Gravitational Attraction
What would happen if two people out in space a few meters apart, abandoned by their spacecraft, decided to wait until gravity pulled them together? My initial thought was that …
Football Physics
Why I'm not Convinced the Patriots Cheated
In #articles
In another post, I outlined how the drop in pressure was entirely consistent with what was measured with the laws of physics. That post was done when the only data was the drop in pressure - nothing specific about the methods, or the data. Then the 243 page Wells report came out with the methods and the data, as well as a sophisticated statistical report (see the Appendix A, page 229). Once I saw (one page 231 (A-2)) that the pre-game pressures were "Assumed Pressure at Start of Game", I realized that there was nothing that the report could say. The fact that there weren't measurements taken at the beginning of the game invalidates nearly any analysis. I was going to leave it at that, and possibly explore the problem as an introductory statistics problem, but basically dropped it.
Then, I was forwarded this critical analysis of the Wells report by the American Enterprise Institute (AEI) and my interest piqued again. There is a nice New York times piece to go along with the detailed report. Suddenly it became clear that:
- the methods used in the Wells report were unorthodox, and basically incorrect
- there is another alternative explanation for their finding that the Colt's footballs were significantly more inflated than the Patriot's footballs - physics again!
From the Wells report plots, the time constant of a football going from one equilibrium pressure to another with a change in temperature comparable to that observed on the day is about 10 minutes. What I hadn't realized in my initial analysis was that the Patriots' footballs were measured first during the half-time, and the Colts footballs measured afterward - right at the end of half-time. This is a delay of about 10 minutes. This leads to the following two consequences:
- The Patriots' footballs are measured when they are the lowest pressure, or near lowest pressures, right after coming in from the cold.
- The Colts' footballs are measured when they have had an ample chance to warm up by the end of half-time. A delay of 10 minutes would bring the pressure up to about 66% of the distance from the cold temperature equilibrium pressure to the high temperature equilibrium pressure given the measured time constant of the football. It would be closer to 75% if the delay is nearly a full 15-minute half-time.
You don't even need to throw in some confusion about which gauge was used a the beginning of the game vs the middle of the game (with a difference of 0.4 psi!). You easily have a situation where, plausibly, all footballs could have been in regulation at the beginning of the game yet end up with one set higher pressure on average than the other in the middle of the game - even with no foul play.
Frankly, I've found this so-called sophisticated quantitative analysis a great example of a smoke screen for alternative motivations.
Finally, I want to add that although I am not convinced that the Patriots cheated, I am also not convinced that they didn't. However, the burden of proof (as in the court of law) lies squarely with the prosecution, not the defense - and they have clearly not made their case.
