h a l f b a k e r yCogito, ergo sumthin'
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I've been a staunch opponent of the vacuum baloon ideas put up in the past, mostly because of shortcomings with thin walled vessels under compression. [Vernon] mentions something similar to this in his opus "Balloon notions" - but then he's talking about helium/hydrogen mixes, and honestly, he's lost
me.
Anyhoo, the concept is pretty simple. A balloon, of whatever arbitrary size, with two walls, which are close together with respect to it's size. These walls are very tightly bound together with tensile fibres, in much the same way that modern high pressure inflatable kayaks and mattresses are. Then, inflate the outer zone between the walls to a very high pressure (although technically, just a little over 2 atm should do it). This will pull the baloon into spherical shape, after which you carefully evacuate the inner zone down to hard vacuum.
Some computational mathematics would be needed to determine the ratio between the inner wall and outer wall diameters, this essentially setting up the buckling resistance of the structure. Ditto the pressure required.
spin it up and you have ....
_22Prayer_20Wheel_22_20Vacuum_20Blimp
[FlyingToaster, Dec 11 2012]
Inflated_20Shell_20for_20Vacuum_20Balloon
Redundant [spidermother, Dec 11 2012]
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I'm pretty sure that won't work without somehow bracing the wall on the inside. |
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[Marked-For-Deletion] Redundant (link). |
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I'll take the MFD however when I read [pashute]'s version I had images of some sort of composite or ribbed outer shell, and then he talks about making the whole thing arbitrarily small, which threw me off. |
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Anyhow, I still reckon this could work as I've described. A sufficiently strong membrane material (easily made with modern aromatic fibres) and sufficient strapping between the inner and outer shells, combined with huge intersitial pressure should be able to support a vacuum within. As a mechanical engineer, I don't see a problem with this concept, and given the high strength/weight possible with modern fibres, I'm pretty sure this could be made work. Certainly this has a much higher potential to work as compared to hard shell structures. |
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Yes, you could hold vacuum using an inflated tank,
assuming mechanical ties between the inner and
outer tank walls, but those ties are going to be
critical. Essentially you're inflating the outer tank,
and those ties have to be strong enough to keep the
volume of the interstitial space small, even against
your high inflation pressure. This would especially
be a problem since the inner chamber will try to
buckle at any point away from the ties. |
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I think you'll find that this will always be denser than air - even if you ignore the structural mass and buckling resistance, resisting the hoop stress alone will require as much air as would uniformly fill an equivalent volume. A gas has no strength in tension (of course), and its compressive strength is directly proportional to its density. An arbitrarily thin cross section of any *pressure balloon (uniform or shell) needs the same average pressure, and hence average density, to resist the external forces normal to that section. Thus, redistributing the gas in any way cannot decrease the overall density of the balloon (in the absence of compressive structural elements). |
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A rigorous proof is a bit beyond me without some serious revision; the above may be flawed. |
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* By pressure balloon I mean one that uses internal fluid pressure to resist external pressure. |
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I'm not sure that's true, the inflated shell
essentially becomes a rigid body, with stiffness as
a function of the pressure between the walls,
which is limited by the tie strength, however, you
can make it arbitrarily large with size limited by
tension in the outer skin. These two are not
directly correlated. |
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That being said, I don't think it would actually
work, as a LTA balloon, since your structure is
going to be relatively heavy. My comment above
was directed at creating a vacuum chamber or
storage tank more than a floating object. |
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I'm not disagreeing with you, [MechE]. I'm sure you could contain a vacuum in this way - probably even with real-world materials. But I'm fairly sure that it can be rigorously proven that it cannot be made lighter than a uniform volume of gas - that is, it cannot be LTA if air-filled - even with arbitrarily strong and light materials. |
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(The idea doesn't mention LTA, but one assumes that that is the goal for a vacuum balloon.) |
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Afraid I don't really have access to the computational resources required to see if this would work or not. |
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Certainly it wouldn't compete with hydrogen or even helium baloons, and even more certainly not at higher altitude, but as a mechanism, I'm sure you could sustain vacuum. But whether you could achieve LTA - I'm afraid I can't say. |
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Perhaps rephrasing the question would help. How does the magnitude of the compressive stress in a hollow spherical shell compare to that in a uniform sphere of the same size, with the same external pressure? If the ratio of stress is not less than the ratio of the volume of material, then LTA is impossible. |
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Ah, but I'll contend that compressive stresses are more difficult to withstand with modern materials, or rather the reverse - tensile forces are more easily withstood than compressive ones. In this design the entrained air is the compression member, everything else is in tension. You scale the pressure such that any forces encountered are exceeded by the tensile forces holding this in shape. |
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My main argument against thin rigid shelled vacuum balloons is that of thin wall buckling. It might just sit there for a second, almost humming with instability, before a tiny surface imperfection, somewhere, will cause it to buckle and collapse. A useful analogy would be a steel rod, say 10mm diameter, two metres long. In theory, you could prop up a weight ontop the rod, the same mass as that which could be held if the rod were in tension. And most FEA packages will tell you it's okay. But in the real world, eccentricity comes into play, and you need lateral support to prevent buckling. It's my contention that a thin walled sphere under compression will be metastable at best, - the compressive stress that this thin shell is under will cause buckling with any external force or surface imperfection. If you're trying to go LTA, it would most certainly be so fragile as to be useless, even if you could manufacture out any imperfections. Which is why I've suggested a "tension in everything other than the gas" design. Whether it works as LTA - I dunno. |
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But I'm contending (or rather, assuming) that _all_ the compressive load is borne by the air; and I'm allowing the (non-gaseous) tensile structure to have negligible mass. Which is why I asked about the compressive stress alone. |
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Sorry mate that was me not getting your question. |
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I agree, zero compressive forces in the materials, only in the gass shell. Of course there will be local shear stress around the ties between the shells, but these will scale down with the number of ties used. |
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The cool thing about the gas pressure is the force applied is only with respect to surface area, not volume. Hence an arbitrarily thin shell gap, or at least a very thin gap, thick enough to still be practical. You'll still have issues with localised bending of the double wall structure, hence it will need some thickness. |
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Yebbut the hoop stress in a thin-walled sphere is inversely proportional to the wall thickness. So halving the thickness halves the volume (again, thin-wall approximation), but doubles the pressure, resulting in the same mass (ideal gas law). That's my point; resisting the force normal to the skin (to keep the two walls apart) requires an arbitrarily small amount of gas, as you say, but resisting the force parallel to the skin (the hoop leading) does not. |
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I think I have a more rigorous proof: |
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Take a uniform sphere, with unit radius, at unit pressure. Its volume is 4/3 pi units, and volume * pressure is also 4/3 pi. |
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Now take a thin-walled evacuated vessel, with wall thickness t, at unit external pressure. Its material volume is 4 pi * t units, its hoop stress is 1/(2t) units, so volume * pressure is 2 pi units. |
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So resisting hoop loading alone requires 2/(4/3) = 3/2 as much gas for a thin-walled high pressure vacuum balloon as is contained in a uniform sphere of atmospheric pressure gas of the same size. |
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