Would a metal sphere containing a vacuum float?

30 May 2010


An airship in flight



Would it be possible to make a hollow metallic sphere float if you suck out all of the air and create a vacuum inside?


We asked Dominic Ford from Naked Astronomy.

Dominic - Yes, it certainly would be. What's important is whether the average density of the sphere plus whatever is inside it is greater or less than the density of the water that it will be floating in. So for example, a ship floats because although a ship is made of steel and that's very heavy, it's got air in there as well and the air is much less dense than the water it's floating in, so a ship as a whole floats.

Now, if you take a sphere, the metal outside of the sphere will be much heavier than the water, but because it hasn't got anything in it, that doesn't contribute to the density. So its average density be quite low. So it will float. It will actually float better than if you filled it with hydrogen or helium which, although they are lighter than air, they still have some mass to them, more than the mass of the vacuum which is nothing at all.

Chris - Indeed. It's a good party question that, isn't it? Which is going to float more, a sealed barrel full of air, a sealed barrel full of hydrogen, or a barrel with a vacuum? Most people will go for the hydrogen, but, actually, it's the vacuum that floats the best!

Dominic - Yes, of course. You don't see barrels "filled" with vacuums very often, because it's so hard to suck air out of a barrel!


I too was wondering about the feasibility of vacuum for buoyancy, to help with flying cars. My intuition jumped to the presumption, posted above, that no material can surmount the pressure challenge. But two thoughts: 1) Isn't the real question, then, what the percentage gain (space saving?) from vacuum compared to helium, since helium is already feasible. 2) Compared to other technological miracles, wouldn't it seem that merely finding a material solution that can withstand a vacuum, would be rather pedestrian compared to for instance editing DNA? Maybe a bad example, but you get my point. I read the conclusion that even diamond wouldn't do it. But it the problem seems an odd one to have a status of "metaphysical illogicality," while granted, a vacuum is a special, spacial, spatial thing.

So I just did my own research and calculations, and given that a Boeing 747 weighs approximately 368 tons, the amount of pure-zero air displacement (as afforded by a vacuum) necessary to reach a weight of zero would be an astonishing 9.21 mil cu ft. The goal doesn't have to be zero, however, but rather just a significant reduction in weight overall. Still, given that total weight, it seems unlikely that any implementation of vacuum technology in commercial aircraft would be able to make a noticeable impact without a significant redesign, likely eschewing all currently-used materials, such as steel, in favor of much lighter materials. Perhaps we will be at a place in the future where carbon nanotubes or some yet undiscovered material is able to bridge the gap between thought experiment and reality with regard to the feasibility of such a technology.

This is not a new idea: https://en.wikipedia.org/wiki/Vacuum_airship
No known materials can achieve the strength-to-weight ratio required for this to happen in Earth's atmosphere.

The answers above reflect my own suspicion, but it makes me wonder if a large enough vessel, made of a light enough material, containing a vacuum within, would float in air. For instance, if you made a thin-walled rigid plastic sphere, weighing less than 0.08 lbs and of a volume greater than 1 cu ft, would it float away? As air weighs approximately 0.08 lbs/cu ft, logic would seem to dictate so, yet this seems like it shouldn't be possible. Is there some rule of physics which says that any known earth material constructed at the necessary dimensions to inhabit a large enough volume at a low enough mass to float in air would necessary be too fragile to support the vacuum within? If not, it seems like it would be useful to incorporate such devices into aircraft in order to reduce fuel costs. Imagine a passenger liner whose wings, tail, fuselage walls, and nose weigh less than air, such that the entire vessel's weight is reduced and therefor requires less energy (i.e. fuel) to achieve and maintain flight.

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