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What Weighs More......

Discussion in 'Bicycle Mechanics and Repairs' started by stephec, 17 Jul 2007.

  1. stephec

    stephec Legendary Member

    Location:
    Bolton
    ...an inflated wheel, or an uninflated one?

    No honest, it's a serious question. It's been a long day sat in traffic jams today, I was going to solve the meaning of life but this question got in first.

    I know I could go and get a wheel and try it myself but I thought I'd see if anyone had tried it before.
     
  2. chris42

    chris42 New Member

    Location:
    Deal, Kent
    Inflated is heavier but don't know how you would weigh it
     
  3. stephec

    stephec Legendary Member

    Location:
    Bolton
    I was going to use the kitchen scales, when my missus goes out later that is!!!
     
  4. chris42

    chris42 New Member

    Location:
    Deal, Kent
    I just use them even if she is in!
    I'm brave!
     
  5. stephec

    stephec Legendary Member

    Location:
    Bolton
    Only 'cause you're not married to my missus!!!!!!
     
  6. chris42

    chris42 New Member

    Location:
    Deal, Kent
  7. Monty Dog

    Monty Dog New Member

    Location:
    Fleet
    Of course, the inflated tyre is heavier. A litre of air weighs about 20g - so all you need to do is measure the volume of air in your tyres. If only I could remember the formula for calculating the volume of a toroid....
     
  8. TheDoctor

    TheDoctor Man-Machine

    Location:
    Stevenage
    Well, cross sectional area of the inner tube is given by pi*r*r where r is half of however 'fat' the tyre is (in mm). The length of it is pi * (622 + 2r) Multiply them together and that's your volume in cubic millimeters. Assumming you're on a 700c wheel...

    That's treating the toroid as a cylinder whose ends just happen to be stuck together, which should be OK.
    OK, working this for a 700*28 , pi*14*14 = 615.75mm^2
    Length is pi * (622+28 ) = 2042.033 mm

    volume is therefore 1257385 mm^3 or 1.26 litres. At a pressure of 6 bar, that's 6*1.26*20 g or 151g of air in your tyre.

    I'm going away now. I can't believe I just bothered with that!

    I also can't believe I looked up the formula on t'interweb, and the above logic is OK. I need to get out more.
     
  9. hubgearfreak

    hubgearfreak Über Member

    if we imagine a tube, it's cross section of width x length

    so for a 700 x 28

    3.14 x r x r x l

    3.14 x 0.014 x 0.014 x 2 = 0.00123

    is around 1.25 litres

    at 5 x atmospheric pressure (75psi)

    it contains around 6 - 7 litres of air

    so at the value given above of 20g/litre
    (presuming this value is at sea level)

    an inflated wheel & tyre assembly would be 120 -140g heavier.

    what we really need is a physics graduate, to pick tiny faults in my ballpark figures.



    :eek:
     
  10. hubgearfreak

    hubgearfreak Über Member

    at least we agree :blush:

    saddos together :eek:
     
  11. andrew_s

    andrew_s Veteran

    Location:
    Gloucester
    The only quibble is that a flat tyre is only flat at the bottom.
    The rest of it contains air at 1 bar, so if your tyre is pumped up to 7 bar, there's only 6xVolx20g extra weight over the flat tyre (disregarding the difference in volume between a round tyre and one with a flat bit at the bottom).

    (tiny fault courtesy of a physics graduate, though extremely rusty as I haven't done any physics since graduating)
     
  12. B1ondini

    B1ondini New Member

    Location:
    Norfolk
    What if you fill the inner tube with Hydrogen??
     
  13. Keith Oates

    Keith Oates Janner

    Location:
    Penarth, Wales
    There's always one :eek: !!!!!!!!!!!!!!!!!!!!!
     
  14. TheDoctor

    TheDoctor Man-Machine

    Location:
    Stevenage
    I think hydrogen is about 1/6 as dense as air, so whatever figure I came up with last night, it'll be about a sixth of that. Just to chuck a spanner in the works, various internet sites allege that air weighs about 1.3 grams per liter, not 20g. But I'm not working it out again! :eek:
     
  15. hubgearfreak

    hubgearfreak Über Member

    you're being entirely silly.
    both figures are estimates, so to quibble for 1/7th is a nonsense.
    but i get you're point :eek: