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?
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.
Isn’t Earth a rotating space habitat?
I think you mean artificial rotating space habitat.
I’ll go away now.
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.
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 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.
Is that relevant in a rotating-in-orbit-or-free-space, as opposed to a space-elevator application?
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.
Why have spokes at all? Just reinforce the circumference, like a steel belted tire, to handle 1G.
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 (mqgsin(q) d(q)). Integrating from 0 to pi/2 gives you reaction R = mg, 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[sup]TM[/sup], 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
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
You can do that, but it’s more limiting than using spokes.
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).
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
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?
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?
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.
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?