Limits on the scale of Space Habitats

[Hornblower]

Well, I'm wondering if this rotating cylinder can, say, have framing in a hexagonal shape on the outside (not ends), and use some kind of internal ties, along with lighter, less thick material sufficient to hold up between the hexagonal grid, or something like that, in order to both provide pressure retention (i.e. atmosphere) and sufficient safety factor for a 1G environment.

But I'm sure this complicates the analysis. And I'm not a civil engineer, so maybe I could just be wrong in assuming that using a variety of materials in some creative fashion might give better results.

I find no reason to disagree with Isaac's opinion that a simple circular ring or hoop is the strongest possible structure for resisting centrifugal stress with a given amount of material.

There are a number of advantages to making the shell thicker; a thicker shell would allow a larger payload, and would give better protection against space radiation.

In a rotating habitat the amount of payload (landscape, life support systems, atmosphere and people) the hoop can support depends on how strong the hoop is. If you have a thin hoop near the limit of hoop strength for that material it can only support a tiny payload. But a thick hoop of the same material with the same radius could support a larger payload.

The payload can be regarded as a fraction of the total mass - if that fraction is necessarily small for a habitat of a given radius, then you can support a bigger payload by increasing the mass of the load-bearing material as well.

I never intended to imply otherwise. If the shell is under the spin rate that would break it in the absence of a payload, of course a thicker one could carry larger payloads. I was just looking at the extreme theoretical case of an empty shell coming apart under its own centrifugal stress.

[adapa]

Someone may have already mentioned this but I think using a "hub and spoke" type structure would be very helpful. This could relieve much of the tensile stress experienced by the outer shell and result in more of a semi-monocoque structure. Also, the "spokes" could be made of composite material with the outer shell being made of steel. The outer shell would protect the spokes (and the occupants) from the radiation while the tensile strength of the spokes would reinforce the structure.

Also, if you have more spokes than needed, this would make maintenance slightly easier because the spokes could be maintained one at a time.

Anyway, I could be wrong because it's been a long time since I have studied engineering.

[Philippe Lemay]

@adapa
It's an idea, anyway I seriously doubt most designs would have the central axis be completely empty. Especially if we go for the non-window approach, we're going to need some form of illumination which would most likely be located at the central axis. Add in some maintenance infrastructure to go with it, a few zero-G labs, and maybe even just some recreational facilities, and you suddenly have a need to transport people quickly to the axis. Spokes could support elevators to do this.

And if the hab is large enough, the spokes could even serve as a method of quickly travelling from one end of the hab to the other, rather than crawling all the way along the inner rim.

[swampyankee]

Digging through my structures books (I'm not a structures guy, but some stuff is basic)....

There are two stresses on a cylindrical space habitat: the hoop stress from internal pressure and rotation, which is going to be something like:

σ_hoop = PR/t + ρω²R² (the t's cancel in the second term)

and an axial stress which will be

σ_axial = PA/t

where "A" is the area of the endwall of the pressurized shell. This need not be the same as the area of the end of the cylinder; e.g., if the "cylinder" is a Stanford torus.

For some perspective, the sea level atmospheric pressure is about 100 kPa, and structures on Earth are typically designed for live loadings -- that's everything except structural weight -- of about 3.0 kPa (there are also deflection limits, say 1cm in a 5m span, which may actually force the structure to be much stronger than 3.0 kPa) over its entire surface, with the possibility of more intense local loadings.

Rewriting the hoop stress equation so the second term is in terms of acceleration gives:

σ_hoop = (P/t + ρa)R

Picking a rather high allowable stress level -- say 700 MPa -- and what I would view as a fairly realistic value of ρa, 30,000, and P/t -- 100,000 -- let's me solve for some value of R, which is about 5400 m. Ignoring the pressure would permit a larger R -- about 23000 m. Clearly, one wants a structure where the pressure and rotational stresses are not carried by the same structure

I'm going to dig up the formulae for stresses in a thin-walled torus. These are a little bit trickier, but I suspect that they are more applicable to the most likely rotating space habitats than those of a cylindrical pressure vessel. Oh, yes, I've ignored the axial stresses. Think of it as homework.

[Philippe Lemay]

I'm really not a math guy... I don't know what half those variables mean (what's the little w, work?).

Clearly, one wants a structure where the pressure and rotational stresses are not carried by the same structure

Well... if the envelope of air wants to hold a gravity, it's going to have to spin, which will submit it to the rotational stress.

The only way I can figure preventing this is if you put the entire rotating frame inside of a bigger pressurized envelope (I think something like this was suggested on page 1), but then the rotating part is subject to some friction from the gas it's immersed in.

[swampyankee]

Oh, sorry.

P is pressure.
A is area
a is acceleration
t is thickness
σ is stress
ρ is material density
ω is rotational velocity.

Use consistent units, and all will be fine.

Actually, it's easy to have the rotational and pressure loads carried by different structures: just picture something like the Millenium Wheel where the individual cars are pressure vessels.

[JeffD1]

If a threat to carbon fiber or other exotic materials is UV and cosmic rays, then could you not simply(like any of this is simple) surround the rotating cylinder with a non-rotating one made of steel or other type of shielding?

[swampyankee]

If a threat to carbon fiber or other exotic materials is UV and cosmic rays, then could you not simply(like any of this is simple) surround the rotating cylinder with a non-rotating one made of steel or other type of shielding?

The UV is easy: use paint. Actually, the environmental threat isn't so much against carbon fiber (although atomic oxygen will do a carbon fiber very little good) but against the long-chain polymers that make up the matrix that holds all the fibers together. This is why I suspect that metal-matrix composites would be a better solution for structural elements exposed to space.

Any structure that is under primarily tensile loads, such as a rotating space habitat or even a pressurized, non-rotating space habitat, will need constant maintenance and inspection.

[Hornblower]

Let's not complicate things by pushing the tensile strength envelope so aggressively. Just make the radius small enough to have a generous safety margin. If we need more capacity, enlarge it by means of a longer cylindrical structure. That will not add any centrifugal stress.

[swampyankee]

I think an interesting question is "what is the least radius for a habitat rotating to simulate Earth's surface acceleration that is practical for long-term human habitation?" I'm going to put in a vote for about 100m. Much smaller than that and I suspect that the difference in perceived acceleration with changes in posture would be too noticeable.

[IsaacKuo]

2rpm may be the practical limit, or about 1/5 radians per second. To provide about 10m/s/s artificial gravity at 2rpm, the radius would have to be 10*5*5 = 250m.

A 250m radius sphere would have a volume of about 62,500,000 cubic meters, or enough volume for a population of 450,000 at I.S.S. population density (6 per 837 cubic meters).

[Philippe Lemay]

It depends on how long you plan on being aboard station, the ISS crew manages to handle zero G for a few months, simply adding 0.25 G would help endure these or longer periods. I'm sure there some relation between how much gravity you have and how long you can stay in space before your health starts to be affected. Going from a few months at near zero to indefinitely at 1.0 G. And yea, I ran the numbers a while back and ran into a similar number to Isaac's, 200 - 300 m. It depends on how much spinning the people are able to handle before they start to get motion-sickness.

But while I acknowledge that 250 meter stations may be more efficient in the near term, I really wanted to know if we could have true cities in space. Baring the economic hurdles of course. I'm hoping that one day we figure out a way to divert near-Earth-asteroids into Earth orbit, assuming people can get over their fear of giant space rocks... Think of it... bringing billions of tons of ice and ore into medium Earth orbit, it would be like having a tiny second moon. MUCH closer to us than the actual moon, and thus much easier to reach. From there we can use it as a platform upon which to build, and from which we can extract resources. Eventually we can hollow it out, reinforce the outer-shell, set it to spin just right, and turn it into a cylinder colony.

It's my fondest hopes that within a few centuries, humanity has several of these asteroid-cities zipping in orbit between the Earth and our moon.

[Ara Pacis]

Thanks for the math, Swampyankee, I was wondering about it myself. As for the smallest rotating habs, the research I've done suggests 3 RPMs is a maximum, which is what I use for simplicity and utilitie's sake (1g=100m radius). Since I wanted to minimize the mass, e.g. shielding, of the craft I was planning on using for interplanetary travel (a mars-earth cycler trajectory) had decided to use 3 RPM and max it out near Mars Equivalent gravity (~.37g = 37m radius), although there would be one more "downward" rotating deck used for engineering space. After determining the mission scale and population density, I arrived at a deck width (cylinder axial length) of about 20m, increasing in width towards the axis (I thought this might help maintain balance if it had a triangular cross-section (sideview)). Outside of this are several non-rotating envelopes, one for water (outward of the habitat deck width only), two for air at lower but still substantial pressure and then a vacuum envelope inside a mass shielding envelope. Each of these envelopes has about 1.5m of crawlspace (floatspace) between them to allow for manned maintenance, and they also act as a bit of a Whipple shield in the event of an impact, while the shield mass, air mass (and water mass) and envelope geometry might help alleviate bremsstrahlung.

Think of it... bringing billions of tons of ice and ore into medium Earth orbit, it would be like having a tiny second moon. MUCH closer to us than the actual moon, and thus much easier to reach. From there we can use it as a platform upon which to build, and from which we can extract resources. Eventually we can hollow it out, reinforce the outer-shell, set it to spin just right, and turn it into a cylinder colony.

Well, it might be better to send it to Mercury for processing, or anywhere sunward of Earth if you can't process it in situ and then send finished products or refined material in bulk to Earthspace.

[Ara Pacis]

A 250m radius sphere would have a volume of about 62,500,000 cubic meters, or enough volume for a population of 450,000 at I.S.S. population density (6 per 837 cubic meters).

Not if you wanted them all to experience the same acceleration.

[Ara Pacis]

Let's not complicate things by pushing the tensile strength envelope so aggressively. Just make the radius small enough to have a generous safety margin. If we need more capacity, enlarge it by means of a longer cylindrical structure. That will not add any centrifugal stress.

I agree. It's good to know the theoretical maxima, but realistically, we need to know what is affordable. Some systems scale well and some will have diminishing returns. At some point it may be cheaper and safer to construct a new or additional habitat. I'm not sure what size that is. Even with skyscrapers on Earth, elevator shafts eventually take up too much of the structure to make it affordable for non-elevator use. Some, like the WTC, get/got around this by using way-stations (called sky-lobbies), where people get off and wait for a new set of elevators. However, this just means that you sacrificed time for space. That doesn't mean the issues are insurmountable, just that there are trade-offs, and whoever builds it will have to figure out what the market will bear.

[JeffD1]

Let's not complicate things by pushing the tensile strength envelope so aggressively. Just make the radius small enough to have a generous safety margin. If we need more capacity, enlarge it by means of a longer cylindrical structure. That will not add any centrifugal stress.

Is an extension of that thought the creation of a ring around the planet that orbits at a sufficient speed to create 1 g on its spaceside inner surface? With such a habitat you have less wasted volume because the inner to outer thickness can, and would have to be, kept to a minimum. Off the top of my head I'd say five to ten meters would be sufficient. Unlike an orbiting cylinder which will go from daylight to night every orbit, a ring will always have 1/2 of its spaceside outer surface in sunlight meaning you have less need for power storage from solar cells.

And it offers a lot more real estate than any relatively short cylinder.

[IsaacKuo]

But while I acknowledge that 250 meter stations may be more efficient in the near term, I really wanted to know if we could have true cities in space.

A population of 450,000 would be a "true city".

I'm hoping that one day we figure out a way to divert near-Earth-asteroids into Earth orbit, assuming people can get over their fear of giant space rocks...Think of it... bringing billions of tons of ice and ore into medium Earth orbit, it would be like having a tiny second moon.

It is easier to deflect an asteroid out of a collision course with Earth than it is to deflect one into Earth orbit. By the time we seriously consider deflecting a large asteroid into Earth orbit, we will have already proven the techniques with deflection missions (or at least practice missions).

I find it more plausible to deflect smaller NEOs into Earth orbit. They are much easier to deflect, and may pose little or no danger. Small NEOs burn up in Earth's atmosphere every day.

A 250m radius sphere would have a volume of about 62,500,000 cubic meters, or enough volume for a population of 450,000 at I.S.S. population density (6 per 837 cubic meters).

Not if you wanted them all to experience the same acceleration.

I wouldn't. The variety of gravitational levels available would be a good thing, in my opinion.

Still, if you would prefer a habitat with a more "even" distribution of artificial gravity levels, there are several options. One is to use a dumbbell configuration with a counterweight. This is the ideal thing for a small habitat, like an interplanetary spacecraft. Another is to place supplies, farms, water systems, and other hardware in the low gravity zone.

[IsaacKuo]

Is an extension of that thought the creation of a ring around the planet that orbits at a sufficient speed to create 1 g on its spaceside inner surface?

Such a ring has a number of serious problems. No material is strong enough, so it would need to use magnetic coupling to a non-orbiting "support" ring to keep it from flying apart. Then there are various instabilities to worry about. It isn't gravitationally stable, so you would need tethers to anchor the support ring to the planet's surface. There are also firehose instabilities which will want to rip the thing apart. It's a nightmare.

[SkepticJ]

The UV is easy: use paint. Actually, the environmental threat isn't so much against carbon fiber (although atomic oxygen will do a carbon fiber very little good) but against the long-chain polymers that make up the matrix that holds all the fibers together. This is why I suspect that metal-matrix composites would be a better solution for structural elements exposed to space.

Give it an outer layer of aluminum. An ultra thin film of aluminum is how Eric Drexler suggests molecular nanotechnology (built from diamond etc.) be shielded from UV.

[neilzero]

Since the O'Neal students knew that we would not build an 8 kilometer cylinder in the 20 th century, they assumed modest improvements in the strength of materials. Besides the centripetal force, the air pressure is not trivial at 14.7 pounds per square inch, and the cost to make flaws non-existent in that large a cylinder is extremely high. If the cylinder is shaded by Earth several hours per day the heat cool cycle fatigues the cylinder. My guess is 4 kilometer diameter is more realistic for long term high reliability and safety and we should think as low a 5 psi for oxygen enriched air pressure. Neil

[SkepticJ]

Why not put them where they were intended to go? the Earth-Moon L4 and L5 points.