Internal Shielding for Space Habitats

 This is a direct followup to my last post, where I ask "what specifically do we get in the yellow region?" That is, what works for the "small" habitats?

Further fueling this, I got a good comment from the internet on the material-specific shielding needs.

"But metals are actually about the worst possible GCR shielding material, they create enough secondary spallation radiation that two tonnes per square meter of solid aluminum is ... actually worse than no shielding!"

and the given pdf link

To recap, I gave 3 regions of space habitats based on the physics.

1. yellow - so small the pressure vessel by itself is insufficient for shielding
2. green - pressure vessel is sufficient(?) for shielding and thermal conduction
3. blue - pressure vessel is so big that heat removal becomes the limiter

It is most likely to be made out of Aluminium just due to what we know is available on the moon, and in that (realistic) case, the yellow region intrudes into larger R values. What I thought was the "green" region actually has insufficient shielding. The solution in both cases is the same - to add more shielding!

The Problem with Adding More Shielding

My goal was to describe a habitat where the shell covers a number of functions, those being:

• (p) pressurization of the habitat
• (h) heat removal from the habitat (the shell _is_ the radiator)
• (r) radiation shielding from all kinds deep space radiation **needs solution**

The problem with adding additional (r) to the outside is that (h) is then blown! This is a philosophical engineering contradiction. It makes me think of the baseball "hand over hand" game. Shielding wants to be on the outside, problem! Now the radiator wants to be on the outside! This isn't just limited to my weird ideas, but a real general strangeness, I asked about it for _micrometeroid protection_ here, which again, is another thing that wants to be on the outside!

To re-state the obvious, if you surround the radiator with shielding, the radiator no longer works.

Alternative - use some kind of fluid (heat pipes) or active heat transfer to go from the surface of the habitat, past the shielding, to a separate radiator on the outside of the shielding. This just loops us right back around to (p), (r), (h) all being separate functions. Can we do any better?

Introduction of Internal Shielding

So let's keep the radiator on the outside, which is the same as the pressure vessel, which is (p) + (h). And we will separately solve the problem of radiation shielding (r), because this does have more flexibility. It physically matters where we put the radiator, but it doesn't exactly matter where we put the shielding. As long as radiation gets stopped sometime before it gets to the humans, we have done our job.

Put the shielding inside the pressure envelope. This was also the size range in which we said that we introduce a _new problem_ of _thermal_ shielding, so both of these structures will be inside, one enveloping the other. It's not obvious which would go in the most-inner location. However, I drew a nuclear power plant in various pictures, so I will put the shielding on the outside, so that the plant can get a lower temperature heat sink without a higher dose. In general, not exposing people working on the thermal barrier to radiation would be nice.

You could also partially coat the _habitat exterior_ in a thermal barrier, since the problem is basically that the radiator works _too well_ in this configuration. Actually, that might help to declutter some of this diagram, so I'll give that snapshot here. It's also useful, because, conceptually, if you get this, you get the overall thing going on with thermal.

That really does help to declutter things. The "thermal blocker" might just be white paint, which is sufficient to decrease the emissivity of the surface. Better, would be "blinds" that could increase or decrease the thermal emissivity on-demand. This would give a thermostat for the space station. The design for this (even though in vacuum) is dramatically more simple than thermal insulation in the atmosphere, so it's hard to see how anyone would choose the in-atmosphere idea. After all, people keep talking about how the vacuum is such a good insulator... this leverages physics more effectively.

This doesn't yet fill in the details of what we would have at the radiation barrier. Because if nothing else, we need heat removal to go through the radiation barrier - bringing us to the central problem here. Can you block radiation, but not block air and movement of people and other things? Yes.

Geometries for Optical Blocking

I know that radiation is more complicated than just this, but to a first approximation you can think of radiation as traveling in a straight line. So bear with me, and let's first focus on the purely "optical" problem. For heat removal, we need air to move freely through the shielding, so it needs to be porous. But no straight line should be able to go through this. This isn't actually fancy or difficult to a first approximation.

First draft internal shielding design - shielding materials are solid lines

This works. In the diagram, the radiation shielding is illustrated with straight lines. There are 2 layers here. One layer has gaps in it, with shielding going perpendicular to the wall, but not all the way to the next layer. The next layer just has gaps and shielding. As long as you can not draw a line that goes straight from one side to the other, this accomplishes the basic concept. This is a 2D sketch, and the 3D version would just require symmetry going out of the page, and that should work.

This comes with additional costs in terms of:

1. constricts flow area of air, which is also our coolant, meaning higher head or higher Delta T
2. needs more shielding material

Exactly _how much_ extra it costs in both cases is interesting, and I have ballparked some numbers. For (1) I got that we preserve 33.3% of the flow area (losing 2/3rd). Before I tried this, I tried it with holes, with a 3-layer design.

holes-and-patches concept for porous shielding

This holes-and-patches idea seemed to get 20% flow area, which is worse. But it is also interesting that the better you do for (1), the worse you might do for (2), and I think this is a legitimate tradeoff in these two geometric examples. That might not necessarily hold for all designs, and truly, I believe some designs may be better in both categories than the ideas I've given here.

I found some form of prior art to say, yes, you can do better. I got some weird places with the AI suggestions. The names get truly weird, like "Gyroid Triply Periodic Minimal Surface". And it was hard to tell if they were still obeying the "optical" blocking idea. But for this one I have relatively good confidence.

https://kenbrakke.com/evolver/examples/periodic/periodic.html

specifically

https://kenbrakke.com/evolver/examples/periodic/gyroid/gyroid.html

This is said to get >80% flow area. Intuitively, I strongly believe that the boxy diagram I drew above can be beaten.

Conclusions

But in any case, we are very good here to say positively that this is possible. Let's bring it back to answer some likely questions - are these segments I drew just floating in air? Mostly. This is microgravity. It just needs some minimal tethers to hold them in place. Next - could people (and possibly cargo trucks) just float through this? Yes, that's the idea. I'd assume there will be hand-holds, or guide tethers to help them.

Next big question - where does the optical assumption break down? Well your shielding would still be primarily basaltic oxides and glass-ceramic from the moon. But in addition to that you need an air gap, plus some low-Z material, and then a thin layer of special neutron absorbers. These are all still relatively abundant from lunar sources. The only real potential conflict with this design is the large size needed for the gap. However, you could just repeat the shielding pattern twice (different materials in each) to give yourself an abundantly large gap. So I would say these constraints could hurt our metrics (flow area, shielding size), but don't conflict fundamentally.

So, I like it. I want to keep it as a decent reference design.

What sizes? Referring to the prior diagrams, starting at sizes of R=0.1 km = 100 meters, it seems kind of plausible. You might not have full flow-dividers for gravity modules, but I expect you could have some kind of gravity module in some sense to stave off bone loss, and I could see this still fitting inside of internal shielding. We haven't really ruled windows, but getting light through the shielding will give extra challenges.

Then for max size, I think it's best to assume some Aluminum given lunar materials for the structure. Going by the argument that it's just not good for shielding at all, we might still need internal shielding, even at R=30km, and maybe even bigger.

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.