Just like a balloon of Helium lifts about 1.02g for being less dense than the air. Does the same principle applies to vacuum being less dense than air? And if so, how much can a ballon (1L) of vacuum lift? Ignoring the condition that to have a pressure resistant balloon would make it heavier than the whole experiment.
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2 Answers
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At 101.325 kPa (abs) and 15°C the density of air is 1.225 kg m$^{-3}$, so a balloon made of massless but very rigid material will lift 1.225 kg for each cubic meter of volume.
answered Apr 19, 2021 at 22:30
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6$\begingroup$ Of course, this is a pure thought experiment, in the sense that hydrogen and helium are the lightest gas in nature. An empty vessel with no gas in it would have to be at the same time very lightweight and very resistant to pressure in order to resist being crushed by atmospheric pressure, which seems impossible to achieve in practice, as illustrated by: youtube.com/watch?v=3s9psf01ldo $\endgroup$ Apr 19, 2021 at 23:12
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$\begingroup$ @SergeHulne I assume you mean impossible to achieve with currently known materials. If you are saying something more than that, it probably deserves elaboration. $\endgroup$ Apr 20, 2021 at 15:22
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$\begingroup$ Yes, I mean "impossible to achieve with currently known materials." $\endgroup$ Apr 20, 2021 at 15:30
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Your intuition is correct - with current materials.
Gas based and vacuum based balloon constructions respond to altitude differently.
Any volume of helium always weighs 14% of the displaced amount of air (assuming the same temperature and the same pressure between the air and helium). If the helium bubble is able to expand at high altitudes, its lift per liter goes down, but its volume goes up - the two effects cancel each other and the total lift is preserved. If, however, the helium is forced to escape or to compress at higher altitudes, the total lift goes down. Typical gas balloon constructions therefore aren't terribly sensitive to altitude or elevation which makes them so popular for travel, haulage and even stratosphere exploration.
This is different with vacuum based balloon constructions. Their rigidity and thus weight has to be optimized for a particular pressure differential; if you assume a near total vacuum on the inside, they have to be optimized for a particular atmospheric pressure. The higher the balloon sits, the lower the net lift is.
With current envelope materials, helium fares better than vacuum. Hydrogen fares better than helium (it weighs only 3.5% of the displaced air, and so its lift factor is about 112% over helium). If and when future envelope materials surpass helium and/or hydrogen, the gas based balloons will still initially retain their ability to climb without gradually losing lift.
However, if vacuum based balloons become practical with future materials, they may be able to offer the practical advantage of lift ratio control through volume control. Compare this to throw-away ballast used to control buoyancy of gas balloons.
And even if those imaginary envelope materials are infinitely rigid and infinitely light, the vacuum balloon will never be able to achieve more than 104% lift factor over hydrogen.
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$\begingroup$ A similar effect could be created by not only using rigid material, but instead pre-stressed elastic material that will relieve stress when pressure drops. (Just like under a bench press some materials will elastically bend, "shrink"). An engineering problem to make it a balloon and lightweight but not inconceivable. $\endgroup$– paul23Apr 20, 2021 at 15:13
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$\begingroup$ @paul23 - Sure. Or a hot air balloon. I was only comparing the technologies mentioned in the OP. $\endgroup$ Apr 20, 2021 at 15:34