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Old 04-18-2010, 07:28 PM   #1
Agemegos
 
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Default O'Neill Cylinders

I'm writing a bit of background material and I have come to the point where I want to briefly mention the construction of some really big habitats in space. I don't want to interrupt the flow of the text (which is historical overview material), but I would like to give the readers an idea of what the structures are: hollow cylindrical worlds spinning on their long axes, about the size of Arthur C. Clarke's Rama. That is, fifty kilometres long, twenty kilometres wide, and with an interior surface larger than the land area of Rhode Island or Luxembourg.

Now, the term "O'Neill cylinder" is sometimes used for this design in SF, and I propose using "O'Neill" as the in-setting term for these large cylindrical habitats (as opposed to the smaller "Stanfords", which are wheel-shaped rather than fully enclosed). But O'Neill's design was actually for a much more elaborate and specific design, with two cylinders counter-rotating, a separate agriculture ring, windows for natural lighting, etc.

Question: is "O'Neill cylinder" going to be misleading if used in the common sense without explanation?

Supplementary: anyone know off hand the limits for stability for a hollow cylinder rotating about its axis?

Last edited by Agemegos; 04-18-2010 at 07:42 PM.
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Old 04-18-2010, 09:28 PM   #2
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Default Re: O'Neill Cylinders

I don't think most people have read High Frontier. Plus calling all the big cylindrical habs "O'Neils" is just the kind of popular corruption that would reasonably propagate.

I think you'd be okay.
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Old 04-18-2010, 11:35 PM   #3
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Default Re: O'Neill Cylinders

Quote:
Originally Posted by Brett View Post
Supplementary: anyone know off hand the limits for stability for a hollow cylinder rotating about its axis?
To be stable, the cylinder bust be rotating about the principle axis with the largest moment of inertia (this gives it the lowest rotational kinetic energy for a given angular momentum, meaning it cannot shed energy into other rotational modes).

A thin cylindrical shell - a hollow cylinder without endcaps - with mass M and radius R has a moment of inertia of MR^2 for rotation around its center axis.

A uniform circular disk - one of the endcaps of the cylinder - with mass M' and radius R has a moment of inertia of M'R^2/2 for rotation around its center axis. The cylinder will have two of these endcaps.

Thus, the moment of inertia for the entire hollow cylinder is MR^2 + 2 * M'R^2/2 = R^2 (M + M').

A hollow cylinder of length L, radius R and mass M without endcaps rotating around an axis perpendicular to its primary axis has a moment of inertia of M(L^2/12 + R^2/2).

A disk M' of radius R oriented perpendicular to its axis of rotation at a distance of L/2 - the endcap - has a moment of inertia of M'(L/2)^2 + M'R^2/4. Again, there are two endcaps.

Thus, for a hollow cylinder tumbling end over end, we have a total moment of inertia of ML^2/12 + MR^2/2 + 2 * (M'(L/2)^2 + M'R^2/4) = L^2 (M/12 + M'/2) + R^2 (M + M')/2

If the cylinder and endcap both have a uniform areal density D (probably equal to 1 ton/m^2, as this is sufficient to cut the dose from cosmic radiation down to levels without known long term health risks), then M = 2 * pi * R * L * D, M' = pi * R^2 *D.

For rotation about the cylindrical axis, this gives
I_z = pi * R^3 (2 * L + R) * D.
For end-over-end tumbling, on the other hand
I_x,y = pi * L^2 R (L / 6 + R / 2) * D + pi * R^3 (L + R/2) D
And we need
I_z > I_x,y
for stability. This gives us the condition
R^3 + 2 * L R^2 - L^2 R - L^3 / 3 > 0
Since it is late, I'm not going to solve this cubic inequality now (or check my work, for that matter - others may wish to look it over for accuracy), but will note that cubic equations do have closed form solutions, so you can find the allowed values of R in terms of L that give you a cylinder that rotates stably about its axis rather than tumbling end over end.
http://en.wikipedia.org/wiki/Cubic_equation

Luke

Last edited by lwcamp; 04-18-2010 at 11:50 PM.
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Old 04-19-2010, 12:12 PM   #4
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Default Re: O'Neill Cylinders

Quote:
is "O'Neill cylinder" going to be misleading
Nope. That _is_ the meaning of the term now, even if the meaning isn't proper given the origin of the word. Happens all the time.
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Old 04-19-2010, 12:50 PM   #5
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Default Re: O'Neill Cylinders

Quote:
Originally Posted by Brett View Post
Question: is "O'Neill cylinder" going to be misleading if used in the common sense without explanation?
I concur with other respondents: almost certainly not. The cylinder design (for purists, the double counterrotating cylinders, which allow you to maintain attitude control without using reaction mass) might be more accurately known as Island Three, but I don't see that getting into slang. "O'Neills" does seem a pretty likely candidate term for "free-floating space habitats large enough to be livable".
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Old 04-20-2010, 11:15 AM   #6
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Default Re: O'Neill Cylinders

Quote:
Nope. That _is_ the meaning of the term now, even if the meaning isn't proper given the origin of the word. Happens all the time.
Agreed.

Quote:
This gives us the condition
R^3 + 2 * L R^2 - L^2 R - L^3 / 3 > 0
If you plug this equation into Wolfram Alpha, you can get solutions for R and L given the other number. Examples:

R = 20:
L < 33

L = 50:
R > 30

In other words, if lwcamp did his math right, your O'Neil cylinder isn't going to be stable if it's got a radius of 20 kilometers and a length of 50 kilometers.
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Old 04-20-2010, 11:27 AM   #7
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Default Re: O'Neill Cylinders

Quote:
Originally Posted by RogerBW View Post
The cylinder design (for purists, the double counterrotating cylinders, which allow you to maintain attitude control without using reaction mass)...
Unfortunately, not so. Each cylinder individually acts as a gyroscope and if you try to keep both pointed at the sun, one will twist up, the other down (but with no net change in angular momentum). To get them to work as O'Neill described, you would need a massive and strong structure linking them, not the flimsy cables depicted by O'Neill. His design is badly understrength.
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Old 04-20-2010, 04:44 PM   #8
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Default Re: O'Neill Cylinders

Quote:
Originally Posted by Langy View Post
In other words, if lwcamp did his math right, your O'Neil cylinder isn't going to be stable if it's got a radius of 20 kilometers and a length of 50 kilometers.
Yeah, I noticed. It's worse than that, actually, since I am going for a diameter, not radius, of 20 km. And the fact that my end caps are hemispheres rather than disks is not going to be anything like enough to save me. In fact, the inequality is rather discouraging. It looks to me as though cylinders have to be so short in relation to their length that roofing over the cylinder floor would be cheaper than capping the ends. That produces a Stanford rather than an O'Neill.

Which means I'm stuck with active stabilisation, I think.
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Old 04-20-2010, 06:01 PM   #9
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Default Re: O'Neill Cylinders

Quote:
Originally Posted by Brett View Post
Which means I'm stuck with active stabilisation, I think.
Even with a ring rather than a cylinder, Larry Niven discovered he needed active stabilization. So scaling up doesn't seem to help.

The "natural" stability of L4 and L5 gets overrated too. You need to maintain your physical plant, you're going to need to maintain your stability too.
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Old 04-20-2010, 08:00 PM   #10
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Default Re: O'Neill Cylinders

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Originally Posted by Fred Brackin View Post
Even with a ring rather than a cylinder, Larry Niven discovered he needed active stabilization. So scaling up doesn't seem to help.
Sure, though that's a slightly different issue: translational stability of the centre of mass. I'm concerned about the thing tumbling, Niven's problem was with drifting off centre on the star.

Quote:
The "natural" stability of L4 and L5 gets overrated too. You need to maintain your physical plant, you're going to need to maintain your stability too.
Yeah, you're right. I guess it's not a big price to pay, except in engineering elegance.
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