The Physics of Natural Football Deflation

Discussion in 'Fred's House of Pancakes' started by SageBrush, Jan 21, 2015.

  1. SageBrush

    SageBrush Senior Member

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    Slate published on amusing FAQ on the controversy over possible play with too low pressure footballs in this week's game between the NE Pats and the Indy Colts.

    They published that the footballs would have had to be inflated in a 85F room for the reported drop of 2 psi to be due to bringing the balls out to 50F weather. I was curious about the math, and came up with quite a different number, so the physics is below along with my calculation. Please correct any error(s):

    The ball is presumed to keep its shape, so volume is constant
    pressure is proportional to temperature
    50F is 10C
    Absolute zero is -273C

    To make the arithmetic easier, I presumed the ball was 12 psi before the game started, and 10 psi when checked at halftime

    So... If the ball was 10 psi at 50F, the pre-game inflation ball was 20% higher pressure, and therefore 20% higher temperature. 283K*1.2 = 340K. That is a pre-game inflation pressure of 67C. Not natural, and way over 85F.
     
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  2. hkmb

    hkmb Active Member

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    I've noticed that American so-called "foot" "balls" have some sort of inflation problem. They seem to end up in some sort of ovoid shape, rather than the correct spherical shape. This also seems to prevent them from having adequate contact with the players' feet. The objects are therefore neither foot-related, nor balls.

    I hadn't realised it was a physics problem. Interesting.
     
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  3. wjtracy

    wjtracy Senior Member

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    Dr. Sage did you assume P1 = 14.7 + 12 = 27 psia
     
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  4. bisco

    bisco cookie crumbler

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    there's a lot of deflated balls around here this week.:oops:
     
  5. SageBrush

    SageBrush Senior Member

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    I didn't!
    I see what you mean though, the pressure ratings should be calculated off an absolute zero, just like the temperature.

    Thanks for the correction.

    Revised calculation:
    The ball pressure dropped from 26.7 to 24.7,
    So the initial T in kelvin would have been (26.7/24.7)*283 = 306K
    306K = 33C, or 93F.

    Hmm. Still too hot as a reasonable explanation, but if the balls had been laying on the ground they may have cooled down to quite a bit below the ambient 50F.
     
    #5 SageBrush, Jan 22, 2015
    Last edited: Jan 22, 2015
  6. bwilson4web

    bwilson4web BMW i3 and Model 3

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    Well if any of the officials drove a Prius, they would have pulled out their pressure gauge and made sure their balls are fully inflated. Reminds me of:


    Bob Wilson
     
    #6 bwilson4web, Jan 22, 2015
    Last edited: Jan 22, 2015
  7. wjtracy

    wjtracy Senior Member

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    Yes it's just like tire pressure calcs.
    Constant volume assumption probably good (works for tires).

    I am not following the news story too closely but possibly the compressor heats up the air a little so I guess that's plausible.
    Of course I assume football managers they know all that from experience, so no excuses please.
     
  8. SageBrush

    SageBrush Senior Member

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    I've thought about this a bit more and checked the calcs again:
    If the pre-game balls were inflated at 80F and then checked at half-time at 41F, a 2 psi drop in pressure is expected.

    Since the balls likely lie on the ground most of the time, a 41F temperature sounds reasonable to me.
    All in all, natural variation is a reasonable explanation and no further action should be taken by the NFL against the team unless a smoking gun appears. Just my opinion, of course.

    And who knows, the NFL may decide to set a pressure and a temperature range in the future. Could physics actually triumph ?
     
  9. fuzzy1

    fuzzy1 Senior Member

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    ^^ Did anyone perform some due diligence by checking the game balls provided by the other team? The temperature shift should change both equally.
     
  10. bwilson4web

    bwilson4web BMW i3 and Model 3

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    Ahhh, the football incubator with constant pressure and temperature regulator.

    Both teams played with the same d*mn ball. If it helped one quarter back and receivers, it helped the other. Someone is smoking something to claim just one team benefited.

    Perhaps just coat the ball with lard and be done with it. The fumbles would make the game more interesting . . . and boxi^i^x^o^b hockly-like. (i.e., rugby for those who drive on the wrong side of the road)

    Bob Wilson
     
  11. fuzzy1

    fuzzy1 Senior Member

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    I'm seeing multiple statements that the balls are changed very frequently. Each team supplies the balls for its own offensive plays, and different balls are used for kicking. So, no, they are not using the same single ball in the same way.
     
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  12. SageBrush

    SageBrush Senior Member

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    There is quite a bit of room for legal gamesmanship:
    • One team could put the balls on the cold ground, while the other team could put them in the ball boy's lap
    • One team could inflate the balls in a conditioned interior while the other team inflates at outside temperatures
    • One team could inflate the pre-game ball to the minimum required while the other team chooses the maximum permissible.
    Unless the league normalizes the pressure to temperature, there is going to be substantial variation in ball pressure between teams since they already allow each quarterback to set the ball pressure the way each one prefers.
     
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  13. bisco

    bisco cookie crumbler

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    a lot of chatter around here, but no answers so far. i'm waiting for someone to ask the refs, since they handle the ball between every play, why didn't they notice anything, yet the indy receiver who intercepted it did?
     
  14. SageBrush

    SageBrush Senior Member

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    I think the Colt's footballs were also checked. I'd like to know how much the pressure changed from pre-game to halftime.
    Just out of curiosity .... the burden of proof that cheating occurred is on the NFL.
     
  15. FL_Prius_Driver

    FL_Prius_Driver Senior Member

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    The balls are neither a fully rigid enclosure (where only the pressure varies with temperature) nor a fully elastic enclosure (where essentially only volume varies with temperature). There is some amount of elasticity, so more air needs to be let out than what is noted to reduce the pressure than what the calculation show. I do not know what this factor is.
     
  16. fuzzy1

    fuzzy1 Senior Member

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    • One team could being compressing (heating up) ambient air for injection into the ball just before handing the balls over for inspection, while the other could be using highly compressed air already cooled to ambient (or even a liquid CO2 cartridge), so it cools upon injection.
     
  17. bisco

    bisco cookie crumbler

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    this is why the umps just keep chucking out new balls in baseball. if the pitcher even looks sideways at the ball, ump chucks out a new one.
     
  18. wjtracy

    wjtracy Senior Member

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    I am recommending they fill with N2.
    Just kidding...
     
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  19. wjtracy

    wjtracy Senior Member

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    ...sounds like the balls are approved (weighed?) by the Ref before the game. So to show up "light" low weight a few hours later the implication would have to be someone is tampering with the balls after approval. The Colts are saying what they noticed is the balls they intercept are light-weight.

    Unless something really sinister going on (see below), once the Ref approves it, the NFL cannot say well we approved it, but we did not check well enough.

    Or how about filling with O2 which diffuses 4x faster than N2? Or any molecule (Argon?) smaller than N2 on a molecular scale...no way these guys are not that smart?? Any chemistry majors on the team? Or finding a way to make a slow leak? or selecting balls ahead of time they know have a very slow leak rate? Mositure/water I guess could be played with.

    Anyone know how much pressure a fully inflated football would lose over 24-hrs?

    Check this out...sounds like they really manipulate the balls heavily before use...
    Qbs Get On The Ball, Reach Goal - Sun Sentinel
     
    #19 wjtracy, Jan 22, 2015
    Last edited: Jan 22, 2015
  20. bisco

    bisco cookie crumbler

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    funny story in usa today, if you believe the science.
     
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