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Lakes on a space station


SargeRho

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I can't imagine how you would go about repairing corrosion caused by your groundwater soaking against your outer hull for a decade.

Corrosion is always a concern, but we manage harsher problems than that on a routine basis. Big steel offshore rigs sitting in salty water, for example. An impressed EMF can channel the corrosion towards easy to replace sacrificial anodes, rather than your hull.

I imagine you'd have a pretty robust water barrier at the bottom with an engineering space underneath to allow for maintenance. It would be easier and tidier to put all your services under the "ground" anyway.

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What are Bishop Rings? Can you explain that.

An more realistic ringworld, say 200 km in diameter with an transparent roof. HALO is set on one of them as I understand.

Nice design but I would give it an central hub with 2-4 towers, this would make docking easier and would give you an zero-g zone who would be nice for manufacturing and great fun.

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An more realistic ringworld, say 200 km in diameter with an transparent roof. HALO is set on one of them as I understand.

Nice design but I would give it an central hub with 2-4 towers, this would make docking easier and would give you an zero-g zone who would be nice for manufacturing and great fun.

Okay then.

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What's the largest Stanford Torus we can construct before the structure fails under the stress of a 1G environment?

Without the spokes, cross-section has to support 1/À of its own "weight". So diameter is equal to the longest homogeneous structure you can suspend in 1G. Steel has density of about 9g/cm³ and can support about 9GPa at a maximum. That's almost exactly 100km at 1G. Since there are a number of things you can do to improve on that, I'd claim 100km as the most conservative estimate. Between adding spokes, using carbon nanotubes, perhaps some other fancy materials, and doing some clever fractal design, 1,000km wouldn't be fantasy. But I don't know if you could make it safe. I think, going larger would require materials we have not discovered yet, but given sizes of typical cities, and ability to "stack" Stanford Tori *, from perspective of material science and engineering, we can build a large enough station to fit any existing metropolis.

Naturally, from perspective of resources, this is far beyond our capability. The limitations, however, are purely in getting construction materials, workers, and equipment to the required orbit. Advances in asteroid or Lunar mining might be able to change that rapidly.

* Stacking rotating stations isn't as trivial as it may seem. Having them rotate on independent hubs would allow any slight wobble in each to shake the structure apart. Building a rigid connection, in contrast, can result in instabilities. Specifically, a station whose two principal axes of inertia are very close may start to tumble, which would be catastrophic. However, stacking a "few" rings with rigid connection is fairly straight forward, so long as you look after possible resonances.

True, laundy isn't liquid, but I don't see what mechanism would evenly distribute water along the torus if uneven distribution occurs. K^2, can you explain it more thoroughly?

It's a little hard for me to tell exactly which part is causing problems, but here are a few things to consider.

First, there are no external forces. So center of mass of the station cannot accelerate, no matter how fluids slosh around inside. That means that the station can only rotate around center of mass. (Any other rotation causes accelerated motion of CoM.) So if there is more fluid on one side of the station, the center of rotation will be shifted there.

That leads immediately into the most simple way to get a general idea for the effect. The polar plot of a circle of radius R plotted around a point shifted by d from center of the circle is given by the following expression.

r(θ) = Sqrt(R² + d² - 2Rd cos(θ))

Plot this from -À to À as a regular plot to see that it has a minimum at 0. Since the centrifugal force is going to be purely radial, this means that the point closest to CoM on the ring is the one that's "highest" in terms of artificial gravitational (centrifugal) potential. So fluid is going to tend to flow to the side opposite of the CoM, trying to shift CoM closer to geometrical center.

The more abstract of seeing this is by recognizing that total angular momentum is conserved, so the total rotational kinetic energy, E = L²/(2I), is minimized whenever the structure has maximum moment of inertia, I. If the fluid is distributed along the floor of the station in a "thin" layer (compared to size of the structure), then around center of rotation, moment of inertia is same as for the ring, MR², regardless of how fluid is distributed. Here, M is the total mass of ring and the fluid. Now, there is a theorem that states that moment of inertia around arbitrary point is greater by Mr² that moment of inertia about center of mass, if the point is located distance r from center of mass. So if center of mass is located distance d from geometric center, and what we just computed is moment of inertia about geometric center, then about center of mass, moment of inertia is given by the following.

I = MR² - Md²

This is trivially maximized for d = 0. So if at all possible, the system will try to tend towards that to minimize energy.

All of the above assumes that station is in perfect balance if you remove the liquid. It turns out, that adding liquid can actually help reduce wobble of a slightly unbalanced station. But this requires more complex considerations. The simplest example, however, is balancing in rotors and drums of washing machines. If there is a spring trying to keep drum centered, then the whole problem is of a driven damped harmonic oscillator given by r'' + 2ζÉ r' + É0² r = d eiΩt. Here, Ω is the drum's rotation speed. If you solve this equation, you'll find that stead state has a wobble in the opposite direction to the center of mass shift whenever Ω >> É. So if you ever wondered why the washing machine's drum has such a soft spring, it's to reduce É, allowing it to self-balance at lower RPM.

If you remove the spring, the effect isn't quite perfect. The liquid will never remove wobble completely. But it can help reduce its effects, because again, the station will rotate around the center of mass, which will cause fluid to "prefer" the opposite end, helping shift center of mass a bit towards geometric center.

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Steel has density of about 9g/cm³ and can support about 9GPa at a maximum. That's almost exactly 100km at 1G. Since there are a number of things you can do to improve on that, I'd claim 100km as the most conservative estimate.

In reality I think the conservative figure would be well under that. You wouldn't want to be operating at anywhere near 100% of your yield strength, 50% would be more realistic and for a critical structure with many human lives at stake you'd want to be going even lower. Your 9GPa figure seems somewhat high, too. The best high strength structural steels are still well under 1GPa UTS, some aluminiums get up to about 500MPa IIRC.

For a rotating structure you're also looking at cyclical stresses (and at low temperature, fun!) so fatigue and brittle fractures would need to be looked at. Brittle fractures are always the lowest energy type of failure, so even if something looks good in nice ductile fracture land it could go snap if you stick it in the freezer and wiggle it enough.

However, like you say we don't know anything about geometry and what materials are available so it's hard to say.

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I've jumped the gun on that 9GPa figure. You can get that from a perfect lattice under tension as a matter of theoretical limit, but not from a real world steel wire, you are right. But you can definitely do much better than 1GPa if you are interested in just raw tensile strength. Resulting alloy will be brittle, and so structural steel is usually much less, yeah, but you should be able to get up to 2-3GPa if you really have to.

I agree that it's probably not a good idea. And yes, I've pointed out as well that this is ignoring any safety margins. Cyclic stress you don't have to worry about. The whole thing will be under very consistent load. But you don't want it to be too brittle or too close to limits, so even if something somewhere breaks, the whole thing doesn't fall apart.

But that's why I used just a raw torus as a basis. Throwing some suspension cables down from the hub would already greatly reduce stress on the main structure. If you want to be more elaborate, you can build a support structure with multiple inner rings connected with cables. That will allow you to support even more of the station's "weight" suspension bridge style. And, of course, you don't have to build from steel. In fact, in space, composite materials are probably a better choice. And you can get much better UTS/weight with these.

So I still say that 100km is a very safe bet. There should be no reason, in terms of materials and engineering, that we couldn't build a 1G station that big. As you go larger, it gets worse rather rapidly, so the real cutoff with materials we know might not be that much larger.

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Actually, I have, and my laundry machine has loose bearings in the outer ring specifically to self-balance. The reason clothes don't self-balance is because they get stuck to the walls and each other. Anything that's free to move around the perimeter, however, will improve balance.

I can tell you more, given a spring, such as wheel suspension, there is a minimum spin speed at which the system self-balances. But in free space, any rotation with free flowing liquid or other free-moving mass is going to self-balance.

Would you like to see derivation of that from the first principles?

There are a lot of things you might know better than me, but mechanics isn't one of them, trust me. I'm happy to explain further to satisfy your curiosity, but you ought to leave any hope of proving me wrong on this at the door.

Actually the big difference is this: A washing machine has an axle. A spinning space ring (presumably) doesn't. The presence of an axle mechanism, in which only a portion of the machine spins, and another portion of the machine is stationary, and there needs to be some attachment point at the pivot point of that rotation, causes a *forced* pivot point. The washing machine cannot spin around the center of mass if the center of mass isn't on that predefined axis, thus the washing machine gets wobbly.

The fact that the clothes stick to the walls isn't the cause of the imbalance. The fact that the axis is forced to be where it is regardless of how the mass it distributed is.

By the time a washing machine is spinning at high speed (rather than agitating back and forth), it has drained out all the free-standing water and the only water left is that which is sponged into the clothes, the spin being there to press the water out through the holes in the walls.

Are you sure it would balance if the holes were stoppered up, the clothes were removed, and the normal control mechanism was 'hotwired' and bypassed to just make the machine spin with only some water (say, 1/4 full) in it?

I think in that case the problem of the unstable equilibrium causing the water to eventually migrate over to one side causing unbalance would still happen in that case. Because the relevant reason the washing machine can develop wobble while the space station can't isn't because it has solid stuck to the walls instead of liquid in it, but because the washing machine has machinery that is preventing the axis of rotation from moving offcenter. The axis of rotation is being forced to remain in the geometric center of the washing machine's cylinder even when that's not where the center of mass is. The space station doesn't have such a mechanism forcing that to happen, and is free to rotate about whatever axis line it naturally happens to rotate around, and THAT is the reason that a washing machine can develop unstable wobble where a space station can't. An axle mechanism disallows the spinning part from spinning around an offcenter point.

Edited by Steven Mading
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I think in that case the problem of the unstable equilibrium causing the water to eventually migrate over to one side causing unbalance would still happen in that case.

I address that case in second to last paragraph of this post in this very thread, including conditions under which such a system is self-balancing. And yes, on a real washing machine, this is going to be the case.

If you read that entire post, you'll see that I've addressed all other peculiarities of both systems as well.

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you can definitely do much better than 1GPa if you are interested in just raw tensile strength.

Well, even if you can't we're still only in vague guess territory. As you say, geometry comes into it a lot, and you can't really judge the overall loads on a structure just from it's general layout. Some parts of the structure will be under higher loads than others, etc.

Cyclic stress you don't have to worry about.

Hmm, disagree with this. You always have to worry about cyclical stresses. Vibrations and imbalances are a fact of life, and the failure mode associated with fatigue is sudden, low energy and catastrophic. But I'm probably just being picky.

And, of course, you don't have to build from steel. In fact, in space, composite materials are probably a better choice. And you can get much better UTS/weight with these.

For sure, but again we're in vague guess territory. This kind of thing is always a cost effectiveness decision, and we can't know the costs. Practicalities come into it too. Is the material available in large enough quantities? In the right shape and size? Can it be repaired easily?

Actually the big difference is this: A washing machine has an axle.

When was the last time you pulled a washing machine apart? All the ones I've seen inside have either had the motor as part of the sprung mass or used a belt drive that has allowed movement. The drum is fully suspended, so the axis of rotation can move.

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This kind of thing is always a cost effectiveness decision, and we can't know the costs. Practicalities come into it too. Is the material available in large enough quantities? In the right shape and size? Can it be repaired easily?

The fact that costs are impossibly high and there is no way to get sufficient quantities of any kind of materials for this are pretty much a given. If we ask a truly practical question of, "How big we can build it, given budget constraints," then the answer is, "About the size of ISS," because that's all we've been able to build given the budget constraints. So I've disregarded that aspect of it completely.

On the subject of cyclical stress, yes, of course there is always going to be some. But it's going to be very small compared to the constant load. To be honest, though, I don't know at which point we need to start considering it as a serious threat.

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In a really massive habitat station like that it would be possible to have a much more biomimetic life support system than our current technology.

I doubt it needs to be even close to that big. Biosphere 2 probably would have worked just fine if it was designed better (some serious design issues there)...

EDIT: Of course their CO2 levels varying so much would have been better with more air volume relative to plants, I think, but I think they could have supported the people with way less plants if they hadn't tried to replicate all those Earth ecosystems. Design it like a farm (with air as a crop) not like a mini-copy of Earth, which doesn't really work on that scale.

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Curious to see in a gaming community that no one's brought up the Citadel from Mass Effect. (link to picture on wikia) It had a water body that ran along the middle of the ring section basically dividing the whole interior into two sets of river bank property, with fountains for decoration and humidity control. The lake acted as one of a set of potable water reserves; no mention of using it to help with mass balance, but I could see it working that way too.

-- Steve

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Curious to see in a gaming community that no one's brought up the Citadel from Mass Effect. (link to picture on wikia) It had a water body that ran along the middle of the ring section basically dividing the whole interior into two sets of river bank property, with fountains for decoration and humidity control. The lake acted as one of a set of potable water reserves; no mention of using it to help with mass balance, but I could see it working that way too.

-- Steve

They have artificial gravity in the mass effect universe. If you can manipulate that, then theres really no problem anywhere (except for giant robotic octupus invaders).

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Actually the whole Citadel rotates for spin gravity. The outer Wards get slightly more than 1G and the Presidium ring gets about 3/4G if I remember the in-game journal entries correctly. The Council Chamber at the top would be in microgravity, but it gets a mass effect field for comfort.

Of course the game itself only modeled 1G, except for the scripted zero-G bits. I gather that was a limitation of the game engine.

-- Steve

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They have artificial gravity in the mass effect universe. If you can manipulate that, then theres really no problem anywhere (except for giant robotic octupus invaders).

Technically they were Squid.:P

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