Just for fun: Lighter than air

Maybe you’re heard someone joke, or snark about filling up your tires with helium? But it does bring up an interesting question. How much does air weigh? Most people might say nothing as common sense. But that’s not right, and I sometimes forget this.

Inflated to 1 bar (left) and 9 bar (right)

The weight at 1 bar at 794g for my 700×23 tires. 9 bar weighed 802g. 8 bar difference, 8g difference. Weight gain was linear and proportional with tire pressure, 2 bar at 795g, 3 bar at 796g and so on.

So why is this? You might remember from your school days that air is made up of atoms and actually has mass, and therefore weight. Grams are actually a measure of mass, weight is a force that is equal to the mass times gravity that is used to approximate mass (I know a great brain teaser about why heavier objects fall faster than lighter ones by the way, Aristotle was right all long! Sort of…)

Lighter than air balloons float really because they’re less dense than atmospheric air. The metric unit for pressure is the bar, which means one atmospheric pressure. A helium filled balloon floats because air is heavier, and the relatively heavier air sinks and falls to the ground and takes up space, pushing the helium balloon up. Just like Archimedes was heavier than water, and displaced the water up and out of his tub when he had his famous eureka moment.

What’s a little confusing is how pressure is measured. Pressure can be measured in absolute terms, bar(a) relative to a vacuum, or bar(g) measure by a gauge such as on your pump, and relative to atmospheric pressure. Atmospheric pressure varies with elevation, but on earth, in simple terms, bar(a) = bar(g) – 1. Meaning that when there is 1 bar(a) a gauge will read 0 bar(g). 1 bar(a) is maintained by the external pressure of the atmosphere shrinking the volume of the tube so that the pressure inside the tube is equal, creating an equilibrium. When pressure is increased, the pressure is acting on the tire casing and the rim which holds the air within a given volume. When Diogenes asked Plato if his cup was empty, he should have said it was filled with air at 1 bar(a).

Things get a little different when we increase the pressure. We increase the pressure by pumping more air into the tires, that’s how a pump works, we’re all familiar with it. In other words, putting more air in the same space, more mass per volume, we’re increasing the density of the air inside the tires. The air inside the tires is no longer just as dense as atmospheric air. 2 bar(a), twice the pressure, twice the air, 3 bar(a), thrice the pressure, thrice the air and so on. It’s denser, and therefore the air in our tires is “heavier than air.”

A back of the envelope approximation confirms this. Assuming that the 700c x 23mm tire is a perfect torus, and ignoring the fact that we should be measuring the internal volume of the tube, and the fact that the casing stretches and so on, we get a volume of 842 cm3. Multiply this times the density of atmospheric air at room temperature (hot air balloons work on the principle that air is less dense when heated), 0.001225 g/cm3, and we get 1g. Right in line with our experimental results.

There are lots of reasons to not overinflate your tires, tires exploding off your rims, uneven tread wear, discomfort, worse rolling resistance on anything but glass smooth velodrome track. And weight. So I can rest easy that I save about 5 grams over someone that inflates their tires to the max pressure on the side of the tire at a cost of $0. That’s some prime value right there.

Seriously, look up the appropriate front and rear tire pressures for your weight, it’s well worth it.

Edit: I again forgot something, that gauge pressure measurement is relative to the atmosphere, 1 bar, not absolute. The post has been edited to reflect that.


One thought on “Just for fun: Lighter than air

  1. Petre Craciun March 7, 2017 / 9:48 am

    Great stuff ! You should calculate it with Helium if possible :))


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