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Can Floating Cities Really Exist?

My impossibly delightful friend Veronica Belmont interviewed me on her show âFact or Fictional?â, a program where she talks to sciencey types about whether some plot point in a movie or TV show can really happen or not.

For this episode, she asked me if we could really build a floating city like in the movie âOblivionâ or the game âBioshock: Infiniteâ. I cranked the numbers, and determinedâ¦well, spoilers, sweetie.

One thing I want to make clear: I misspoke in the video making a small mistake (oops). I said it would take a balloon the size of the Empire State Building to float the Empire State Building. What I meant was that the balloon would have to be a sphere with the *radius* equal to the height of the building. That has a *lot* more volume than the building itself, which makes sense. The doodle I made of the building that you see in the video is actually about the right scale.

Doing the math for this was fun, and actually pretty easy. The density of air at sea level is about 1.2 kilograms per cubic meter. The density of helium is only 0.2 kg/m^{3}. Thatâs why helium rises; itâs less dense than the surrounding airâit weighs less than the air itâs replacingâmaking it buoyant. If you had a balloon with a cubic meter of helium in it, itâll rise as long as it has a mass less than 1.2 kilograms, the mass of the air itâs replacing.

That means a cubic meter of helium can lift 1.2 â 0.2 = 1 kilogram of mass. Easy peasy.

The Empire State Building weighs 365,000 (Imperial) tons, which is 330 million kg. So you need 330 million cubic meters of helium. Crank the math, and you get a radius of 430 meters, or about the size of the building itself. Thatâs the radius, not the diameter, which is where I made my mistake. But still, the point it, you need a *really* big balloon to float a building. So Iâm not buying this idea, even if it is totally cool and kinda steampunky.

Thatâs why I said itâs possible theoretically, but in reality would be silly.

Now that I think about it, this topic was similar to the last time Veronica had me on, when we talked about whether the Helicarrier from âAvengersâ was possible. I hedged a little bit there to, saying essentially the same thing. Possible, but why bother? I think she needs a new category: Factional.