What's the most logical shape for my city in space (space station)?

Science fiction shows us two common shapes for large space stations, rings and tubes:

Deep Space 9 (image source):

Similarly, 2001: A Space Odyssey (image source).

On the other hand, we have Babylon 5:

(Image source.)

The International Space Station isn't a city in space (it holds fewer than 10 people), but it's the only actual data we have. It follows the latter approach.

Which style makes more sense for a city-sized space station, one where people live permanently, work, and do commerce? Does it depend on what it's in orbit above (if anything)?

In your answer please consider factors that go into both building it and maintaining it. If one is more expensive to build but would be less expensive to maintain, then it's possible that it's still better in the end. (Expense isn't the only factor; usability factors matter too.)

Assume we've already identified a site for this station.

Assume we are limited to things we know how to build, and have the materials to build, today.

• One potential problem with tube-shaped stations is weather patterns inside. The difference in angular velocity between the center and the outside edge is going to create some pretty turbulent air patterns and potentially very strong winds in places. Nov 24, 2014 at 9:18
• Does your civilisation possess artificial gravity? Rings and tubes are good because you can spin them and use inertia to fix things down. If you can generate your own gravity you don't have that constraint. Nov 24, 2014 at 9:24
• @superluminary artificial gravity would be needed, yes. I"m looking for things we have the knowledge to build today; I know we can get gravity from spinning, but if there's some other way to do it with today's knowledge, an answer based on that would be just fine. Nov 24, 2014 at 19:09
• Gravity is a force which causes acceleration in the direction of the gravity well. Rotation replaces this with acceleration towards the hub. Current technology mimics gravity using acceleration. Nov 24, 2014 at 20:09
• It's noteworthy to set DS9's ring shape apart from current toridial designs which are meant to provide "artifical" gravitation by spinning. Looks like the Star Trek Franchise offers another technological means for that. Nov 28, 2014 at 13:25

Tube shaped will be your best bet

Space stations are expensive to produce, so there is going to be a strong preference for choosing shapes which are efficient at accomplishing their goals.

One of the goals of a space station is gravity. Most Sci-Fi books choose to have a source of a gravity-like force because there is just too much evidence that humans don't do well without it. Barring fictitious gravity engines, centripetal acceleration is the easiest answer.

Centripetal acceleration has an interesting flaw. As discussed in Rendevouz with Rama, any rotation also causes centripetal acceleration's bothersome cousin, the Coriolis effect. Human brains seem to have trouble with this (though there is little research into how we would handle it if we grew up on a station). The solution is always to keep the angular rate slow, to minimize Coriolis. This means big radii to get the "gravity" you want.

For the smallest of stations of this sort, rings are popular. It is common to want to have lots of your space at one common G force, so much of your station should be at on radius from the center of rotation. This minimizes materials per volume at 1G. Often this is supported with "elevators" that go through the center of rotation to short circuit the long distance along the ring.

As the station gets bigger, and transit becomes more of an issue, there is a desire to expand in a second direction. The ring widens, becoming a revolved ellipse instead of a revolved circle, looking more like a wristwatch band. This transition from "maximize volume of space to 1G" to "balance volume of space at 1G with the distance between points in the city" separates the simple rings from these widened rings.

At some point, the ring becomes so wide that another shape takes over: the cylindrical tube. A ring has to maintain pressure-grade materials on all sides. At first this is efficient, but when the ring becomes wide enough, it starts to look like there's extra material to be shed. The station starts to look like {wall} pressure-space {wall} vacuum-in-the-center-axis {wall} pressure-space {wall}. In fact, it starts looking like a cylinder, but with no end caps and double-walls on the rest of it. If you skin the end caps, and pressurize the whole area, you can ditch half the walls. If the ring is wide, this can be a substantial boon.

Arthur C. Clarke's Rama was of this shape and size. It was 54km long and 20km in diameter, which rotated with a period of 4 minutes per rotation. It is a reasonable size for a city spaceship.

Of these shapes, the one that is conspicuously missing is the sphere. This is because of the desire to have a constant "gravity" over large areas. Spheres are great at material-to-volume, but they have a constantly varying radius as one changes "latitudes," which could be undesirable. However, if one is comfortable with differing gravities like that, the sphere is the most efficient shape you can have

• Tubes need active stabilization. If you spin one along its long axis and let it sit, random perturbations will cause the axis of rotation to shift until it's spinning end-over-end.
– Mark
Nov 23, 2014 at 8:54
• How much active stabilization? And are rings immune to this need? Rocket fuel costs money/resources. Can the stabilization be set up with something like E-sails? Nov 23, 2014 at 10:55
• @Mark: A long rigid cylinder spinning around its axis (minimum moment of inertia) is stable for the same reason as a ring spinning around its axis (maximum moment of inertia). Of course, that only applies as long as the rigid body approximation is valid, which it may or may not be for a large space station. Nov 23, 2014 at 17:21
• @Mark: The same principle still applies: a rigid object will rotate stably around an axis that is a strict local extremum (i.e. maximum or minimum) of the moment of inertia; otherwise, i.e. if the rotation axis can gradually shift without changing the moment of inertia, it will tend to do so. Nov 23, 2014 at 22:21
• I do not think this answer is correct because expanding a toroidal station does not make it a revolved ellipse. It becomes a set of parallel toruses, like the two of them in 2001's space station. So from false premises, false conclusion. Nov 24, 2014 at 9:02

Toroidal.

Bear with me here. This is going to take some explanation, but maybe I can explain myself.

Shokhet and Cort Ammon solved the problem of making sure that the station spins properly. A cylinder is probably the simplest solution to that problem, because it's easy to build and maintain. The problem, though, is that it soon becomes hard to get from one end to the other. As you mentioned, Cort Ammon,

As the station gets bigger, and transit becomes more of an issue[.]

This is going to be a huge problem if you want to make a city. You could make a disk-shaped station (to save the rotational aspect and thus gravity, while making it easier to get from one spot to another), but this still requires the station to be large. It'll look like a giant pancake. Eventually, you're going to want to extrude it into a cylinder.

My solution (independent of Shokhet's suggestion, and implemented completely differently) is to create a toroidal space station. This essentially takes Skohet's and Cort Ammon's cylinders and bends them around so the ends meet. Voila! You can get around easily. The reason that toroidal space stations are so popular, as Shokhet said, is that you can rotate them along an axis going through the open center of the torus. My idea is a bit different.

The cross-section of a torus is a circle. You can form a torus pretty easily by graphing a circle on the Cartesian plane and rotating it about some line (you can calculate its properties using calculus). The point, though, is that you can break up a torus into a series of circles. This can be exploited to generate artificial gravity. Instead of rotating the entire space station along one axis, I would rotate lots of smaller circular segments along an axis going through the center of each segment. This would create artificial gravity along all sides of the torus. Rotating a torus about its center wouldn't create this effect, because the "top" and "bottom" would not be effected. The advantage of this design is that it creates artificial gravity along all parts of the surface - which is necessary to fit everyone into a city-sized space station!

The idea has its plusses and minuses, of course.

Pros:

• Artificial gravity wherever you like. I'm really pushing this point, but there's another upside: You could rotate each segment at different rate, providing different gravities (or no gravity at all). Think about how useful this would be for a space station containing many different alien races. Each one is accustomed to a planet with a different gravitational field. If you have a space station with one strength of artificial gravity, most would be unhappy. Here, this is fixed. Note: You could break up a cylindrical station just as easily.
• You can get just about anywhere pretty easily. Part of my motivation for this configuration was that you can't easily get from a point on one end of a cylindrical space station to another. This could of course be solved by planning - that is, designing the station such that people on one end won't need to go to the other. But it's probably best to make all areas equally accessible. On this station, all you have to do to get form one point to another is to simply travel through the center of each segment. You could also bridge the central gap by creating "bridges" from each segment to another.
• It's compact. Let's say you want to make a cylindrical space station that has a surface are of 10 cubic miles. You also want a radius of half a mile, to make it easy to make the artificial gravity you want. The formula for the surface area of a cylinder is $V=2 \pi r^2 + 2 \pi r h$; some algebra leaves us with $h=\frac{10 - 0.5 \pi}{2 \pi (0.5)}= 2.68$ miles. That's pretty long. A torus with the same area is a bit shorter. The formula for the surface are of a torus is $4 \pi ^2 (Rr)$, where $R$ is the radius of a circle whose circumference equivalent of the height of a cylinder and $r$ is the radius of a circular cross section. This is explained better in this graphic:

$R$ is the radius of the pink circle; $r$ is the radius of the red circle. We set $r$ to 5 and find $$R=\frac{10}{4 \pi ^2 (0.5)}=1.59$$ The width of a torus is $R+r$, which becomes 2.09 miles, a slight improvement. Note, though, that a sphere would be the shape which is the easiest to travel through.

Cons:

• Not easy to build. It's tough to build a circle or a cylinder because of their curved side(s). This is even harder in the case of a torus, because it has many curved sides. It's highly irregular. Your best bet would be to build it in the segments which will be used to generate artificial gravity.

Frankly, I think the pros outweigh the cons here.

Let me end by addressing some of the specific things you mentioned in your question.

Does it depend on what it's in orbit above (if anything)?

From a logistics standpoint, the answer is yes. You need to re-supply any station that is not self-sufficient. However, this is simply a problem for all of the proposed ideas, not just this one. And it can be avoided by making the station completely self-sufficient. I'm being vague here on purpose, because there are a lot of factors that would go into solving this problem.

In your answer please consider factors that go into both building it and maintaining it. If one is more expensive to build but would be less expensive to maintain, then it's possible that it's still better in the end.

I don't think that there would be a huge change in expense among the different ideas. You need to have $X$ dollars/pesos/pounds/yen/euros to maintain a station of a given surface area. Unfortunately, all of these stations that have artificial gravity need to have the same surface area, so this isn't going to change.

Peteris recently said

Umm, How do you propose to rotate sections of a torus? A torus cannot be made of cylindrical segments without gaps or overlap; in a torus, the "inside" part of each section is narrower than the outside, and can't rotate along the red circle in your drawing.

I completely forgot about explaining this part. My "toroidal" space station wouldn't be a perfect torus. As I said, it would be made of segments. However, I didn't explain that the segments would be closer to cylinders than slices of a torus. Think of small cylindrical pieces connected by wedges. Each piece rotates, creating artificial gravity. The torus isn't perfect; it's an approximation.

• Umm, How do you propose to rotate sections of a torus? A torus cannot be made of cylindrical segments without gaps or overlap; in a torus, the "inside" part of each section is narrower than the outside, and can't rotate along the red circle in your drawing. Instead of a single enclosed station, you'd have a set of cylindrical stations each rotating separately, with a gap between them (especially on the torus-outside part) and connected only in the middle. This would create a transit bottleneck as well as greatly increase the surface area that needs protection from leaks of air, heat, etc. Nov 23, 2014 at 19:52
• If your torus is made of linked individual cylindrical segments, why even make them into a torus? You could connect your cylinders in much more efficient ways. You could just attach all the segments together into a dense grid couldn't you? Or stack them all like a pile of logs. It would make moving between the cylinders a little tricky, but your design already allowed for segments spinning at different rates and it would reduce travel times drastically. Nov 23, 2014 at 21:40
• Building an airtight rotating joint is hard. Building enough of them that a group of cylinders adequately approximates a torus, on the scale you're picturing, would be a nightmare.
– Mark
Nov 23, 2014 at 22:29
• When I say "I'm not convinced", I don't mean I have the knowledge to rule it out, I just mean I'd need evidence because it sounds too good to be true. It will be interesting to see what Space Exploration come up with... Nov 24, 2014 at 1:11
• @githubphagocyte Here's the question. We'll see what happens. Nov 24, 2014 at 1:13

Why would you choose a ring (or torus) over a tube (or cylinder)? First, you would choose either over other shapes because they spin. If you're not spinning, there's no point in either shape. This is why the International Space Station (ISS) is neither tube nor ring. It's just a bunch of modules stuck together. It's a little closer to a tube shape, but it's actually shaped more like a series of buildings connected by tunnels. So the main reason to choose a ring or tube is because you can spin them.

The fictional Deep Space 9 (DS9) has the same problems as an example as the ISS. It looks a bit like a ring, but it actually isn't one. People live in the center of DS9, not on the edges. This is because DS9 doesn't have to spin to create gravity. It has artificial gravity that works in a way unknown to our physics. If we do build ring shaped space habitats, it is unlikely that they will look like DS9. They will have more on the edges and less in the middle.

The primary advantage of a ring is that it can be smaller than a tube for the same radius. You want to maximize the radius because gravity is generated by the illusion of centrifugal force, that is force away from the center of the spin. This is actually a fictitious force, as the real forces are inertial (in the direction of the spin) and centripetal (from the floor keeping you from following the inertial force). Increasing the radius reduces the side effects of the spin (e.g. the Coriolis effect). For a small radius, you are constantly changing direction. A larger radius makes the change of direction more gradual.

It's easier to make a ring that uses less atmosphere. You can make a tube with another tube inside it, but for a similar expenditure of material, you could make a larger radius ring. The rings are generally shown with a center that is either hollow or contains spokes. You could make a disc instead of a ring, but that would have a lot of unused atmosphere in the middle. We can guess that rings are cheaper in atmosphere while cylinders are cheaper in structural material.

There is some reason to believe that structural material is easier to obtain in space than atmosphere. In particular, we can mine the asteroid belt for structural material while we'd have to mine comets, moons, or planets for atmosphere. After Earth, Venus is the closest planet. Everything else is at Jupiter's orbit or farther. Comets can come closer but they are small and move comparatively quickly. So we'd spend a lot of energy to match speeds. Saturn's rings might be the best source, but they are far away and still partly in the gravity well.

The ring provides more structure. Note that the spin will affect objects that are attached to the "ground" or floor most, then objects that rest on the floor, and will affect things like atmosphere the least. The obvious result would be that the side of a building that faces into the spin would have a thicker atmosphere than the sides or the leeward portion. How much of a problem will that be? What kind of weather side effects would occur?

It would be easier to run an elevator from point to point on a ring, as there's already structure there (the spokes of the ring). It would be more difficult with a cylinder, as you'd have to create the structure for the elevator. Cylinders are more compact though, so it might be easier to run a shorter track along the edge of a cylinder than to run through the middle of a ring. You could also fly in a cylinder.

A ring would likely be forced to use artificial light. Rings have too much structure to work well with windows. A cylinder can be constructed such that windows let in light regularly. Unfortunately their rotation speed doesn't support a day/night cycle, so it's unclear if we'd do this. We might be able to give a night cycle by "shutting" the windows. This is either an advantage of cylinders or irrelevant. Perhaps both use artificial illumination.

The real truth is that we don't know whether we'd prefer a ring to a cylinder. Unfortunately, we've never had the resources to try either of them. Our current International Space Station doesn't have artificial gravity. We don't have any real understanding of when the simplicity of the wider ring of the cylinder outweighs the advantage of a decreasing side effects from a greater radius. We have no experience of how either would impact atmospheric effects.

Our best guess is that we'd start with rings, as they are easier to build for smaller capacity. As our needs increased, we'd switch to cylinders, as it is easier to move from point to point on them. So for something big enough to be a city, it is more likely that it would be cylindrical. But that remains speculation at this point, as we have no experience with either.

• Centrifugal forces are real! As long as you're in a rotating frame of reference, that is. See: xkcd.com/123 Nov 23, 2014 at 23:43
• Thanks for the DS9 correction. I didn't know how their gravity worked. Nov 24, 2014 at 19:23

I would suggest that tube-shaped cities would be the better setup for a city, because it would be a lot easier to travel and transport materials around the the city if all you had to set up was a series of elevators that go up and down, instead of carts on a weird track that travel around your ring.

A note on setting up floating cities:
Most science fiction I've read assumes that a torus-shaped (ring-shaped; not Taurus-shaped) is the best arrangement for cities in space, because spinning them around their center can provide a sense of gravity through centripetal force -- basically, as the structure spins, the inhabitants are pressed against the inner-side of the outer wall to imitate gravity. This is also possible with a tube-shaped structure.
But if you want gravity, make sure it spins.

• On your note, good point. Babylon 5 spins along the center (lengthwise) axis, for instance. Nov 23, 2014 at 2:44
• @MonicaCellio I didn't know that, but that's exactly what I'm talking about :-) Nov 23, 2014 at 2:48
• The outer shell of the station would tend to move in a circle due to centripetal force, but he artifical gravity would be due to centrifugal force similar to what goes on in a centrifuge. Nov 24, 2014 at 17:51
• On a torus you could always have cylindrical "bridges" connecting opposite sides of the station (sure, there would be no gravity in the middle, but it would only be for transportation purposes)
– k_g
Apr 10, 2015 at 23:57
• @k_g Of course. Those are always fun :) Apr 12, 2015 at 1:30

TL;DR: Neither. The easiest thing would be to populate an asteroid, small moon, pseudo planet or comet.

Longer explanation: Space stations (of the unknown distance future) will be big. And that means that we need resources. And wasting them isn't an option. We can't afford to loose them on our home planet. And the needed resources boil down to where the station gets built.

Built in space

That means that we would have either travel long distances to get hold of the needed materials and bring them to our factory place or that we would have to bring them up from a planet. In both scenarios we loose a lot of time and waste a lot of resources just to transport semifinish and parts.

Built on the surface

No matter on which surface we build it, we need to bring the whole thing into some orbit or into some place where it stays (relatively). Again we are wasting resource. Maybe even more as the structure would probably need to levitate and raise itself into position.

Populating asteroids

Depending on the building materials, we can find a lot of the needed resources in place. We also have a finished outer shell. And depending on the mass we could easily rotate it. Also they come in various sizes and drilling rings and tubes into it, sealing the walls off with fluid concrete (or a similar material mixed with the gravel already in place) could be done quickly. Pretty much like we build tunnels through mountains nowadays. Oh, and it's easily exchangable as nature showed us.

There is an interesting document for a small spacestation-city called Asten on the NASA homepage. While I don't understand enough to follow all the Details it sounds reasonable and goes not only in the Question of construction (Form/Materials/and so on) but also things like infrastructure and supplies for the Population.

Since I can't reliably condense the 93 pages, here is a link:

http://www.nss.org/settlement/nasa/Contest/Results/2009/ASTEN.pdf

For only the form of the spacestation they suggest a cylinder constructed out of individual rings.

I believe it comes down to artificial gravity.

A torus can be set to spin at the proper rate in which case it would have a centrifugal force pushing outwards and producing a false gravity to the outside of the ring. The 2001 space station does this.

In the case of the cylinder, if the city is in transit to another system it could accelerate at a constant 1G (~10m/s/s) and then there would be an artificial gravity towards the rear of the vessel. In this case floors could be stacked transversely to the direction of travel. This sort of vessel would accelerate towards its destination and then at the half way point perform a maneuver to turn around and then decelerate at the same constant rate until it reaches its destination. Such a vessel could spend several generations in space.

IMO, those are the two most realistic scenarios.

Alternatively, a vessel in transit could also be set to spin and could have floors within it designed to have a camber that matches the balanced forces somewhere between the the centrifugal forces and accelerating forces.

Note that the DS9 station pictured above does neither of these relying instead on some other fictitious gravity generation devices. AFAIK, there is no known way to generate such gravity.

• Thanks for the DS9 correction. I didn't know how their gravity worked. Nov 24, 2014 at 19:23