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How can I determine if a rotating thin shell cylinder space station is stable? Its dimensions are:

radius = 895m
length = 1150m
thickness of the shell = 15m

The interior is filled with lunar regolith, weighing 10+ tons/m3. RPM=1 and rotational speed is 95.2952m/s.

The shell is to be composed of kevlar and carbon fiber. The structure is intended to be used as a human settlement. Can you help me to figure out if it's stable or not?

What i mean by stable is- As the station rotates generating gravity on the inside, there are forces acting in different directions and if it is not right it might wobble. Here moment of inertia can be taken into account and according to thumbs rule in order for a station to rotate stably it's major axis moment of inertia has to at least 20% greater than the minor ones.

(I am doing this for a competition. The idea is to design a settlement, and I have designed one. I am still in grade 9, but I'm really interested in physics and if one of you could help it would be highly appreciated.)

Punit Sai
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  • What do you mean, stable? What's its structure? – Nathan Tuggy Sep 18 '16 at 21:29
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    I think that this has to do with using the breakup limit. However, the question does not provide enough information. What velocity is the space station rotating at? Or are you just trying to find the maximum velocity it can rotate at? And what is the tensile strength of the material holding it together? Or is it orbiting something which could cause breakup? – Phiteros Sep 18 '16 at 22:09
  • Stackexchange's purpose is to answer questions that are of general interest, not just of interest to the OP. This question gives no explanation of why the particular numbers chosen are of interest, and it also doesn't give enough information to allow anyone to give an answer. –  Sep 18 '16 at 23:49
  • I have edited your question for grammar and included details from your comments. It is still a little bit unclear what you mean by "stable," however. Are you asking, for instance, if centrifigual force might tear it apart? – Jerard Puckett Sep 20 '16 at 04:16
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    @PunitSai you might want to read Appendix A of Chapter Five of this document http://www.saintannsny.org/depart/computer/classes/spacol/articles/sp-413(1975_nasa+oneill.pdf. (It's a very large download. NASA report SP-413, one of the early studies of O-Neill colonies.) Might gve you some idea of the mechanical design, though this is college-level engineering really. – Andy Sep 20 '16 at 08:43
  • @NathanTuggy It's structure is a "think shell cylinder" – Punit Sai Sep 21 '16 at 00:17
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    @PunitSai: I mean the details: how much of what material is used where? "Kevlar thick shell cylinder" could mean anything from a sheet of 1mm kevlar holding the whole thing together to 7m of kevlar and 7m of carbon fiber with 1m of regolith, to give the crudest examples from what I understand of your specs. Those are going to have very different characteristics. – Nathan Tuggy Sep 21 '16 at 00:23
  • Not yet sure on the thickness of Kevlar but will be using 10+tons/m lunar regolith.. – Punit Sai Sep 21 '16 at 00:25
  • As the space station will be place in GEO it needs more radiation shielding. – Punit Sai Sep 21 '16 at 00:26
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    I have edited your question further. You still need to define stable. –  Sep 21 '16 at 07:23
  • @JanDoggen: I believe in this context it means structurally stable - not tearing itself apart due to the forces being exerted (centripetal of its own mass and the regolith, pressure 1 bar (human habitable)). And this makes it an engineering problem, way more suited for Engineering.SE – SF. Sep 21 '16 at 10:32
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    Is that ten tons per cubic meter, or per square meter? – 2012rcampion Sep 21 '16 at 14:23
  • The design study @Andy mentioned is indeed very helpful. Here is a link to a table of contents so you can load just the section of interest. Jan is right, this site is here to help also the people who come later looking for the same information. It is important that you edit the question to be clear what you are asking. SF's guess sounds right, but that needs to be in the body of the question. – kim holder Sep 21 '16 at 14:24
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    As people still seem interested I've added my vote to others who've asked to re-open the question. If @PunitSai can edit the question to add what "stable" means this can be a useful question worth keeping. By the way, at first I interpreted stability as avoiding gyroscopic precession - which is why some designs proposed two counter-rotating cylinders. But that may be a different matter... – Andy Sep 21 '16 at 14:37
  • @PunitSai should also give an estimate of his Kevlar type/tchickness –  Sep 21 '16 at 15:19
  • For information there's an earlier one what-stability-issues-plague-long-artificial-gravity-cylinders with a few interesting answers though not directly answering this question. – Andy Sep 23 '16 at 09:13

1 Answers1

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The moments of inertia of a hollow cylinder of uniform density without end caps is:

$$I_z={m\over 2}\left(r_1^2+r_2^2\right)$$

$$I_x=I_y={m\over 4}\left(r_1^2+r_2^2+{h^2\over 3}\right)$$

where $m$ is the total mass, $r_1$ is the inner diameter, $r_2$ is the outer diameter, and $h$ is the height.

Mark Adler
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