Stabilizing a McKendree Cylinder Habitat

Question

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 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:

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.

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?

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.

Answer 6

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.

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

Answer 7

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.)

Answer 8

Add a flange around the “equator”, a wide annulus of dense material coaxial with the cylinder, protruding from the cylinder wall into space halfway between the end-caps. Perhaps make its rim especially dense or thick. That would increase the moment of inertia about the longitudinal axis by more than the moment of inertia about the transverse axis.

Answer 9

Given the assumption that the cylinder cannot survive without a technological society running it, then the solution would be to use active compensation systems such a moving weights or liquids and accelerometers to cancel all unwanted motions and achieve active stability. A fly by wire system such as the one of the X-29 and other modern fighters.

Answer 10

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?

Answer 11

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

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.

Answer 12

Use the sun to keep it steady. Not the Sun, mind you, but assuming you don't want to do the silly idea of making it half windows, you need to have a little sun inside the cylinder that you power with the solar panels on the outside if you happen to be near a star. I'll assume it can be as heavy as you find convenient - you only need a shell that emits light, but the local sun also makes a great place to hide ugly industry while taking advantage of zero gee conditions.

Since people don't want day all the time and it's a waste to build a giant portable sun just to turn it off half the time, that sun is going to get passed all the way up and down the main axis of the cylinder each day. Each time it passes up or down that axis, it is reeling in some of the filaments (you said nanocarbon) that tether it and letting out others. It may have a track infrastructure tethered to the poles to help. Of course, very efficient regenerative braking makes this process "elastic" - you're not really throwing away much energy when you use the filaments to steer it.

Anyway, by controlling the path of the sun, or equivalently which directions the sun applies more force during its daily round, under the careful technical control of Chief Engineer Ra, the sun will exert enough torque in enough directions on this cylinder that it can be kept spinning the right way despite all the minor motions on the surface.

Answer 13

You might use the high strength of the materials required for construction to create a gravity anchor towards the sun. A sufficiently high gravity gradient should create a force capable of stabilizing the cylinder. Something like this, but at scale:

A new attitude control approach is presented here that overcomes most of these limitations. The proposed system configuration assumes a downward deployment of a ‘pendulum-like’ small mass from the satellite through a pair of identical tethers attached to its two distinct but symmetrically off-set points around the mass center.

Answer 14

Use the axial light source as a harmonic counterweight

Most of the solutions suggest that we move something around the outside to keep the rotational axis consistent, but that would be a complex mechanism because you'd have to actually change the size of the containers to keep them from sloshing as you moved the fluids around.

What I'm suggesting is more akin to the tuned mass damper, except that we're countering uneven load instead of a vibration.

Every implementation I've seen of this kind of cylinder has a light source that runs along the central axis. This light source also acts like a hub, and spokes would radiate out to keep it centered. In this case, we would increase the mass of the axial tube, and adjust the length of the spokes to move the tube away from where the extra mass was added.

Note that this is just a short-term measure. You still have to deal with the linear energy added to the system, which will attempt to pull the tube to one side. For that, you're going to need station-keeping thrusters.

Or...

Use tidal force

This is like the Integral Trees. You have the tube be long enough that the tidal force of some object exerts enough tension to counter-act any rotational forces. Obviously, this means it would have to be really long, and in orbit around a massive object.