# What Weighs More......

#### stephec

##### Squire
...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.

#### chris42

##### New Member
Inflated is heavier but don't know how you would weigh it

OP
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#### stephec

##### Squire
I was going to use the kitchen scales, when my missus goes out later that is!!!

#### chris42

##### New Member
I just use them even if she is in!
I'm brave!

OP
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#### stephec

##### Squire
Only 'cause you're not married to my missus!!!!!!

#### Monty Dog

##### New Member
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....

#### TheDoctor

##### Noble and true, with a heart of steel
Moderator
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.

#### 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.

#### hubgearfreak

##### Über Member
at least we agree

#### andrew_s

##### Legendary Member
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)

#### B1ondini

##### New Member
What if you fill the inner tube with Hydrogen??

#### Keith Oates

##### Janner
There's always one !!!!!!!!!!!!!!!!!!!!!

#### TheDoctor

##### Noble and true, with a heart of steel
Moderator
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!

#### hubgearfreak

##### Über Member
andrew_s said:
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)

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