I posted this at the Kraft apology thread.............
If Mortensen's initial report was inaccurate then I agree this was much ado about nothing. One still must be curious, if he is objective, as to why one ball would register 2.0 psig below regulation.
Here's a link to the Headsmart page which directs to the findings of Tom Healy's experiement:
http://www.headsmartlabs.com/#in-the-news
Mr. Healy found that in this test a total pressure loss of 1.82 psig was measured, taking 12 footballs from 12.5 psig in dry 75F conditions to 50F wet conditions.
I've reviewed Healy's report and have commented on the two threads here at Cowboyszone that have dealt with this issue. I still find Healy's attempt to reproduce real-time conditions to be somewhat flawed.
Healy, based on the combined gas law and Ideal Gas Law derived a delta P of 1.07 psig based on temperature differential alone.
I posted my calculations and underlying assumptions on the two topic threads here and derived a delta P of 1.03 psig. Unlike Healy, I corrected for a lowering in barometric pressure during the game of roughly 2 mm Hg (0.09" Hg). Accounting for change in P-atm lends to a more accurate calculation of P-gauge when solving for absolute pressure.
I also started at an indoor temp of 72F (versus Healy's 75F). Both are within reasonable range for indoor conditions. Likely, many household and office thermostats are found within this range. I took the halftime temp of 49F from real-time meteorological data (vs 50F for Healy). Again, a minor difference. I accounted for some equilibration of air temp inside the footballs when they were brought into the officials' locker room at the half, allowing for a positive delta T of 2F, arriving at 51 F. My overall delta T in running the Ideal Gas Law, assuming constant volume (V1 = V2) was 23F; cf. Healy at 25F. I assumed the balls were brought into the officials locker room in either a ball bag or ball cart and allowed about 10 minutes for the officials to get coffee, use the restroom and get to the task of measuring the ball pressures.
Again, I was trying to be conservative and reasonable in my underlying assumptions.
Healy wetted the balls by immersing them in cold water, thereby saturating the leather completely. He then placed them in a 50F room with a fan blowing on them.
This is where I must critique his experiment - and I have shared my thoughts here previously. We must look at how teams take care of footballs during outdoor games in inclement weather. Home teams provide 12 more balls during outdoor games than indoor. Ball care is not an issue in September (for the most part) or during most games that the Dolphins play at home, but it becomes an issue later in the year for many teams playing outdoors. In bad weather - snow or rain - ball boys keep their team's balls covered and out of the elements. Balls coming to the sidelines from the official following change of possession, or prior to a kick (FG or punt) are immediately towel-dried and then covered in a cart or bag. Pre-game warm-ups do NOT involve game balls which are turned in to the officials more than two hours before kickoff. Game balls are kept as dry as possible throughout the game. By keeping them covered and in a ball cart or ball bag, that may provide a small, yet measurable, protection from ambient temperature drops experienced during outdoor games. So, to derive empirical data based on wetted, saturated balls left with air blowing over them in 50F is not a real-time simulation of game conditions. Not unless the NE Patriots and Indianapolis Colts - and very other NFL team - has their 12 game balls sitting on the bench or on the ground exposed to the rain and cold (or snow in Green Bay or Chicago or Pittsburgh......) for the entire game. Let us be realistic here: teams do NOT do that. Mr. Healy did in his experiment, but this is not normal practice, either in the NFL or collegiate level.
Healy derived an additional pressure drop of 0.75 psig (11.43 psig - 10.68 psig) based on the wetting/exposure to ambient conditions phase of his experiment, which incidentally followed two hours of balls sitting in a cold room at 50F. His overall delta P was therefore 1.82 psig (12.5 psig - 10.68 psig).
A more accurate reproduction of real-time conditions would be to maintain the balls in a 50F room for 2 hours, wet a ball while keeping the others dry, approximate a time the ball "in play" would remain wet to mimic the possession time of each NE possession during the first half, then dry the ball thoroughly, place it in a ball bag with the other 11 balls, take another ball, saturate it, keep it exposed to the elements (as Healy did, a wet ball with a fan blowing over it in a 50F room), dry that ball, place it in the ball bag and repeat the process for the length of time the first two quarters took.
This would replicate real-time conditions better. I suspect it would also result in less volume expansion as calculated (from Boyle's Law, which demonstrates an inverse relationship between pressure and volume at constant T) by Healy.
Mr. Healy, using a delta P of 0.75 psig and assuming P-atm of 14.7 psi arrives at a volume expansion of 3% to account for the 3% reduction in absolute pressure. Here, Healy should have confirmed his findings. The volume of a footbal is: V = 4/3 * pi * a * b^2, where a is half the length of the ball along the major axis, b the radius of the ball along the minor axis of the football (2a = length of ball; 2b = diameter of ball at fattest part, center of the laces). A 3% increase in volume (volume of football based on a = 14.0 cm, b = 8.5 cm is 4237 cm^3 or 4237 cc) would increase V from 4237 cc to 4364 cc. Increasing V by a factor of 1.03 is equivalent to increasing b by a factor of 1.0149 (1.015). This would increase the circumference of the ball at its fattest part from 53.41 cm to 54.2 cm. The experiment should have measured initial and final diameter and circumference to verify the inferred volume increase based on Boyle's Law.
One thing that must be answered: if Healy's findings support New England's position, then that would appear to contradict (a) rebuttals of Mortensen's position, which Rogah and HoustonFrog seemingly support; and (b) the findings that the Colts balls were ALL within spec. You see, if the Colts' balls were generally at the high end of compliance, i.e., 13.5 psig, then based on a delta P of -1.82 psig (accounting for delta T and saturation effects on pebble-grained cowhide) all of the Colts balls would be found to be at approx. 11.7 psig - hence they would fail to meet NFL specs. In effect, if Healy were to "clear" the Pats, he would simultaneously place the Colts balls out of spec and in violation; however, the NFL did not find the Colts balls to be out of spec. Thus, Healy did not reproduce game conditions on the visitor's side of Gillette Stadium on January 18, 2015.
One more critique of Healy's experiment: composition of the air he used to inflate the balls at 75F to 12.5 psig should have been included. Was he using dry air? What was the % water vapor of the air if not dry? A complete analysis of delta P should include the effect (potential effect) of vapor pressure of water as a function of T. Using Dalton's Law of partial pressures, one can approximate the loss in internal ball pressure based on the % by volume (correlates to decimal equivalent of molar fractions of air and water vapor) of water comprising the air in the ball. For example, water has a vapor pressure of 26.7 mm Hg at 75 F (27C) and about 10 mm Hg at 50 F (11 C). That is a change of vapor pressure of about 16.7 mm Hg, which is roughly 0.32 psig. If the air used toe fill the balls was relatively dry, one need not account for the delta P due to decreased vapor pressure, but composition of the air would be needed to know for certain.
I would be interested to see if other engineers peer review Healy's experiment.
I have worked for years with attorneys preparing cases, and I know that data (when cases do go to court) and conclusions based on said data are thoroughly scrutinized.
If this in is an issue of seeking an unfair competitive advantage or simply a major misunderstanding of facts, I would hope that if one party relies on Mr. Healy's study that it would undergo careful analysis by competent engineers and scientists.
I've taken it probably as far as I care to go, and am not sure if anyone is even following this any longer.
I find it interesting that Rogah rebuts virtually everything that runs counter to his position, but I have not seen him respond or attempt to refute anything I've said following my initial post.
-MV
