# How can I determine if a rotating space station is stable

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.)

• 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
• @PunitSai you might want to read Appendix A of Chapter Five of this document saintannsny.org/depart/computer/classes/spacol/articles/…. (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 8:43
• @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 0:23
• I have edited your question further. You still need to define stable. – user10509 Sep 21 '16 at 7:23
• Is that ten tons per cubic meter, or per square meter? – 2012rcampion Sep 21 '16 at 14:23

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.

• It is correct, but there is a relation. Thumbs rule state that Iz>=1.2Ix – Punit Sai Sep 25 '16 at 4:50
• You already knew that. I was filling in the blanks. – Mark Adler Sep 25 '16 at 5:21
• Yeah..I did know that. And by the way it is a thin shell cylinder not hollow cylinder. And also thank you at least for leaving a comment. – Punit Sai Sep 25 '16 at 14:55
• Those formulae do not depend on the shell being thin. They work all the way to $r_1=0$, a solid cylinder. – Mark Adler Sep 25 '16 at 15:11
• I didn't understand? – Punit Sai Sep 26 '16 at 3:41