

In addition, with limited information available, and the fact that the Colts balls were not on the field in a way similar to the Patriots drive leading up to halftime, the Colts ball pressures measured in the locker room are consistent with the pressures measured at halftime by the four Colts balls, as has already been determined in the Wells Report.

Appendix A

Analysis of Figure 21 of the Wells Report.

This graph is the result of experimentally modelling the changes in temperature experienced by balls, done in a controlled environment by the Wells Report scientists.  This is their game day scenario.  (This curve does not take into account the effect of a cold artificial turf field.)

Figure21
The Wells Report game day scenario depicts the game ball pressures expected from exposure to the ambient air temperatures as the game progressed. This does not take into account sitting on the artificial turf for extended periods of time leading up to half-time at 240 minutes.

 

The brown curves show the Patriots balls starting at 12.5psig. The blue curves show the Colts balls starting at 13.0psig.  The pressure drop at 120 minutes (balls brought to the field) appears to be an exponential curve (see Appendix C), and doing a rough fit, has a time constant of 15 minutes (i.e. it drops 63% in about 15 minutes).  The pressure rise at 240 minutes (halftime) does not as closely match an exponential curve, but with another rough fit, using the outer parts of the curve, the wet ball curves have a time constant of 20 minutes.  This extra time is significant because of the timing of the last Patriots drive, and subsequent measuring of the ball pressures at halftime.

Extrapolating to the Presence of a Cold Artificial Turf Field

So where would a ball recently used on the field be on this chart?  Suppose the pressure was reduced by .65psi by the field (effectively a 10oF temperature drop for .5psi, and then an additional .15psi because of the wet ball effect as shown in this chart).   It should be starting out 5 to 10 minutes before halftime at the 10.75psig point (well off the bottom of the chart).

If we had a sequence of such balls, starting at the 220th minute, and rising towards  the 11.25-11.4 psi pressure, we would find a range of pressures when the ball bag is finally opened, and the pressures start to be measured in the Officials Locker room.

Appendix B

January Boston area temperatures (from The Weather Underground — wunderground.com).

january-full
Weather chart for the month of January, 2015

 

Figure 3. Weather chart showing the temperatures in the Boston area during the month of January, 2015.  From Weather Underground (wunderground.com)

temp-expanded
Expanded view of the weather chart including the day of January 18. Note the sharp rise in temperature during the day of Jan 18.

 

Figure 4. Weather chart, expanding the section from Figure 3, to highlight game day on January 18th.  Note the dramatic rise in temperature (the red line) shortly before noon on that day.  The temperature leading up to that time averaged near 25oF.  The ground underneath the Artificial Turf, and the sand within the turf are expected to have been near that average temperature.

Appendix C

Explaining the exponential behavior of temperature changes.

Most objects warm up or cool down by exponentially approaching a final temperature from a starting temperature.   This is because the rate of temperature change is proportional to the difference in temperature.  I can go through the physics of this elsewhere, but it does involve calculus, so we will leave it out of this paper.   This is the resulting equation below for the simple ideal case, but it is written in terms of Pressure because in this case of no leaks and constant volume Pressure is directly proportional to Temperature via the Ideal Gas Law

P(t) = P1 – (P1-P0) * exp( -t/t0)

In words, this says that the Pressure as a function of time equals the final pressure P1 minus the difference between the two pressures P1 and initial pressure P0 times an exponential function which is decreasing in time, with a special timing constant t0.

The constant t0 is important.  If t0 is 15 minutes, that will mean that the pressures will be roughly 63% towards equilibrium in 15 minutes, after 30 minutes will be 87% towards equilibrium, and after 1 hour will be 98% towards equilibrium.That means balls on the field can be expected to maintain a significant Pressure differences resulting from the field even after 15 minutes.

Appendix D

An alternative explanation to the data was reached by the Wells report.  

The Wells Report reached the conclusion that a person must have released some air from the Patriots footballs sometime between the initial measurement and the halftime measurement.

The motive for this was to allow the Quarterback better handling of the ball.

By examining the distribution of pressures we find that this person must have let the air out of some balls and not others, and then relatively random amounts were removed, leaving the Quarterback with a wide distribution of pressures in the balls.

In their report, the uncertainty in the pressure measurements put the average pressure in the Patriots balls just outside the predicted values, close enough, so the verdict from the Wells report scientists was only “probably” this happened.

Inclusion of another source of cold temperatures (i.e. the Artificial Turf) should cause this model to be re-examined, and may change that “probably” rating.

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