I did some calculations on popular cylindrical rotating space habitat designs, from the almost-practical Kaplana One to the ridiculously huge Banks Orbital. What would they be made from, and how much would they weigh? The O’Neill Island Three Cylinder was designed to the theoretical limit of steel, and the Mckendree Cylinder to the theoretical limit of carbon nanotubes, but are those really the best materials? And how much would we need? How much material could we save by reducing the gravity or air pressure? What kind of material would we need to construct a Banks Orbital?
|Name||Length (km)||Radius (km)||Floor Area (km2)||Earths||Cap height (km)||People (dense)||People (sparse)||People (really sparse)|
The sparse figure is 510 people/km2, the density of South Korea.
Really Sparse is 32 people/km2, the density of the United States
Structurally, space habitats are a cross between a balloon or pipe and a flywheel. Much of the pressure that the structure needs to contain comes from air, with the mass needed for radiation shielding also a significant consideration. Air pressure on earth is 15 psi, or 10 tonnes per square meter. That’s five 2 ton cars per square meter! Smaller habitats would be completely full of air at an essentially uniform pressure, while McKendree Cylinder sized structures would have a vacuum in the center (on Earth the air extends up about 100 km).
Materials I considered are metal alloy and fiber composites. The best modern steel and aluminum alloys have similar strength to weight ratios, with titanium alloy being slightly higher. Fiber composites have a strength to weight ratio 10x-15x the best metal alloys. Examples of composite material are carbon fiber, fiberglass, and aramid (kevlar) fiber. These materials derive their strength from the fiber part, which is essentially a fabric, and which is held together with a plastic substrate. Carbon nanotube materials (aka graphene) have a theoretical strength to weight ratio of about 20x current composites. Constructing a Banks Orbital, with a diameter of 3 million kilometers (10 times the distance to the moon, or 10 light seconds), would require a new exotic material with a strength to weight ratio 500x better than carbon nanotubes.
|Materials||titanium||steel eglin||aluminum||basalt (glass) fiber||kevlar||graphene||exotic|
The relevant properties for space habitat materials are tensile strength and density. Tensile strength (strength under tension or pulling) has the same units as pressure, usually expressed as MPa or psi and is the amount of force per unit area the material can resist before breaking. Density has units of mass over area, often expressed as g/cm3 or kg/m3. Because the space habitat structure needs to support itself, the ratio of strength to density is critical.
It makes sense to build such a habitat out of materials mostly manufactured in space, probably mostly on the moon initially. The obvious material for radiation shielding is simply lunar regolith (sand). Water tanks and other bulk supplies would also presumably be located on the floor/shell of the habitat to act as shielding. Iron, aluminum, and titanium are all available on the moon, although the necessary processes to extract them, especially in sufficient quantity, need to be developed. One particularly interesting type of glass fiber is Basalt fiber, which can be extruded directly from certain types of rock and may be convenient to manufacture on the moon. Chemically, lunar regolith is basically oxygen + metal + silicon, so it may turn out that a single machine can produce both metal and glass (silicon + oxygen) fiber from lunar regolith. There is almost no carbon on the moon, so the plastic part of the composite would need to be manufactured from carbonaceous asteroids.
It’s unclear how to get megatons of nitrogen gas into earth orbit for the station atmosphere, since there isn’t much nitrogen on the moon or on near earth asteroids (oxygen is abundant on the moon). Comets and Trojan asteroids with frozen Ammonia (NH3) are a possible source.
The following table shows the wall thickness of the habitat shell in meters, using various materials. It follows the O’Neill cylinder and Kaplana One papers in using 1G and 0.5 atm of air pressure (42% oxygen, 58% nitrogen). We assume 5 t/m2 of shielding material as well as 1 t/m2 of contents (i.e. people, furniture). We have ignored the mass of thermal radiators, solar panels, and other parts which might be attached to the hub. Calculations use a 1.5x factor of safety on the material stress limit, which is common for aircraft designs.
|Name||t (steel)||t (Al)||t (glass)||t (kevlar)||t (graphene)||t (exotic)|
A steel Kaplana One would be 3cm thick, and a composite version only 1cm. The O’Neill cylinder made of steel as originally envisioned would be nearly a meter thick, but the same cylinder made of the exotic material sufficiently strong to support a Banks Orbital could be only 10 microns thick. The following table shows masses. We assume that the end caps are half as thick as the floor, and that the Bishop Ring and Banks Orbital have 200km tall edge walls.
|Name||Shielding||Furnishings||Air 1atm||Air 0.5atm||m (steel)||m (Al)||m (glass)||m (kevlar)||m (graphene)||m (exotic)|
The mass of Kaplana One is mostly shielding and contents. A metal O’Neill cylinder would not need any shielding beyond the shell, since the mass of the shell exceeds the mass of required shielding. An exotic matter O’Neill Cylinder would still weight 20,000 tons, or 200 100t SpaceX Starship launches. A steel version would require about 50 million launches for the shell and another 27 million for the air and contents. The masses of the larger habitats are dominated by the air.
The following table shows the wall thickness for the habitats while varying atmospheric pressure and spin gravity.
|Name||Material||t (1 atm, 1 G)||t (0.5 atm, 1G)||t (1 atm, 0.5 G)||t (0.5 atm, 0.5 G)|
The International Space Station is pressurized to 1 atm, while the Apollo missions used pure oxygen at 5psi or 0.33 atm. Pure oxygen atmospheres are impractical for large habitats, since they greatly increase the risk of fires (as in Apollo 1) and require significant adjustment times for people coming from Earth atmospheres to avoid problems with nitrogen decompression sickness. A 0.5 atm pressure seems like a reasonable compromise and has significant mass savings. Reducing the spin gravity doesn’t actually reduce the mass all that much.
We calculated the masses of various space habitats when built with various materials and parameters. Fiberglass or another composite seems like a more practical material for near-future space habitats than metal alloys, with a ~10x reduction in mass. A practical design taking into account more factors like micro-meteorite protection, space weathering, etc, would likely use a combination of materials.
An interesting consequence of the importance of air pressure in habitat design is that rotating space habitats would not consume significantly more materials than large pressurized domes on, for example, Mars. Of course it’s more difficult to access materials in orbit.
The type of steel I considered is Eglin Steel, which was designed by the USAF and is about twice as strong as the 4130 cro-moly steel in my bicycle, itself about twice as strong as the standard structural steel used for I-beams. Another interesting superalloy is Maraging steel which contains about 20% nickel by weight – coincidentally similar to the ratio of iron to nickel in many nickel iron meteorites (and asteroids).
Carbon fiber (as far as I can tell) has similar properties to kevlar composite, so I’ve only included kevlar in the calculations.
t=((Pa+G) R)/(s - a p R)
m=2 pi (R h + 0.5 (R^2 - r^2)) t p
s stress limit of structural material (Pa)
p density of structural material (kg/m3)
R radius of cylinder (m)
r radius of top of end cap wall (R – Cap Height) (m)
h height of cylinder (m)
t thickness of cylinder (m)
Pa pressure of atmosphere (101,325 Pa for 1 atm)
G pressure of contents (Pa, aka kg/m2)
a acceleration due to gravity (9.8 m/s2)
The above equations are derived from the hoop stress equation
s = P R / t
and flywheel stress equation
s = p R^2 w^2
where w is angular velocity (rad/s) and
w^2 = a / R
End caps / side walls are assumed to be half the thickness of the floor
- Kaplana One: https://space.nss.org/kalpana-one-space-settlement/
- Bishop Ring: http://www.iase.cc/openair.htm
- McKendree Cylinder: http://www.zyvex.com/nanotech/nano4/mckendreePaper.html
Shouldn’t the mass be 2 pi r h t p + pi r^2 t p / 2 ?
You are right! My spreadsheet actually had the formula you provide, but I screwed it up in the notes.
I also made a mistake calculating the mass of the end caps for open ring habitats like Bishop Rings – it should be `2 pi (R^2 – r^2) t_e p` where R is the outer radius and r is the inner radius. I had been calculating it as `2 pi (R-r)^2 t_e p` which is a much lower value. (note that we are assuming end caps are half the thickness of the floor, so t_e is t/2)
Anyway thank you for noticing and telling me, I updated the equation and table of habitat masses.
Excellent analysis. Reminds me of the one done in the Journal of the Traveller’s Aid Society No. 23 for Traveller, but much updated.