Interactive DeflateGate Simulator
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On January 18, 2015, the AFC Championship Football game between the Patriots and Colts, was played. The Patriots were accused of
deflating footballs in what has infamously become called DeflateGate. A subsequent investigation by the NFL led to a report about the pressure
of those footballs, and how much of the pressure change was do to the weather that day, and how much, if any, was due to tampering by the Patriots.
This computational model takes us from the initial measurement of the footballs before the game, to their measurement in the officials locker
room at half-time, where the pressure of the footballs was rising while the measurements were being taken. The question of which gauge was used,
and reconciling the difference in measurement between the Colts and the Patriots balls are important to this consideration.
While the simple computations of the Ideal Gas Law of Physics can be performed quickly, the complexity of the real situation, with changing pressures
temperatures, and a large number of permutations of starting conditions make testing of the conclusions of the NFL Report difficult.
This simulator puts that capability into the hands of everyone.
What you will find!
Contrary to the conclusions of the Wells Report, there are solutions to the problem where the Patriots balls and the Colts balls are consistent with one another using the Logo gauge.
Figure 27, a lynch pin of the conclusions reached by the Exponent Report cannot be reproduced, and does not agree with the Ideal Gas Law.
In a surprising result, the solution where the pre-game Patriots balls were measured with the Logo gauge, and the pre-game Colts balls were measured with the Non-Logo gauge produces the best fit.
The simulator is designed to be run without much guidance for those familiar with the Wells/Exponent Report.
Check out the DeflateGate Workbook for more informationThe only thing you really need to know is the definitions of the fields. Each
field is restricted to a choice of values within the ranges specified by the Paul Weiss group as reported in the Exponent report.
Click on the icon beside each field for the definition of each field. Just select a new value for that field
and see how the chart changes.
You should try to get the border of the round balls to glow green. One ball on the chart -- the blue one -- represents the average value of
the referee football measurements at halftime for the colts balls, and the the red ball represents the patriots balls. If you get any piece of
the ball to lie between the wet curve and dry curve for the respective teams, it should glow green.
The border color represents one of three conditions:
Red - The pressure lies outside the acceptable range for that ball.
Yellow - The pressure is within 2 standard error of the acceptable range
Green - The pressure is within 1 standard error, or lies within the acceptable range
The cooling of footballs is about heat transfer out of the football. Since the heat energy is proportional to the temperature, we can simply talk
about the rate of Temperature change. This rate is proportional to the temperature difference. This yields the differential equation:
f'(t) = dT/dt = alpha * (Tf - T)
This leads to a simple exponential.
In addition, there is heat lost to a wet football due to evaporation loss on the surface of the football. The final temperature of the football
will be at a point where the heat loss due to evaporation equals the heat gain due to the temperature difference. This must be at or above the wet-bulb
temperature, and below the actual air temperature. If we determine this temperature experimentally as Te, we can, as a first order approximation,
estimate the governing equation to be:
f'(t) = dT/dt = alpha * ((Tf - Te) -T)
This is not completely correct, as we might expect that the actual Temperature dependence to depend on the saturation vapor density near the
surface of the football, which itself has a complex Temperature dependence which rises non-linearly with Temperature (i.e. things evaporate faster
at higher temperatures. This might cause the curve to appear slightly flatter than a full inclusion of this process would suggest).
Finally, there could be other effects, such as contact of a portion of the football with a cold field. These can be tested by modifying the
underlying code, and adding the heating and/or cooling rates to this governing equation.