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Background

A McKendree cylinder is a rotating cylindrical space habitat comparable to the more well known O'Neill model. It was proposed by NASA engineer Thomas McKendree in 2000 as an update of O'Neill's, using carbon nanotubes instead of steel and aluminum to allow for much larger structures – up to 10,000km long/1,000km radius, compared to O'Neill's 32km length/8km radius.

A couple looks into the distance within a cylindrical habitat; the landscape is pastoral

A single McKendree cylinder therefore has millions of square kilometres of habitable space along the interior surface and potential for even more within the hull itself and interior structures.

Problem

Wobble. More precisely: rotational instability.

A capped cylinder as described has two principal rotational axes and moments of inertia: along the length of the cylinder (in blue, below), and another perpendicular to this between the end caps (in red). The former is the smallest principal axis, and the latter is the largest principal axis:

A cylinder with two axes of rotation indicated

Given a space habitat as described above its inevitable that the interior space won't be perfectly and symmetrically balanced at all times: people will need to move around, cargo has to be shifted, vehicles will traverse the surface in every direction, air will flow in complex ways, water will slosh about, and so on. Because this structure is in space, momentum is conserved, but kinetic energy is not: movement of objects within or on the surface of the habitat will dissipate kinetic energy unequally and result, inevitably, in the cylinder tumbling end-over-end as it seeks equibilirum with the largest axis. For sake of discussion let's assume this tumble-point is somewhere between a few days and a few years of normal use. Any potential solution will need to work in either extreme case.

Partial Solutions

The classic solution found in both O'Neill's and McKendree's proposals is to pair each cylinder with an identical counter-rotating cylinder connected by a superstructure so each cylinder's wobble is countered by its neighbour's.

A pair of O'Neill-style space habitats

Similarly, Orion's Arm's implementation proposes nesting a second cylinder within the larger external cylinder and counter-rotating it. The site doesn't go into technical detail about how this is achieved, but presumably the internal cylinder is connected to the external cylinder at the end caps in a way that allows it to spin freely in the other direction. (Whether this would work is a question for another time.)

These may (or may not) solve the problem for those specific configurations of habitat, but do not work for a single cylinder.

Question

Given a McKendree cylinder (singular, unnested) habitat of arbitrarily large dimensions and suitable mass, what is the best way to prevent wobble from destabilizing the rotation and orientation of the structure?

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  • $\begingroup$ The wobble should be self correcting due to the gyroscopic effect. If your cylinder is rotating on 1 axis of rotation, it will resist any other axis of ration that is generated. Just keep adding energy to keep it spinning along the cylindrical axis. $\endgroup$ – A. C. A. C. Aug 29 '17 at 22:26
  • $\begingroup$ I always thought carbon nanotube(CNT) can withstand enormous radial and hoop stress, no? CNT is known for its tensile strength, lightweight and very elastic. $\endgroup$ – user6760 Aug 30 '17 at 5:49
  • $\begingroup$ @user6760 Surely. But the concern is not the hull falling apart, but the clean, homogenous artificial gravity getting funny or dissaeparing and throwing things around. $\endgroup$ – b.Lorenz Aug 31 '17 at 6:14
  • $\begingroup$ A bunch of extra gyros and control systems. They measure and counteract any wobble. $\endgroup$ – Donald Hobson Aug 31 '17 at 13:40
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    $\begingroup$ @A.C.A.C. That is what intuition says will happen, but (for example) Explorer 1 ended up tumbling end over end. $\endgroup$ – rek Sep 14 '17 at 4:31
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Pumping water back and forth to squash wobbles has long been proposed. If you have enough water being moved around just under the outer skin, you can not only damp out any wobbles but it can act as radiation shielding too.

It is just that it would take an awful lot of water and plumbing to work that system for a cylinder as large as you are talking about.

Another method would be deployable solar sails.

Also, if the cylinder is big enough, the random movements inside should cancel themselves out.

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  • $\begingroup$ Do you have a reference of some sort I could follow up or more details on the use of water as described? I'm leaning toward a combination of your answer and @Lex's below, but while yours came first, his is a bit more precise about the where and why of it working. $\endgroup$ – rek Sep 27 '17 at 13:30
  • $\begingroup$ I couldn't find any specific references but I found this: nss.org/settlement/physicstoday.htm that might have some useful info. I want to say that I saw it in The High Frontier but I don't have the book on me and Google didn't help. $\endgroup$ – ShadoCat Sep 27 '17 at 17:05
  • $\begingroup$ I don't think random movements are likely to result from large amounts of humans living together. If anything, you would expect to see emergent predictable behavior as you increased the scale. $\endgroup$ – Pasqueflower Feb 11 '18 at 16:22
  • $\begingroup$ @Pasqueflower we're die of radiation exposure when we pass the next star because we all just had to go to Phil's birthday party at the same time. $\endgroup$ – candied_orange Nov 11 '18 at 19:01
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Arbitrarily large dimensions, you say? Well, then...

Just make it so large that it can't tumble.

Specifically, make it long. On sufficiently large scales, everything is non-rigid, so eventually you will get to a point where the cylinder doesn't just wobble, but rather starts twisting and bending like a strand of wet spaghetti. Now I know what you're thinking: "That sounds like a terrible idea! I don't want my colonists thrown around at the end of a whiplike carbon-nanotube spaghetti strand as the structure tears itself apart!" Well, you just haven't made it big enough yet.

Because the structure cannot be perfectly rigid, there is some (very large) minimum radius of curvature around which you can bend the entire cylinder without breaking it, and it'll keep happily spinning while all of the superstructure is periodically compressed and stretched over each rotation. At a several-times-larger radius, the stresses will become unnoticeable, and the local deviation from perfect straightness completely unmeasurable to human perception. At that point, you can bend the entire megastructure into a loop, tie the two endcaps together (so that it still technically counts as a distorted cylinder, rather than the torus you get if you eliminate the end caps entirely), and you will then find that the bent structure, consisting of a single extremely long tube with no pair,

a) has zero net angular momentum, b) cannot tumble, because its ends hold each other in check, c) has billions of times Earth's living space, and d) can push against itself to spin up / down--no strict need for solar sails or reaction mass.

It can be set vibrating by asymmetries in local mass distribution around the curved axis, but damping those kinds of vibrations is a much simpler task, and material can be moved along the spin axis arbitrarily.

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  • $\begingroup$ Nice out-of-the-box thinking :-) $\endgroup$ – cmaster Nov 11 '18 at 22:15
  • $\begingroup$ Why not turn it into a torus? Then you can have hilarious arguments between the toroidalists and the straight-cylinderers. $\endgroup$ – Joe Bloggs Nov 12 '18 at 8:55
  • $\begingroup$ @JoeBloggs Because if you do turn it into a torus, then it's technically outside the scope of the question. :) $\endgroup$ – Logan R. Kearsley Nov 12 '18 at 19:53
  • $\begingroup$ @LoganR.Kearsley : Well you’re no fun! $\endgroup$ – Joe Bloggs Nov 13 '18 at 15:39
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The moments of inertia are only as listed assuming the cylinder has uniform density. By increasing the density along the 'equator' you could make the axis of rotation the largest principal axis. This then removes the need for active stabilization.

One way of accomplishing this might be to add a large lake/sea along the equator. The depth and width of this body of water will depend on the weight of the superstructure it needs to balance out. I assume this is a biome you would want present somewhere in such a large structure anyways, so why not around the equator.

Rigid spars radiating from the equator would also alter the moment of inertia, but it is my understanding that the radius of a McKendree cylinder is limited by the tensile strength of carbon nanotubes, so I do not know what could be used to extend structures out past that radius.

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  • $\begingroup$ Any idea how to calculate the needed excess mass/density at the equator to make that the largest principal axis? Open seas are a waste of space (and present problems if you need to move the cylinder; see Rendezvous With Rama), but sequestering it "underground" would solve that problem. $\endgroup$ – rek Sep 14 '17 at 4:42
  • $\begingroup$ Moments of inertia can be calculated fairly easily with calculus, but it depends on the density/distribution of mass in your cylinder overall. If you are worried about maximizing useful space, then your entire cylinder would probably filled with a 100s of kilometers thick arcology which would have a different moment of inertia then a thin shell filled with atmosphere. $\endgroup$ – Lex Sep 18 '17 at 18:10
  • $\begingroup$ If your cylindrical sea were 100km wide and required a 100m sea wall to keep from spilling during acceleration, then the air pressure at the bow would drop to something similar to that at the top of Mount Everest during acceleration. $\endgroup$ – Lex Sep 18 '17 at 18:22
  • $\begingroup$ By "waste" I meant it's unlikely a terrestrial species devising to bring its biosphere along would design a significant portion of the habitable area to be marginally habitable at best and a hinderance to transportation (in both senses). $\endgroup$ – rek Sep 25 '17 at 18:06
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This potentially violates the original premiss but what about making it a very short cylinder, sure this reduces the amount of available living space but would also not give the station a longer axis that it could turn around. I was thinking in the order of the cylinders length being the same as its radius.

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    $\begingroup$ That is the rationale behind the Kalpana One design, but as you said it isn't in keeping with the design proposed above. $\endgroup$ – rek Sep 25 '17 at 18:08
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A long, thin cylinder is dynamically unstable, and over the long time span that a McKendree cylinder would be in operation, it is almost a certainty that some condition or set of conditions will arise to create dynamic instability and cause the cylinder to tumble.

Given the enormous scale of the cylinder, using movable ballast or even rocket thrusters seems infeasible, the amount of materials needed to to be moved or the amount of reaction mass being expended will be vast (indeed, the very act of moving megatons of ballast or pumping billions of litres of reaction mass may be enough to cause the cylinder to become unstable).

My suggestion would be to use giant solar sails attached to the cylinder to provide gentle, long term torques to the cylinder to maintain stability. The form of the sails will be a "Heliogyro", which provides control of individual "blades" to provide some fine control of the amount and direction of the torque. The illustration is of the proposed heliogyro for a mission to Halley's comet, and given the rather low amount of "thrust", the scaling of the heliogyro blades for a McKendree cylinder will be on the scale of the cylinder itself.

enter image description here

JPL Heliogyro proposal

Since the size of the cylinder will provide a massive amount of inertia, the gentle and long term application of torques by the heliogyro blades should keep the cylinder spinning within the limits that discourage instability.

Edit to replace dead link

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  • $\begingroup$ The sails would need to be anchored at the end caps and remain stationery, wouldn't they? A cylinder 2,000km in diameter would need to rotate 0.03 rpm or 188.5 km/min (at the outer surface of the cylinder) to produce 1 g, which strikes me as destructively fast for solar sails. $\endgroup$ – rek Sep 14 '17 at 4:21
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    $\begingroup$ They would be anchored to the cylinder much like helicopter blades are attached to the hub of the helicopter's rotor head. They apply torque through changes in "pitch". Since the sails can be tension structures due to the rotation of the cylinder, they can be strong and light. $\endgroup$ – Thucydides Sep 14 '17 at 4:46
  • $\begingroup$ Moving the fuel around can cause the cylinder to lose stability, but releasing the intrinsic chemical energy of that fuel cannot undo or outright reverse it? Something doesn't seem right. $\endgroup$ – B.fox Feb 11 '18 at 15:02
  • $\begingroup$ @Thucydides Your link has deaded. Do you have an updated version? $\endgroup$ – wizzwizz4 Nov 11 '18 at 20:24
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There doesn't seem to be an answer suggesting the only obvious solution besides the ones you mentioned (and discounted) in the question: simply make the moment of inertia larger along the axis of the cylinder, so that rotating along that axis becomes its most stable state.

This of course requires adding a lot more mass. But since this kind of structure has to be built in space anyway this isn't necessarily a big issue. Simply attach a number of captured asteroids in a thick ring around the midpoint of the cylinder, and stick them together with carbon nanotubes. The ring should extend out from the cylinder as far as possible given the material limits of the nanotubes holding it together.

Of course, your cylinder might be so big that you're at the limits of carbon nanotube tensile strength already. In that case this plan won't work at all, since the mass of the ring will exert even more centrifugal force than the cylinder itself. Because of this, a cylinder using this stabilisation method would have to be a lot smaller than the theoretical maximum. It could still be enormous, though.

(I should note that this answer is somewhat tongue in cheek. I'm not sure it would really work, because an object on that scale wouldn't really behave like a rigid body. The ring would want to spin one way while the two ends of the cylinder want to tumble, and that might cause the whole thing to tear itself apart. I don't know whether it's possible to prevent this or not. I suspect that in reality the only ways to do it are some kind of active stabilisation or some kind of counterrotating mass, with the latter probably being far more practical.)

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The best way is the way you mentioned. If you simply don't need that much space, consider multiple smaller cylinders. If you are opposed to this for aesthetic reasons though I supposed we can consider a few other options.

You could also try a counterbalance system. A computerized system shifting weight can offset the impact of movement inside the cylinder. Shifting liquid ballast could possibly prevent rotation, but it's not exactly energy efficient.

Stabilize through the use of thrusters, or similar means. One more way to stabilize would be through using rockets or some other future propulsion system to counteract unwanted spin. Rockets however can run out of fuel, so maybe it uses magnets to manipulate itself within a magnetic field from a planet or sun?

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  • $\begingroup$ Multiple cylinders is outside the parameters of the question, and obviously making them smaller doesn't solve the problem of cylinders tumbling. $\endgroup$ – rek Sep 25 '17 at 18:22
  • $\begingroup$ @rek multiple smaller cylinders = same total space as one large one. Also that is only a third of my answer. $\endgroup$ – Braydon Sep 25 '17 at 21:34
  • $\begingroup$ And I'm telling you that part isn't a solution within the parameters of the question. $\endgroup$ – rek Sep 27 '17 at 13:20
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Flywheel gyroscopic stablizers

Two of them, one for each of the axes you describe. These flywheels would oppose shifts of the cylinder and hold it in position. Gyroscopic stabilizers work via conservation of angular momentum. Or maybe you only need one - tt seems to me a giant spinning cylinder like this would already act like a flywheel. So you might only need one additional flywheel to stabilize it.

from http://veemgyro.com/wp-content/uploads/2015/11/White_Paper_1403-How_Gyros_Create_Stabilizing-Torque.pdf

pdf on gyroscopic action via conservation of angular momentum

The more momentum the more stabilization you can get. You could have large flywheels exterior to the cylinder. Or you could have very fast spinning flywheels. Or you could have many, moderate sized flywheels that act together.

You are in space, so you do not need to worry about atmosphere slowing down your flywheels if you keep them outside.

An (additional) cool thing about flywheels is that you can also store energy in them as kinetic energy and so these flywheels would serve double duty. You can tap that energy for readjustment of the cylinder or whatever other needs you have.

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  • $\begingroup$ The question does specifically say a single cylinder. That being said I did also have my first suggestion being just having two smaller cylinders instead of one big one. $\endgroup$ – Braydon Aug 29 '17 at 23:36
  • $\begingroup$ How big would a flywheel capable of stabilizing hundreds of millions of tons of hull and soil and water and such need to be? $\endgroup$ – rek Sep 27 '17 at 13:24
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I am not sure I understand your problem. Presumably your "tube" would orbit a star or a planet and the gravitic field would stabilize it and prevent tumbling. This is because the force keeping the near end "down" is significantly larger than the force pulling the far end away from "up".

So your actual problem IMHO would be to keep the interaction between gravity and inertia from tearing the structure apart. I am afraid you would need those "partial solutions" for that, you need to counter the inertia. This would actually IMHO be a good thing since, if the counter-rotating mass is an outer hull, it would work as radiation shielding AND allow you to rotate the actual habitat without actually ejecting reaction mass, a non-trivial benefit as rotating a structure that large is not a simple problem. It would also work as armor against physical impacts. This would also make having a "non-rotating" middle-layer you probably want for docking space, storage, sensor system, solar power and such fairly trivial.

So while the counter-rotating outer hull sounds complex, I think it is actually the simplest solution overall, if you consider all the other issues relevant to building a large habitat. Most importantly, it is a robust solution that depends on the overall structure of the habitat, not on sophisticated active and dynamic systems. It won't fail because of a software bug or a fuse breaking. Any failures will be obvious not hidden or deceptive. And it would probably work for a very long time even without maintenance if designed for that.

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  • $\begingroup$ I don't see the connection you're making between the local gravity well (if present) and an object like this tumbling. If the attraction is such that the cylinder is held pointing down-well, collision is a more pressing concern. Doubling the number of cylinders wouldn't solve the problem you're identifying (tearing itself apart due to the interplay of its inertia and the local gravity well) either. $\endgroup$ – rek Sep 25 '17 at 18:19

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