An interesting fact about the Eiffel Tower

I overheard one pupil tell another yesterday morning that:

“The air in a cylinder that contained the Eiffel Tower
would weigh more than the Eiffel Tower itself.”

It sounded feasible, but I wanted to check the maths.

The metal structure of the Eiffel Tower has a mass of 7300 tons, or 7.3 million kilograms. The design of the tower is very space-efficient: if you melted down the pure iron* that it is made of, it would occupy a volume of only 930m3, equivalent to a sphere with a radius of just six metres.

The Eiffel Tower is 324 m tall and sits on a square base with sides of 125 m. It would therefore fit inside a cylinder with a radius of 88 metres, giving the cylinder a volume of just under eight million cubic metres. This much air would have a mass of 10 million kilograms.

So yes, that pupil was telling the truth. The air contained in a cylinder that could hold the Eiffel Tower would be 2.7 million kilograms heavier than the Eiffel Tower itself.

I am particularly fond of the Eiffel Tower as it lists, around its base, the names of seventy-two important French scientists, mathematicians and engineers, including Ampère, Arago, Becquerel, Daguerre, de Coulomb, Foucault, Fourier, Fresnel, Gay-Lussac, Lagrange, Laplace and Poisson.

* More accurately, the tower is made from puddled iron, a type of wrought iron that has a density of 7850 kg/m3.

29 thoughts on “An interesting fact about the Eiffel Tower

  1. I believe there are some problems with this…

    A. The total weight of the tower is closer to 9,400 tons, and even the weight of the iron alone is being reported on at least one site as 8092 tons.

    B. Air loses density with altitude, so the average air mass can’t be figured at sea level pressure. Even though, see below.

    C. When I figured this using cubic feet, I came up with a cylinder of 177,795,743 cubic feet — π x r2 x h (3.14 x 53,824 x 1052). Multiply by .081 lbs per cubic foot of air (sea level) and you get 14,401,455 lbs, or 7201 tons.

    Maybe I’m missing something?

  2. Reply/correction to my previous comment… I had bad information on the tower base width, which is in fact 410 feet. Considerably greater than the 328 ft. figure I was working with. New calculation = 11,244 tons of air at sea level pressure, compared with the 9,441 ton weight of the tower. You are correct!!

  3. That’s sort of the point – it’s very well constructed, and so can support itself with only a small amount of metal. And it’s made from puddled iron – not steel.

  4. I think that today, with the computer power available for CAD and other technical advances, we could construct a tower of the same dimensions and strength with 40 % less material (identical, of course). Maybe even 50 % less material.

  5. And if you melted down the iron into a 125m square of even thickness, bounded by the four legs, it would be only 6 cms deep.

  6. There are several problems with this. A ton is imperial weight. A tonne is metric and thus 1000 kg weighs one tonne. So which is it ton or tonne. If it is ton 7300 of them is not 7 million kg.

  7. I really need to understand how come the EIffel tower weighs less than air if I were to make a cylinder around it. Or how come the pressure at the bottom is so small as if something were lifting it? I really do not get it. Can anyone explain it in simple terms please!!!

  8. I don’t know the dimensions of the Eiffel Tower but when its said that if a cylinder were placed over the tower to the same dimensions, the air inside the cylinder would weigh more than the metal. So, what that means is if you put the tower on some scales out would weigh approx 7000 tonnes. Of you had a giant imaginary cylindrical container that weighed nothing itself and was the same diameter as the base of the tower and the same height as the tower this would weigh more than the tower. This is because air weighs one kilogram per cubic metre and the volume of that cylinder will need to be more than 7000 cubic metres for this fact to be true. I don’t know the details. To grasp the concept of the air weighing one kilo, if you had a one cubic metre box full of air, you wouldn’t notice the weight if you picked it up(note the box is imaginary and doesn’t weigh anything). This is because the surrounding air ie the atmosphere weighs one kilo per cubic metre. Now if you picked up the same one cubic metre box with the air in it on a vacuum you would then notice the weight.

  9. If the tower weighs less than the air around it, that is, the air it displaces, why does the tower not float away, like a zeplen?

  10. Joseph, it’s because the density of steel is just a little bit higher (6000 times higher) than the density of air.

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