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