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There are other questions (c.f. What gas is used in airships to give them buoyancy?) that discuss the use of lifting gasses such as Helium and Hydrogen in airships. Helium is rare and Hydrogen is flammable.

If one could build a light-enough and strong-enough rigid outer frame, then couldn't one use a vacuum rather than lifting gasses? At ground level, the frame would only have to withstand 15psi (100,000 pascals), which isn't a tremendous amount of force. Theoretically, a vacuum should provide even greater lifting force than any gas.

Have there been any attempts at vacuum based rigid-dirigibles -- and if not, what are the technical or mechanical limitations to doing so?

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  • $\begingroup$ en.wikipedia.org/wiki/Vacuum_airship suggests that you would require a material with a lower propensity to buckle than pure diamond. $\endgroup$ – Hugh Nov 24 '14 at 6:27
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    $\begingroup$ which isn't a tremendous amount of force.? It's an enormous force. About one ton per square foot if you are on the old system still. $\endgroup$ – Simon Nov 24 '14 at 8:20
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    $\begingroup$ "Which isn't a tremendous amount of force." Actually, it's pretty big. $\endgroup$ – David Richerby Nov 24 '14 at 12:00
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    $\begingroup$ @Michael it looks like a vacuum is just 179 grammes per square meter lighter than helium, if I understood pericynthion correctly. I'd be surprised if it's possible to make such compartments without using more than 179 grammes of material per square meter $\endgroup$ – user56reinstatemonica8 Nov 24 '14 at 18:11
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    $\begingroup$ Lighter than air craft work by displacing air from an enclosed volume with a gas which has less mass per volume (ie less density) than air. The achieved lift per volume = mass_new gas - mass_air - mass_enclosing structure. When vacuum is used the lift = mass of air per volume less support structure. As air masses about 1.2 kg/m^3 at STP (~= sea level, 25C) the support structure needs to mass less than 1.2 kg of enclosed volume to get any lift at all. Larger volumes gain some advantage due to cubed-squared law as volume increases with side cubed but area wity side squared. HOWEVER .... $\endgroup$ – Russell McMahon Nov 25 '14 at 5:50
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what are the technical or mechanical limitations to doing so?

There is no known material that has a sufficient combination of lightness and strength to support a vacuum that would support the weight of the container on Earth at sea-level.

There was a similar question with a good answer on Physics.se

Is it possible to make a solid rigid evacuated "balloon" out of Beryllium or other elements or alloys?

The currently first answer runs through the maths

calculated it over a database of almost 3700 materials including all common aerospace composites, metals and alloys.

and concludes

So in short, the best materials fall short of achieving our aim by a factor of just over 2. It is conceivable we might push up the stiffness / density ratio by perhaps developing some kind of Beryllium foam. For example, a closed cell foam of this Beryllium with a relative density of 0,041 would give a value of about 920 at the expense of lowering the Young's modulus to about 600MPa - however, I have no idea if such a foam is even possible. Alternatively it might be possible to come up with some clever engineering of the envelope geometry to overcome the buckling constraint. However, I suspect the effort is unlikely to pay off with a better boyancy ratio than is already achievable by conventional balloons.

Other related questions

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  • $\begingroup$ What if you only wanted to add some bouyancy to an otherwise 'normal' airplane or something? We're making a huge assumption, that we want to float the whole ship by itself. What if we just want something that's "light" enough to be a better ground effect vehicle or something like that? Where's the cutoff - how much bouyancy could be acheived? $\endgroup$ – Jasmine Nov 24 '14 at 16:33
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    $\begingroup$ @Jasmine: It's not a case of cutoff, you can not achieve any buoyancy at all with this approach, you can only make your vehicle heavier. The vacuum balloon cannot lift itself, let alone anything else. Even if you constructed your vehicle from metal foam and somehow evacuated the gas (air) from the foam, it would almost certainly still be either heavier than conventional construction or too weak to support the structural forces on top of atmospheric pressure. $\endgroup$ – RedGrittyBrick Nov 24 '14 at 16:43
  • $\begingroup$ Oh thanks, that makes total sense. $\endgroup$ – Jasmine Nov 24 '14 at 16:46
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    $\begingroup$ @Jasmine: Even if one had a magical magical vacuum foam which weighed nothing and could be easily controlled, such a thing would be of very little use in an airplane. Replacing a cubic meter of interior airspace with magical vacuum foam would add less than 1.5 grams of lift. The interior volume of an Airbus 380 is less than 4,000 cubic meters, so replacing all of it with the magical foam couldn't generate more than 6 kilograms of supplemental lift. The only way to add a meaningful amount of lift would be to make the craft a lot bigger, and the only way that would save any fuel... $\endgroup$ – supercat Jul 31 '15 at 16:43
  • $\begingroup$ ...would be if the craft's airspeed was extremely low. Having an airship stay aloft at zero airspeed requires almost no energy, but propelling it any significant speed will require a lot more energy than would be necessary for an airplane of comparable payload capacity. $\endgroup$ – supercat Jul 31 '15 at 16:45
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The other answers correctly point out the extreme (impossible) materials strength and stiffness requirements of a vacuum balloon. Another notable point is that the advantage in lifting capacity is small; at standard temperature and pressure the buoyancies of helium, hydrogen and vacuum are respectively 1.096, 1.185 and 1.275 kg/m^3. So even if you could hypothetically build a vacuum balloon with the same envelope mass as a hydrogen or helium balloon, it wouldn't be able to lift much more payload.

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Beneath the argument that it's impossible to build a structure which can withstand the outer pressure, pericynthion pointed to another argument: The buoyancies of gas and vaccuum is similar and the higher mass of a vacuum-airship will cancel the benefit.

But there is even more:

Airships usually include a balloon filled with air. If the ship ascends, the gas expands and the air is pressed out. (see http://www.americanblimp.com/fly.htm) This way, the inner and outer pressure is equal and there is no additional stress on the hull due to overpressure.

Also, the buoyancy does not decrease: In an altitude of about 5.8km, air pressure is reduced to 50%, and so is the buoyancy for a fixed volume. If you let the gas expand, it will expand to twice its volume. Twice the volume times 50% buoyancy gives you 100% buoyancy again.

But a fixed volume of vacuum will not expand and have only 50% of its buoyancy at sea level.

Of course, 5.8km altitude is very much for an airship, but the numbers are nice to show the effect. And due to the exponential nature of the air pressure, a gas-filled airship which allows the gas to expand has a higher buoyancy than a vacuum airship with fixed volume above 600m for hydrogen filled and 1200m for helium filled ships. Here is a plot comparing the buoyancy of 1m³ of vacuum to 1m³ gas at sealevel: enter image description here

(By the way: This is the reason why weather balloons have a flexible hull or seem to be partially filled only at sea level)

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All of the links I've seen are to sites where it is implicitly or explicitly assumed that the dirigible is a homogeneous sphere. This approach does have some merits - any failure has to originate at some point, and if the sphere is absolutely uniform then there is no obvious point of first failure; and in the analogous situation of deep sea exploration spherical construction has been shown to have its uses. However, in practice no material construction is ever completely uniform, and even if one was, until the dirigible was aloft there would be a difference between those points which were in contact with the ground or supporting structures, and those which were not.

It seems to me that a much better approach would be to have something which is approximately spherical, but which is supported internally by a complex system of ribs and buttresses, akin to what can be found in a gothic cathedral.

For a starting point, take a look at e.g. http://www.cutoutfoldup.com/905-spherical-model---cube.php. Imagine this structure scaled up and manufactured to extremely high precision using the strongest available materials, and covered by a thin film so that the interior is completely enclosed. What you'd have is essentially a sphere which is very thick at certain points (i.e where the ribs are) but very thin at others. The ribs would be able to withstand enormous pressures. The other points - not so much. As it stands, it would fail at one of the non-ribbed points. So, not a great advance. But now imagine that the material of the faces is quite strongly curved; that each face is a portion of a sphere which is much smaller and therefore more strongly curved than the overall sphere. These smaller spherical segments should be able to withstand a much larger external pressure than a large sphere of the same thickness.

Now imagine each of these bubbles is itself ribbed, with the facets between the ribs occupied by still smaller ribs and bubbles. The construction is effectively fractal, with the repetition at smaller scales occurring as often as is required. The very smallest bubbles would be very highly curved, and therefore very strong. The external pressure exerted on them would be directed to small ribs, which would in turn be directed to larger ribs, and so on. I don't know of any attempts that have been made to construct a vacuum dirigible along those lines, but I don't see why it shouldn't work.

EDIT: If we understand that any vacuum achievable on Earth using a mechanical pump is in fact just a partial vacuum, and we therefore use the word "vacuum" as an abbreviation for "partial vacuum", it follows that "vacuum dirigible" and "lifting gas dirigible" are not mutually exclusive terms. It should be possible to construct a dirigible containing hydrogen or helium at significantly reduced pressure, instead of the slight overpressure that is normal. The rigidity would then have to come from the structural rigidity of the shell instead of from the internal pressure.

The big advantage, in the case of a reduced pressure helium dirigible, is that under normal circumstances the loss of helium to the atmosphere should be negligible, unlike a normal balloon where losses are substantial and have to be continuously replenished. The major gas seepages would be from the higher pressure exterior to the lower pressure interior, and any potentially escaping helium would be in effect swimming against that current. It would also be seeping through a rigid material which is likely to be more impervious to the flow than a more flexible material would be. This advantage will become increasingly significant as the price of increasingly rare helium continues to skyrocket.

Not that it should be necessary to employ reduced-pressure helium, it's just that doing so would make construction easier by decreasing the pressure difference between interior and exterior to something more easily manageable. But I'm fairly sure that with an intelligently designed shell it would be possible to create a working dirigible even with the interior close to being a hard vacuum. The article cited by RedGrittyBrick in his answer states "the best materials fall short of achieving our aim by a factor of just over 2", and I am sure that a better structural design would result in MUCH more than double the rigidity of a simple homogeneous sphere for the same mass of material. Supercat's anecdote, below, helps to illustrate that.

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    $\begingroup$ When my father (and lots of helpers) built a sandbag wall around his house (which held up to a flood with standing water almost 4' above ground level, plus substantial waves on top of that), rather than building it as a circle or ellipse, he built it as a scallop-shape, with substantial buttressing at every concave point. That greatly reduced the radius of, and consequently increased the strength of, all of the non-buttressed portions of the wall. $\endgroup$ – supercat Nov 24 '14 at 18:42
  • $\begingroup$ @supercat. That shape also deflects cannon fire. $\endgroup$ – TRiG Mar 8 '15 at 2:20
  • $\begingroup$ the reduction in helium leakage seems compelling. wonder what the cost advantage would be... $\endgroup$ – ivo Welch Mar 22 '16 at 23:17
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According to our finite element analysis (US patent application 11/517915 (Akhmeteli, Gavrilin, Layered Shell Vacuum Balloons, you can find it at USPTO site or at http://akhmeteli.org/wp-content/uploads/2011/08/vacuum_balloons_cip.pdf ), it is possible to construct a vacuum balloon using commercially available materials and sandwich structures. In his comment, @Hugh refers to a Wikipedia article that emphasizes our calculation proving that one cannot make a vacuum balloon as a homogeneous spherical shell made of currently available materials, but does not clearly quote our conclusion on a possibility of inhomogeneous (sandwich structure) spherical shell vacuum balloon.

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  • $\begingroup$ Sandwich material, of course. Like stated in a comment of the physics site, this is awesome. $\endgroup$ – Koyovis Jun 8 '17 at 2:22

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