Given futuristic materials, could a structure ever be strong enough to contain a vacuum, yet light enough to provide buoyancy under standard atmospheric pressure?

Obviously "futuristic materials" is highly ambiguous because we don't know what exists in the future... but what properties would it take? Are there theoretical materials that provide the right properties that are at least compliant with the laws of chemistry?

So, for example, if you created a woven carbon fibre bag and then somehow impregnated it with seamless industrial diamond, would that be sufficient?

  • $\begingroup$ Mythbusters successfully flew a lead balloon (albeit with He fill). As the answers suggest, it's all in how you stiffen your structure. $\endgroup$ – Carl Witthoft Feb 8 '18 at 14:15
  • $\begingroup$ You know an egg is a remarkable piece of structural engineering. Rather than speculate, blow out some eggs, reseal and evacuate the interior. It will require a shellac type sealant to prevent air passing through the shell (thats how the embryos breathe) but at that point you will have a thin, structural shape that with some perseverance will provide some answers for your question. All you need to determine is how large a volume is needed to generate bouyancy per gram of shell mass. Not a difficult calculation if you try. $\endgroup$ – Donald Gibson Feb 8 '18 at 19:41

Start out by doing some basic calculations. Air is mostly N2, with a atomic mass of 28, and O2, with a atomic mass of 32. There is more nitrogen than oxygen, so let's say air has a average atomic mass of 29.

At 0 °C and 1 atm, one mole of ideal gas occupies 22.4 liters. Let's say 20 °C is more realistic, so we'll scale that by the absolute temperature ratio (22.4 l)(293 °K)/(273 °K) = 24.0 l. So the density of what we will call "air" is (29 g)/(24 l) = 1.2 kg/m3.

So for every cubic meter you can enclose, you get to use 1.2 kg of material. That by itself is not a big deal. The gotcha is that the surface has to somehow be able to withstand about 15 pounds per square inch, or about 11.4 tons per square meter, or 101 kN/m2.

Let's say you want to make a sphere 10 m in diameter. That has a volume of about 524 m3, so you can use up to about 630 kg of material.

It should be pretty straight forward to calculate the thickness of various materials required to make a 10 m diameter sphere than can withstand 1 atm of external pressure. None of the materials we have today come close.

However, that's a really naïve way to make a vacuum tank. A suitable internal lattice structure will save well more than its own weight in weight of the skin material. The real engineering issues are with the clever design of the internal supports. The optimum arrangement of internal supports depends on the relative strengths and densities of the available materials, so you can't just create one design then work backwards to see what the material properties need to be.

To really answer the question, you'd have to pick some material properties, iterate to find the optimum structure design, see where you're at, adjust the material properties, adjust the structure to the new tradeoffs, etc.

Note also that scale matters. A sphere with twice the diameter gives you eight times the mass budget, but only four times the surface area. There is obviously some win in going larger. On the other hand, larger diameters give you less advantage from the arch effect due to the curvature, and the interior supporting structures don't scale the same way.

In the end, I expect that this is solved with a multi-dimensional iterative design process.

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  • $\begingroup$ I'd use a sphere made of transparent aluminum with support struts made of unobtanium. $\endgroup$ – Carl Witthoft Feb 8 '18 at 14:17
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    $\begingroup$ On the serious side: an incandescent light bulb can withstand quite a few atmospheres' worth of pressure (ask scuba divers). Obviously that glass is too thick to be buoyant in air, but I would go for a manufacturing process which produces near-perfect spheres, as a sphere is the most structurally strong shape. To get uniform wall thickness, might want to "blow bubbles" on the ISS so there's no gravitational sag. $\endgroup$ – Carl Witthoft Feb 8 '18 at 14:20
  • $\begingroup$ @ Olin: I think you can take an internal support structure for the sphere and work backwards to see how strong the material of the structure needs to be, Buckminster Fuller has shown that the Octet Truss is the optimum configuration for any support / beam structure. So with a spherical "envelope", you would have a spherical internal strut system based on the octet truss . $\endgroup$ – William Hird Feb 8 '18 at 15:17

It is possible with materials that is "lightweight" and "high compressive stress".

Or create a wireframe globe that covered with thin rubber on the outside and then we can vacuum it.

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    $\begingroup$ downvoted because this is qualitative speculation. $\endgroup$ – Carl Witthoft Feb 8 '18 at 14:16

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