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Geocritter's avatar
Geocritter
Explorer
Apr 22, 2014

How many cubic feet of air does my 16" tire hold?

I’ll be frank, I’m mathematically challenged. Don’t get me wrong, I can read a formula and plunk numbers into a calculator I just don’t “think” mathematically. So my question is how many cubic feet of air does one of my 235/85R16 tires hold when empty and when filled to 70psi?

I’ve googled the question already and found numerous responses that eventually turned to gibberish in my non-mathematical brain, plus posters would argue with one another about their calculations. It didn’t give me a lot of confidence.

FWIW I solve most physics type problems by 3D visualization. I mentally construct a working 3D model of the problem. I’m nearly always correct in my assumptions; I just fail when it comes to supplying the math needed to prove it.

Steve
Class A

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  • BB_TX's avatar
    BB_TX
    Nomad
    Apr 22, 2014
    Excluding the expansion of the tire, the volume of space inside the tire would be the same at 70 psi as at 0 psi (relative to atmospheric pressure). However there would be more air in the tire at 70 psi than at 0 psi due to the fact that it is compressed.
    If you took 1 cubic foot of air from a compressor at 70 psi and put it into a balloon, that balloon would expand to a much greater volume than 1 cubic foot. The compressor takes a large volume of air and compresses it into a much smaller volume.
    I remember studying the change in volume vs pressure in my college engineering days, but far to distant in my memory to remember how to calculate it.
  • rgatijnet1's avatar
    rgatijnet1
    Explorer III
    Apr 22, 2014
    Geocritter wrote:
    I purposely didn’t mention why I needed this information because I didn’t want the thread to go off on a tangent. But here goes, I’m planning on a keeping a 2,000psi nitrogen tank (and regulator) on board for my compressed gas needs. I’m torn between a 55 gallon and an 80 gallon tank (both size and $$ issues) and I’m trying to figure out how much useful gas volume I’ll have with the 2,000psi tank. I want it for topping off tires and possibly the occasional use of a rented air tool such as an air impact wrench for breaking loose the Godzilla sized bolts this beast is held together with.


    I think that your tanks are NOT gallons but cubic feet. ie 50 cu ft and 80 cu ft tanks. That cubic feet designation is the amount of air that is compressed in to the tanks, not the volume of the tanks themselves.
  • Kemahsabe's avatar
    Kemahsabe
    Explorer
    Apr 22, 2014
    If you're willing to assume the tire is a torus, then the volume is:

    V = 19.84Rr² where R and r are the "major radius" and "minor radius", respectively.

    Problem solved!
  • Geocritter's avatar
    Geocritter
    Explorer
    Apr 22, 2014
    I purposely didn’t mention why I needed this information because I didn’t want the thread to go off on a tangent. But here goes, I’m planning on a keeping a 2,000psi nitrogen tank (and regulator) on board for my compressed gas needs. I’m torn between a 55 gallon and an 80 gallon tank (both size and $$ issues) and I’m trying to figure out how much useful gas volume I’ll have with the 2,000psi tank. I want it for topping off tires and possibly the occasional use of a rented air tool such as an air impact wrench for breaking loose the Godzilla sized bolts this beast is held together with.

    Ooops! I mean 55 and 80 cubic foot tanks, dang brain pharts!
  • Kemahsabe's avatar
    Kemahsabe
    Explorer
    Apr 22, 2014
    rgatijnet1 wrote:
    The cubic feet of air remains the same with the tire, inflated or not, only the pressure changes.
    Now, if you want to know how many cubic feet of air must run through an air compressor to inflate the tire to 70 psi, that is an entirely different question.

    True. (Let's ignore any stretching of the tire, OK?)

    To help with the second part, the density of air at 0 psi (gauge pressure) and 70°F is .075 lb/ft³, and at 70 psi is .432 lb/ft³.

    All you have to do is figure out the volume of the tire in cubic feet.
  • Geocritter's avatar
    Geocritter
    Explorer
    Apr 22, 2014
    rgatijnet1 wrote:
    The cubic feet of air remains the same with the tire, inflated or not, only the pressure changes.
    Now, if you want to know how many cubic feet of air must run through an air compressor to inflate the tire to 70 psi, that is an entirely different question.

    Excellent point and better expressed than the way I did. I'll restate.

    What is the 235/85R16 tires cubic foot volume at 14psi (atmospheric pressure at sea level)and next how many cubic feet of air would be required to fill one of the tires to 70psi?

    Steve
  • Dog_Folks's avatar
    Dog_Folks
    Explorer
    Apr 22, 2014
    Geocritter wrote:
    I’ll be frank, I’m mathematically challenged. Don’t get me wrong, I can read a formula and plunk numbers into a calculator I just don’t “think” mathematically. So my question is how many cubic feet of air does one of my 235/85R16 tires hold when empty and when filled to 70psi?

    I’ve googled the question already and found numerous responses that eventually turned to gibberish in my non-mathematical brain, plus posters would argue with one another about their calculations. It didn’t give me a lot of confidence.

    FWIW I solve most physics type problems by 3D visualization. I mentally construct a working 3D model of the problem. I’m nearly always correct in my assumptions; I just fail when it comes to supplying the math needed to prove it.

    Steve


    The size(cubic feet) would be the same empty and under pressure. It does not change, just becomes pressurized.

    A cubic foot is a cubic foot at 10 PSI and also a cubic foot at 100 PSI.

    The math to determine how MANY cubic feet you have, I can't help you help there, I join you in the non-math part.
  • rgatijnet1's avatar
    rgatijnet1
    Explorer III
    Apr 22, 2014
    The cubic feet of air remains the same with the tire, inflated or not, only the pressure changes.
    Now, if you want to know how many cubic feet of air must run through an air compressor to inflate the tire to 70 psi, that is an entirely different question.
    To add 70 psi is equal to 4.76 atmospheres so what ever the actual cubic feet of your empty tire is, (Guessing it to be somewhere around 2.2 cu. ft.) than it would take 2.2 x 4.76 or about 10.5 cu. ft of air compressed in to your tire to equal 70 psi.
  • DutchmenSport's avatar
    DutchmenSport
    Explorer
    Apr 22, 2014
    Wow, that's probably a tough one. But when it comes to dealing with pie, I'd rather just eat it than mathematically try to figure it out! :B
  • downtheroad's avatar
    downtheroad
    Explorer
    Apr 22, 2014
    Don't take this the wrong way...but how come do you want to know?
    Just interested and wondering if this is something I should know also about my tires...

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