### Sports

As I did at the end of 2013 & 2014, so I do again here at the end of 2015 to recount some travel experiences, which I don’t normally write about here. I need not give the whole setup again for the premise of such entries and see my blog from the end of 2013: Travels of Spocklogic. The notables this year (travel blogs I finished or made additions to) include:

That’s the summary for 2015. Some are carry overs from 2014, but I finished the blogs in 2015, after my last post on travels (see: Travels of Spocklogic II) in December 2014 or earlier if I made additions. As I alluded to in recent entries, I will take a break from this Cogito Ergo blog for a while in 2016. I’ve had 20 years of internet exposure and been blogging for 10 years (see: 20 Years of Internet and Mapping the Internet). I hope to return again with a fresh perspective down the line. There’s plenty to explore in the Cogito Ergo blog archives until then (see the link to: Browse Blog Posts). Best wishes for the New Year 2016! See you in the future…

The controversy surrounding the Patriots deflated footballs in the AFC Championship game on Jan. 18, 2015 has made some headlines in the news, and raised some physics questions. There has been talk of the ideal gas law, guage pressure vs. absolute pressure and relative temperature vs. absolute temperature. So, I take this as an opportunity to explain some of what all this means if you have followed it or have an interest in this. Lets begin with the NFL rule book stating:

The ball shall be made up of an inflated (12 1/2 to 13 1/2 pounds) urethane bladder enclosed in a pebble grained, leather case (natural tan color) without corrugations of any kind. It shall have the form of a prolate spheroid and the size and weight shall be: long axis, 11 to 11 1/4 inches; long circumference, 28 to 28 1/2 inches; short circumference, 21 to 21 1/4 inches; weight, 14 to 15 ounces.

By “pounds” it is assumed this means “pounds per square inch” or psi. However, this term refers to a guage pressure, so the actual pressure is really guage pressure + atmospheric pressure. To understand this remember that the pressure measured with a guage, such as you would with a tire, indicates pressure relative to the atmospheric pressure. Scientists often speak of atmospheres of pressure or atm and define Standard Temperature and Pressure for sea level at 273.15 K as 1 atm = 101325 Pa, or 14.69595 psi. (Note: Pa is another pressure unit called the Pascal and K is a temperature unit called Kelvin). So, consider 1 atm of pressure inside some container, that is, there is the same pressure inside the container as outside of it. Taking a gauge will not show 1 atm, but zero atm, since the pressure in the container is just the same as the pressure outside. This means that relative to the outside there is pressure in the container and it is in balance or equilibrium. This is the meaning of gauge pressure. Now, absolute pressure is technically more accurate when speaking of pressure as it is the force that some gas is applying to the container surface area, by virtue of the fact that on the order of 1E23 molecules are bouncing around off each other and the container wall because of thermal stimulation (heat), a form of kinetic energy.

Heat is not the same thing as temperature, though they are related to each other. Heat is a form of energy that flows from a hotter substance to a colder one, which have higher and lower temperatures, respectively. So, there must be a temperature difference for heat to flow. Consider our container again, and it has a certain amount of heat associated with it, which can be probed by measuring the temperature. Another container made of a different substance may have more heat associated with it but still measure the same temperature, because the second container has more mass. Anyway, that’s the concept, and wanted to get that out of the was to talk about temperature specifically. Temperature scales we commonly use everyday to speak about the weather are measurements relative to some reference value. In the Celsius scale, for example, the reference value is the freezing point of water, or 0 °C. Fahrenheit uses 32 °F as the freezing point for peculiar scientific historical reasons. All measurements are made relative to these reference values, for example in speaking of above or below freezing. The Celsius scale and the Fahrenheit scales are relative temperature scales and can have both positive and negative numbers. This is not so with an Absolute temperature scale, which has only have positive numbers. The Kelvin scale and the Rankine scale are absolute temperature scales. The Rankine scale, in which the degree intervals are equal to those of the Fahrenheit scale and in which Rankine (R) equals −459.7° Fahrenheit. The Kelvin scale, in which the degree intervals are equal to those of the Celsius scale and in which absolute zero is 0 degrees Kelvin and the triple point of water has the value of approximately 273 degrees Kelvin (K). The triple point is the temperature and pressure where the three phases of a substance (solid, liquid and gas) are in equilibrium. The triple point of water, 273.16 K at a pressure of 611.2 Pa, is chosen basis of Kelvin definition.

I explained all this (more than you the reader maybe wanted to know) because it is important to understand the difference between relative measurements and absolute measurements. This is important in scientific discussions describing values of things like pressure and temperature. So, we now have a better feel for things like gauge pressure vs absolute pressure and relative temperature versus absolute temperature. This allows discussion of the Ideal Gas Law that has been in the news. A good description of an ‘ideal gas’ is as follows: “An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces. One can visualize it as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other.” The Ideal Gas Law is characterized by three variables: absolute pressure (P), volume (V), and absolute temperature (T) and written as:

$PV = nRT$

where n = number of moles of the gas, with each mole (abbreviated as mol) containing 6.02214129 × 1023 atoms or molecules, known as Avogadro’s number. R is the gas constant (known as universal or ideal gas constant) universal  having a value of 8.314  J/K-mol or 10.731  ft3 -psi -lb/R-mol. As will be seen, we won’t need these constants, but just note them for reference. The utility of this equation is that one can hold any variable constant and see how the others change. In the case we want to examine, our container is a football, and we can tentatively take the volume to be constant and see how the pressure changes with a known temperature change.

Before proceeding, let’s review the scenario that transpired in Foxborough, MA on the afternoon and early evening of Jan 18, 2015 before and during the AFC championship game between the New England Patriots and the Indianapolis Colts. The timeline of events can be found here – Timeline: Key Deflategate events probed in Wells Report. Key events needed for calculations are that footballs were checked at 3:45 pm and found to be at or above the minimum 12.5 psi gauge pressure, though they were not recorded. At 8:28 pm during halftime, the footballs are retested and found to be below psi specifications. The exact measurements of the under inflated footballs can be found here – Finally, the halftime PSI numbers are known. A couple of additional pieces of information are needed: (1) the temperature at which the footballs were and the atmospheric pressure in Foxborough at that time and (2) the field temperature and atmospheric pressure when the footballs were taken off the field. Data is available about the weather conditions and can be found here – Foxborough Weather Conditions (Jan. 18, 2015). This is actually data from Norwood, MA about 20 miles away from Foxborough. Only a guess can be made of the locker room temperature (say 70° F or 294.26 K) before the game, but the atmospheric pressure was approximately 29.9 Hg (or 14.686 psi) from the weather data. During halftime the temperature was approximately 50° F (or 283.15 K) and the atmospheric pressure at 29.6 Hg (or 14.538 psi). We have the needed data now for some calculations on all the footballs, but let’s play with the ideal gas law, and assume a constant volume for the football at time 1 (3:45 pm) and time 2 (8:35 pm), that is V1 = V2 and

$P{_1}V = nRT{_1}$

$P{_2}V = nRT{_2}$

Combining these equations, V, n and R cancel out and we are left with:

$P{_2} = {{T_2}\over{T_1}}P{_1}$

I ran the numbers, correcting gauge pressure to absolute pressure from the weather data and using the Kelvin scale temperatures, for both alternate referee measurements (Piroleau and Blakeman). Initial minimum pressure was assumed to be 12.5 psi and 13.0 psi for the Patriots and Colts footballs, respectibvely, at T =294.26 K and atmospheric pressure of 14.686 psi (with absolute pressure being 27.186 psi), while final temperature was 283.15 K with an atmospheric pressure of 14.538 psi. The results for the final absolute pressure on the 11 Patriots footballs and 4 colts footballs are:

Patriots Footballs, based on initial pressure of 12.5 psi

Colts Footballs, based on initial pressure of 13.0 psi

Taking the average of the two alternate referees measurements, gas law results and difference between the them, results in the following:

Patriots: Initial pressure = 27.186, average halftime measured pressure = 25.836, gas theory pressure = 26.10, average ∆P = -0.324
Colts: Initial pressure = 27.686, average halftime measured pressure = 27.069, gas theory pressure = 26.64, average ∆P = 0.429

This means that the actual alternate referee measurements and the gas law agree to within 0.324 psi with the actual measurement for the Patriots footballs, being slightly lower than what the gas law would predict, while they agree to within 0.429 psi for the Colts footballs, being slightly higher than what the gas law would predict . Said in another way this is only about 0.32 to 0.43 in 27, or approximately 1.2 to 1.5% difference in measurement and theory. The total average pressure drop, gas law aside, for Patriots footballs is 1.35 psi and for Colts footballs is 0.617. Both teams show an average drop in pressure, so something happened to both teams footballs that caused them to measure lower pressure. With that said, it is also curious that Prioleau’s measurements are consistently higher than Blakeman’s measurements for Patriots footballs, while Prioleau’s measurements are consistently lower than Blakeman’s measurements for Colts footballs. I don’t understand this unless they switched gauges between measurement of Patriots and Colts footballs. This appears to be the case. There are a lot of unknowns here: Initial pressures of the footballs before the game were never recorded, the initial temperature in each locker room is not known, the time between when the footballs were taken off the field and when they were measured is not precisely known, and the football pressures at games end were presumably not measured. In addition, only 4 Colts footballs were measured because referees ran out of time according to the Wells Report, implying the Colts footballs were measured after the Patriots footballs, which may have given them more time to warm up. What was the time gap from officials going from the Patriots to Colts locker room? All we really know is that halftime was around 13.5 minutes, where measurements and reinflation took place.

Based on this analysis the conclusion would be (from a scientific point of view) that the footballs were not tampered with and pressure differences are partly explained by the Ideal Gas Law. Hooray for physics! The footballs were re-inflated at halftime, but it doesn’t see that anybody bothered to measure them again at the end of the game. Nevertheless, the Wells Report seems to reject the Patriots explanation using physics. The scientific analysis of “Exponent”, the consulting firm used in the Wells report, seems thorough. However, the Wells Report may have cherry picked what they wanted from the scientific report by Exponent to phrase what they wanted to say. A key statement in the Wells Report is: “Exponent concluded that, within the range of likely game conditions and circumstances studied, they could identify no set of credible environmental or physical factors that completely accounts for the Patriots halftime measurements or for the additional loss in air pressure exhibited by the Patriots game balls, as compared to the loss in air.” True, but both teams footballs lost pressure when measured at halftime, and the Patriots footballs measured 0.733 psi lower in lost pressure than the Colts footballs, according to my analysis. The Wells Report makes this to be ~ 0.7 psi. Interestingly, the difference in pressure of the footballs explained by the Ideal Gas Law -0.324 for the patriots and 0.429 for the Colts, an absolute difference of 0.753 psi. The point is that both teams have a pressure discrepancy that has to be explained by something. Instead, the Wells Report states, “According to our scientific consultants, however, the reduction in pressure of the Patriots game balls cannot be explained completely by basic scientific principles, such as the Ideal Gas Law, based on the circumstances and conditions likely to have been present on the day of the AFC Championship Game.” So, what about the reduction in pressure of the Colts footballs? What is that explained by? This is not thorough, unbiased science as presented in the Wells report. Somebody should scrutinize the Wells Report more, as it’s full of assumptions and goes so far as to say science does not explain the Patriots footballs pressure drop. If true then by the same token, what has caused the pressure drop in Colts footballs, and science must not be able to explain that either?

Well, the NFL punishment has been doled out and it seems more about Patriots lack of cooperation in the investigation now, or more specifically, Tom Brady’s participation. I can’t say I blame him for not cooperating in today’s hypersensitive society where every little detail is scrutinized and people are presumed guilty until proven innocent. Maybe the Patriots real flaw is a culture of trying to gain a competitive edge without actually breaking any rules. It’s a grey line on morality, but part of sports, past and present. Some of the ways players try to get an edge up seem based more on psychology or physiology than physics. Athletes will be athletes and rely on brawn more than brains most of the time. Coaches or managers on the other hand often know more than they admit to, but it’s like protecting the commander in chief and players do that as they should. Maybe the Patriots did tamper with the footballs, but maybe they didn’t – it’s a stretch at best (without complete data) to conclude they did. To single out Tom Brady just seems unfair to me. He seems an honest guy and others say that of him too. His character is at stake here and I hope he come out on top in challenging the Wells Report!

Enough said, and here are some facts about footballs:

The NFL rule says it must be a prolate spheroid. It has a volume V = ${4\over 3}{\pi}{a^2}c$, where a is half the length of the long axis and b is half the length of the short axis, called the major and minor axes, respectively. Since 1959, the inch has been defined and internationally accepted as being equivalent to 25.4mm, so with 1″ = 2.54 cm,  an NFL regulation football is 27.94 to 28.575 cm along the long axis (giving b = 13.97 to 14.2875 cm) and 53.34 to 53.975 cm around the short circumference, which requires using the formula for circumference = $2{\pi}r$ (giving a = 8.489 to 8.59 cm). Using these numbers in the formula for an oblate spheroid to be V = 4216.95 to 4416.02 cm3 (or 257.33 to 269.48 square inches).

A football weight is 14 to 15 ounces. With 1 ounce = 28.349 gm, a football is 396.886 to 425.235 gm. It is generally assumed that the air in a fully inflated football accounts for only about 10 grams of its mass. Is this true? Assuming a gauge pressure of 13 psi (89632 Pa) at standard temperature and pressure (T = 273.15 K and P = 101325 Pa = 14.69595 psi) gives the absolute pressure of the football to be and knowing the volume of a football in addition to the molecular weight of O = 15.9994 and  molecular weight of N = 14.0067, we can figure it out. By weight, dry air contains 23.2% O2 and 75.47% N2 by weight, which accounts for 98.67% of the weight of air. The actual major constituents of air are shown below:

Gas Ratio compared to Dry Air (%) Molecular Mass
M –
(g/mol)
Chemical Symbol Boiling Point
By volume By weight (K) (oC)
Oxygen 20.95 23.20 32.00 O2 90.2 -182.95
Nitrogen 78.09 75.47 28.02 N2 77.4 -195.79
Carbon Dioxide 0.03 0.046 44.01 CO2 194.7 -78.5
Hydrogen 0.00005 ~ 0 2.02 H2 20.3 -252.87
Argon 0.933 1.28 39.94 Ar 84.2 -186
Neon 0.0018 0.0012 20.18 Ne 27.2 -246
Helium 0.0005 0.00007 4.00 He 4.2 -269
Krypton 0.0001 0.0003 83.8 Kr 119.8 -153.4
Xenon 9 10-6 0.00004 131.29 Xe 165.1 -108.1

So, we can be a little more exact and include carbon dioxide (CO2) and argon (Ar) to account for 99.99% of air composition by weight. Adding the numbers scaled by weight fraction gives:

Molecular weight of air = (0.7547 x 28.02) + (.2320 x 32) + (.0128 x 39.94) + (.00046 x 44.01) = 29.1 g/mol

The volume of a football we know is 4216.95 to 4416.02 cm3 , so take V = 4316.5 cm3 as the average. Using the Ideal Gas Law we can calculate the number of moles of air in a football at standard temperature and pressure as: n = PV/RT = [(190957 Pa) x (0.0043165 m3)]/[(8.314  J/K-mol) x (273.15 K)] = 0.362 moles. Each mole has Avogadro’s number of 6.02214129 × 1023 molecules. With the molecular weight of air as 29.1 g/mol, we find that a football has and incredible 2.18 × 1023 air molecules (more that 2 billion billion) that add to approximately 10.5 gm. So, indeed it is true, and air only accounts for ~ 2.5% of its mass. We may conclude from this that the NFL source who reportedly told Kravitz (Bob Kravitz at WTHR in Indiana) that “officials took a ball out of play at one point and weighed it”, and would investigate the deflation of footballs by the Patriot’s, is sort of half-baked. Kravitz broke the story and posed it as possible cheating. That’s how these things start and take on a life of their own. Anyway, that’s all I have to say or share on this matter, and a wild one it is for sure. Here are some other links I can offer:

1.) Ideal Gas Law – Hyperphysics
2.) Gas law calculators – WebQC
3.) Humid Air and the Ideal Gas Law – The Engineering Toolbox
4.) Heat and Heat Vs. Temperature – Online Physics Tutorials
5.) Calculate mass of air in a tyre from pressure – Physics StackExchange

As I did at the end of 2013, so I do again here at the end of 2014 to recount some travel experiences, which I don’t normally write about here. I need not give the whole setup again for the premise of such entries and see my blog from the end of 2013: Travels of Spocklogic. The notables this year are a couple of blogs I finished and some reviews that may be of interest:

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That summarizes some travel selections for 2014. I did travel to Italy also in July 2014, and have some links to share for photo collections I put together for a special year in Erice to celebrate a 40th anniversary of the International School of Atomic and Molecular Spectroscopy (ISAMS):

Rino: 40 Year Erice Celebrations (2014) – Erice, Italy
2014 Erice Workshop: 30 July – August 5 – Erice, Italy
People (2014) – Erice, Italy
Places (2014)
– Erice, Italy

In addition, I traveled to China again this year in November 2014, but am still working on my travel blog for that, so it will have to wait until my 2015 account of my travels. I will make this type of entry something traditional at years end to cover where I have been and what I have done in travel ways. It’s all rather like the City on the Edge of Forever perhaps…

I don’t often write about my travels in this WordPress blog (Cogito Ergo) as I have another site for that (TravBuddy). In this year of 2013, I completed a number of travel blogs on that site that are worth noting and I give the links to them here. Mind you, I don’t know that any of my travel blogs are ever really completed. Each one is like a child I nurture and raise up, but always needs attention in future ways. Anyway, I suppose I list them here for my own reference and also to offer it to others who may be interested in my travels. There is some connection of the blogs, one to another in embedded personal ways, but are also self-contained. Here they are:

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Some of these blogs have been posted for some years, and I either added to them, made them more complete, and/or formed connections between them. Some of them are entirely new in 2013. They do tell a story in total I suppose and maybe that’s why I decided to make a sort of review of the Travels of Spocklogic here. They were also all the blogs featured on TravBuddy for me this year. My Italy blog (L’Avventura Dell Italia) seems never-ending and I have some more work to do on it, but the majority of important events are there for the most part. The last one in this list, the blog on China, is something I am still working on too, but intend (or hope) to complete it before the end of 2013. I suppose this collection of blogs forms a personal journey of sorts that I tried to form this year regarding my life and relation to travel. When I finish the China blog, maybe I will know what I have been endeavoring to understand and ultimately discover in my life. It’s not a teaser, or cliffhanger, but maybe more a matter of what I will embrace. Sounds enigmatic I suppose, but not really. It’s my personal perspective, the choices I make and what is ultimately best for me in a world of possibilities…

Boston Strong! insignia on the Green Monster

Congratulations to the Boston Red Sox on being 2013 World Series Champions! It is their third Championship in ten years and that is quite an accomplishment. Beyond that I think this team in 2013 was not just winning for sport or for personal glory, but also for the victims of the Boston Marathon bombing on April 15. Boston Strong! has been the phrase that New Englander’s have rallied around, and the nation has embraced. I’m not sure where it originated from, but supposedly it was first used in a Tweet by Red Sox third baseman Will Middlebrooks. Some have tried to capitalize a profit on it, which is reprehensible, but it has been something of a statement to give substance to what was felt in the aftermath of the Boston Marathon bombings. The Red Sox unified a city, in part, during a crisis and sports can sometimes do that like no other public endeavor.  Though the Red Sox won the World Series in 2013, it may be true this was a personal journey for many Red Sox players, baseball fans and the city of Boston!

Boston Strong! World Series Champion Red Sox

Another ring for Boston fans in a World Championship, but it says much more in a statement of perseverance from a team that went from worst to first in a year to capture “The Precious” in a World Series title and it speaks a lot about sportsmanship in what the team accomplished, and that they did it with heads held high, despite setbacks. Something to be admired in the face of adversity; Something we can all use as an an example in tribute to living – Boston Strong! When David Ortiz accepted the World Series MVP trophy, held it up high and said, “This is for you Boston!” – That spoke volumes and embodied the character of this 2013 Red Sox team.

Boston Strong! Full Page Tribute in Boston Globe

The New England Patriots have had a hard road as an NFL team. Between 1959 and 1970 the franchise played in four different fields (including Boston University Field, Harvard Stadium, Fenway Park and Boston College Alumni Stadium), until finally finding a home at Foxborough in 1971. They played their first game at Schaefer Stadium on Aug 15, 1971, defeating the Giants 20-14. Since then, the New England Patriots have had their ups and down. They earned a wild card berth in 1976 , but lost to the Oakland Raiders 24-21. Despite having some outstanding players over the years, the Patriots never managed to achieve any greatness. Unfortunately, their loss in Super Bowl XX to the Chicago Bears with a score of 46-10 embarrassed the franchise greatly. It was a long period languishing in mediocrity for the New England Patriots in the mid 1980’s to mid 1990’s.

Robert Kraft bought the team in 1994, promising to bring a an NFL championship to New England. In 1996 the Patriots made it to the Super Bowl again, but lost to the Green Bay Packers in Super Bowl XXXI, 35-21. Things were looking up for the New England Patriots, however, and they hired Bill Belichick as head coach in 2000, who molded the Patriots in the course of a year into a team capable of competing with the elite teams in the NFL. In 2001 the Patriots had a new stadium and all the pieces were in place, when disaster and magic happened at the same time. In the 2nd game of the 2001 season, Drew Bledsoe was injured and the backup Tom Brady was substituted. Bledsoe returned in game 3, but wasn’t quite right and Brady in the two games he appeared in was unimpressive. Once he found his zone, however, he was amazing and has been so ever since. It’s been a great decade of Patriots football since Tom Brady lead the Pats to their 1st Super Bowl victory in 2002 – and the Patriots are 3 for 4 in Super Bowl chances in that time and hungry for more. Interesting Fact – All 4 of those Super Bowls were decided by 3 points (that’s a sobering perspective):

2/3/2002 Super Bowl XXXVI: Pats – 20 ; Rams – 17
2/1/2004 Super Bowl XXXVIII: Pats 32 ; Panthers – 29
2/6/2005 Super Bowl XXXIX: Pats – 24 ; Eagles – 21
2/3/2008 Super Bowl XLII: Pats – 14 ; Giants – 17

So, don’t hate the Patriots because they are great. They have struggled long and hard to have this decade of success. They are great because they have struggled and eventually found their stride. Sure, it has come all at once and is equalling the kind of greatness that storied franchises have enjoyed for a long time. The New England Patriots are enjoying the kind of success that is rarely seen in sports and that is something to be applauded. The patriots are great because they have a good stadium, good management, good coaching, good players and good fans. That’s a recipe for success. This is not something that has always been there, but came over time, hard work, circumstance and perseverance.

I am favoring the Patriots in Super Bowl XLVI, and I composed a Pats vs. Giants poem in tribute: Here is the pre game tribute:

Do Not Go Gentle (Pre-Game)

Do not go gentle into an over confident role,
Patriots confuse and confound at opening play;
Rage, rage against Giants this Super Bowl.

Patriots pass, drive and find the hole,
Let Patriot deeds find Giants in dismay;
Do not go gentle into that good Super Bowl.

Offense, defense, special teams, all with soul;
Patriots remember 2008, and aim to take the day;
Rage, rage against Giants this Super Bowl.

Wild men, encounter any Giant in flight,
Challenge him to fumble on his way;
Do not go gentle into that good Super Bowl.

Giants will stumble without sight,
Patriots will have perfect vision this day;
Rage, rage against Giants this Super Bowl.

The outcome will surprise and delight,
Patriots are looking for Giants to slay;
Do not go gentle into that good Super Bowl.

BMW 1/26/2012

Do not go gentle – Super Bowl XLVI – Something to enjoy what ever side you are on…

Phenom is a word that describes Mark Fidrych, who died April 13, 2009, in an apparent accident on his farm. In 1976 he was as close as it comes to being as being as good as it gets. Rookie of the year, second in Cy Young voting, American League ERA leader, and top five in wins and shutouts. That’s pretty darn phenomenal for a rookie. What really made Fidrych a household name, however, in addition to his talent, was his personality. He talked to the baseball, fixed the dirt on the mound with his hands and congratulated his infielders for a good play inside the diamond. He only played baseball 5 years and retired after the 1980 season due to injury. There are few instances of someone who played so few years in a sport and are remembered for their character and accomplishments more than 30 years later. Mark “The Bird” Fidrych is one of them. He was one of a kind.

Mark Fidrych (1954 -2009)