A glass O'Neill cylinder in LEO

A $200 billion space straw.

Source

No self-respecting sci-fi fan can go without designing a space habitat, so I’ll try my hand here.

Of the different designs, O’Neill cylinders are the most appealing and practical, relatively speaking. Simply spin a large tube to create gravity and fill it with atmosphere. Almost all of the mass that goes into the structure actually translates to usable surface for habitation, unlike designs that spin spheres or discs. And it doesn’t require exotic materials like bishop rings. They can be scaled up by making more of them or extending their length.

So let’s look at how to design one¹. I’m going to assume a few things are already in place once construction starts:

1. A system of space tethers to transfer mass between the moon and low earth orbit. There are other ways to move stuff in cislunar space, but this system will make the O’Neill cylinder less unprofitable and one of the tethers will act as an atmospheric scoop.

2. Rudimentary industry on the moon, mainly to scoop regolith and send it to LEO.

3. Manufacturing capabilities in LEO, mostly to make large structural elements like the wall of the cylinder and the buildings.

The plan

1. The cylinder will be assembled in LEO due to the lower radiation, higher economic value, faster communications, and easier staff changes.

2. Regolith will get processed on the moon to ensure that only useful mass gets shipped and to avoid contaminating the structure with regolith particles.

3. The structure will mostly be made from glass fiber, because it’s more abundant, easier to make, resistant to oxidation, has lower thermal expansion, and has a higher specific strength than aluminum or steel². Better yet, glass fibers pulled in microgravity can be even stronger than those found on Earth. Lunar industry can separate silica from the regolith and send blocks of fused silica to LEO to be pulled into fiber. Aluminum and steel can also be used for certain structural elements³⁴.

4. Unlike O’Neill’s original plan, the cylinder will be small, since housing a lot of people isn’t the goal. More cylinders can be built and linked together if the station needs to grow.

5. Oxygen for the station’s atmosphere comes partially from the moon. Nitrogen and oxygen can also be obtained from tether-based atmospheric scoops.

6. No panes of glass to let sunlight in since this creates fragility, adds engineering complexity, and makes people dizzy. Internal light sources to mimic the sun are used in its place. Titanium dioxide paint on the outside can reflect sunlight to reduce heating.

7. The structure gets its energy from a combination of nuclear power and solar panels placed outside with some assistance coming from energy beamed by microwaves from Earth.

8. Complex products like pharmaceuticals, food, and computer chips are imported from Earth.

9. Orbit raising comes from a combination of electric propulsion and solar sails

Specs

As we’ll see, the uses of an O’Neill cylinder don’t require massive amounts of space, so to make construction easier and lower the mass requirements we’re going to use a small cylinder.

Orbit: Low-Earth orbit

Length: 1 km

Radius: 100 m

Internal surface area: 0.7 km^2

Gravitational acceleration felt at the surface: 0.5g⁵

Population: 10,000

Population-weighted density: 20,000 people/km^2 (Similar to Seoul, South Korea)

Built area: 0.5 km^2

End caps: Aluminum hemispheres

Structural material: S-2 glass fiber

Thickness: 1 m

Tensile strength: 4890 MPa

Compressive strength: 1600 MPa

Density: 2460 kg/m^3

Breaking length: 203 km

Atmosphere: 78% nitrogen, 22% oxygen, 1 bar pressure

I consider the population density to be a low estimate, some cities on earth have higher population-weighted densities and in space people have to be comfortable with tighter living quarters. I also consider the mechanical properties of the glass fiber to be conservative estimates, because we can pull stronger fibers in microgravity and cool them to make them stronger.

In the appendix, I check that the structure can handle the stresses from the rotation, buildings, and atmospheric pressure and find that these stresses are almost two orders of magnitude smaller than the strength of glass fiber.

Flying, interior design, food, and sunlight.

One of the benefits of making such a tiny tube with low gravity is that you can fly places. With a 100m radius and half of Earth’s gravity, you only have to get 50m off the surface to reach a quarter of your weight relative to earth⁶ and at the center you’re weightless. With a strong enough drone, you can take off from the ground⁷⁸! This is the ultimate transport system, it has faster transit times than any place on Earth with no need for cars, planes, or monorails. With only walkways and bike paths between the buildings, the city itself enjoys a form of walkable mixed-use urbanism that terrestrial city planners can only dream of.

The diameter of the structure is 200 meters, about the height of a 50-story skyscraper. For fun, you could even have a few skyscrapers span the structure. These would provide structural support and dense housing, though the gravity might make the more central floors unlivable⁹. From a few stories up, you can launch right off your balcony and fly wherever you’d like.

Since the buildings take up a smaller footprint, a larger area (30% or more) can be devoted to green spaces. The soil has to be imported from earth, so it can’t be too thick; plants with shallow roots will predominate. Careful monitoring of particulates and gasses released from the soil and constant replenishment of the soil microbiome will be required. Hanging gardens and planter boxes can provide more greenery per unit mass than an open field. Adding a large lake creates valuable scenery while requiring less mass than soil. The lake serves many other purposes since it can moderate temperatures, provide humidity, and act as a propellant depot.

For food, the cost of importing from earth is so high and space is at a premium, so it makes sense to use vertical farming, precision fermentation, or peptide nanotechnology to produce food. Human waste and exhalations can be atomically recycled back into food.

For lighting, the glass panes used for sunlight on the original design never made sense to me. They seem hard to build and worse, knowing how fast the outside is rotating might make people dizzy. Artificial lighting designed to mimic the sun should work fine. I imagine a small version of the sphere in Vegas set in the center of the lake would produce a spectacular sunset.

Cost

It’s hard to estimate the costs of such a structure since most of its mass is produced by industries that don’t exist yet. Once construction equipment is put on the moon and in LEO, the opportunity cost of using the equipment is quite low. The moon doesn’t have useful resources to sell to earth, and massive quantities of glass fiber in LEO aren’t useful for much else¹⁰. So the main costs are buying the equipment, putting it in space, and replacing it when it breaks.

We can easily upper-bound this cost using launch costs to LEO, since sourcing material on the moon will have to be cheaper than launching from Earth to justify the effort. Long term, I expect the moon can offer an order of magnitude lower cost of getting bulk material to LEO.

With the dimensions I’ve given, the density of S-2 glass fiber, and a cost to LEO of $100/kg¹¹. The total comes out to $160 billion. I had to rerun the numbers a few times because this is extremely low for a government project; even with a 10x fudge factor. Heck, Jeff Bezos, an avid fan of O’Neill cylinders, could fund this today if he wanted to.

But that’s just the cost of the outer shell, we also need to move people (1E6 kg), atmosphere (4E7 kg), buildings (3E7 kg), soil (1E8 kg), and water (4E7 kg) up to LEO, adding $21 billion. I’m not sure how to price-in the cost of other raw materials, but S-2 glass fiber costs $20/kg, so that adds $32 billion (though the price would fall with scale)¹². That brings the grand total to $212 billion.

The real headache is when we need to safely transport people to the station and assemble all of the parts. Fortunately, most of the construction can be done with teleoperated robots since the latency to LEO is tiny. Once built, the station will require constant support from Earth to repair damaged parts, replace crew, and replenish supplies.

While these costs are manageable for governments, there’s real value in cutting costs further so that smaller countries and other groups can build their own foothold in space. It looks like launch costs could bottom out at $10/kg, but orbital manufacture can bring the price down much further.

Uses

Though I don’t expect it to be profitable, there are many uses for this structure that make it less-unprofitable. Once you’re in LEO, you’re halfway to anywhere and there are plenty of uses for a town that straddles the path between earth and the stars.

The station can do all sorts of medium-complexity tasks required for space industry. It can convert raw materials from the moon into structural components and combine them with complex parts made on Earth.

These manufacturing capabilities are particularly valuable for satellite repair and repurposing. Repair is hard to automate given the variety of ways satellites can get damaged, it requires a team with experience assembling satellites and access to spare parts.

The facility can also act as a propellant depot and clearinghouse for all sorts of products. Oxygen is a biproduct of refining metals on the moon so the colony can deliver LOX (which makes up almost 80% Starship’s mass) to ships in LEO¹³.

But perhaps most interesting is the provision of nuclear fuel. The moon has massive amounts of uranium and thorium; separating it from the regolith is relatively easy. It doesn’t make sense to bring these supplies to Earth, we have plenty of nuclear fuel already. The fuel is more valuable in space where they can provide nuclear propulsion and power. But enrichment is technically and politically tricky. A colony in LEO would have the kind of oversight and support needed to enrich these fuels and is in the right location to provide fuel to ships bound for other parts of the solar system¹⁴.

Imagine how much this could help the space industry. Groups that want to build something in orbit need only send a blueprint along with some bespoke parts like computer chips or sensors. Struts, solar panels, solar sails, cooling systems, antennas, tanks, LOX, nuclear thrusters, and other heavy parts can be provided and assembled in-orbit. Satellites will last longer with regular repairs, and when its time to decommission a satellite, it can be sold for scrap rather than burn up in the atmosphere.

These factors put the station in an excellent position to service the $2 trillion telecommunications industry. Counterintuitively, a station in LEO can communicate faster with any place on earth than places on earth can communicate with each other. This also makes it an excellent platform for things like stock exchanges. The colony can also support many of the other opportunities I mentioned in a previous post, including tourism.

In spite of these opportunities, it’s probably still too expensive to cover costs. But it’s not too costly, eventually some government or group will just foot the bill on their own. The social value of research in space is likely far larger than its costs.

Conclusion: how this fits into space exploration more broadly

The cylinder’s location lends itself naturally to assisting all sorts of orbital activities. By interfacing raw materials from the moon with complex products from Earth, the colony can support a huge (and profitable) industry in cislunar space.

The design is intentionally small to lower the initial cost, but can be extended to greater lengths, forming a “space straw”¹⁵. With more experience, people can build larger structures and tackle challenges farther from Earth¹⁶.

An established industry on the moon and a colony in LEO will make it much easier to move material to Mars and Venus and the lessons learned from living and working in orbit will transfer to these new colonies.

As people explore the outer reaches of the solar system and head to other stars¹⁷, I imagine this will be one of the first things they build. A familiar habitat made from abundant materials that can cocoon us from the emptiness of space.

See also

The artificial gravity lab. Notice how unintuitive the Coriolis effect is but how quickly Tom Scott adapts to it.

Con Hathy on rotating spaceships for artificial gravity. It turns out you can train your inner ear to get used to small radius centrifuges.

This video shows what the interior of a 1 km diameter O’Neill cylinder would look like, this is the closest example I can find to compare to the 0.2 km diameter I’m proposing here. See also: Medina station from the TV show The Expanse, which is 0.5 km.

The High Frontier: A Technical Critique.

Appendix

It was surprisingly hard to find resources on mechanics of O’Neill cylinders, so I hope this can be a reference for fellow travelers.

There are a few terms we need to specify:

Cylinder

inner radius: r (meters)

wall thickness: t (meters)

outer radius: R = r + t (meters)

height: h (meters)

Rotation

angular frequency: omega (radians/sec)

acceleration: a (meters/sec^2)

Note that a=(omega)^2*r

Material

density: rho (kg/meter^3)

tensile strength: s (MPa)

breaking length at acceleration ‘a’: B_a = s/(a*rho) (meters)

Note that the free break length or break length is equal to B_a when the acceleration is equal to Earth’s gravitational acceleration (g, 9.8 m/sec^2).

Let’s make sure the structure can handle all of the stresses on the system. For these calculations, I’m often going to make a thin-walled assumption which is common in the literature. Specifically, we assume that the radius (r) is at least 10 times longer than the thickness (t). I’m also going to ignore the mass and area of the hemispherical caps on the ends of the cylinder, they make a negligible contribution to the overall mass and area since they only have to hold back the atmospheric pressure (and don’t change the mechanics much).

First, observe that the ratio between the volume (V) and inner area (A) of a cylinder is:

\(\frac{V}{A} = \frac{\pi h (2rt + t^2)}{2 \pi r h} = t(1 + \frac{t}{2r})\)

With the thin-wall assumption this becomes:

\(\frac{V}{A} \approx t\)

Since the overall mass is just the density times the volume we get:

\(\frac{M}{A} \approx \rho t\)

We want to minimize this number, since we want to produce the largest amount of livable area (A) for a given amount of mass in orbit.

On to the mechanics. Let the pressure from the atmosphere be p_atm and the pressure from the buildings be p_b. In a cylinder, there are three kinds of stresses it experiences:

Hoop stress or circumferential stress is a tension along the circumference of the cylinder. It has components that come from the rotation of the cylinder, the atmospheric pressure, and the weight of the buildings. It will end up being the largest stress the cylinder experiences. Here’s the formula for each component:

Atmospheric pressure:

\(\sigma_{\theta, atm} = \frac{p_{atm} \cdot r}{t}\)

Building pressure:

\(\sigma_{\theta, b} = \frac{p_{b} \cdot r}{t}\)

Rotational stress:

\(\sigma_{\theta, rot.} = \omega^2 r^2 \rho = ar\rho\)

Axial stress is a tension along the cylinder’s length due to the atmosphere pushing on the end caps.

\(\sigma_z = \frac{p_{atm} \cdot r}{2t}\)

(note that some people use sigma_z to refer to the hoop stress)

Radial stress pushes radially outwards (or down into the floor of the O’Neill cylinder) compressing the walls (this is important because glass fiber is weaker in compression than in tension). It comes from the atmospheric pressure and the weight of the buildings.

Atmosphere:

\(\sigma_{r, atm} = \frac{p_{atm} \cdot r}{2t}\)

Buildings:

\(\sigma_{r, b} = \frac{p_{b} \cdot r}{2t}\)

Just to be clear, the pressure of the buildings is:

\(p_b = \frac{m_b \cdot a}{A_b}\)

Where m_b is the building mass and A_b is the area of the buildings.

Notice that the hoop stress contains terms that are larger than the terms in the other stress components. So let’s focus on the hoop stress for now. Setting the hoop stress equal to a safety factor (f) times material’s tensile strength we get:

\(f \cdot s = \frac{p_{atm} \cdot r}{t} + \frac{p_{b} \cdot r}{t} + \omega^2 r^2 \rho\)

Solving for t we get:

\(t = \frac{r(p_{atm} + p_b)}{fs - \rho a r}\)

Going back to the mass over area formula:

\(\frac{M}{A} \approx \rho t = \frac{\rho r(p_{atm} + p_b)}{fs - \rho a r}\)

Flipping the expression, substituting in B_a, and simplifying:

\(\frac{A}{M} \approx \left( \frac{f \cdot B_a}{r} - 1 \right) \cdot \frac{a}{p_{atm} + p_b}\)

Remember, we want to maximize the amount of area we get for a given mass. Other tricks like nesting cylinders and denser living quarters only change this ratio by a constant factor.

The first term in parenthesis is the ratio of the maximum safe radius (with the safety factor included) relative to the radius. As this approaches 1, the thickness has to increase to accommodate the stresses, and the area per mass falls to zero. As you can see, we want r to be as small as possible.

Let’s calculate what the thickness should be under the design parameters at the beginning of the post and use a conservative safety factor (f) of 0.1. Atmospheric pressure (p_atm) is about 0.1 MPa. I’m going to assume the cylinder is filled with 50 story skyscrapers that weighs 250,000 tons with a footprint of 3000 meters^2 that offer no structural support (very conservative assumptions) which creates a pressure of 0.37 MPa.

Putting it all together, t is 0.0964 meters or about 10 centimeters, much smaller than the 1 meter used in the design.

Practically, this means is that the thickness is going to be determined by factors other than the stresses on the cylinder. Things like weird mechanical effects, the need for radiation shielding¹⁸, fixed costs, passenger comfort, and the rate that damage from space debris can be patched will all constrain the thickness to some minimum value.

Assuming there is a minimum thickness value, we can calculate what the mass and area per unit mass are.

\(M = \pi h \rho \cdot (2rt_{min} + t_{min}^2) \approx \pi h \rho \cdot 2rt_{min}\)

Where the last formula comes from the thin wall assumption. Total mass scales linearly with the radius.

If this wasn’t enough math for you, you can try to redo these calculations without the thin-wall assumption. For that you’ll need the Lamé equations, this presentation might help.

Some other links:

Cylinder stress

Pressure vessel

Rotating bodies - stress

Implications of Molecular Nanotechnology Technical Performance Parameters on Previously Defined Space System Architectures

1. Note that usually two counter rotating cylinders need to be linked together.

2. Glass fiber can also be cooled to increase its strength, which is one potential application of liquid nitrogen produced from orbital atmospheric scoops. Cooler external layers also have a higher neutron cross section, improving their shielding abilities.

3. A side effect of all of this mass moved to LEO is that it can be used to spin-up a space tether which is another source of profit.

4. The structure may need to include modular tiles so that the parts of the wall damaged by radiation or debris can be swapped out. Inspired by seeing how Dragon’s beard candy is made it might be best to make small spools of glass fiber and link them together like a chain link fence. Broken spools can be swapped out while leaving adjacent elements intact. A loose, nestlike structure makes it more accessible to robots.

5. When I put these parameters into SpinCalc they look fine, though the angular velocity is slightly too high.

6. There are more whimsical ways to reach the weightless center: you could walk up a “stairway to heaven”, ride a helium balloon, or launch off a slingshot. Care must be taken when landing as the other side of the cylinder is moving at an apparent velocity of twice the rotational velocity. Just to be sure, we should add some foam pits with aerogel blocks, fun colors optional.

7. If I understand correctly, you could float to the center with a small amount of lift by flying anti-spinwards fast enough to cancel out the rotational velocity. Then you could fly along the axis until you reached your destination. To land, you would need to fly fast enough to catch up with the ground (or just land on a platform near the center and climb down). Alternatively, if you can produce enough thrust, you can fly spinwards towards the center, get deflected back towards the ground, and glide to your destination. But you’re probably safest climbing to a platform, flying at a constant altitude along the axis, and landing on a platform at the same altitude and climbing down.

8. It would be fun to play a VR game that simulated all the little details like the density gradient of the air, the Coriolis forces, and the differences when travelling in spinward and anti-spinward directions.

9. These can be used as a zero-g research facility.

10. This isn’t entirely true, the fibers could also be used to make huge space tethers. It may be cheaper to make tether material on Earth and launch it up, but the mass ratio on some tethers is pretty high, suggesting that bringing in mass from the moon could work.

11. This is a high estimate given the fact that SpaceX plans to reduce costs to $10/kg. Tethers and new jet engines can reduce costs even more.

12. If launch costs get low enough, this could start to be a larger portion of overall costs. At that point, the choice between manufacture on the moon or Earth comes down to the relative quality of fibers made in microgravity, since the cost of lifting the equipment to LEO would be negligible.

13. Two elements that are hard to get in cislunar space are carbon and hydrogen. I expect liquid methane (or something like methanol) will be the bulk of the mass launched to LEO from Earth in the future.

14. Could enriched fuel come from Earth? Of course, but for applications requiring large amounts of fuel, the costs and hazards of putting lots of enriched fuel on a rocket are too great. See also: SNAP-X: The Space Nuclear Activation Plant.

15. A small design increases the speed of construction which means that designers can iterate more quickly. Costs could potentially fall due to learning effects.

16. A neat way to transfer a cylinder to other places in the solar system: make solar sails from thin sheets of lunar material and fly them to your destination, melting them down and assembling into a cylinder upon arrival.

17. If they’re not Em’s by that point.

18. The radiation shouldn’t be too bad in LEO behind a meter of glass. Though regular crew changes may still be required. Glass should have similar radiation protection as concrete, which has a half-value thickness of ~1.5 meters. See here, here, and here for more. There have also bee recent developments in active shielding.