Bare Metal Sphere Habitat

 This post will show "convergence of functions" for a space habitat, presenting a design that is surprisingly simpler than expected - the bare metal sphere habitat! The first thing I have to address here is the categorization of functions that a habitat must provide.

Space Habitat Requirements

Hard requirements are non-negotiable things with a physical basis. In this classification, there are 5 of these, aside from the noted location-specific caveats. For any particular design, we want labels for (p), (r), (e), (h), and (g). Otherwise we don't really know what we're looking at. The payoff is that some of these functions converge onto the same structure in some designs.

• (p) Pressurization to 20 to 100% of sea level so humans can breathe
• Much agriculture requires N2 air content, pointing to the upper end of that range (out of scope here)
• (r) Radiation shielding of 2 to 10 tons per square meter
• caveat: some LEO locations can meet requirements with much less
• (e) Provision of energy, could be from external solar, or internal like nuclear
• (h) Heat removal, all energy from prior point plus any radiative ingress from sunlight
• (g) Artificial gravity via rotation

The key distinction is when multiple requirements are served by the same structure, and where they are not. Then, for my own original ideas to be presented with that categorization applied. Why? Because this illustrates the whole point, as functional groupings are *different* in different designs, and I have a very different grouping (compared to prior art) that I want to present to the world.

Habitat Design Families and Lewis One

I'm a little obsessed with the Lewis One space station concept. If you compare to other ideas like Island Three, Lewis One separates functions that might otherwise have been integrated. Specifically, Lewis One separates the shielding into an outer envelope. If you look at its literature, you'll find computer graphics from 1991. It's a bit of a shame that I couldn't find any updated drawings. The internet has maybe three images, not enough to understand what's going on at a glance. So here is my humble redraw.

Later, many of the same people pitched Kalpana One, which goes back toward the classical “everything rotates” design, like 2001's Space Station V. We haven’t built rotating habitats at all, so there is no path dependence yet. Any commercial station currently taken seriously is selling microgravity, not the opposite. At some future point I am convinced we add back in artificial gravity. At this point, absolutely nobody knows how that will happen because it is not anywhere in major current space priorities, private or public. You might start with bearings between the rotating part and other station modules, like Nautilus-X, which was a serious idea. Even assuming that type of thing, it's not easy to say what the next step is. That's why it's a great time to talk about this now - before the industry is ready to talk about this in the first place. That begs the question of what we should be assuming. What is scarce, and what is valuable? By the time we are able to build these... maybe mass-optimization isn't as big of a deal. My philosophically more complex motivation is that, if ASI arrived tomorrow, do we have something worth asking them for? Maybe everything we have yet seriously imagined is too modest. Maybe.

Now, put Lewis One and a classical fully-rotating design into this requirements language. I’ll use “Kalpana One” as the name tag for the classical design family.

Comments directly on these diagrams:

• Whether or not the "external solar" is co-rotating or not depends on design. The Kalpana One writeup makes a surprising choice of remote power transmission.
• Also note that both designs require extra shielding. In Lewis One, this just happens to be separated & stationary.
• Exactly how heat removal and power transmission in Lewis One makes it into the rotating pressure envelope is not spelled out in the Lewis One writeup.
• Lewis One is providing an extra pressurized microgravity habitat inside the shielding. You could argue Kalpana One and others have a near-zero-gravity environment in the center. I don’t buy that as equivalent.
• This is all as-reduced-as-possible, only containing hard requirement features for the most part. Mentally picture these being shiny space habitats crawling with robots and spaceships.
• The "grav module" wording comes from Lewis One. I call the analog structure in this blog just "tubes". I switched my wording to that here. Just temporarily.

Bare Metal Sphere Functions

Now let's get to the "what if" of this all. What if we throw everything away and start all over from the start. We need to hold in pressure. Physics students will make a sphere, so do that. Easiest to assume steel, if not aluminum or something else you can send from a mass driver on the moon. Those have good heat conduction.

We have covered (p), and next up, we ask: do we even need (h), or (r)? Specifically, is there a parameter space where the metal sphere we already imagined (because we have atmosphere) can take care of these functions? This is not obvious, because they go in opposite directions - thicker walls, better shielding, but worse conductivity.

For a first-pass baseline to keep the math clean, assume:

• deep-space thermal conditions (think Pluto vicinity), i.e., minimal radiative ingress from sunlight
• an internal power source, so (e) is satisfied by a nuclear reactor

Now for the hard part, we have one item left out - (g), provision of gravity. Well, that is the subject of this blog. Read my introduction post (link on right) for a basic description of the mechanism, but the idea is that you can rotate a tube inside of the microgravity atmosphere, but you need to add multiple shrouds to have the flow be managed and well-behaved. There are open questions related to how you maintain placement of those shrouds as I described in some recent posts, but I am very serious about proving solutions with experiments. I have little doubt that it is possible, and that is what I am here to convince the world of. So, that's where (g) is satisfied, and the completed diagram is below.

This differs from the pie-in-the-sky idea I've presented before where pressurization (p) is satisfied by rock weight around the sphere.

So with this formalization, I will acknowledge the advantage the bare metal sphere can have over a gravity balloon. The wall thickness is ~10 meters for bare metal sphere, but ~10 KILOMETERS for the gravity balloon. You can get away with conduction in the first case (numbers given below) but not for the second case in a million years. This requires that gravity balloons have some form of active heat removal. See the Orion's Arm article on gravity balloons, which shows a radiator. The large walls are why this is the canonical (and fair) portrayal.

Numerical Analysis of Viability Range

None of what is written here is from AI, but I am now using AI significantly to more quickly arrive at the answers I'm looking for. So here is my folder with details for the analysis, made by Codex / ChatGPT and my prompting.

https://github.com/AlanCoding/gravitational-balloon-mathematics/tree/master/bare_metal_sphere

Referring to the above diagram, there are 2 questions we are asking.

• At what point will the wall be thick enough to cover radiation shielding all on its own?
• At what point will the inhabitants be generating so much heat (due to increasing volume-to-surface area ratio) that the heat cannot be rejected fast enough?

To accomplish this, we have to start putting in specific numbers. Some are simple hand-waves, like using 0.8 for emissivity. Possibly the most complex one to pin down is the heat produced per volume, which comes from assumptions about the society that lives there. I will not go too far into justification, but here is where my spitball number comes from.

$$ q''' = \frac{23{,}000\ \mathrm{W}}{\mathrm{capita}} \cdot \frac{1{,}000\ \mathrm{capita}}{\mathrm{km}^3} $$

$$ 1\ \mathrm{km}^3 = 10^9\ \mathrm{m}^3 \quad\Rightarrow\quad q''' = 0.023\ \mathrm{W/m^3} $$

This is to say: 23 kW per person and 1,000 people per cubic kilometer. Convert units and it becomes 0.023 W/m^3, which is the `q_expected` parameter in the scripts. Shielding is set at 2 tons / m^2.

Put these into the scripts (python -m hab_sphere.numeric_summary --epsilon 0.8 --q_expected 0.023 --mu_req 2000), and getting specific numbers:

• steel
• shielding min: 0.63 km
• thermal max: 26.6 km
• Al
• shielding min: 2.0 km
• thermal max: 36.7 km

This is our first good news! It was not obvious at all that the constraints would "agree" with each other at all. The first number didn't have to be smaller than the second, but it is. Al has better thermal conductivity which is mostly the reason for the difference according to materials.

This is the literal convergence: (p) and (r) are served by the same metal wall at around the kilometer scale.

To give better sufficiency for this analysis, here are the "good" and bad regions plotted:

Neither the yellow or blue regions are fully idea-killers. If the thing is too small, you just need to add extra shielding - and this is exactly what Lewis One is doing (with some other differences). If you are in the thermally-limited zone, then you either need to generate less heat, or make the sphere bigger. Making the sphere bigger in this case might be "wasteful" of materials, but this would be judging prematurely, not understanding the true constraints of our future (possibly post-abundance) society. The ultra-large scales start to describe something more like the world of Virga, where distances between tubes become vast by necessity of heat balance.

Variations on the Bare Metal Sphere

This still needs additional scrutiny. In the good region, we find that the radiator is actually too good. In this case, we would need to add an insulator so that the temperature of the air does not drop too low.

Thermal power plants, inside the atmosphere, would prefer to exchange heat with the walls for efficiency, no matter how uncomfortably cold that is.

What if you wanted to use solar instead? It would be fairly straightforward to add penetrations to the sphere to run wires. After all, this is a non-rotating structure, and you would probably align its orientation with the light source. However, this in any configuration other than perfectly shielded from the sun will decrease the heat rejection capability. If you do extend a radiator outward, it would then be in the penumbra direction. The graphs and numbers here are kind of best-case, if around Pluto or something.

Yes, the temperature of the inner surface of the sphere must be slightly lower than the air due to convective losses, and this should be accounted for in a more accurate script (it is not now). However, I have published many blog posts on how to "globally" circulate the air, so I believe this is only a local problem and solvable in-atmosphere, making it vastly easier and "ordinary" engineering which is what we want.

The next predictable concern is whether increasing to mega-scale sizes might actually decrease the total amount of heat you can produce in the interior due to increasing wall thickness at some point. This does not appear to be the case after running the numbers.

You can see you can make it bigger and bigger, and still put more people in the habitat. The trend appears to continue forever, and breach at least the PW level. Breaching the TW level happens at only (lol) ~200 km radius. Considering the number of people this could house (43 million), that might not be unreasonable.

As a technical note, the mass of both air and metal wall scales linearly with the volume. This is because structural support (assuming some strength value) scales with the (pressure)x(volume) product. That means that, given the material, the habitat requires a constant ratio of air to metal, which is on the order of ~3 for steel with engineering margin. Once you start to think about this, it reveals that if we have mass drivers sending mass from the moon, the air materials, specifically nitrogen, quickly becomes the limiting factor. This is an interesting detail, but not in scope here.

The next objection I'd predict is that my math is wrong. Well, let's look at the breakdown and ask if it looks intuitive.

What we're seeing here is that the low-R regions are under-powered compared to what the steel can handle as a radiator (surprised me). But once we reach the thermal-limited range, we have to allow more temperature drop across the wall due to its increasing thickness. This hits hard due to the T^4 term. At the extreme values of R > 200 km, it would become extremely profitable to add some other heat rejection methods. However, these do not necessarily have to be active. A passive means to increasing heat rejection would be to mix some thermally conductive materials with the structural materials at the cost of a bit more materials.

But overall, I rate the overall idea as almost trollishly effective. Like the gravity balloon itself, I'm sure the reason other people haven't seriously put it forward is because of the apparent uselessness of a large volume of air-filled microgravity. To this, I have a very simple answer, which is to use the flow-dividers to add whatever gravity tubes you want inside of it. This is flexible and evolvable. By using metal structural pressurization, we allow a bare metal sphere hab to be built in cislunar space from mostly lunar materials, which can open up days-scale travel time to a place that has an actual shot at offering an experience, in the long-term, better than suburban existence on Earth, to put it in summary.

We also shouldn't ignore the "vibes" factor of it all. A great big metal sphere with a question mark for what goes inside feels very messy in a good way, similar to a cell of biology. This allows for multiple layers of governance, which is something you want when multiple millions of people are involved. Gravity structures are possible in engineering & economics-wise via flow-dividers, which is important due to human biology. This is more exciting IMO than other designs which say "made your world, here you go!" Starting with an atmosphere and re-arranging the interior ad-hoc feels more like Alpha from Valerian than a sterile space stations. Even extending beyond the pressure envelope, the idea has decent resilience to revisions. Put in literal windows? Should be possible. Docking should be taken for granted, which is large penetration, and might need material reinforcement around it, but that's all.