How big could a rotating space habitat be?

[Lumpy]

Not counting hypothetical gigastructures like NIven's Ringworld which would have be be built of unobtainium. I know that with the structural steel bridges and skyscrapers are built of, you could have a rotating habitat a couple of miiles in diameter. I presume if something like graphite composite could be mass produced cheaply enough it could be bigger, and if you could make carbon nanotube cable even bigger. Assuming the latter is realistically achieveable, then how big a 1-g rotating habitat could be built with it?

[Dromish]

Considering that the current plans for a space-elevator hinge on a ribbon cable made of carbon-nano tubes up to geostationary orbit, how about 200 odd miles in diameter? The practical limitations have more to do with balance, weight distribution, and tethering than the structural integrity of the cable. It may sound simple to say "Spin the doughnut to make gravity" but actually getting everything moving in the right direction at the right time without falling askew is a heck of a trick.

[Lobsang]

Isn't Earth a rotating space habitat?


I think you mean artificial rotating space habitat.


I'll go away now.

[Chronos]

Considering that the current plans for a space-elevator hinge on a ribbon cable made of carbon-nano tubes up to geostationary orbit, how about 200 odd miles in diameter?

Make that 40000 odd miles. But that's starting to get to the point where the weight-to-strength ratio is straining even nanofiber, so the practical limit is probably somewhere around there. Theoretically, you could make one of any radius at all from any material at all, but you need to taper your cables so that the parts under less strain weigh less. For a nanofiber space elevator, you'd need a taper ratio of something like 5 to 1 (that is, the thickest part of the cable has a cross-sectional area 5 times the thinnest part), but as you go to longer lengths, or to worse materials, the necessary taper ratio grows exponentially.

[Glazer]

I don't understand why you couldn't use any material that can take 1G of force. The larger your ring the slower it rotates. What am I missing?

[Chronos]

The problem is that the material has to support its own weight, too. Let's say that I have some sort of cable that can support 100 pounds, and 10 feet of it weighs 1 pound. If I'm holding a foot-long length of it, there's no problem: I'm only supporting a tenth of a pound, but it's strong enough for a thousand times that. Suppose, though, that I attach one end of a very long strand of it to a helicopter, and fly up to 10,000 feet. Now, I've got a thousand pounds of cable being supported by the top end of it, but the cable's only strong enough to support a hundred pounds. So what I have there is a broken cable.

[sunacres]

Is that relevant in a rotating-in-orbit-or-free-space, as opposed to a space-elevator application?

[Chronos]

It's a little more complicated for a space elevator or rotating habitat than for something just dangling out of a helicopter, since the effective strength of gravity will vary along the length of the cable, but yes, it's basically the same effect, and relevant in all three.

[Glazer]

Why have spokes at all? Just reinforce the circumference, like a steel belted tire, to handle 1G.

[Stranger On A Train]

Originally Posted by Glazer

I don't understand why you couldn't use any material that can take 1G of force. The larger your ring the slower it rotates. What am I missing?

The problem is that the larger you make the structure, the more of its own mass it has to support; even though it is rotating slower the larger you make it, to develop 1G of centripetal acceleration on the inside surface it still has to have a tensile strength in proportion to the mass.

For the purpose of calculating static loads a large spinning ring structure can essentially be treated as a suspension bridge with no endpoints, i.e. a circle rather than a parabola (as frequently noted by Larry Niven). If you take a ring with a linear density m per unit radian rotating in plane such that the centripetal acceleration is g and cut the ring in half, the tensile reactions at each of the endpoints are -integral (m*q*g*sin(q) d(q)). Integrating from 0 to pi/2 gives you reaction R = m*g, plus whatever reactions you get from whatever mass you've attached to the ring. The yield limit of high strength structural steel is 80-100 ksi, and I'll leave it as an exercise to the reader to figure out how large you can make a steel structure spun to develop any arbitrary acceleration. (Note: just making it thicker doesn't help because you're adding mass at the same time.) You can reinforce with other materials like graphite, Kevlar^TM, carbon nanofiber, whathaveyou, but in the end you're still going to have a size limited by the tensile strength of the material.

As a practical matter you have other problems to deal with, including structural resonance modes, gyroscopic stability of the structure, resistance to impact, et cetera. A long tubular structure is also going to have to deal with torsional shearing stresses, bending modes, rotational instability, et cetera. So the practical size of any real structure is probably going to be significantly less than dictated by the material strength.

Stranger

[Raguleader]

Wouldn't a rotating structure also have the problem of Coriolis effect making everyone stumble into the walls when they try to move their heads?

[Stranger On A Train]

Originally Posted by Raguleader

Wouldn't a rotating structure also have the problem of Coriolis effect making everyone stumble into the walls when they try to move their heads?

If it is sufficiently large enough the rate of rotation will be low enough that the Coriolis component is negligible, at least for the speeds at which a person moves; something moving very quickly, like a bullet, will still describe a spiral path in the rotating reference frame. Similarly, as long as the change in angular momentum from movement is low, the Euler acceleration will be tiny.

Stranger

[Chronos]

Why have spokes at all? Just reinforce the circumference, like a steel belted tire, to handle 1G.

You can do that, but it's more limiting than using spokes.

[scr4]

Originally Posted by Glazer

Why have spokes at all? Just reinforce the circumference, like a steel belted tire, to handle 1G.

If you do that, you are essentially relying on the curvature of the "rim" to counteract the centrifugal force. But as the curvature gets smaller, the tension required to counteract the centrifugal force gets significantly larger. It's like stringing a heavy cable between two poles; it doesn't require much tension if you let it droop down a lot (large curvature), but you have to pull really hard to make it taut. It requires infinite force to pull it perfectly taut (perfectly straight).

[jimpatro]

You need spokes because that's where the artificial gravity happens. Not on the inside of the ring surface as 2001, A Space Oddysey would have you believe. Centrifugal force happens because of gravity. If you're in zero gravity there's no gravity to first push you against the ring wall. LIke spinning a bucket of water around in a circle. In zero gravity the water is pushed against the wall of the bucket, not the bottom.

[Stranger On A Train]

Originally Posted by jimpatro

You need spokes because that's where the artificial gravity happens. Not on the inside of the ring surface as 2001, A Space Oddysey would have you believe. Centrifugal force happens because of gravity. If you're in zero gravity there's no gravity to first push you against the ring wall. LIke spinning a bucket of water around in a circle. In zero gravity the water is pushed against the wall of the bucket, not the bottom.

Urk? There is not one statement in the above post that makes sense.

Stranger

[Alex_Dubinsky]

Right, right. In a spokeless ring everything is under "1G", but g's don't measure force. Force is 1G*mass, and the bigger you make the ring, the bigger will be the mass.

There is a size limit on a steel (or nanotube) ring before it tears itself apart (even ignoring all the "non-load-bearing walls"). What is it?

[jimpatro]

Each spoke would essentially be a floor. As the wheel spins you are forced against the spoke/floor. Why would you be forced into the inner ring floor?

[sailor]

Originally Posted by jimpatro

You need spokes because that's where the artificial gravity happens. Not on the inside of the ring surface as 2001, A Space Oddysey would have you believe. Centrifugal force happens because of gravity. If you're in zero gravity there's no gravity to first push you against the ring wall. LIke spinning a bucket of water around in a circle. In zero gravity the water is pushed against the wall of the bucket, not the bottom.

You might want to rephrase or redo that post in such a way that it makes sense and that it is not full of errors which make no sense.

[jimpatro]

So let's say that you're floating in zero gravity in the habitat before the ring starts spinning. You're not touching ceiling (spoke), floor (spoke) or the curved wall of the ring. Now the wheel begins to spin. The floor comes up to meet you and you're forced against it. Why would you be thrown against the curved wall instead?

[scr4]

Originally Posted by jimpatro

So let's say that you're floating in zero gravity in the habitat before the ring starts spinning. You're not touching ceiling (spoke), floor (spoke) or the curved wall of the ring. Now the wheel begins to spin. The floor comes up to meet you and you're forced against it. Why would you be thrown against the curved wall instead?

Centrifugal force.

If the ring starts out stationary, and continues to acclerate (spin faster and faster), then you'd also be pushed against a spoke. But that's not how a rotating habitat would work. It'd be rotating at a constant speed, so the only force on you is centrifugal force.

[jimpatro]

Okay let's get rid of the spokes. The wheel starts spinning. You should continue floating in the same spot without moving towards the ring wall.

[chrisk]

Originally Posted by jimpatro

Okay let's get rid of the spokes. The wheel starts spinning. You should continue floating in the same spot without moving towards the ring wall.

That is quite true. Let us assume that Bob starts in the center of our space habitat. Bob experiences no gravity, spokes or no spokes.

If there are spokes, with ladder rungs or something, and Bob can reach or otherwise get to one of the spoke walls from where he is, then he could pull himself along the latter, moving away from the center and spinning with the rest of the habitat. Bob will gradually develop weight, and then he will need to climb down the rest of the ladder in traditional fashion.

If there are no spokes, and Bob is shoved away from the center at a gentle speed, he will drift towards the 'floor' in a still mostly weightless way. As he gets towards the floor, there will be some wind effect of air that is mostly rotating along with the floor, pushing him in that direction, but I don't think that would be enough to give him a full affect of gravity, depending on the size of the habitat. (If someone has the numbers, or just common sense argument, to prove me wrong on this, I'd be glad to see it.)

and IF he approaches the floor while it's spinning away under him, then he'll probably acquire that spin speed and gravity very quickly when he touches it - along with some scrapes and bumps.

Does this help clear anything up?

[scr4]

Originally Posted by jimpatro

Okay let's get rid of the spokes. The wheel starts spinning. You should continue floating in the same spot without moving towards the ring wall.

True. So if the ring is about to start spinning, and you want to end up on the floor, you need to grab onto the ring before it starts spinning. After the ring is up to speed you can walk around normally on the floor (or "ring wall" if you insist, though it will look and feel like a floor to you).

In practice, the ring would be rotationg all the time. And if you want to arrive on it with a spaceship, the spaceship needs to match speeds with the ring (constant 1-G thrust so it's following a circular path right next to the ring), and then connect to the ring. Either that or you dock at the "hub" and take an elevator down to the surface.

[jimpatro]

and IF he approaches the floor while it's spinning away under him, then he'll probably acquire that spin speed and gravity very quickly when he touches it - along with some scrapes and bumps.

Right, I see how this would work like say on a ride at a carnival. But that's on Earth with gravity having an effect on centrifugal force. All I see in the space ring scenario is the ring floor just sliding beneath me as it rotates.

[Stranger On A Train]

Originally Posted by jimpatro

So let's say that you're floating in zero gravity in the habitat before the ring starts spinning. You're not touching ceiling (spoke), floor (spoke) or the curved wall of the ring. Now the wheel begins to spin. The floor comes up to meet you and you're forced against it. Why would you be thrown against the curved wall instead?

Because of the radial acceleration you experience as your linear momentum vector is forced to change as you rotate (i.e. you would go in a straight line if not restrained by the ring).

The tangential acceleration you would experience as the rotational speed of the ring increases or decreases is called the Euler (azimuthal) acceleration. However, once the ring is spinning at a constant speed you no longer experience this acceleration.

Stranger

[scr4]

Originally Posted by jimpatro

All I see in the space ring scenario is the ring floor just sliding beneath me as it rotates.

You still have friction in space. If you floated towards the inner surface of the ring and hit it, the friction will bring you up to speed. (Though that's not the most pleasent way to match speed with the ring.)

[Rapier42]

Originally Posted by jimpatro

Right, I see how this would work like say on a ride at a carnival. But that's on Earth with gravity having an effect on centrifugal force. All I see in the space ring scenario is the ring floor just sliding beneath me as it rotates.

You're right, to a certain extent. If you and the ring are stationary in 0g, and then the ring begins to spin, you're going to stay in the same place, assuming you have no physical contact with the ring.

Until you encounter one of the walls dividing the rooms along the ring wall/floor. Then you will rapidly and rudely be accelerated to the speed of the rotating ring, at which point you will also accelerate towards the floor (outer ring wall).

[Chronos]

Or slightly less rudely, if you don't hit a wall, then eventually air resistance will bring you up to the same speed as the outer wall (floor).

LIke spinning a bucket of water around in a circle. In zero gravity the water is pushed against the wall of the bucket, not the bottom.

Think about this a bit: Water being pushed against the wall of the bucket means that effectively, the side of the bucket is "down". So if that's the way it worked, the effect would be like setting a bucket of water down on the ground on its side.

[DanBlather]

Originally Posted by jimpatro

Right, I see how this would work like say on a ride at a carnival. But that's on Earth with gravity having an effect on centrifugal force. All I see in the space ring scenario is the ring floor just sliding beneath me as it rotates.

Have you been on one of those? At the top you are still being squashed outwards towards the rim.

ETA: Oh, and an object on a spinning ring is being accelerated even when the ring is revolving at a constant speed. Acceleration is change in speed or direction.

[sailor]

Originally Posted by jimpatro

Right, I see how this would work like say on a ride at a carnival. But that's on Earth with gravity having an effect on centrifugal force. All I see in the space ring scenario is the ring floor just sliding beneath me as it rotates.

You are TOTALLY misunderstanding centrifugal force. It has nothing to do with gravity. Nothing.

[Lumpy]

Bump.

Stranger On A Train lost me at the word "integrate", so maybe this'll work: I know that a common figure cited for big cylindrical O'Neil colonies built with structural steel was 3km in radius. I presume the stress on the structure goes up as the square of the radius. So if someone can cite me strength/weight ratios for structural steel and the expected achievable ratio for nanofiber, that would do.