The Earth is just too small and fragile a basket for the human race to keep all its eggs in.

Robert A. Heinlein.

A home from home

Living at the bottom of a gravity well is, in the long term, suicide. Sooner or later, a bigger fatter lump of rock from further away than you expected will show up faster than you expected and smack the object whose gravity well you're in, and you aren't going to survive. Thankfully, the timescale on that is fairly forgiving: we can reasonably expect to get away with somewhere between many millions and a large fraction of a milliard of years before the next time our home planet gets smacked; and its two closest neighbours (Mars and Venus) are about as safe. All the same, we know the clock is ticking; we don't know when the unexpected will next come around; and don't keep all your eggs in one basket isn't exactly original advice.

That, in itself, is a strong argument for establishing autonomous habitats as far afield as we can. They need to be autonomous so that a catastrophe which takes out some will still leave the rest viable. They need to be far-flung so that no catastrophe can catch all of them. Ultimately, we know the star we call Sun will blow its gaskets: that'll take several milliards of years yet, but we're sure it'll happen. Life won't survive that unless it's made it out at least as far as the Kuiper belt – a mess of comets and random debris left over from the formation of our solar system, far out beyond the orbit of even Pluto. We don't need to worry about that for a while yet; but we do need to bear it in mind in our long-term planning.

Meanwhile, folk are eyeing up the planets nearest us – particularly Mars – and wondering whether we can make them habitable – Earth-like enough that life as we know it can survive in the wild there. That transformation is known as terraforming; and we have to face the fact that, if we do it to a planet, we'll destroy most of the archaeological evidence of its past and wipe out any life – however it may be – that may have been there before. Worse yet, if our efforts to make the place like home go sour, we may merely end up creating an ecosystem in which we can't survive – whether because vestiges of indigenous life prove too virulent or because the life-forms we (engineer and) introduce to do the job evolve into something with which we can't share a world. These worlds would then be closed to us.

Before anyone goes attempting terraforming on another planet, it may be a good idea to do some experiments in space. For this, one will need a substantial habitat involving large expanses of surface at which gravity is roughly similar to that on the Earth's surface; one will need to ensure that an atmosphere is prevented from escaping, in so far as one can get one started; and one will need a light-source, as near as possible like sunlight filtered by the Earth's atmosphere. That happens to be exactly the same set of requirements we'd need to meet for autonomous habitats in which life can propagate and survive such catastrophes as would sterilize our cozy planets.

A solution presents itself: a spinning cylinder (e.g. formed out of the rock of asteroids or Kuiper-belt objects) and some work with mirrors (and glass plugs in the end-plates to let the light in while keeping the air in) and light-scattering materials positioned along the cylinder's axis.

Structural Viability

Mechanics: consider such a cylinder, of axial length Z, radius R; suppose the skin to have thickness h (presumed small compared to R) and to be made of a material with density D and ultimate tensile stress S (to which I'll return); suppose it to be turning with angular velocity w (so it completes a whole revolution every 2.π/w seconds). The apparent gravitational field strength (which we want to see near 10 m/s/s or 30ish ft/s/s) on the inner surface of the skin will be w.w.R.

To keep the skin accelerating inwards (or, to the observer standing in it, to prevent the skin's weight from tearing it apart) the skin must then sustain tension. Let the tension in the skin be T and consider two half-planes radiating out from the cylinder's axis, with a small angle a between them. These cut a slice of the skin; the slice has (straight) radial edges of length h, (straight) axial edges of length Z and (slightly) curved edges of length a.R; so its mass is (roughly) a.R.h.Z.D. Construct the bisector of the angle – another half-plane radiating out from the axis, meeting the original planes in angles a/2 on opposite sides of itself. The slice of skin is moving tangentially – so (roughly) at right angles to this plane – but only accelerating radially inwards. This requires a net force on it of w.w.R times its mass. That force can only be supplied by tension in the skin: which acts perpendicular to the flat faces in which our outer planes cut the skin. Luckily, these aren't quite parallel to one another.

The tension in each face pulls almost perpendicular to the bisecting plane; each makes an angle a/2 with the actual perpendicular. Each tension's component perpendicular to the bisector is T.cos(a/2) and they pull in opposite directions, so cancel one another out; their components parallel to the bisector are both radially inwards of size T.sin(a/2), so we obtain a net inward force 2.T.sin(a/2). Since a is small, and in particular because we're only interested in the limiting case when a is very small, I can use the approximation sin(a/2) = a/2 to obtain a net inward force a.T, which must be equal to our mass, a.R.h.Z.D, times acceleration, w.w.R; i.e. a.T = a.R.h.Z.D.w.w.R.

Cancelling out the small angle a, we obtain T = h.Z.D.(w.R).(w.R), in which I bracket w.R because this is the speed at which the skin is moving (tangentially). Meanwhile, T/h/Z is the tensile stress (tension divided by area across which it acts) in the skin: this has to be less than the ultimate tensile stress, S – the tensile stress at which the material breaks. This limit on T/h/Z places an upper limit, S/D, on T/h/Z/D = (w.R).(w.R), so the square root of S/D is a velocity which characterizes the strength of the skin: call this V and our constraint becomes w.R < V, i.e. the strength/density ratio of the skin imposes a constraint on its sustainable tangential velocity.

See my page of data on materials for illustrative values of ultimate tensile stress, density and V, the square root of their ratio (called densile speed there but limiting velocity here). I am not a civil engineer, so don't necessarily take my use of the numbers too seriously … but all I really want them for is the orders of magnitude we need to play with. Practical materials offer limiting velocities of order 100 m/s (a.k.a. 224 miles per hour); wackier materials like carbon nanotubes offer several kilometres per second. For a cylinder ship of diameter 1 mile (1600m, R = 800m) a velocity of 100 m/s limits w to at most 1/8 radians/second or just over one turn per minute.

Crucially, R is bounded above by V.V/(w.w.R) and w.w.R is our apparent gravitational field strength, so our desire to have an Earth-like value for this, coupled to the practical limitations on V, imply an upper bound on the radius of our cylinder ship. A limiting velocity of 100 m/s will allow us Earth-like gravitation at up to 1km radius; materials offering 1km/s will allow us around 100 km as radius; and carbon nanotubes would appear to offer at least a factor of 10 beyond that. A cylinder ship with the same radius as the Earth (roughly 64 mega metres) and the same (though outwards, rather than inwards) surface gravity would require a material with limiting velocity at least 7.9 km/s; which carbon nanotubes may well be able to deliver. Of course, such a huge structure would be hard to manoeuvre out of the way of incoming disasters, and would make the cost of being hit by one immense; so I'm not especially enamoured of them. None the less, it is nice to know that plausible materials will suffice to make cylinder ships at least as large as we can sanely want.

Payload

That's for an empty cylinder ship. Of course, we'll actually want some rubble, soil, water, air and other stuff inside the cylinder; this effectively increases D (without affecting S), thereby reducing the limiting velocity a bit.

To deal with the plain weight of rubble, soil, water and similar is easy; just add, to D.h, the mass of detritus per unit area strewn about the interior of the cylinder; call that E. To deal with the air, we'll be having some specific air pressure at the skin, P; our sliver between two planes an angle a apart has surface area a.R.Z so the force on it will be P.a.R.Z. As before we can cancel a from all terms; and Z appears as a common factor in the load, so we obtain:

whence, dividing through by h, we get (D+E/h).(w.R).(w.R) + P.R/h bounded above by the ultimate tensile stress of our skin-material. Since our ultimate tensile stresses are all better than 20 mega-Pascals, which is roughly 200 atmospheres, the air pressure contribution will be ignorable as long as R/h is ignorable compared to 200, i.e. the skin thickness needs to dwarf R/200 – in our 1-mile diameter example, we can ignore air pressure if the skin thickness dwarfs 4 metres (13 foot and a few inches).

Now E will be the typical density of your rubble, water and soil times its depth; its density is similar to D so D+E/h will be ignorable if the depth of rubble, water and soil is negligible compared to h. To have any chance of terraforming our cylinder ship, the 4 metres h needs to dwarf for atmospheric pressure to be irrelevant sounds like a reasonable depth of rubble, water and soil (though we might want rather more – perhaps as much as 10 metres), so it sounds like ignoring the payload won't be wise !

Note that air pressure p varies with height r as dp/dr = density.w.w.r, and density is the average molecular mass of the air times p/k/T, where k is Boltzmann's constant and T is the temperature. Ignore temperature variation inside the cylinder and assume the air is well mixed, so relative molecular mass divided by k.T is constant; this constant has the dimensions of the inverse square of a velocity (and we're about to halve it), so take it to be 2/u/u. We thus have dp/dr = 2.p.w.w.r/u/u so log(p) differs from (w.r/u).(w.r/u) by a constant and we obtain

so that, on the axis, the air pressure is lower than at the skin by the factor exp((w.R/u).(w.R/u)). Let g = w.w.R be the local gravity at the skin to make this exp(g.R/u/u). To simulate conditions at the surface of Ocean, where air density, 2.p/u/u, is about a kilogram per cubic metre at one atmosphere, so u is 450 m/s and u.u/g is over 20 kilometres or nearly 13 miles. Thus, in our one-mile diameter example, air pressure at the axis will be 96% of air pressure at the skin: we can realistically ignore variation in atmospheric pressure.

Good Gravity

Now, we want subjective gravity inside the skin to be roughly g = 10 m/s/s. Subjective gravity is w.w.R or (w.R).(w.R)/R, bounded above (if we ignore payload) by V.V/R so, in turn, R is bounded above by V.V/g, of order 1 kilometre. The limiting 1-mile diameter ship considered above has subjective gravity of about 12.5 m/s/s; if we let it spin slightly slower, at one turn per minute, we get a subjective gravity of 8.8 m/s/s, which would probably feel quite nice.

The worst material in my list is the week end of glass's range; glass makes a reasonable approximation to granite, which is a reasonable caricature of the materials at one's disposal in space; this gives a limiting radius of V.V/g = 739.6 metres or just over 800 yards – with no payload.

For the sake of a handy reference, consider a slightly smaller cylinder ship with circumference 1 mile (so R is 256 metres or 280 yards); to attain 9.81 m/s/s (i.e. standard gravity; only slightly more than the speed of light per year, 9.5 m/s/s) requires 1.87 turns per minute giving a tangential velocity of 50m/s (112 miles/hour), which is respectably within the limits imposed by strengths of materials. That completes a whole turn each 32 seconds or so; if we slowed it down to take 40 seconds/turn (i.e. one and a half turns per minute) we'd get a surface gravity of 6.3 m/s/s, roughly 2/3 standard gravity, with a tangential velocity of roughly 40 m/s or (since we're doing a mile every 40 seconds) exactly 90 miles/hour.

So, as model example, consider a cylinder ship with circumference a mile rotating once every 40 seconds. Local gravity is about 2/3 that on the surface of planet Ocean, at 6.3 m/s/s or (quite accurately, as it turns out) the speed of light per year and a half (light per 1.5032 years). The axis is 280 yards overhead, or 256 metres for those who like bytes.

What's that like ?

You might have trouble growing sequoias, at least once they're tall enough to be intruding into the low-gravity region near the axis, but most living things are going to be happy enough in a world that small. The world's tallest tree is, I gather, 367 feet tall; that's a bit over 100 metres, so not quite half way to the axis. Trees might grow taller than that in lower gravity, of course.

It's going to be fun for the birds; flying up near the axis, they're going to have to learn how to fly without gravity. But I reckon birds are intelligent enough to positively enjoy doing that – especially swifts and their kin. It's going to confuse the hell out of bugs, though – but the birds will apply plenty of evolutionary pressure in that department.

If you build a road round the inside, a biker doing 90 mile/hour in one direction is going to experience double local gravity, about one and a third times standard gravity; going the other way, our biker will be in free fall. Cute, huh ? Do a tun that way and you'll have a little gravity to hold you on the road; while the serious grand-prix-scale racer at 180 miles/hour can experience local gravity again. Some bikers I have known probably wouldn't be able to resist the weird experience of going through 90 miles/hour in the latter direction, albeit you'd have trouble doing it unless the road varied its altitude (i.e. distance from the axis), since otherwise you'd have no traction with which to accelerate as you approached 90 from below (or, indeed, tried to slow down again from the other side).

Now, swifts can fly that fast, so expect to see a swift discover that it's going fast enough that it can fold up its wings and just float in mid-air, albeit while travelling at 70 miles/hour, or some such (depending on altitude). That's going to be fun to watch, in its own right. Flying the wrong way will give them amplified gravity, which they can probably exploit to attain serious accelerations; and how long will it be before swifts evolve competence at taking Coriolis forces into account ? [The Coriolis force is at right angles to one's velocity; its magnitude, per unit mass, is 2.w/radian times one's velocity; and 2.w/radian is about 0.3/second in our case, a factor of 2160 up on that for residents of planet Ocean.]

Why Bother ?

Well, for a start, growing your food on a cylinder ship has one spectacular advantage over growing it on a planet. It's not at the bottom of an enormous gravity well.

As Crazy Eddie might point out to you, in a comparatively sensible moment, every kilogram of mass at the surface of planet Ocean owes the universe 63 million Joules of energy. Now, OK, so Big Al tells us that a kilogram of mass is equivalent to almost 90 petaJoules, so 63 megaJoules is a mere .7 parts in a milliard (that's a billion to North Americans). However, it's rather like a mortgage on an absurdly high rate of interest; paying it off will break you. If you want to break free of the loan shark (the gravity well), you're going to have to work very hard to do it.

If you want to live anywhere but at the bottom of a gravity well (where the loan shark can't stop your equally-indebted neighbours from trading with you) you need to (breathe, but air's light, …) eat and drink. If there's nothing you can (breath, …) eat or drink that isn't up to its neck in debt, you're going to have to pay off its debts before it's any use to you. So either you get an economy going that's not up to its neck in debt, or you live … up to your neck in debt. Sound familiar ?

On the other hand, if you set up an ecosystem on a cylinder ship, at the top of the gravity well (i.e. a debt-free local economy) you're in a position to get pro-active about your situation. For one thing, it's a lot easier to get a few more cylinder ships up to speed on this once you've got one of them going – the resources the first had to work so hard to get going will actually be looking for somewhere to move to, once the first cylinder ship gets reasonably crowded. Life behaves like that – get it going and it fills the available space, then it starts wanting somewhere else to fill. Now I, and Crazy Eddie, am all in favour of this (nothing but life is any good to eat, for instance), so let's help it to find somewhere else to fill – by building more cylinder ships.

At the same time, the International Space Station is going to be severely resource-strapped as long as it costs the Earth to feed even a handful of folk living on it. Whereas, if it were down-hill from a cylinder ship with a herd of pigs living in a forest, a good expanse of arable land and a large lake full of fish, the food would be about as cheap on the ISS as it is on a Pacific island. What's more, the human ordure the ISS has to dispose of would find a place where it's welcome.

So, even if you don't get a buzz off the thought of Life expanding its sphere of influence, the raw economic advantages of an ecosystem at the top of a gravity well should persuade you this is valuable. Anyhow, I value it: and so will Crazy Eddie. So, basically, get out of the way and let us get on with it !

Another advantage of cylinder ships is that all your structural materials go into making surface. If you divide the volume of The Earth by its surface area, you get 2117 km (a third of Earth's radius). If you can make cylinder ships with hulls less than 212 metres thick out of the rubble in our asteroid belt, Kuiper belt and the like, even allowing that you can only use 1% of the rubble mass to make the strong materials you need for your hulls, you'll still only need one hundredth of the Earth's mass, in rubble, to build enough cylinder ships to equal The Earth in surface area. All the other Earth-like planets, plus The Moon, collectively only have a surface area of about one and a half times that of Earth: and their immensity is, at every turn, an obstacle to making them habitable. Furthermore, the habitable space gained in the form of cylinder ships has the enormous advantage that each pocket of it is a separate target for any disaster: one large comet can ruin your whole planet in a single blow, but it can generally take out only one target at a time. Furthermore, a cylinder ship can dodge much more readily than a planet can.


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