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Is it possible to build a vacuum balloon with a near perfect void that can lift heavy objects and doesn't collapse and buckle under the atmosphere?

I expect perhaps a honeycombed or lorimerlite lattice infrastructure with toothpick-like filaments spanning across the honeycomb or lorimerlite voids in an alternating double helix pattern. These "toothpicks" would be slightly thicker in the center and thinner at their ends where they connect to the inside of the honeycombed or lorimerlite lattice. This would be made made of titanium. I would choose a toroidal (donut) balloon.

Would this design work, or is there another design that would?

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    $\begingroup$ I seriously doubt the titanium structure could achieve average density lower than hydrogen. $\endgroup$ – Jan Hudec Jun 6 '18 at 5:23
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    $\begingroup$ Using vacuum doesn't get you more than a marginal advantage over hydrogen. Air averages ~29 g/mol, H2 is 2 g/mol. The 0 of vacuum is only about a 7% improvement over hydrogen, and 14% over helium. $\endgroup$ – jamesqf Jun 6 '18 at 6:08
  • $\begingroup$ Air pressure at ground level is 1 kg/cm2. That's how much force your vacuum tank has to withstand. $\endgroup$ – Hobbes Jun 6 '18 at 12:18
  • $\begingroup$ There is no material strong enough to contain a vacuum that doesn't weigh more than the displaced air plus equivalent aluminium structure. $\endgroup$ – RedGrittyBrick Jun 6 '18 at 15:25
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    $\begingroup$ Vacuum would implode instead? $\endgroup$ – CrossRoads Jun 7 '18 at 12:43
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You can load a decent titanium alloy to about $500 \mathrm{MPa}$ (the ultimate compression strength is quoted at least $850 MPa$, but you need to stay below the elastic limit and have some safety margin). That is $5000$ times more than the pressure at sea level. Therefore, the supporting elements have to take about $\frac{1}{5000}$ of the volume. At density about $4500 \frac{\mathrm{kg}}{\mathrm{m}^3}$, the average density comes at least $0.9 \frac{\mathrm{kg}}{\mathrm{m}^3}$. That is just slightly better than the $1.225 \frac{\mathrm{kg}}{\mathrm{m}^3}$ of air, but way worse than the $0.09 \frac{\mathrm{kg}}{\mathrm{m}^3}$ of hydrogen or the $~0.17 \frac{\mathrm{kg}}{\mathrm{m}^3}$ or helium. And this is only weight of the support—for containing vacuum, the skin will be much heavier as well.

Therefore there is no way this could be better than traditional hydrogen or helium-filled aerostats and it's unlikely to get off the ground at all in practice though the above back-of-the-envelope estimate suggests it just barely might.

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    $\begingroup$ Note: that calculation is hyper-optimistic. The best-case crushing strength of 3D materials is C*S*(d/D)^1.5, where S is original material strength, D its density, d the foam's density, and C<1. This limit is mathematically impossible to exceed with any structure and any material. At d/D<100 with any known metal, the collapse is elastic at C times S*(d/D)^2. So average density to withstand air pressure will be ~10 kg/m3 ideal (C=1, 1 GPa loading, plastic collapse) and ~50 kg/m3 realistic (elastic collapse). $\endgroup$ – Therac Jun 7 '18 at 15:10
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If there was a reason to do this, ideally, you would want to use a structure similar to an open cell foam with a focus on minimizing cell size. Metallic microlattices would do much better than honeycombs.

But even better than microlattices would be some very compressible structure that would automatically adapt to the outside pressure. You need a very strong structure to withstand atmospheric pressure at sea level, but dense air also provides a lot of lift. As altitude increases, aerostatic lift decreases. So you need an increasingly lighter structure, but it will be under increasingly less pressure and can be much weaker.

A material that solves this problem actually exists - it's called gas. As atmospheric pressure decreases with altitude, gas expands and makes itself less dense. With the gas vented outside, the balloon literally makes itself lighter as it ascents.

The problem with the 'vacuum balloon' concept isn't even the lack of sufficiently strong materials. It's the decrease in lift with altitude. A balloon 100 meters in diameter will produces 5,000 tons of lift at sea level, but less than 2.5 kg of lift at the Karman line, the lower edge of space.

In theory, if the envelope could be light enough, an edge of space balloon isn't absolutely impossible. But, for any given finite level of material strength, it will fly higher with hydrogen (or helium) inside than with vacuum and a structure.

Any hypothetical material is better used to make a thinner shell to contain more gas. Since there's literally no limit to how light a gas can get, as pressure is reduced, there's no altitude where you'd have a reason to switch to vacuum.

There's also a practical advantage for gas - it equalizes the pressure, so a gas-filled balloon won't suffer explosive recompression and rapid sinking once a tiny dust speck makes a hole in it.

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