Engineering a vacuum zepelin?

[Ziggurat]

There's no perpendicular load; the fabric is arranged symmetrically on all sides of the column. There's a huge compressive force, which, yes, may cause ordinary buckling. But hoop compression on a sphere can buckle it, too, so the real question is whether "buckling of a column" and "crushing of a sphere" have different r-dependencies, and maybe whether one is more favorable than the other. I kinda doubt it, but I'd like to see the math.

They're the same r dependencies. Your pillars are holding back an area that scales as r², and so the force they have to withstand also scales as r². That means we have to increase their own cross-sectional area by r². And since their length scales as r, their volume scales as r³. The structure could conceivably have an advantage if the prefactor is lower (ie, you can make light pillars easier than you can curved surfaces), but the scaling offers absolutely no advantage. It's always r³ scaling for the weight of the structure as the best case.

 

[quarky]

I appreciate the feedback on this. Thanks.
If Zig is correct; i,e, no advantage in scaling up, as per the weight of the structural requirements to allow x amount of exterior load, and he very well may be, then this seemingly is a non-obtainable device.

Yet, it doesn't look like unobtanium, in a fundamental way. As in, forbidden thermodynamically.

Is it possible?

 

[MikeG]

Jumping away from the maths for a minute, and back to speculating about a suitable structure......

The only way I can see this even getting close to working is with a honeycomb-type structure entirely filling a spheroid. The honeycomb would have to be open-celled, to allow for the air to be extracted.....and my mind boggles at the difficulty of designing, let alone constructing, a spherical open-celled honeycomb structure, presumably out of something like carbon fibre.

Mike

 

[catsmate]

A variant sprouted from Iain M. Banks' fertile imagination has the zeppelin filled with evacuated buckyballs. This also has the benefit of turning the "vacuum" into a pumpable medium. Net gain in lift, in his opinion (presumably not strictly calculated - we are talking rip-roarin' SF here), would be just a few percent beyond hydrogen filling, and the entire apparatus "something that tended to be done because it could be done, and not for any real pactical purpose".

Jumping away from the maths for a minute, and back to speculating about a suitable structure......

The only way I can see this even getting close to working is with a honeycomb-type structure entirely filling a spheroid. The honeycomb would have to be open-celled, to allow for the air to be extracted.....and my mind boggles at the difficulty of designing, let alone constructing, a spherical open-celled honeycomb structure, presumably out of something like carbon fibre.

Mike

LTA solids already exist; there are lattice materials (link link) that are lighter than an equivalent volume of air, though not by very much (about 300g less and air per cubic metre).
Aerogel solids have been around for twenty years or so.

LTA solids are a moderately common sci-fi concept, a "foamed vacuum" similar to aerated plastics but without the gas filler. Compared to hydrogen or helium it has slightly more lift but it requires less structural material (no gasbag for example) though you'd need a ballast mechanism as you couldn't valve gas to reduce lift. The "vacuum airship" is not such an impossible concept as people might think, there are people working on it.
Of course compared to nullification of gravity it doesn't provide much lift capacity.

Another SF concept is the "stasis drigible" from Niven's Known Space series.


Materials science, no longer the bastard child of physics and chemistry.

 

[DavidS]

If Zig is correct...

Consult historical posts. Figure the odds. Place your bets.

...i,e, no advantage in scaling up, as per the weight of the structural requirements to allow x amount of exterior load, and he very well may be, then this seemingly is a non-obtainable device.

Yet, it doesn't look like unobtanium, in a fundamental way. As in, forbidden thermodynamically.

Is it possible?

The scaling relations Ziggurat presented clearly don't say it can't be done, they say a big one isn't more doable than a little one. Add in consideration that, in addition to the pressure forces, the structure will have to support its own weight and resist buckling over its span, and it looks like bigger is actually harder than smaller.

 

[quarky]

Consult historical posts. Figure the odds. Place your bets.
The scaling relations Ziggurat presented clearly don't say it can't be done, they say a big one isn't more doable than a little one. Add in consideration that, in addition to the pressure forces, the structure will have to support its own weight and resist buckling over its span, and it looks like bigger is actually harder than smaller.

I yield to Zig's wisdom, but in an effort to better understand the forces involved myself, I hope it's not an insult to post further musings on the subject.

The exterior 'crush' on the structure, at maximum, will be aprox. 15 psi.
This is nothing like the load at the bottom of the ocean.
This could be folly and wrong-think, but picture a sphere, constructed of pressurized, truncated hexagonal identical units, with slightly angled sides.

These would be glued together to create a tightly fitted sphere. Ideally, their exterior aspect would be slightly curved. If, individually, these hollow plastic units, pre-pressurized, could handle 5-10 lbs of pressure (per sq. inch) on their outside, wouldn't evacuating the interior volume of the enclosed space squeeze more or less uniformally on the whole structure?

In such a structure, I don't quite grasp why scaling up wouldn't give gains in the potential of lift-off.
If the units were pressurized, and had an outward, partially spherical face, as evacuation of the interior enclosed space began, their collective outer face would be squished into a flatter configuration, forcing the whole into a tighter, more stable configuration.

If my description is lacking, I'll try harder.

Pre-thanks for educating me.

 

[Ziggurat]

The scaling relations Ziggurat presented clearly don't say it can't be done, they say a big one isn't more doable than a little one.

Quite so.

Add in consideration that, in addition to the pressure forces, the structure will have to support its own weight and resist buckling over its span, and it looks like bigger is actually harder than smaller.

That's actually not much of a concern. Remember, the whole structure is lighter than air. That means that the weight of the structure pressing down on the bottom of the structure is less than the weight of the air you displaced. In other words, the stress on a 1 meter tall balloon sitting on the ground won't be any better than a 10 meter tall balloon sitting on the ground, due to that additional 9 meters of air weighing down on it.

Since anyone considering building such a balloon will have to engineer in some tolerance above the nominal pressure the balloon will operate at, the pressure differentials between the top and the bottom of the balloon won't be important until you get to positively colossal sizes (at which point you start engineering the top of the balloon differently than the bottom of the balloon anyways). If your balloon can't tolerate more than the pressure differential of the atmosphere between the balloon's top and its bottom, it's going to collapse in a gentle breeze.

But there is an incredibly significant advantages to going small, which is simply cost. A smaller balloon will cost less than a big balloon, and these things would be expensive.

 

[quarky]

Idle curiosity, but have any of you made soap bubbles with helium?

 

[ben m]

They're the same r dependencies. Your pillars are holding back an area that scales as r², and so the force they have to withstand also scales as r². That means we have to increase their own cross-sectional area by r².

That's true if you're looking at the crushing strength. But the main failure mode for a long, thin column is buckling, which happens at loads far below the crush strength. So the scaling is somewhat worse than r^3 for my caltrop. (I think?) Maybe this isn't true for some properly-designed lattice structure.

The thing is, I don't know what the equivalent is for spherical shells. I don't know if there's a buckling-failure that forces you to increase the shell thickness far beyond the naive hoop-stress/material-limit calculation. Maybe? Maybe not?

And, yeah, prefactors, but it's possible that the prefactors are large.

 

[DavidS]

That's actually not much of a concern. Remember, the whole structure is lighter than air. That means that the weight of the structure pressing down on the bottom of the structure is less than the weight of the air you displaced. In other words, the stress on a 1 meter tall balloon sitting on the ground won't be any better than a 10 meter tall balloon sitting on the ground, due to that additional 9 meters of air weighing down on it.

Point taken with regard to vertical compressive load. OTOH, the structure will also be subject to the shear and bending forces of its own weight and lateral extent. A quick peek through a rusty brain at this and that suggests:

r¹ Characteristic length, e.g. diameter
r² Weight per unit length, scaled to resist pressure forces
r² Shear strength
r³ Shear load grows faster than shear strength

r⁴ Bending moment
r⁴ Area moment of inertia, assuming equal vertical and horizontal scaling to resist pressure forces
r² Deflection grows faster than size with equal vertical & horizontal scaling

Unless I did or interpreted something wrong (neither would be news), that indicates there will be a size beyond which scaling up to resist the pressure forces won't be enough for the structure to maintain shape against its own weight. Using more material -- and weight -- to increase shear strength won't help, because that increases the shear load, too. Appropriately different vertical/horizontal dimension scalinb could keep deflection <~ r¹, which I'm guessing is necessary to avoid compressive buckling, but that won't save you from shear failure.

Doesn't that imply there's a maximal buoyant size for any construction material, scalable design, and external density? Lighter/stronger materials could make that size bigger, but couldn't make it go away. I leave as an exercise whether that size is too ridiculously humongous to worry about.

Above, I presume a simply supported, uniformly loaded beam of uniform section is a suitable proxy for scaling rules (not for quantitative relations). If that's a bad presumption, then I'm not right. Again.

But there is an incredibly significant advantages to going small, which is simply cost. A smaller balloon will cost less than a big balloon, and these things would be expensive.

Of course, the incredibly significant disadvantage of going small is simply less excess lift to carry payload. Whether many small ones is merely a construction detail of the group considered one big one is mere nomenclature. Whether many small ones are easier/cheaper to build and employ in combination than one big one, with appropriate allowance for connections complexity and weight, is an implementation detail. Unless I'm mistaken (I often am), such design may influence the maximal buoyant size, but not the existence of a maximal buoyant size.

 

[rwguinn]

There's no perpendicular load; the fabric is arranged symmetrically on all sides of the column. There's a huge compressive force, which, yes, may cause ordinary buckling. But hoop compression on a sphere can buckle it, too, so the real question is whether "buckling of a column" and "crushing of a sphere" have different r-dependencies, and maybe whether one is more favorable than the other. I kinda doubt it, but I'd like to see the math.

Keep on dreaming, ben m. Keep on dreaming.
Draw the free body.

 

[Ziggurat]

Point taken with regard to vertical compressive load. OTOH, the structure will also be subject to the shear and bending forces of its own weight and lateral extent. A quick peek through a rusty brain at this and that suggests:

r¹ Characteristic length, e.g. diameter
r² Weight per unit length, scaled to resist pressure forces
r² Shear strength
r³ Shear load grows faster than shear strength

r⁴ Bending moment
r⁴ Area moment of inertia, assuming equal vertical and horizontal scaling to resist pressure forces
r² Deflection grows faster than size with equal vertical & horizontal scaling

Hmmm... let's think about this in terms of our model, rather than a simply supported beam. Consider, for example, a spherical shell balloon, and examine the forces at an equatorial cross section. The pressure exerted downwards from the top half of the shell, due to the atmosphere, will scale as r². The circumference of the shell scales as r, and the thickness of the shell will have to scale as r, so the area of shell to support that downward pressure will also scale as r². But the area of the top half of the shell scales as r² and the thickness as r, so the volume of material in the top half and hence the mass does indeed scale as r³. So that scaling does indeed work against us.

But prefactors matter. What's the prefactor involved here? Again, the weight of that top half of the sphere is going to be less than the weight of air it's displacing (because otherwise it's not a balloon). That weight serves as an upper limit to the force we'll experience from internal stresses. So how does that weight compare to the weight of the column of air pressing down on our sphere (which we have to withstand regardless of size, and which we know scales properly?) Well, if we make our balloon 10 km high, then we've got a problem. But even if we're talking about something the size of the Goodyear blimp, or even a supertanker, the weight of air within the structure (and hence the weight of the structure itself) will be a tiny fraction of the weight of the column of air sitting on top of it. So we don't need to worry about it until the weight of the displaced air becomes a significant fraction of the weight of the above air column, and that won't happen until our balloon reaches a significant fraction of the total air column height. And that is absurdly large (we're talking > 1 kilometer), and that's also the point where we can no longer assume constant pressure everywhere around our balloon. In fact, we can start designing the balloon to be weaker and thus lighter at the top than on the bottom, so scaling might change at that point anyways (though I haven't tried to figure out if the bouyancy scaling will match the weight scaling). But if you're not working with something that monstrously large, the small prefactor makes the internal stress scaling basically irrelevant next to the design margin you would need just to keep a modicum of safety.

But there is effectively a maximum buoyant size: the height of our atmosphere. Beyond that, you automatically lose boyancy by making it bigger. And given the relationship between pressure, atmospheric density, buoyancy, and gravity, the finite height of the atmosphere is actually built into the problem.

 

[Ziggurat]

The thing is, I don't know what the equivalent is for spherical shells. I don't know if there's a buckling-failure that forces you to increase the shell thickness far beyond the naive hoop-stress/material-limit calculation. Maybe? Maybe not?

Hmmm...

Buckling failure modes should only come from forces the structure isn't already specifically designed to resist (ie, lateral stresses for your rods, etc). We've got it resisting the atmosphere, and the prefactor for resisting its own weight are low. So what other forces are in play?

Well, presumably we want to move this thing. If we can ignore air resistance, then the acceleration requires a force that scales as r³, since that's how the mass scales. To do this gently, we want to apply it over an r² surface area, leaving a pressure that scales as r. That's the same scaling as the stresses from our internal weight. And that actually makes sense: the internal weight is trying to provide a constant acceleration of g, and we're trying to provide an external acceleration a. As long as a < g, then, the force required to put our balloon in motion should be less than the internal weight stresses, which we know have a tiny prefactor for balloons that aren't absurdly big. I think air resistance scaling actually works in our favor here, since the cross-sectional area is only r² so the air resistance should scale slower than our locomotive force. Of course, we're assuming that the force we're applying can be evenly distributed over an r² area (or, for a lattice/skein design, over r² contact points), but that may not be terribly practical. If we need to apply our locomotive forces in a more concentrated manner, then maybe the scaling will work against us more strongly, and the prefactors might not rescue us.

Now we also need to worry about stuff like impact stresses, like if a bird hits it, but those sorts of stresses shouldn't scale as r³.

 

[quarky]

In my napkin math, a sphere with a radius of one mile, could have a shell of 18" thick reinforced concrete, which would weigh less than half of the air inside.

I have no illusions of that being an effective approach, due to a large variety of structural issues, including the exterior air pressure loads being non-uniform.

At the other end of this; the tiny; we see heavier than air particles aloft...dust particles and such. The same is true in water solutions, wherein floculating long chain polymers are employed to clump together various floating crud; allowing them to sink to the bottom of the pool, even though they were denser than the water to begin with.

 

[Ziggurat]

In my napkin math, a sphere with a radius of one mile, could have a shell of 18" thick reinforced concrete, which would weigh less than half of the air inside.

I doubt 18" of concrete, or even steel, is going to withstand the force from a mile radius vacuum sphere. But try calculating the net downward (or upward) force on one half of the sphere, and see what pressure that puts in your shell.

At the other end of this; the tiny; we see heavier than air particles aloft...dust particles and such.

Dust falls. It just falls more slowly than turbulance can lift it, because viscosity scaling makes it harder for small particles to move through the air. Air resistance scales as r² while mass scales as r³, so viscosity/weight scales as 1/r, and viscosity dominates at small r. But that won't help with our balloon, because "small" in this context is really small.

 

[quarky]

An odd friend of mine assembled a bunch of slightly tapered styrofoam cups into a spherical unit; the size was dictated by the angle of the individual, truncated cones.
It was an interesting structure; serving no purpose beyond amusement in beholding it.

IIRC, it was approximately 3' in radius.
This is what got me pondering the sphere of assembled units as described above.
I never got around to it, but I thought it would be very interesting to wrap that sphere of foam cups in thin plastic; replace the air inside with He, and evacuate just enough of it to cause a sucked-in look; the opposite of a balloon.

If it floated, it would be an interesting structure to behold. I think that is do-able, though I didn't do it. It would serve no purpose other than a visual anomaly, but it got me wondering about this larger feat, as per the o.p.

 

[Beerina]

Cool.

One of my thoughts on the matter was to create a sphere of balloons, wrapped in mylar. The balloons would merely comprise the outer shell of the structure, possibly being a lot lighter than a geodesic frame work. As the interior air was evacuated, the shell of balloons would squish against each other tightly, gaining structural integrity with the increase of outside pressure.

That's pretty awesome. Scientists just built robot hands that were basically rubber balloons with sand in them. They act like it -- it will mold easily over an object. But suck the air out and suddenly it's a rock hard gripper. You seem to have described the exact same principle.

 

[rwguinn]

Keep on dreaming, ben m. Keep on dreaming.
Draw the free body.

OOps--I just did.
If you get the geometry exactly right, you do have all compression.
But slenderness ratio is gonna kill you.

 

[Myriad]

Besides getting the scaling exponents right, you also have to make the right comparisons.

For a spherical shell, the compressive force due to the outside pressure (which applies along the surface at every point in every tangential direction) scales as r², and the strength resisting that force (assuming thickness scales with r) also scales as r². To stay intact, the latter must exceed the former.

The mass scales as r³, and the lift also scales as r³. To be buoyant, the latter must exceed the former.

So basically, a given design (shell materials, internal gas, interior pressure, and ratio of thickness to radius) works or fails at any scale. So, you might as well do your early testing on basketball-size spheres or smaller.

Respectfully,
Myriad

 

[rjh01]

In my napkin math, a sphere with a radius of one mile, could have a shell of 18" thick reinforced concrete, which would weigh less than half of the air inside.

I have no illusions of that being an effective approach, due to a large variety of structural issues, including the exterior air pressure loads being non-uniform.

At the other end of this; the tiny; we see heavier than air particles aloft...dust particles and such. The same is true in water solutions, wherein floculating long chain polymers are employed to clump together various floating crud; allowing them to sink to the bottom of the pool, even though they were denser than the water to begin with.

What was the density of the concrete? The weight would mostly be stone. However some stones (volcanic) can contain a LOT of air and actually float in water. Do your calculations again using concrete that has the same density as water or less.