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Would a spoked, rotating torus work as a method of colonizing space? If so, how feasible would it be? As in, what would be the cost, where would we get the materials for it, how fast does it have to rotate to simulate earth gravity, etc.

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I'm actually thinking of a design somewhat like a wagon wheel. The outer ring is where everything happens, and the inner ring is where ships dock and such.

The questions, to be specific, are

  • How fast would one have to rotate to offset the slight gravitation from its own mass and simulate Earth gravity?

  • Where would be the best place to put one of these?

  • What is the best size for one of these?

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  • $\begingroup$ There are a lot of questions in there, and some of them are subjective. Could you break this into separate questions, one about materials and construction, and one about application and location? $\endgroup$ – Frostfyre May 27 '15 at 0:24
  • $\begingroup$ Earth diameter? Wouldn't work, because there is no material strong enough. The best size is way smaller, say a few hundred meters in diameter. $\endgroup$ – jamesqf May 27 '15 at 0:53
  • $\begingroup$ I've done some calculations before, and I think a couple km was the sweet spot balancing material requirements and comfort. $\endgroup$ – 2012rcampion May 27 '15 at 0:56
  • $\begingroup$ @Frostfyre Are the new questions good? $\endgroup$ – Desolationgame May 27 '15 at 1:29
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    $\begingroup$ @2012rcampion Can you lead me to where I can find the equations? $\endgroup$ – Desolationgame May 27 '15 at 1:30
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The spoked wheel is the classical design for space stations and colonies. It was introduced as far back as the 1930's (if not before), popularized by Von Braun in the 1950's, appeared in the movie "2001, A Space Odyssey" and reappeared as the "Stanford Torus" in the 1970's when Gerald K O'Neill popularized the idea of space colonization.

To calculate the force felt by the colonists by a rotating colony (or any rotating structure, for that matter), use the following equation:

$a = \omega^2 r$ where $\omega$ is the angular velocity of the station (rad/s) and $r$ is the radius of the station. Acceleration, a is measured in $m/s^2$.

The Stanford Torus is 1790m in diameter and rotates once a minute to simulate a 1 g environment

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On Earth:

$$ a_G = 9.81\text{ ms}^{-1} $$

That's acceleration due to gravity. On a spinning torus, you simulate gravity by living on the outer edge and using centrifugal force, for which the formula is

$$ a = \omega^2r $$

where, as Thucydides says, $\omega$ is the angular velocity and $r$ is the radius.

The comments have it right: about a 2km radius is the sweet spot balancing material limitations and having a decent size station, so to simulate gravity $\omega$ must be $0.070 \text{ rad/s}$.

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    $\begingroup$ Usually we use a little $a$ for acceleration... also I think your math is off, I get 0.07 rad/s or about 0.6 rpm. $\endgroup$ – 2012rcampion May 27 '15 at 13:39
  • $\begingroup$ @2012rcampion is correct, you forgot to square the $\omega$ term. $\endgroup$ – Samuel May 27 '15 at 16:14
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A fictional rotating station much larger than the Earth diameter is described by Larry Niven in Ringworld. He invents a fictional material with extraordinary strength. Not hard science, unfortunately ...

Slightly smaller are the orbitals in Iain M. Banks' Culture series. Again fantastical science is used.

A hard design in 1976 was the O'Neill Cylinder. Compared to your cylinder, it is longer and has an air-filled center. Also consider the Centrifuge Accommodations Module -- much smaller, but also much closer to reality. Those two don't look like spoked wheels, but the principle is the same.

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  • $\begingroup$ You can build a Ringworld without unobtainium, although obviously not exactly like Niven's. Instead, imagine a train half a billion miles long with neither head nor tail. It's riding on an equally impressive track. The track is stationary, not in orbit. The track must be much more massive than the train--gravity pulls down on it with the same force the train pushes up. His walls are impossible but you can make a curved bottom that will accomplish the same thing, albeit at a far higher material cost. $\endgroup$ – Loren Pechtel May 31 '15 at 3:16
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A LOT of thought has gone into the question of how to build space stations and use rotation to provide simulated gravity.

Space Station built from Shuttle External Tanks
Space Station built from Shuttle External Tanks

I don't see anything wrong with prior answers but thought I'd add my $0.02.

Minimum size constraint
It turns out that any rotation speeds >= 3 rpm makes people motion sick. For design purposes, designers felt a maximum rotation speed of 2 rpm would ensure very few people would suffer motion sickness. Scientists felt that most people could acclimate to a rotation of 10 rpm but I think I'd reserve such a design to mission specific applications (e.g. a small military ship crew).

So the minimum size of your cylinder is constrained by human physiology.

Maximum size constraint
As many others have pointed out, the maximum size of the station is constrained by the tensile strength of the construction materials.

I don't feel like doing the math and others have commented on it so just use their numbers.

More information
The most excellent Atomic Rockets web site has a vast store of useful information for world builders. Even better, it has a whole (& very large) page devoted to Space Stations.

For people looking for math, numbers, and other reference materials - including actual design studies for rotating stations (as well as other issues that might arise), run to the web site and be prepared to spend a couple of weeks reading.

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As for location, it depends on your story setting.

The International Space Station (ISS) is orbiting around 400 km above Earth. This is about the optimum with the technology we have today. Go too low and atmospheric drag will slow down the space station causing it to lose altitude and eventually re-enter in a giant fireball. To prevent this from happening, the ISS occasionally gets its altitude boosted by visiting Soyuz crew capsules. Go too high, and it becomes more expensive to reach the station.

If the station altitude is higher than 1000 km, then some sort of radiation shielding will need to be considered. The Van Allen belts are high radiation regions between 1000 km and 60,000 km. Satellites passing through this region need shielding to protect their electronics. People probably need more shielding if they are going to be living here.

Other places to consider would be the Lagrangian points. These are stable points in Earth's orbit around the sun. Colonies placed at these points would require minimal station-keeping. They would, however, be pretty hard to reach with current tech.

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