Shell Worlds: "Man Caves: Humanity’s Next Home" by Ken Roy

[Mark K]

The shell would bounce around the planet like on springs and and would create shear stresses with huge component forces.
These things are not even in dynamic equilibrium without restoring force

How is a spring not in dynamic equilibrium, providing a restoring force?

Some analogies don't work. In this case the blob of matter inside the shell is not held in place by any strong force. The air between the shell and the surface can move freely to anywhere inside the interior, which means that it won't act as a spring to keep the blob of matter in the shell centered.

While the concept is interesting, the laws of physics won't allow it to exist without active forces (i.e. LOTS of energy being expended) to keep the blob of matter centered in the shell. Wouldn't be a safe place to live... 

I agree completely!

Two points - to answer the earlier question first -
I meant the shell arrangement with no pressure gradient. It is not in equilibrium at all so the only posited forces to keep it in place would have to be the pressure gradient. Any little force must be counteracted by the pressure difference before the shell hits the center mass because nothing else is stopping it.

Second, having a pressure gradient strong enough to matter means that all the nice features related to not needing super strong structure in the shell go out the window. The shell needs to be strong enough to be pushed on by these pressure gradient forces which are not all normal to the shell so there are tension and shear forces. These forces - if the pressure gradient is really enough to stop the multi-megaton shell from moving in a short enough distance to not hit the central mass and then reversing its direction - will be astronomical in the bad sense. Plus since there is no equilibrium and no damping from it, any "bouncing" of the shell will not really go away - it might heat up the air inside over time, but that will be the cause of more forces on the shell - higher pressure which won't be evenly distributed. It could be slowly damped by moving the material of the shell - tearing it or bending it apart as well.  Aerodynamically inside you would get interesting air currents, pressure waves, i.e. winds from the back and forth...

Since there would be so little damping, lucky resonances would likely just build up... It could be quite spectacular quite quickly for such a huge object.

[Paul451]

The air between the shell and the surface can move freely to anywhere inside the interior

Ah, now I get it, that's the part you haven't understood. The air is gravitationally attracted by that "blob of matter", but not by the shell (which has a uniform internal gravity field). As long as the blob-of-matter has a gravitational potential sufficient to create an pressure gradient across the gap between surface and shell (8-10km or so), then that pressure difference will act as a counter-force to any tendency of the shell to drift towards the surface (or vice versa.)

If the contained mass is too small, then it won't have enough gravity to create a sufficient pressure difference. But Ceres does. And I suspect that most of the dozen largest main belt asteroids would.

[Paul451]

The shell needs to be strong enough to be pushed on by these pressure gradient forces which are not all normal to the shell so there are tension and shear forces.

No, all the force is perpendicular. There's only compression between the atmosphere and the mass of the shell.

Plus since there is no equilibrium and no damping from it

Not sure why you keep saying that. Why isn't there an equilibrium? Why isn't there damping?

[RotoSequence]

Gas floated structures will drift and settle with the ebb and flow of the atmosphere, which is highly compressible. Balancing the roof of an air supported structure requires consistent and equal pressure distribution.

[Mark K]

The shell needs to be strong enough to be pushed on by these pressure gradient forces which are not all normal to the shell so there are tension and shear forces.

No, all the force is perpendicular. There's only compression between the atmosphere and the mass of the shell.

Plus since there is no equilibrium and no damping from it

Not sure why you keep saying that. Why isn't there an equilibrium? Why isn't there damping?

There is no (i.e. negligible) damping because this is like an air spring not a shock absorber. There is very little loss of energy (i.e. damping) from anything - or the shell breaks. The pressure differential just gives restoring force, no damping. All the energy from tidal forces, from hot air in some place rather than others, from things landing on the top of the shell, from radiation pressure on one side of the outside and not the other and so on, is going to get translated into motion of the shell relative to the core.

The only only thing you have mentioned that is going to stop that motion from causing the shell to hit the center is the pressure -differential- between the bottom and the top of the inter shell zone. Not the pressure inside, say 1 bar average - that doesn't help at all, but only the difference between bottom and top - much less.

So as the shell moves the pressure on the inside of the shell moving toward the center increases slightly and the pressure on the other side decreases. Great we have a restoring force - an almost perfect spring. If this force is enough to stop the shell from hitting the center mass (unlikely over time in my opinion, but not calculated) then the shell is going to "bounce" back the way it came, and squish and stretch the shell. the forces will NOT be perpendicular, normal, to the shell.

If the shell is weak it will break. It has to be strong enough so support the whole bounce strains and stresses at all the angles. If it is that strong then little energy will be lost in the bounce - very little damping - so all the "bounces" will over time be added together. If there are any resonances, and there almost certainly will be, look out something will give.

[sanman]

Could you have towers or pillars linking the shells, in order to transmit force more effectively than atmospheric pressure? What complications would that introduce?

[Coastal Ron]

The air between the shell and the surface can move freely to anywhere inside the interior

The air is gravitationally attracted by that "blob of matter", but not by the shell (which has a uniform internal gravity field). As long as the blob-of-matter has a gravitational potential sufficient to create an pressure gradient across the gap between surface and shell (8-10km or so), then that pressure difference will act as a counter-force to any tendency of the shell to drift towards the surface (or vice versa.)

Gravity would NOT create "pressure" within the shell, the air pressure would be created by how much air is maintained in the area between the "blob of matter" and the shell. And since the air can move freely, it does nothing to keep the "blob of matter" centered within the shell.

Gravity is the weakest of the four known fundamental forces, and not just a little, but by a lot. And since gravity is a force that applies in all directions, I don't see how there is a true centering force.

For instance, as the "blob of matter" moves off center, gravity will attract the portion of the shell that is closest stronger than it will attract the portions of the shell that are moving away. No doubt the part moving away is going to be of greater mass, but that means the centering force of the gravity is going to be even weaker.

If the contained mass is too small, then it won't have enough gravity to create a sufficient pressure difference. But Ceres does. And I suspect that most of the dozen largest main belt asteroids would.

Again, it is NOT gravity that determines the air pressure, but how much air has been pumped inside of the shell, and how air tight the shell is.

[Paul451]

Balancing the roof of an air supported structure requires consistent and equal pressure distribution.

Air supported structures have trivial amounts of internal pressure (relative to external pressure). Typically on the scale of a couple of hundred Pascal. Ie, less than half the pressure of Mars' atmosphere. Around 100 grams of force-equivalent per square metre. 1atm pressure gives around 10,000,000 grams per square metre.

[Paul451]

The only only thing you have mentioned that is going to stop that motion from causing the shell to hit the center is the pressure -differential- between the bottom and the top of the inter shell zone. Not the pressure inside, say 1 bar average - that doesn't help at all, but only the difference between bottom and top - much less.

Uh, dude, that's the whole point of shell worlds. It's not something that I've personally tacked on. If you don't understand why the pressure differential occurs, you don't understand the concept enough to criticise it.

If this force is enough to stop the shell from hitting the center mass (unlikely over time in my opinion, but not calculated)

It's not hard to calculate. It's the pressure difference between the ground and shell.

On Earth, as an example, a 5km shell height gives a pressure difference of over 40%, producing a difference in upward force between a pushed down shell section of 2 tonnes-equivalent per square metre.

For the input disturbances, let's use the tidal force due to the moon, which gives around 150 grams of force per square metre of shell.

A difference of four orders of magnitude more restorative force than input disturbance. The shell will barely budge.

Of course, on smaller bodies, the scale pressure difference is less, on Ceres a 10km shell height gives just 4% pressure difference, so 400kg per square metre. But the tidal force from the sun is a tiny fraction of that from the moon on Earth, although the mass of the shell (per square metre) is higher, so it's almost break even. But you still end up with three orders of magnitude difference between the two forces.

the forces will NOT be perpendicular, normal, to the shell.

Compression can't be anything but perpendicular to the surface, because it's ultimately due to gravity, regardless of the disturbing force.

[Paul451]

For instance, as the "blob of matter" moves off center, gravity will attract the portion of the shell that is closest stronger than it will attract the portions of the shell that are moving away. No doubt the part moving away is going to be of greater mass, but that means the centering force of the gravity is going to be even weaker.

The gravitational force inside a hollow shell is uniformly zero, regardless of your position within the shell. I think some guy from the Royal Mint worked it out awhile back. Isaac something. Google "gravitational force inside a hollow shell is".

it is NOT gravity that determines the air pressure

The pressure of the air at ground level is caused by the weight of the air column above it. That weight depends on the mass of the air times by the strength of gravity.

All the shell is doing is substituting for the air that would be above that height in an unconstrained system. It doesn't change the process that creates a pressure difference between the ground and the height of the shell. Hell, there's a pressure difference between the floor and ceiling of the room you're in.

[edzieba]

While the effective gravitational attraction of the shell is uniform inside it, you also have a load of atmosphere sloshing around inside it. e.g. for an earth-mass internal planetoid you have on the order of 5 petatons (5x10^18 kg) of atmosphere. As your internal planet displaces freely it will compress this springy mas and the shove it around inside your shell, causing all sorts of fun pressure differentials and oscillating masses. And by 'fun' I mean 'extremely high energy disruptions to your fragile eggshell pressure vessel'.

[rakaydos]

Instead of a free floating shell around an entire planet, 12 planetary scale pentagonal "domes" might be a better choice. The walls hold the shells in place, and the pressure in adjacent domes help hold up the walls.

[kenny008]

I've read thread several times, and I don't think I understand how this setup supposed to work.  If I'm reading this right:

- You put a shell around a planet
- You pressurize the atmosphere inside the shell to support the "weight" of the shell, keeping it thin and manageable.
- The shell is self-centering.  As it drifts, the air pressure will rise on one side as the shell approaches the planet, pushing it back into position.  This is due to the atmospheric pressure rising as the shell goes deeper into the atmosphere.
- You then propose additional shells with different pressure regimes to allow additional atmospheric pressure options.

     If this is all correct, I don't see at all how this works.  The self-centering mechanism just doesn't click with me.  Won't the atmosphere just move from the "high-pressure" side to the "low-pressure" side?  I can see this maybe generating a pretty significant wind on the planet, but I see no way that it would push against the shell. 

     The reason there is a CONSTANT pressure gradient from sea level to space is because gravity is pulling on the atmosphere, AND also because there is nothing pushing on the atmosphere from above.  Once you start bringing the shell down toward the planet, the atmosphere would have to push back UPWARDS on the shell to move it back into position.  This would cause the atmosphere to not just push up, but also sideways.  In effect, the atmosphere would just move around the planet to the other side, and the shell would not self-center.

     This seems to be equivalent to putting a small ball inside a larger ball.  I can shake the large ball, and the small ball just impacts the sides.  It doesn't build up a pressure on one side and float to the center, where it is stable.  Even performing this experiment in a zero-g environment wouldn't change the results.  The inner ball will just bounce around the outer ball.
     I know in this experiment there is not already a gravitationally-induced pressure gradient, but Pascal seems to indicate that this pressure gradient would shift around the planet.

     Sorry if I'm missing something here.  Just trying to picture this system.

[Stan-1967]

The primary assumption for the system stability is that you are dealing with completely uniform gravitational attraction of the outer shell by the mass contained inside the shell.  This is a poor assumption for an even extremely advanced civilization.  If you wanted to build it around an earth sized & shaped mass, the earth is an oblate spheroid, and has a non uniform gravitational field on the order of milli g's.  That should be plenty to tidally lock some part of your inner sphere to the shell. 

I also think the concept has problems with tidal forces from moons & even the central star.  The outer shell will decouple  its rotation rate from the inner planet over time, as well as it center of rotation.  Similar to how satellites have to periodically correct for lunar induced precession.  There is also the problem of Lagrange points & the system barycenter. The whole system will have a barycenter, however the much larger mass of the inner planet will be moving around this barycenter while the outer shell is decoupled from that barycenter.  How will the system stay stable when the inner planet is not actually rotating around it's center point, but some point far off center.  In the case of the earth, this point is some 1700km from the center of the earth.  This means the inner planet will slam into the outer shell without some magical means of aligning the center of rotation.

So many bad assumptions.  Thermodynamics is also a problem.  When a shell is covering a planets atmosphere ( like the Venus example ) it will cool & collapse the atmosphere because it will have much less solar irradiance.  Now you have a shell not supported by the needed atmospheric pressure.

 

[jee_c2]

Reflecting on the problems with relative movements of the shell and the planet/inner body induced either by gravitational forces or by pressure variencies: theoretically could the shell be anchored to the core with some sort of cables? I think the forces could be really big, so perhaps pillars would be needed as well to stabilize the construct. Still I assume, it would be really hard to achieve a stable system.

Anyway, interesting idea.

[Paul451]

you also have a load of atmosphere sloshing around inside it.

"Sloshing". If the windspeed is, for eg, 100mph/160kmh, the pressure difference against the under-surface of the shell is around 0.17PSI. The pressure difference due to altitude, on Ceres, is more than 0.5PSI, around 3.5 times higher. And if you have enough thermal differences to create 100mph winds, you've probably done something wrong. (Indeed, an issue will be the lack of thermal variation under the thick shell.)

The primary assumption for the system stability is that you are dealing with completely uniform gravitational attraction of the outer shell by the mass contained inside the shell.

No, it's just easy to explain the concept. Your own example of non-uniform gravity in the milli-g's shows how trivial a difference it makes.

The whole system will have a barycenter, however the much larger mass of the inner planet will be moving around this barycenter while the outer shell is decoupled from that barycenter.

The barycentre of the shell and core will barely differ from the CoM of the core, because the shell is fairly uniform.

So you presumably meant the barycentre of the core mass and another mass (such as the Earth and its moon)? Externally, the shell acts as a point mass. Being uniform around the core, its CoM will be trivially the same as the core's. Therefore both would move around the same barycentre, their motion will be similarly coupled to the external mass. That is, if Earth is orbiting around a point 1700km away from the CoM due to the mass of the moon, then the shell is orbiting around a point 1700km away from its CoM (which it shares with Earth) due to the mass of the moon. And because they are orbiting about the barycentre of the same mass (the moon) they will even be locked in the same period and phase.

Similarly to their orbit around the sun. They will share an orbit. Here they aren't locked together and can drift apart, but the system is self-stabilising because of the atmosphere. You'd have to have sufficient external forces to overcome the pressure difference caused by the atmosphere in order to make the shell touch the surface, let alone collapse. As I showed in previous examples, when it comes to tidal forces, you have orders of magnitude margin.

When a shell is covering a planets atmosphere ( like the Venus example ) it will cool & collapse the atmosphere because it will have much less solar irradiance.

That's why it's proposed for Venus. Precisely to help freeze out the atmosphere, while keeping the excess carbon under the shell.

Now you have a shell not supported by the needed atmospheric pressure.

Over the thousand or so years it will take to lose the existing thermal energy, the shell's size will need to be reduced about 1/6th of 1%.

[Paul451]

I've read thread several times, and I don't think I understand how this setup supposed to work.  If I'm reading this right:
- You put a shell around a planet
- You pressurize the atmosphere inside the shell to support the "weight" of the shell, keeping it thin and manageable.
- The shell is self-centering.  As it drifts, the air pressure will rise on one side as the shell approaches the planet, pushing it back into position.  This is due to the atmospheric pressure rising as the shell goes deeper into the atmosphere.
- You then propose additional shells with different pressure regimes to allow additional atmospheric pressure options.

Ignore the last part. Until you understand the basic concept, making it more complex doesn't help. But to clarify, it's not "adding additional shells", it's splitting the one shell into several layers. Same overall mass, but we get more use out of it.

- You pressurize the atmosphere inside the shell to support the "weight" of the shell, keeping it thin and manageable.

Not especially thin. The mass has to equal the pressure you want for the atmosphere. So to approximate SL Earth, you need 10 tonne of force per square metre (minus a bit for the scale height, to allow, say 10km of gap between the shell and the planet or asteroid.)

So for Ceres, you're looking over three hundred tonnes of mass per square metre in order to keep the atmosphere at SL Earth pressure. That means several hundred metres thickness.

The lower the mass of the shell, the lower the air pressure under it.

If this is all correct, I don't see at all how this works.  The self-centering mechanism just doesn't click with me.  Won't the atmosphere just move from the "high-pressure" side to the "low-pressure" side?  I can see this maybe generating a pretty significant wind on the planet, but I see no way that it would push against the shell.

In order to do so, it would have to in-effect raise the atmosphere on the other side up 10km. Or compress it an equivalent amount. That increases the pressure on that side (effectively doubling it), which exceeds the pressure difference you've created on the "high-pressure side", so that obviously can't happen. Instead, the pressure is raised slightly everywhere, which creates a counter-force against the shell. Provided the scale pressure difference exceeds the force acting on the shell.

Remember, we're not talking about a small object floating inside a space-station. The core mass (planet/asteroid) has enough mass to pull the atmosphere and shell sufficiently to create the situation in the first place. That gravity means you can't arbitrarily double the height of the atmosphere on the other side, with exerting an enormous force to counter that gravity.

The reason there is a CONSTANT pressure gradient from sea level to space is because gravity is pulling on the atmosphere, AND also because there is nothing pushing on the atmosphere from above.

Not quite. The pressure at sea-level is caused by the weigh of the air on top. The pressure at any altitude is caused by the weight of the column of air above it.

We are replacing the weight of the air above (for example) 10km in height, with the weight of the shell. Nothing else changes. Including the fact that the air just below the shell is only supporting the weight of the shell, while the air at the surface is supporting the weight of the shell and the 10km column of air between.

Once you start bringing the shell down toward the planet, the atmosphere would have to push back UPWARDS on the shell to move it back into position.

And it does. Look, forget the mass-balancing thing. Imagine the shell was inflated, under tension. Like the classic space-domes that everyone obsesses over. Do you accept that the skin is being stretched by nearly 15psi? Do you accept that a small force, much less than this pressure, will not suddenly cause the skin to collapse against the ground?

This seems to be equivalent to putting a small ball inside a larger ball.  I can shake the large ball, and the small ball just impacts the sides.  It doesn't build up a pressure on one side and float to the center, where it is stable.  Even performing this experiment in a zero-g environment wouldn't change the results.  The inner ball will just bounce around the outer ball.
I know in this experiment there is not already a gravitationally-induced pressure gradient, [...]
Sorry if I'm missing something here.  Just trying to picture this system.

Because you are picturing a small (effectively non-gravitational) mass inside a larger volume. The central mass is the source of gravity for the system. Everything is drawn to it. It is the centre. It's not that the system re-centres the inner ball, the inner-ball forces everything else to move with it. Imagine the inner ball was connected to the outer by springs (representing the atmosphere). We are holding the inner ball (somehow), and moving it around, the outer shell is going to follow, yes? You are seeing the atmospheric effect as a small afterthought (I think so are the others) rather than the whole central mechanism.

I think the better starting point is to picture the pressured skin under tension. Once you are comfortable with that, start imagining the skin was heavier, able to counter some of the outward force of the atmosphere. Ask yourself if anything's changed in how the system works except that the skin doesn't experience as much tension.

If you get stuck with that, picture a gas-filled tube on the surface of the planet/asteroid. (The tube is magically frictionless, naturally.) If we have a column of gas high enough, the weight will put the gas at the bottom under a particular pressure. If we instead have a solid mass sitting on top of the column of gas, equalling the mass of gas we've replaced, the situation will be the same. Provided we keep the gas from sneaking past the solid mass.

[edzieba]

And it does. Look, forget the mass-balancing thing. Imagine the shell was inflated, under tension. Like the classic space-domes that everyone obsesses over. Do you accept that the skin is being stretched by nearly 15psi? Do you accept that a small force, much less than this pressure, will not suddenly cause the skin to collapse against the ground?

Here's the problem: with a gravitationally significant inner mass, that is exactly what will happen. A small offset in skin position will end up with the skin drifting and impacting the interior object. The atmosphere is not a helper here: the shifting skin pushes atmosphere to the other side of the volume, but there is no damping here. The atmosphere is free to oscillate back and forth and has a rather enormous mass of its own. As it is pushed to the other side of the volume, it compresses (and increases the perturbation force for this time), then springs back and produces a pressure spike at the antipode as the atmosphere rushes back around the internal mass to that point.

Because you are picturing a small (effectively non-gravitational) mass inside a larger volume. The central mass is the source of gravity for the system. Everything is drawn to it. It is the centre. It's not that the system re-centres the inner ball, the inner-ball forces everything else to move with it. Imagine the inner ball was connected to the outer by springs (representing the atmosphere). We are holding the inner ball (somehow), and moving it around, the outer shell is going to follow, yes? You are seeing the atmospheric effect as a small afterthought (I think so are the others) rather than the whole central mechanism.

The barycentre problem is because your ball-and-shell is not in isolation. It's (one would assume) orbiting a host body (shell around a planet orbiting a star), and may even have that host body orbiting a host body (shell around a moon orbiting a planet orbiting a star). The barycentre offset means that the centre of mass of the planet is not the barycentre of the system as a whole. Even in the basic case of a star with a single planet (and no other bodies) that means your shell will be pulled slightly sunwards.

[Paul451]

And it does. Look, forget the mass-balancing thing. Imagine the shell was inflated, under tension. Like the classic space-domes that everyone obsesses over. Do you accept that the skin is being stretched by nearly 15psi? Do you accept that a small force, much less than this pressure, will not suddenly cause the skin to collapse against the ground?

Here's the problem: with a gravitationally significant inner mass, that is exactly what will happen. A small offset in skin position will end up with the skin drifting and impacting the interior object. The atmosphere is not a helper here: the shifting skin pushes atmosphere to the other side of the volume, but there is no damping here.

In order to push the skin (or shell) down on one side, you have to raise the local air pressure. That takes energy/work.

Yes, the air will migrate out sideways because of the new pressure difference between that half of the atmosphere and the rest. That is not frictionless nor perfectly elastic however, you aren't going to squeeze air (using Ceres) around ~1500km through a gap 10km wide without serious energy losses. Additionally, the local air doesn't just squeeze out the sides, it doesn't "know" anything but pressure. In order to move sideways, you have to increase the pressure, and if you increase the pressure, you increase the force pushing up on the shell. That acts against whatever force is pushing the skin/shell down to the surface.

How much force are we talking about? I did the maths for both Earth and Ceres. Tidal force (moon and sun respectively) is orders of magnitude too small to overcome the atmospheric pressure gradient and force the shell onto the surface. Orders of magnitude is a decent engineering margin, IMO.

And any disturbance large enough to create a force across a wide area of the shell of more than a tonne per square metre is sufficient to destroy anything on or under the surface of that body. Indeed, probably enough to break up many objects, crack the crust of planets, etc.

The barycentre offset means that the centre of mass of the planet is not the barycentre of the system as a whole.

I've already addressed this in more detail.

The CoM of the shell will be the same as the CoM of the planet. Therefore, WRT any external mass, both are functionally point-masses at the same spot. Therefore both will, independently, have the same barycentre offset. Any small variations between the two will be countered by the atmosphere.

Even in the basic case of a star with a single planet (and no other bodies) that means your shell will be pulled slightly sunwards.

Why would there be a higher gravitational force on the shell than on the planet, that doesn't make any sense at all.

[Stan-1967]

Therefore it only needs existing technology, it's the scale that is... ahem... advanced.

This will require extremely advanced technology that does not exist today.  My BOE calculations for the work required to lift a 1 meter thick steel shell to a height of 1km would take Kardashev I type civilization to dedicate it's full power output ( 10^16 W) for 45 days in an earth equivalent gravitational field. 

If the shell was 8-10 km high per the OP, that would make it over a full year of power output from a K1 civilization.  If it is several meters thick of equivalent mass, then multiply that number accordingly.   K1 civilizations need to have harnessed H-H fusion, as well as possibly antimatter production.  Again, this is just the dedicated power needed to lift the steel or equivalent regolith mass.  It does not include the energy needed to mine & smelt the steel, nor does it account that the construction energy budget would be some fraction of the civilizations total energy production.   

Also what technology allows you to get the shell into place for the initial construction without it falling down?  It seems like you need something not invented yet to magically place all that steel, fully connected , welded, and structurally sound, into it position in the sky as a shell.  Existing technology would require something along the lines of 1st generation space elevator technology for the scaffolding to raise it & place it together.  ( might as well leave the scaffolding in place when done, since that would potentially solve the problem with dynamic motion.

The arguments back & forth about stability remind me of the difference between static & dynamic stability as it relates to aircraft & other systems of motion.  A shell around a central world has a mathematical solution for static stability that seems sound.  However the dynamic stability still seems to have problems.  Hand waiving away & assuming that all the dynamic forces are miniscule or orders of magnitude too small to matter are not good assumptions for long timescale ( decades, century's, millenia, etc. )