Limits on the scale of Space Habitats

[Philippe Lemay]

Sorry if this subject has been brought up a dozen times, I did do a search and could only find vaguely related threads.

I'd simply like to know what the realistic limits on the size of a space hab are. For example a simple O'Neill cylinder. For simplicity's sake we'll asume a soild steel cylinder with no windows. I know that it has to do with the ultimate tensile strength, which is measured in Pascals (or MegaPascals to be specific), which are a unit of pressure, also known as Newtons per square meter.

So... at what point exactly would a cylinder become too big to support it's own weight as it spins to produce 1 G. I figure the thickness of the cylinder would affect this, but I find the math is somewhat beyond me.

And yes, I know we will probably never get enough resources or funding to build one of these, assume for a second limitless funds. I just want to know what the physical limitations are for our current best construction material, which I assume is structural steel. If anyone feels up to it they can include carbon fibers or even carbon nanotubes, but that's WAY beyond my math skills.

Added for Refference Purposes:
http://en.wikipedia.org/wiki/Tensile...sile_strengths
http://en.wikipedia.org/wiki/Island_..._Two_and_Three

[Hornblower]

I worked from a pressure vessel calculator I found online.
http://www.engineersedge.com/calcula...l_pres_pop.htm
The centrifugal force is the equivalent of internal pressure in the absence of spin, for the purpose of finding the stress on a cylindrical shell. If we use steel and can tolerate 100,000 pounds per square inch of tensile stress, I find a maximum radius of about 20,000 feet, or about 4 miles. Making the shell thicker does not help, because the total stress goes up in proportion to the thickness, so the stress per square inch stays the same.

If we can find a lighter material with the same tensile strength, we could handle a larger radius. Experimenting with the calculator shows that for a given amount of radial force, the stress along the circumference is proportional to the radius.

With some effort perhaps I could rediscover the calculus for deriving the general formula. For now I will take the author's word for it.

[Philippe Lemay]

Huh... I was expecting more, especially since O'Neill and his students calculated a diameter of 8 kilometers (5 miles) for their large-scale hab, Island Three. According to Wikipedia at any rate http://en.wikipedia.org/wiki/Island_..._Two_and_Three
I guess steel is too heavy, O'Neill must have planned using something lighter in his design. Back in the day I don't think they'd even discovered CNTs yet, so if anything our modern day estimates should be 8 klicks or more.

But at any rate I should be able to say with confidence that 4 mile wide cylinders should be possible. For that at least I thank you. But still! I encourage others to add stuff if they can think of anything.

ETA
One thing I realize though... the propane tank analogy used in that calculator, it calculates compressive strength, doesn't it? From the gas pushing against the inner surface. A rotating cylinder will depend upon it's tensile strength, which (from what I've seen) tends to be stronger than compressive.

[Van Rijn]

Here's some information on material strength issues. Advanced materials make a big difference:

http://www.zyvex.com/nanotech/nano4/....html#RTFToC18

5.1 Maximum Radius of Space Colonies
The maximum radius of such an O'Neill style colony is limited by the hoop stress of the spinning structure, and the tensile strength to density ratio of the material. The formula is

R = HoopStress/gG

Where R is the radius, g is the acceleration of pseudo-gravity at the rim, and G is the density. MNT offers a 5 x 10¹⁰ Pa tensile strength. Using the design rule of 50% safety factors for O'Neill style colonies [12], a 3.3 x 10¹⁰ Pa design tensile strength is reasonable. The associated material density is 3.51 10³ kg/m³. One goal of the architecture is for g to equal 9.8 m/s² [10],[12]. This all gives a possible space station radius of 9.6 x 10⁵ m, or nearly 1000 km. For comparison, the corresponding feasible radius for titanium is 14 km, and even at its ultimate tensile strength with no safety factor, the titanium limit would be 23 km.

At the 9.6 x 10⁵ m radius, the entire available strength (at the safety factor) of the MNT-based material is being used to prevent the rotating structure from bursting, and there is no strength left over to hold the space station's contents, including an atmosphere. To do so, a lower radius must be set.

[Philippe Lemay]

That's... probably exactly what I was looking for, thanks!

But what is MNT? It gives a tensile strength in the GigaPascals... is it Molecular Nanotechnology? Carbon Nanotube sort of stuff? If so, that's pretty damned impressive... I mean, granted we're a long way from being able to mass produce CNTs, but damn... 1000 klicks.

ETA
Solid steel (adding in that "safety factor" they mention, which takes high strength alloy ASTM A514 steel and drops it's 680 MPa strength down to 340) results in a radius of about 4.2 kilometers. Or 8.4 klicks in diameter. Similar to what Dyson got. But that's just for solid steel, I'm sure adding CNTs or even just real carbon fiber should push it up beyond 10 kilometers.

Hey... Can someone tell me what the difference between Yield Strength and Ultimate Strength? http://en.wikipedia.org/wiki/Ultimat...sile_strengths

[HenrikOlsen]

One thing I realize though... the propane tank analogy used in that calculator, it calculates compressive strength, doesn't it? From the gas pushing against the inner surface. A rotating cylinder will depend upon it's tensile strength, which (from what I've seen) tends to be stronger than compressive.

The propane tank walls are still under tension, the gas pressure from inside is trying to expand the tank's volume, hence trying to expand the circumference, hence tension, not compression.

This is definitely a place where steel is far from being the best material, for a current non-exotic material with vastly superior attributes for this application have a look at woven carbon fiber composites. Main problem with this is how the polymer matrix stands up long term to high vacuum and high UV-flux.

BTW, I don't remember that O'Neill spec'ed the habitats for 1g which may be where the larger size came from.

[IsaacKuo]

Overall, I'd say steel is the best material...for now. We have a lot of engineering experience with building large structures and ships with steel, and a lot of hard data on how well large steel structures and ships last over time. Structural steel turns out to be very durable when it comes to dealing with stresses and strains over long time periods.

In terms of strength vs density, aluminum would actually be better than steel. Aluminum would give a superior potential radius. But it's not as durable as steel.

[Philippe Lemay]

A compartmentalized approach might be the best if we want long term survivability. So that as a component rusts or wears out, it's just swapped out and replaced with a new one. Maybe some kind of heavy solid steel skeleton, with tiles of lighter aluminum/carbon-fiber materials to fill the gaps. The skeleton would be heavier and last longer, the tiles would lighten the load and be easily interchangeable. Oh! And maybe some of that kevlar-based foam they were working on for Bigelow's Transhab, to help with radiation absorption.

CNTs may very well beat out everything else, but I see them as a very... hypothetical technology. Like fusion power, they can exist based on the laws of physics but they are so difficult to achieve... I hope they'll exist though, one day. Imagine habs with a radius of hundreds of kilometers!

ETA
And I'm sure we could find a use for titanium... somehow. Making the whole Hab out of titanium is bound to be counter-productive (you could probably build 2 steel habs for the price it would cost you to build 1 out of Ti), but specialty parts or components could be made using it. Maybe hatches or something?

[Van Rijn]

BTW, I don't remember that O'Neill spec'ed the habitats for 1g which may be where the larger size came from.

I'm pretty sure he was assuming one G. The idea was to have a conservative design with an Earth-like environment, and the health effects of long term lower gravity were unknown. I think (though I'm less sure of this) that he was assuming aluminum alloy for the main structure. That could have a better strength to weight ratio than steel, but nothing like carbon composites or advanced polymers.

[Van Rijn]

CNTs may very well beat out everything else, but I see them as a very... hypothetical technology. Like fusion power, they can exist based on the laws of physics but they are so difficult to achieve... I hope they'll exist though, one day. Imagine habs with a radius of hundreds of kilometers!

Keep in mind that existing carbon composites and advanced polymers already beat out steel easily, if your goal is a habitat with a larger radius. But as IsaacKuo says, there is the durability issue. Long term survivability would be a concern.

ETA
And I'm sure we could find a use for titanium... somehow. Making the whole Hab out of titanium is bound to be counter-productive (you could probably build 2 steel habs for the price it would cost you to build 1 out of Ti), but specialty parts or components could be made using it. Maybe hatches or something?

The economics of construction would depend greatly on the source of material. It probably wouldn't be from the Earth, especially for a large habitat. It would almost certainly be from the Moon or asteroids, and titanium might turn out to be the better choice. I suspect the space based production issues would also be the biggest problem with advanced materials too - it's a good bit trickier than producing it on Earth.

[swampyankee]

<snark>The aerospace industry has a lot of experience with inhabited pressure vessels, the vast majority of which are made from aluminum. We call these "aircraft." </snark> Boeing's experience, incidentally, is that mixing graphite reinforced materials with aluminum is not easy, because of (among other issues) galvanic corrosion.

Clearly, the most practical construction material would depend on fabrication technology, but I suspect that the best "near term" material would be metal-matrix composites, such as boron-reinforced aluminum, for the tension members and conventional aluminum for maintaining pressurization. It may also be best if there are radial tension members, instead of relying solely on the outer skin (circumferential tension). Any structures guys out there?

[Philippe Lemay]

I remember hearing somewhere that some meta-materials could actually be easier to produce in the microgravity of orbit/near-Earth space than to produce them down here. Something to do with crystal formation in the absence of gravity forming more... perfectly. I can't remember which meta-materials they were, but maybe some of them could be used as Hab construction materials.

[IsaacKuo]

<snark>The aerospace industry has a lot of experience with inhabited pressure vessels, the vast majority of which are made from aluminum. We call these "aircraft." </snark>

This experience is one reason why we know aluminum wears out over the order of decades. We have a lot of hard earned experience (some of it earned in blood) on how to inspect for this degradation and how to determine when an airframe is simply too worn out to continue safely flying.

Anyway, if you are designing a space station that's only supposed to last a decade or two, aluminum is the compelling choice. A large city in space should be designed to last much longer than that. Steel would make more sense despite the greater mass.

[swampyankee]

Well, there is considerable experience in inhabited pressure vessels made from steel, too, although they usually operate where the external pressure exceeds the internal pressure. I will add that any structure where the dominant loading is tensile will require continual monitoring; the price for not doing so has, as you pointed out been paid in blood. In this regard, steel is not qualitatively different from aluminum. I will also add that many civil engineering structures are designed for finite lifetimes, usually about forty or fifty years, after which they are likely to be quite expensive to keep in service. This is especially true for bridges, which are subject to fatigue failures, at least partly because many US bridges were designed and constructed when the legal limit for truck traffic was about 80% of what it is today, and that traffic was less.

[Philippe Lemay]

I still feel that we would be able to swap out materials as they wore out. Just like today's bridges or skyscrapers, they drill/cut/remove the bad pieces and add in some new ones. It's not cheap, and on the scales we would see for space habitats the price would surely be that much higher... but... Which would be worse I wonder, paying for an extensive refurbishing of the station's worn critical components, or send it burning into the ocean and replace it with a brand new one?

I guess it would depend on a LOT of variables, such as how easy it is to get the new materials to build a replacement station. And like you said, how long they had planned the station to last in the first place. For example if we continue to develop along an exponential curve, a station put up in 2080 might not only be worn out by 2130, it might also be made obsolete by larger/better stations.

[eburacum45]

Iron asteroids could be used to create large iron or steel shells, assuming that carbon nanotubes are not available.

If carbon nanotubes were available in bulk then (according to McKendree) the largest possible cylinder would have a radius of 960 km, or a diameter of nearly 2000km. That is assuming a tensile strength of 50 Gpa (in fact it may be as high as 68 Gpa), a safety factor of 50%, and no payload (ie no internal fixtures and fittings, and no people).

Assuming that the slightly higher strength is feasible, and that a slightly lower safety factor is possible, and lower gravity is acceptable then one should be able to build a Bishop Ring 2000km across
http://en.wikipedia.org/wiki/Bishop_Ring_%28habitat%29
http://www.orionsarm.com/eg-article/460db7f55a8d3

[HenrikOlsen]

This experience is one reason why we know aluminum wears out over the order of decades. We have a lot of hard earned experience (some of it earned in blood) on how to inspect for this degradation and how to determine when an airframe is simply too worn out to continue safely flying.

Anyway, if you are designing a space station that's only supposed to last a decade or two, aluminum is the compelling choice. A large city in space should be designed to last much longer than that. Steel would make more sense despite the greater mass.

But afaik most of that limited wear time is due to the pressure cycles of starts and landing and fatigue cracking due to that and vibrations, an orbital station won't cycle like that but will rather have near constant forces. A somewhat different situation I think.

[Philippe Lemay]

It might not be subject to vibration or sudden force, but cosmic rays will probably deliver just as much of a punishment. And the day night cycle, don't forget that. If the Hab is in orbit of say Terra it will swing in and out of it's shadow. This would subject the materials to a lot of thermal expansion and constriction. I'm no material expert but I think that could cause plenty of metal fatigue.

Though... it might be so much that it wreaks havoc on steel just as badly as it does on lighter materials... lol. In which case where back to square one in trying to find an adequate real-world building material.

[IsaacKuo]

But afaik most of that limited wear time is due to the pressure cycles of starts and landing and fatigue cracking due to that and vibrations, an orbital station won't cycle like that but will rather have near constant forces. A somewhat different situation I think.

A station in LEO will have day/night thermal expansion/contraction on a cycle of 90 minutes. A station in a higher orbit will have varying thermal exposure to the Sun or Earth or both, depending on its specific orbit and whether it is designed to maintain orientation to the Sun or the Earth.

In any case, the hull will experience varying heating that will place cyclic deflections on it. While steel can elastically recover from small deflections indefinitely, aluminum can't. No matter how small the stress, repeated deflections will eventually cause aluminum to fail.

See fatigue limit.

[HenrikOlsen]

BTW, I'm not really arguing for aluminum as the best material, I already mentioned carbon fiber (conventional, not buckytube) composites as structurally superior. I strongly suspect that, as in most cases, the real solution is a combination of different materials for different parts, probably layered, with something like carbon fiber composites for structural strength and steel (or aluminum) for keeping the air in.
In any case it would probably need to be designed with a view to have modular replacement of all parts, including structural members, on a fairly regular basis.

[IsaacKuo]

In any case it would probably need to be designed with a view to have modular replacement of all parts, including structural members, on a fairly regular basis.

We don't design ships or skyscrapers this way. I suspect we wouldn't design a large spin gravity habitat that way either. Now, it's possible to put a ship into drydock for repairs and maintenance, but that's an expensive operation. The equivalent for a large habitat would be to pump out the air and perhaps de-spin (de-spin isn't a practical option if only one section were de-pressurized and the remaining sections are still inhabited).

To contend with general wearing out, I suspect the most sensible strategy will be to replace the outer hull with an entirely new hull. The new hull can be constructed so that it's a bit larger than the previous hull--adding a new lower floor. When the new outer hull is complete, it's pressurized. The previous hull now becomes an inner floor, which can last far longer now that it's relieved of air pressure.

[swampyankee]

As I said before, the optimum material is going to be decided as much by availability and fabrication issues as anything else.

A rotating, pressurized space habitat will have the bulk of its structural loading be in tension. There will be some vibratory loading, from such things as internal traffic, thermal cycling, etc., so it will be subject to fatigue. Note that the concept of "endurance limit," a stress below which fatigue damage doesn't occur doesn't really apply to anything except mild steels.

[Philippe Lemay]

To contend with general wearing out, I suspect the most sensible strategy will be to replace the outer hull with an entirely new hull. The new hull can be constructed so that it's a bit larger than the previous hull--adding a new lower floor. When the new outer hull is complete, it's pressurized. The previous hull now becomes an inner floor, which can last far longer now that it's relieved of air pressure.

That's not bad...

[Ara Pacis]

I don't have any experience with maxima, but I have looked at the minima for a rotating habitat for use as an space station, transit vehicle or interplanetary cycler. I took a multi-layered approach to maximize the benefits of different materials for different needs. If you need a large mass of something for shielding, save your material stress and don't spin that part. Leave it as an unrotating external envelope. Inside of that you might use a second non-rotating metal envelope as an outer pressure hull that uses low pressure atmosphere or even a non-breathable gas like argon as a buffer for volatile materials used in the next envelope that encompasses all non-vacuum spaces. I'd have a second buffer surrounding the rotating habitat that allows for higher pressure and breathing air in case of a penetrating impact. (This allows one to work in a p-suit in the outer atmosphere envelope without worrying about a huge mass spinning right next to them.) The next envelope might be the rotating habitat that uses fiberglass/carbon-fiber and resins for the main human habitating envelope and uses metal struts and tension cables. I might also add toroidal water tanks external to the spinning hab in the non spinning structure to act as extra radiation/impact shielding. I might, however, use radial stirring mechanisms to provide centripetal force for ullage.

One of the upshots of this design is that docking is much simpler since the hangar doesn't have to spin and neither do the main airlocks and neither do your main communications and astrogation/observatory equipment, and neither do your sunshields or radiators (which makes them simpler), and neither do your vehicle propulsion systems (if you plan on using catapult or beam technology to help your residents and visitors get to and from your city in space).

[Ara Pacis]

We don't design ships or skyscrapers this way. I suspect we wouldn't design a large spin gravity habitat that way either.

But skyscrapers and ships (to a large degree) rely upon compressive loading, not tension loading. Skyscrapers deal with gravitational acceleration by using the large bottom to support the mass above it. A arc/segment structure in a rotating habitat has to work in the opposite mode, using the narrow top levels to support the mass of the wider lower levels against acceleration from angular velocity. Building a spinning habitat will have more in common with building bridges (i.e. cable-stayed) than ships and skyscrapers.

So, modularity might be important for adding secondary structures to the main structure or even for expanding the main structure longitudinally. Although if you use my multiple envelope design mentioned above, a major rebuild would still be a major rebuild, modular or not.

EDIT: I forgot to add, many large ships are, in fact, built with modular construction. Samsung invents Terablock construction, up from Gigablocks and Megablocks

[swampyankee]

We desperately need a structures guy to join this thread. I'm a mechanical engineer, but my only structures experience has been in fatigue testing of helicopters.

Steel, aluminum, titanium, magnesium, and composites are all prone to fatigue damage. The plastic matrix of most composites may also be subject to environmental damage from the space environment; I don't know if there is any applicable literature on this.

So we've got at least two immediate issues with material selection: its fatigue properties and its long-term susceptibility to damage from the space environment. Currently, I would argue the latter would rule out conventional composites: we may not know enough about their behavior in space, especially when subject to continuous loadings.

[IsaacKuo]

A arc/segment structure in a rotating habitat has to work in the opposite mode, using the narrow top levels to support the mass of the wider lower levels against acceleration from angular velocity.

This is less efficient than using the floors to support themselves. Just look at any of the classic rotating habitat designs--O'Neill Cylinder, Bernal Sphere, Standford Torus. None of them have radial cables or columns for support. Instead, the floors support themselves with hoop stress. That's because it's a more efficient use of structural mass.

EDIT: I forgot to add, many large ships are, in fact, built with modular construction. Samsung invents Terablock construction, up from Gigablocks and Megablocks

Sure, but modular construction is different from modular replacement. Ship modules are welded together, not bolted together with regular replacement in mind.

[Ara Pacis]

This is less efficient than using the floors to support themselves. Just look at any of the classic rotating habitat designs--O'Neill Cylinder, Bernal Sphere, Standford Torus. None of them have radial cables or columns for support. Instead, the floors support themselves with hoop stress. That's because it's a more efficient use of structural mass.

I'm not a structural engineer, so you may be right... I was wondering how well that would work or if it would merely create a massier habitat. My concerns with a rotating station focus on maintaining alignment with non-rotating and/or counter-rotating sections for the reasons I describe above. But then, I'm trying to minimize the concept, not maximize it.

Sure, but modular construction is different from modular replacement. Ship modules are welded together, not bolted together with regular replacement in mind.

I wasn't making a distinction since either one would be a major operation. In my plan, a lot of the interior partitions would be modular with the aim being regular adjustment due to changing mission requirements and "seasonal" needs, but not the external structures, which would be fixed after installation (with the exception of some ancilliary bolt-on structures). I was thinking of internal struts similar to the Babylon 5 design.

[eburacum45]

Making the shell thicker does not help, because the total stress goes up in proportion to the thickness, so the stress per square inch stays the same.

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.

[jj_0001]

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.