My impossibly delightful friend Veronica Belmont interviewed me on her show “Fact or Fictional?”, 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 “Oblivion” or the game “Bioshock: Infinite”. I cranked the numbers, and determined…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/m3. That’s why helium rises; it’s less dense than the surrounding air—it weighs less than the air it’s replacing—making it buoyant. If you had a balloon with a cubic meter of helium in it, it’ll rise as long as it has a mass less than 1.2 kilograms, the mass of the air it’s replacing.
That means a cubic meter of helium can lift 1.2 – 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. That’s 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 I’m not buying this idea, even if it is totally cool and kinda steampunky.
Photo: Phil Plait
That’s why I said it’s 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 “Avengers” 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.
