Have we been able to construct vacuum buoyant structures yet?

[LSLGuy]

@Shalmanese

…
Still, exactly how close are we to building them now? Are we any closer than we were 5, 10, or 50 years ago? Are there any promising areas of research that might yield one on the future if pursued far enough? Or does there exist some physical law that would make materials approaching the limit of what’s needed to build them theoretically impossible?

Not trying to pile on. Peter Morris’s post led me on a voyage of discovery back through the even earlier history on this perennially popular question.

@Dr.Strangelove

For me at least, it’s because it falls in the domain of extreme engineering problems. It doesn’t violate any laws of physics, and existing materials seem almost good enough if you could arrange them right, but it’s never been done. So it’s like nanomachines and nuclear rockets and electromagnetic launchers and maglev vacuum tunnels and so on.

It’s the “seems” part I wonder about. Though I readily admit your relevant engineering chops are far beyond my decades old academics.
Ref this post from 2008 by an ME/SE: http://boards.straightdope.com/sdmb/showthread.php?p=9581053#post9581053

The strength/weight shortfall between the best known material (diamond) and that required for an engineeringly perfect sphere of the same material is 10 million to 1.

We’ve got aways to go to engineer an improvement by 10 million X over the current best known natural or artificial material.

This isn’t one of those “How much do I have to work out to be able to lift 250 lbs?” questions. It’s more like “How much do I have to work out to be able to high jump over the Moon?”

[Dr.Strangelove]

@LSLGuy

The strength/weight shortfall between the best known material (diamond) and that required for an engineeringly perfect sphere of the same material is 10 million to 1.

That post certainly proves that any thin-wall solution is doomed to failure; that is, anything with a dense, homogeneous wall material. But that just indicates that you need thick, low-density walls instead. It’s like claiming that large cranes are impossible because a solid bar of steel has too high a bending moment. Well no, it just means you need to structure the material better, into a truss or otherwise.

[Stranger_On_A_Train]

@Peter_Morris

Because hydrogen is dangerous and helium is rare and running out (until we are able to mine the Sun)

Hydrogen is fairly dangerous (high detonability and diffusion) but helium is not running out. We have (foolishly) elected to liquidate the National Helium Reserve because of the costs of storage (even though those are largely administrative) but nearly every natural gas field has at least a small fraction of helium that ends up being a large volume, and some produce 10% or more by mass. In many cases the gas is vented into the atmosphere once separated from natural gas not because it is in any way difficult to collect or refine, but simply because it isn’t worth enough for natural gas producers to bother to store or distribute it. Just as there are vast known and presumed untapped resources of natural gas, there are also volumes of helium which could be extracted if the value were sufficient. We can also produce helium by neutron bombardment of [SUP]6[/SUP]Li, and it is a byproduct of tritium synthesis by this mechanism. Once we make nuclear fusion practicable helium (not going to lay money on when that happens but it will almost certainly occur at some point), helium (in the form of ionized alpha particles) is a product of the most probable fusion reactions up to p-[SUP]11[/SUP]B and [SUP]3[/SUP]He-[SUP]6[/SUP]Li. And of course, the Sun throws off thousands of tons of helium every second. While it will likely never make economic sense to collect interplanetary helium for delivery to and use on Earth, it could certainly be a nearly limitless supply of helium for space use, from supercoolant to working fluid to fuel. It is literally the second most abundant material in the Universe, dwarfing everything except hydrogen, and we are nowhere near its disappearance.

@Dr.Strangelove

For me at least, it’s because it falls in the domain of extreme engineering problems. It doesn’t violate any laws of physics, and existing materials seem almost good enough if you could arrange them right, but it’s never been done. So it’s like nanomachines and nuclear rockets and electromagnetic launchers and maglev vacuum tunnels and so on.

Existing materials are no nearly good enough to produce a buoyant vacuum vessel. You can say that it “doesn’t violate any laws of physics,” but material science and structural mechanics are just as much a part of physics as electrochemistry and gravitation, and unless you can postulate a material which is capable of exhibiting virtual rigidity through just a few tens of layers of molecules or lattice planes, vastly beyond any known or hypothesized material, this is just as much science fiction as warp drives and teleportation. Nanomachines are practicable–nature has been producing them on our planet for over four billion years–and nuclear thermal and electric rockets are largely more a matter of engineering (albeit yet-to-be-proven concepts) than basic physics as they operate on known principles. The kind of hyperrigid materials to be buoyant in air while continuing a vacuum, on the other hand, defies basic material science as we know it.

Stranger

[Dr.Strangelove]

@Stranger_On_A_Train

and unless you can postulate a material which is capable of exhibiting virtual rigidity through just a few tens of layers of molecules or lattice planes, vastly beyond any known or hypothesized material, this is just as much science fiction as warp drives and teleportation.

Again, this is only true if you maintain the thin-wall criterion. Dense materials are doomed to fail. But nanostructured materials don’t have to be dense. There are all kinds of possible carbon structures that achieve whatever density you wish to have without significantly affecting the specific strength.

If you really want to reach physical limits, you can go way further than that, with electromagnetic or kinetic structures. Want to achieve really impressive compressive strength with no buckling and unlimited length? Get two pairs of electromagnetic decelerators/accelerators and have them shoot bearing balls at each other. Maintaining stability is a bitch and we’re nowhere close to building useful systems like this, but they don’t exceed any basic material limits or break any laws.

[Melbourne]

@Stranger_On_A_Train

No, not even remotely. The problem isn’t one of material strength as it is geometry, i.e. such a rigid wall vessel would have to have extremely thin walls, and all thin-walled structures are sensitive to local buckling regardless of the tensile and shear strength. Filling it with a reinforcing material such as aerogel helps resist buckling but at the expense of additional weight, and even the lightest aerojels weight more than a low density gas.

No lighter-than-air aerogel is commercially available (now): Aerogel Technologies, LLC | FAQs

But not “all thin-walled structures are sensitive to local buckling”. Remember Eulers buckling theorem depends on length and edge conditions: F=k/(x**x). When x is very small and the ends are constrained, stuctures don’t buckle.

The design of a rigid gas is an interesting problem: if it’s rigid, it’s not a gas. If it’s rigid then it’s not equally incompressible in all directions at the molecular level. And if it’s rigid, and not isotropic, then it’s molecular, so it’s denser.

Still, if you think of a theoretical aerogel that is a constrained gas, rather than starting with the idea of a crystal, it is an area that may still see more development.

[LSLGuy]

ETA: @**Dr Strangelove **just above:

Agree that I ignored the structural design issue. Which is an oversimplification too far. OTOH needing to make up a materials deficit of 10 million to 1 via smarter structures implies a hefty amount of smarter.

You gave me an idea. Could you do something with electrostatic repulsion? I’m imagining a rigid conductive sphere that could *not *withstand much (any?) negative atmospheric pressure. Build the sphere, but with normal atmospheric pressure inside and out.

At the center, place a relatively small but powerful electron source or sink. Crank up the power so the central anode/cathode is repelling the enclosing spherical cathode/anode. Then evacuate the air out of the empty space.

Lotta challenges. And making the entire power supply chain weigh less than the sphere-equivalent volume of H or He is simply not gonna happen. But it might be a way to improve buckling resistance with less weight within the sphere proper.

After all, it’s essentially molecular-scale electrostatic repulsion that’s creating the gas phase phenomenon we call “pressure.”

[TriPolar]

@Dr.Strangelove

I propose making an icosahedron out of fat columns filled with compressed hydrogen. An envelope surrounds the whole thing and the interior is pumped to a vacuum.

A tensegrity sphere makes sense for this, unless that’s what you were thinking off. Buckminster fuller proposed such designs for hot air floating cities using floating members. For anything of size you need far more faces than an icosahedron.

[Chronos]

LSLGuy, I think you overlooked the biggest advantage of that design: You can literally and honestly tell people that it’s held together by a forcefield.

[Dr.Strangelove]

@LSLGuy

You gave me an idea. Could you do something with electrostatic repulsion?

I believe so (and vaguely hinted as much above). There are limits to what you can achieve before the high voltage discharges to ground through the air, but the material can be arbitrarily thin–like gold leaf. It should be self-smoothing due to the 1/r^2 falloff; any parts that get too close will get pushed away by the electric force; too far and air pressure pushes it back.

In principle, you get also get away with an arbitrarily small power supply, but I guess free ions in the air will eventually discharge it. Not sure offhand what that rate would be.

[Dr.Strangelove]

@TriPolar

A tensegrity sphere makes sense for this, unless that’s what you were thinking off.

It’s close to a Fuller-like design in that all elements are purely compressive or tensile. Actually, simpler to think about is a tetrahedrons made of of 6 of the cylinders mentioned above. They’re neutrally buoyant, so they don’t contribute anything to the weight, but clearly have plenty of structural margin. Inside the tetrahedron is a tetrahedral bag pulled apart by tethers attached to the corners of the big tet. You’ll get some amount of vacuum inside the bag no matter what tension you can achieve.

I would say that whether this ends up as a cheat or not depends on exactly how much vacuum is achieved. If you need 1000 m^3 of structure to get 1 m^3 of vacuum, then it’s silly to call it a vacuum balloon. But if the numbers are in the same ballpark then I think it’s fair. I haven’t run the numbers carefully enough yet to know if this is possible.

[Scylla]

@Stranger_On_A_Train

First of all, heat loss from a hot air balloon is primarily by conduction, not radiation, as addressed previously. Because the air, both inside the balloon and in the atmosphere is of such low density, the rate of conduction is low under normal conditions. The air inside the balloon does flow (cold air from the outside falls and forces hot air to rise through the center) but because of the large mass of air and small temperature differentials the flow is slow, and the difference in average temperature is not large; hot air balloons have an average internal temperature of around 200 °F, whereas your stove probably doesn’t even have a measurement below 300 °F, and the primary reason for insulating your stove is to prevent your kitchen from getting hot (unless you have a convection stove) as it cooks largely by radiation. Your Yeti cooler, on the other hand, has to protect a small volume from heat coming from the ambient air into a cold temperature reservoir with essentially infinite heat capacity, and unless you are using dry ice you have a working temperature of not much less than 32 °F which is maintained as long as the total energy flux doesn’t exceed the latent heat of fusion of your ice or other coolant.

It isn’t that a hot air balloon doens’t lose heat energy, but it does so slowly enough that it is not worth adding the extra mass of insulation to offset any savings of fuel for the propane burner. Complex schemes that add more mass in order to achieve a marginal increase in theoretical buoyancy are highly unlikely to be a net improvement.

This isn’t a cheap per se, but realize that once you start increasing the pressure of the hydrogen inside the columns you are increasing density and thus reducing buoyancy. Compared to the external loads (14.7 psia AMSL) which add up quickly you’re going to need a considerable amount of internal structure to support that. You’ve proposed an icosohedral structure (presumably because it is the simplest “sphere-like” classic solid with triagonal faces) but it would be instructive to look at an even more simple structure for scaling without dealing with only axial loading, i.e. take an annular structure, like a backpacker’s alcohol stove, seal and fill the annulus with hydrogen or helium, and cap the open ends (we’ll assume for the moment that the end caps are perfectly rigid) to form an evacuated chamber in the center. In this case buckling is not a concern as long as you keep the pressure in the annulus sufficient to assure positive tension. Now calculate the buoyancy of the structure (both the evacuated center and the high pressure annulus) versus the mass of some real world textile material for the skin. You’ll find that the necessary ratio of pressure in the annulus to the ambient to support the end load is larger than the inner diameter of the annulus squared over the difference of the squares of the outer and inner walls. In short, you’ll end up with a very large annulus to support an evacuated center, even assuming rigid caps. The scaling on a icosohedran will be different but it is actually worse because of the lower mechanical advantage of that configuration. Getting more than a small fraction of lift from the evacuated volume just isn’t plausible.

Stranger

That makes sense and I understand the first part completely. Thank you for going to the effort to explaining it to me.
As for the second part, I’m not sure what evacuating my anus has to do with anything.

[Dr.Strangelove]

@LSLGuy

Ref this post from 2008 by an ME/SE: http://boards.straightdope.com/sdmb/showthread.php?p=9581053#post9581053

Getting back to this again…

I rechecked the math in that post, and everything was fine until the very last line! The E/d[sup]2[/sup] of diamond is not 0.1; it’s nearly 100,000. That’s still a far cry from the necessary 450k+, but we can work with that.

Instead of solid diamond, we’ll use an octet space frame of diamond rod. Since macroscopic buckling is the main constraint, I’ll work from there and then double-check at the end that the other constraints are met.

The space frame in question is composed of octahedrons, and a unit cell consists of length 12 of rod material, with a volume of 1.414, a cell mass of 12pir[sup]2[/sup], and a density of 26.66r[sup]2[/sup]. We’ll also keep in mind a “derating factor” of 8.89r[sup]2[/sup], which is the factor we divide the force on the unit cell by to get the force on the component members (this is just the cross-section of each rod, times 4, divided by sqrt(2)). Or, we might multiply by that number to get the effective limits on a unit cell.

We’ll start with the high-end estimate from before, to allow some margin (especially given that the space frame is not perfectly isotropic; it’s pretty close but not 100% along all axes):
E/d[sup]2[/sup] = 1500000

Our members are made from diamond, which has E=1.22e12 Pa and d=3520 kg/m[sup]3[/sup]. Therefore, for the space frame:
E = 1.22e128.89r[sup]2[/sup] = 1.085e13r[sup]2[/sup]
d = 26.66r[sup]2[/sup] * 3520 = 93800*r[sup]2[/sup]

So:
E/d[sup]2[/sup] = (1.085e13r[sup]2[/sup])/(93800r[sup]2[/sup])[sup]2[/sup] = 1500000

(1.085e13r[sup]2[/sup])/(93800r[sup]2[/sup])[sup]2[/sup] = 1500000
8.22e-4 = r[sup]2[/sup]
r = 0.0287

Ok, not too bad. That r is unitless, by the way–we’re considering it as a ratio. But it means if we built the truss out of 1 m rods, they would have to be 5.7 cm in diameter to meet our requirements. That’s pretty slender, as we’d expect, but not absurdly so.

This material won’t buckle “macroscopically”, but what about the individual components? Specifically, will the rods themselves buckle or otherwise fail?

To make things easier, lets assume a 1x1x1.414 m unit cell (again, all of this is scale-free, so it doesn’t matter if we scale down to micrometers at the end).

The thickness ratio from zut was just:
(t/R) = 0.43/d

We know d; it’s 26.66*r[sup]2[/sup]*3520, so d=77.3, and (t/R)=0.0056.

Hoop stress is:
S = qR/2t = (q/2)/(t/R) = (101325/2)/0.0056 = 9050000 Pa.

We’re considering a 1m cell, so the force is 9050000 N, and the effective force on each member is 3200000 N.

Let’s look at the buckling limit of each member. Euler’s critical load formula for columns is:
F = pi[sup]2[/sup]EI / (KL)[sup]2[/sup]

I is the moment of inertia; we have a circular cross-section, so it’s (pi/2)r[sup]4[/sup]. K is 0.5 since the column is supported on both ends. E is that of normal diamond. L is 1. Therefore:
F = pi[sup]2[/sup]1.22e125.33e-7 / 0.25 = 51330000 N.

That’s 51 MN, and we only needed 3.2 MN. So that’s plenty. What about basic compressive strength? Diamond has a compressive strength of 110 GPa, which comes to 284 MN for our rod. Way more than plenty.

So I’m going to call this plausible. The raw compressive strength is so high that there’s plenty of margin in that regard. We could have reduced the structural member diameter by a fairly large factor and still have compressive margin left over; the lowered density would increase the E/d[sup]2[/sup] even further, but that doesn’t appear to be necessary. I did make some assumptions with regard to the isotropy of the space frame but nothing that would make even a 2x difference, and there is enough margin everywhere to account for that.

All that we need now is a few hundred cubic meters of perfect diamond and a system to machine it down with micrometer precision. Easy.

[Ranchoth]

@Scylla

We could never imagine Hannah Montana swingingnaked on a wrecking ball, but that happened, so you know, I’m still hopeful for my vacuum blimp.

So…you’re saying Hannah Montana is either completely vacuous, or just full of hot air?