Overview
During the Patriots - Colts game on January 18, 2015, the
temperature of the turf field is expected to have been colder than the ambient
temperature. It would be expected to
have an impact on the temperature/pressure of the balls used on the playing
field, as modern artificial turf fields are designed to maintain a reservoir of
cold that is transmitted to the surface using the artificial grass. This keeps the playing surface cool on hot
days. Using reasonable assumptions, the distribution
in the pressures and the lower absolute pressure of the Patriots footballs at
halftime is consistent with this expectation; however, experimentation is
required to confirm this expectation.
Inclusion of this effect removes the requirement of a person removing air from the Patriots footballs. It can be entirely explained by the weather.
This effect was not
discussed in the 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 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.
Undoubtedly, under the turf field was frozen earth, probably
matching the average temperature of the last week, about 25oF (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.
Is it possible the field has 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 20-25 minutes -- probably due to the layer of water on its
surface needing to heat up as well. And those
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, into the 70oF locker room, the ball bags 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:
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.
Figure 2. Pressure
in the Partriot footballs, Gauge 2. Footballs to the left are the ones we
expect were recently used in the field of play.
The three to the right may have been dry and not used.
This top figure was created using the ball measurements
using the Pressure gauge Referee Walt Anderson recalled was the one he used. Since there was some ambiguity in which gauge
was used, the measurements are shown for both gauges. The Wells report noted an average of
.35-.4psi difference in the measurements of the balls. The uncertainty in the actual measurement
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. This 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.
Such a temperature would bring the expected pressure to 10.75psi
(see Appendix A). This is below all the
pressures measured with one gauge, and all but two of the balls with the other
gauge. From there, the pressure is
entirely dependent upon the amount of warm-up time before the half-time
measurement. The amount of time, 5-20
minutes, that we might give for that warm-up entirely explains the distribution
of pressures we see in the Patriots balls.
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.)
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, 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 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).
Figure 3. Weather chart showing the
temperatures in the Boston area during the month of January, 2015. From Weather Underground (wunderground.com)
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
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.