{"id":1057,"date":"2015-02-04T13:51:07","date_gmt":"2015-02-04T18:51:07","guid":{"rendered":"http:\/\/test.pegasuslectures.com\/blog\/?p=1057"},"modified":"2015-02-09T18:47:18","modified_gmt":"2015-02-09T23:47:18","slug":"balls-and-boyles-on-cavitation-and-football","status":"publish","type":"post","link":"https:\/\/www.pegasuslectures.com\/blog\/index.php\/2015\/02\/04\/balls-and-boyles-on-cavitation-and-football\/","title":{"rendered":"Footballs and Boyle’s : On Cavitation and Deflate-gate"},"content":{"rendered":"

\"Patriot_Statue\"OK!\u00a0 Full disclosure: I am a New England Patriots fan through and through, having grown up and lived much of my life in Massachusetts.\u00a0 Leading up to Superbowl\u00a0 XLIX, there\u00a0 was incessant media coverage discussing potential \u201ccheating<\/a>\u201d in the AFC title game through the use of deflated footballs.<\/p>\n

\"\"

Cavitation as Results From a Propeller*<\/p><\/div>\n

Whether or not someone intentionally deflated game balls cannot be disproven by science, but \u2026 science can at least offer a plausible alternative, using the same equation that explains how cavitation<\/strong> occurs during peak rarefactional pressure (and not the peak compressional phase of the pressure \u2013 as is often mistakenly assumed<\/em>).\u00a0 The equation derives from the ideal gas law<\/strong>.<\/p>\n

The term cavitation comes from the Latin term \u201ccavus<\/em><\/strong>\u201d which mean a cavity, pocket, or hole.\u00a0 Remember that cavitation is a rapid<\/span> phase transition to a gaseous state, creating a cavity within the medium.\u00a0 When discussing why cavitation occurs during rarefaction, I usually refer to Boyle\u2019s law<\/strong>.\u00a0 In reality, Boyle\u2019s law is\u00a0 just a special case of the ideal gas law<\/span>.<\/p>\n

 <\/p>\n

PV = nRT<\/strong><\/p>\n

This equation states that there is a relationship between pressure (P<\/strong>), Volume (V<\/strong>), and Temperature (T<\/strong>).\u00a0 The variable n<\/em><\/strong> stands for the \u201camount of the gas, specified in moles\u201d, and R<\/strong> is known as the gas constant.\u00a0 Cavitation typically occurs in an extremely short time duration<\/span>, implying that the number of moles (n<\/em><\/strong>) and the temperature (T<\/strong>) remain constant.\u00a0 This means that the ideal gas law can simplify down to an equation that states pressure times volume equals a constant, also known as Boyle\u2019s Law.<\/p>\n

\"\"How does Boyle\u2019s law explain cavitation occurring during rarefaction and not compression?<\/em><\/strong>\u00a0 During compression, the exterior pressure on the gas bubble increases, making the bubble shrink.\u00a0 In other words, as the external pressure goes up, the internal volume goes down.\u00a0 This is similar to what happens when a balloon is brought deep under water; the balloon collapses but never pops.\u00a0 Conversely, during rarefaction, the pressure exterior to the gas pocket decreases allowing the internal pressure to expand the bubble.\u00a0 Again, since the pressure times the volume is a constant, as the pressure decreases, the volume increases<\/strong>.\u00a0 If the bubble (volume) expands enough, the membrane is stretched too thin and the bubble implodes.\u00a0 This is similar to taking a balloon up in an airplane.\u00a0 As the plane gains altitude, the cabin air pressure decreases and the balloon gets larger. Eventually, the balloon will expand to the point where its latex\/rubber film cannot maintain the stretch, and the balloon bursts inwardly.<\/p>\n

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\"deflate\"Returning to football and \u201cDeflate-gate<\/em><\/strong>\u201d \u2026 How does this same equation potentially exonerate the Patriots from wrongdoing?\u00a0 In this case, we cannot simplify the equation in quite the same way as in our prior discussion since the temperature cannot be assumed to be constant<\/span>.\u00a0 In fact, the whole argument hinges on the temperature NOT<\/strong> remaining constant.\u00a0 In essence, the equation tells us that for a fixed volume (i.e. no conspiracy to remove air from the footballs) as the temperature changes the pressure changes<\/span>.\u00a0 Since Tom Brady of the Patriots seemingly likes the football less inflated<\/a> than some other quarterbacks, the Patriots would naturally inflate the ball to the lowest allowed limit<\/span>.\u00a0 If the footballs were inflated in a warm room, when they are taken outdoors on a winter afternoon in Foxboro, Massachusetts, the temperature decrease could result in a pressure decrease below the allowed limit.<\/p>\n

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\"foxboro\"But why would this not also be true for the Colts?\u00a0 The answer is simple, although the stadium temperature was clearly the same for the Colts, the starting condition could easily be different.\u00a0 Let\u2019s say that the Colts generally inflate their footballs to a higher allowed pressure (perhaps because the ball flies farther when kicked).\u00a0 Let\u2019s also assume that Indianapolis inflates the footballs in a room that is colder than the room in which the Patriots inflate their footballs.\u00a0 Now when that ball is taken outside to colder temperature, the pressure drops less than for the Patriots, still remaining within the allowed limits.\u00a0 Hence, science can provide a reasonable explanation for what otherwise requires assuming that everyone is trying to cheat in a way that makes little to no sense.\u00a0 Besides, the Patriots scored only 17 points in the first half of the game when the footballs had lower pressure, and scored 28\u00a0points after the footballs were re-inflated to NFL specifications.\u00a0\u00a0 It sounds like the argument for advantage just fell into a cavus.<\/p>\n

Frank Miele, MSEE \u00a0President, Pegasus Lectures, Inc.<\/a> ,\u00a0graduated cum laude from Dartmouth College with a triple major in physics, mathematics, and engineering. While at Dartmouth, he was a Proctor Scholar and received citations for academic excellence in comparative literature, atomic physics and quantum mechanics, and real analysis.<\/em><\/p>\n

*<\/strong>\u00a0[Cavitation photo] Reprinted with permission from Ultrasound Physics and Instrumentation, 5e<\/a>.\u00a0Photo courtesy of Professor S.A. Kinnas, Ocean Engineering Group, University of Texas at Austin.<\/em><\/p>\n

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OK!\u00a0 Full disclosure: I am a New England Patriots fan through and through, having grown up and lived much of my life in Massachusetts.\u00a0 Leading up to Superbowl\u00a0 XLIX, there\u00a0 was incessant media coverage discussing potential \u201ccheating\u201d in the AFC … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[16,1],"tags":[],"_links":{"self":[{"href":"https:\/\/www.pegasuslectures.com\/blog\/index.php\/wp-json\/wp\/v2\/posts\/1057"}],"collection":[{"href":"https:\/\/www.pegasuslectures.com\/blog\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.pegasuslectures.com\/blog\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.pegasuslectures.com\/blog\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.pegasuslectures.com\/blog\/index.php\/wp-json\/wp\/v2\/comments?post=1057"}],"version-history":[{"count":26,"href":"https:\/\/www.pegasuslectures.com\/blog\/index.php\/wp-json\/wp\/v2\/posts\/1057\/revisions"}],"predecessor-version":[{"id":1093,"href":"https:\/\/www.pegasuslectures.com\/blog\/index.php\/wp-json\/wp\/v2\/posts\/1057\/revisions\/1093"}],"wp:attachment":[{"href":"https:\/\/www.pegasuslectures.com\/blog\/index.php\/wp-json\/wp\/v2\/media?parent=1057"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.pegasuslectures.com\/blog\/index.php\/wp-json\/wp\/v2\/categories?post=1057"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.pegasuslectures.com\/blog\/index.php\/wp-json\/wp\/v2\/tags?post=1057"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}