Designing a Space Habitat

A range of designs have been proposed for space habitats. Some appear to be mostly artistic concepts, others are much more serious. They include:

(From Wikipedia http://en.wikipedia.org/wiki/Space_habitat)

• Bernal sphere - "Island One", a spherical habitat for about 20,000 people.
• Stanford torus - A larger alternative to "Island One."
• O'Neill cylinder - "Island Three", the largest design.
• Lewis One^[4] A cylinder of radius 250m with a non rotating radiation shielding. The shielding protects the micro-gravity industrial space, too. The rotating part is 450 long and has several inner cylinders. Some of them are used for agriculture.
• Kalpana One, revised^[5]A short cylinder with 250 m radius and 325 m length. The radiation shielding is 10 t/m² and rotates. It has several inner cylinders for agriculture and recreation.

There are other well-known structures from science fiction literature, including

• Rama (a 20x50km rotating cylinder) from Arthur C. Clarke’s novel, Rendezvous With Rama
• Space Station V (from the movie 2001: A Space Odyssey)
• Babylon 5

Of these, the most complete design is “Kalpana One, Revised,” which properly accounts for issues such as shielding and rotational stability. Most designs presume that it is best to provide windows to admit natural sunlight, but there are many reasons to prefer artificial light sources, primarily involving heat, but also the need for shielding. For adequate shielding from radiation and meteors, the outer walls of the habitat must mass about ten tons per square meter. While transparent quartz windows could be built of this thickness, most designs involving natural sunlight use mirrors to deflect sunlight around shields of stone. But the admitted heat is the real problem (discussed below).

In my previous posts, including Our First Colonies In Space, Life in an Asteroid, and Our Homes, the Comets, I assumed that we would tunnel into asteroids and comets, enclose and spin them for gravity if they were small enough, or build spinning structures inside them if they were too large.

But while writing a sequel to my short story Apophis 2029, I realized that the best choice was simply to build one or more space habitats from the raw materials of the asteroids and comets. I came to this conclusion because of considerations for effective use of space, the stresses of spinning large objects for gravity, and (most importantly) thermal dissipation.

People consume energy in their homes, workplaces, and travel. Much more important, food requires a large amount of energy in the form of light for growing crops. After extensive research on plant needs, high-intensity farming, and lighting technologies, I concluded that the minimum light levels needed requires 4 kilowatts of very-high-efficiency LED lights to grow the food for one person (assuming a primarily vegetarian diet – you need more to grow additional crops for livestock). Add to that the per-capita electric consumption in the U.S.A. of about 1.5 kilowatts, add a little more for contingencies, and I realized we need to plan on 6 kilowatts of energy consumption for every human aboard the habitat.

That’s not too bad, especially considering that readily available solar power can easily provide such levels and at a modest cost.

But energy consumption turns into heat, and heat must be radiated away. The bottom line is that we must allot 19 square meters per person of surface area assuming black body radiation at a temperature of 0 degrees C. It does not help to plant little radiators all over the surface, as they interfere with each other. All that matters is the apparent size of the habitat from a distance, and how closely it approaches the ideals of a black body radiator. Of course, we could use active cooling to heat radiators to much higher temperatures while cooling the interior, but I prefer passive techniques so that a failure of the cooling system doesn’t rapidly result in cooking the inhabitants.

There goes my idea that a million people could thrive in a cubic kilometer of comet. There is plenty of room, more than enough materials. Unfortunately, their waste heat would rapidly boil their home away.

Also, solar light has a large content of heat – and that excess, too, must be radiated away. Sunlight is not energy efficient for growing crops in a thermos bottle (which is what a habitat in space effectively is).

So, my revised plan calls for 20 square meters of surface per person. Also, to provide radiation and meteor shielding equivalent to the Earth’s surface requires 10 tons of shielding per square meter of surface – and thus 200 tons of shield mass per person (regolith is fine, slag works well and is dense, ice is best as long as it doesn’t boil away). But the needed surface area and shield mass per person are constants.

My earlier thoughts on structure did not consider rotational stability, and the folks that designed Kalpana One came up with some very strong arguments that a spinning cylinder is best, and that the width of the cylinder should be 1.3 times the radius. Thus, a cylinder of radius 100 meters (spinning at 3 rpm for 1 G gravity along the outer rim) should be 130 meters wide. That gives a 1-G living area of a little over 80,000 square meters, a total surface area of over 144,000 square meters, and thus a maximum population of 7,200. This structure provides 11.25 square meters (121 square feet) per person of 1-G living space. Is that enough?

It’s comparable to the space provided (per person) in many hotel rooms and cruise ships. But few couples want to live in a 242 square foot efficiency for long, although 28 sm (300 sf) studio apartments are common in many expensive cities.

There is no need to live only on the outer 1-G surface. Assuming 3-meter intervals, the next level up provides 97% of a G. Surely that is adequate. And now we have 22.5 square meters per person of available living space, equivalent to 450 square feet per couple – or 900 square feet for a family of 4. A third living level raises the per-person space to over 33 square meters – 675 sf per couple – 1350 sf for a family of four. Not spacious, but certainly comfortable.

Humans need space for living, working, and of course for growing food. We must allot some space for office space, work space, schools. A single level should suffice (11 square meters per person), partly because some people will work in the farms, or in their homes, or outside the habitat entirely (such as in the mines, the smelters, the steel mills, the solar power satellites, etc.).

Each person requires approximately 64 cubic meters for crops, but crops don’t require 3-meter ceilings. Allocating 2 levels for agriculture may be tight, but 3 levels is more than enough and provides some excess capacity for the production of meat, milk, and eggs.

We need a little more space for overhead: storage, aisles, conduits for air, water, sewage. So we add an 8th level for good measure. That still leaves an interior cylinder with a radius of 75 meters as a park or recreation area. It has 3/4ths of a G of gravity. The opposite side is more than 500 feet overhead – it will feel spacious enough, and 15+ acres of playgrounds, hiking paths, trees, and grass will provide a little bit of Earth in space.

But there’s no need to leave the end caps – the walls of our cylinder – as bare metal. We should build offices, low-gravity facilities (perhaps hospitals), hotels, etc. along those walls. Allocating 15 meters of depth along each end-cap for such purposes still leaves a hundred-meter-wide park, now with only 12 acres of usable space, 100 meters wide by 470 meters around. The lowest level of the end caps is a perfect place for shops and restaurants.

The above ramble describes the capacity of a 100-meter radius cylinder, spinning at 3 rpm to provide Earth-normal gravity. This spin rate is often considered the maximum for a rotating space habitat, as most people (but not all) can adjust to it. More people can adjust to 2 rpm, and essentially everyone has no problem with 1 rpm.  So how much room do we get with these and larger structures? Can they be built?

This table shows the size, possible population, and mass (in kilotons or kT) of the external steel shell, the internal steel infrastructure, and the shield (total mass of steel shell plus rock). Note that once the steel shell reaches a mass of 10 tons per square meter, additional shielding is not needed. For a reference point, the total mass of steel in a modern aircraft carrier is about 60,000 tons, about 20% less than the smallest habitat. The dimensions given are of the habitable volume; the outer walls are assumed to be an extra 5 meters in thickness to provide the volume needed to contain the shield mass (but that extra external area raises the maximum population as well). The thickness of the outer steel shell is also given, in meters, and it ranges from 3cm (1.2 inches) in the 100 meter cylinder to 1.31 meters (4 feet) in the largest. The table also shows the percentage of the asteroid Apophis needed to build this structure, or alternatively the minimum size of a rocky asteroid large enough to build it. *Note that the largest structure would require a nickel-iron asteroid, as there is no rocky shield mass needed.

RPM	3.0	2.5	2.0	1.5	1.0	0.8	0.4
Radius	100	143	224	398	895	1,590	4,621
Width	130	186	291	517	1,163	2,067	6,007
Population	8,087	16,010	38,005	117,491	585,398	1,839,804	15,457,797
Central Park	100	156	261	487	1,133	2,037	5,977
Ceiling	150	236	397	745	1,739	3,131	9,191
Acres	12	29	80	281	1,529	4,949	42,625
Steel Shell (kT)	38	105	385	2,092	23,258	129,560	3,154,722
(thickness)	0.03	0.04	0.06	0.11	0.25	0.45	1.31
Steel Structure (kT)	36	71	168	519	2,584	8,117	68,166
Shield (kT)	1,580	3,096	7,216	21,406	93,822	238,401	0
Total Mass (kT)	1,653	3,273	7,769	24,018	119,664	376,078	3,222,888
% Apophis (27 mT)	6.12%	12.12%	28.78%	88.95%	443.20%	1392.88%	11936.62%
min.asteroid	107	134	179	260	445	651	924*

It is clear that Apophis contains enough raw materials to build habitats supporting 125,000 colonists in up to 16 structures. It is interesting that a 1-kilometer nickel-iron asteroid (of which there are approximately 50,000 in the main belt) provides enough iron that (adding the resources of a small carbonaceous chondrite for carbon, oxygen, and water) a 9x6 kilometer cylinder could be built, supporting over 15 million people. Still larger structures may be constructed; steel has adequate tensile strength for structures large enough to support a billion people, but they become wildly inefficient, requiring nearly 10 times the steel per person.

I plan additional posts providing details on farming in space, on solar power satellites, and on the economics of life in space. It is clear that space habitats are feasible, and that commerce based upon tourism and the construction and maintenance of solar power satellites can pay for it. The obstacles are the difficulty of the bootstrap process:

• capturing an asteroid such as Apophis into Earth orbit
• Launching the tools to mine the riches of the asteroid, the tools to smelt its ores into steel and other valuable materials, the tools to shape that steel into the plates, beams, and girders needed to build things
• Launching the people to make it possible with enough consumables to get past the bootstrap.
• Designing and implementing closed-system recycling facilities capable of efficiently converting human wastes (and crop residues) into food, oxygen, and water.

Once enough infrastructure is in place, the colony should not need the addition of oxygen, water, food, or structural materials. High tech tools will be needed, including whatever is needed to construct solar cells, but the raw materials would already be in place. The Earth will export technology, tools, vitamins, pharmaceuticals, and people. In exchange, the Earth will receive bountiful energy from the Sun, with zero carbon footprint.

But that, too, will take time, energy, and especially people. In the long run, the demand for people in orbit is likely to exceed our capabilities of putting them there. And that, too, is the subject of a future post.

A Choice of Asteroids

I began researching this post believing that Apophis (with its April 13, 2029 close approach) was our best opportunity to capture the resources of an asteroid for humanity and the space program.

Soon I realized that the selections are bountiful (or frightening, depending upon your point of view).

NASA maintains several valuable web sites and services, including

• the Potentially Hazardous Object list (over a thousand) at http://neo.jpl.nasa.gov/orbits/ (where you can display an orbit animation)
• the Small Body Database Browser at http://ssd.jpl.nasa.gov/sbdb.cgi which lists 3,000+ comets and 400,000+ asteroids
• the Near Earth Object Program at http://neo.jpl.nasa.gov/
• The Sentry Risk Table at http://neo.jpl.nasa.gov/risk/ listing PHOs in order of threat. Apophis is currently #4, not based upon 2029 or 2036 but the 2068 approach.

As I described in my post Capturing Apophis, these objects are far too large for us to simply man-handle. We must use finesse, or more precisely, we must use the gravitational influence of a body such as the Earth to do most of the work for us. We can nudge small to medium size bodies a bit given months or years of head start. So, we need objects that pass close by, perhaps within the orbit of the Moon.

Plus, I’m interested in objects we can capture in my lifetime.

Here is a list of potential asteroids. Their distance of closest approach is given in Earth radii (1 Er = 6400 km). For reference, the Moon averages 60 Er (Earth radii) away. This list is in order of close approach date.

• 2005 YU55 passes at 25 Er on 8-Nov-2011. It’s 120 meters across, masses 3 million tons. I wish it passed later – it would make a wonderful practice asteroid but we’re not likely to be able to launch a deflection mission in time.
• 2008 UV99 passes at 7.16 Er on 30-Mar-2019, is 400 meters wide and masses 87 million tons.
• 2001 FB90 passes at 13 Er on 24-Mar-2021, is 349 meters wide and masses 58 million tons.
• 2007 RY19 passes within 0.89 Er on 12-Mar-2024, is 110 meters wide, masses 1.8 million tons.
• 2001 CA21 passes at 6.41 Er on 9-Oct-2025, is 677 meters wide and masses 422 million tons.
• 2001 WN5 passes at 37.5 Er on 26-Jun-2028, is 780 meters wide, massing 646 million tons.
• Apophis 99942 passes at 5.86 Er on 13-Apr-2029, is 270 meters across and masses at least 25 million tons.
• 2007 FT3 passes at 22 Er on 03-Oct-2030, is 340 meters wide, masses 54 million tons.
• 2009 UN3 passes at 19 Er away on 09-Feb-2032, is 919 meters wide massing just over a billion tons.

Note that the sizes are estimates based upon the apparent brightness of the asteroid. None of these have been imaged and measured. The masses are estimates based upon a spherical body of that size with a density of 2.6 tons per cubic meter (partly porous). A solid body would mass more, nickel-iron much more.

This list is not exhaustive, and some of these asteroids may be moving too fast (or not have suitable advance rendezvous orbits) for our purposes. But all 9 of these pass close enough to the Earth that their subsequent orbits are changed by the Earth’s gravity, and a relatively small nudge can be used to control a gravitational slingshot and choose its subsequent path. Some may require multiple slingshots and many elapsed years before they can be parked in a suitable orbit, but even the smallest of these (2007 RY19 at 1.8 million tons) contains enough resources to pay for the effort many times over.

There are many other asteroids from which to choose. A number of asteroids are in horseshoe or spiral orbits near the Earth, and may make suitable low delta-V rendezvous targets. Many more are easier to reach (in terms of required delta-V) than the surface of the Moon. Some of these are nickel-iron asteroids, others may be extinct comets containing huge amounts of ice. One estimate is that 6% of asteroids may be extinct comets.

We need better observations of all of the above objects. If one were a carbonaceous chondrite or an extinct comet, its value would be immensely greater due to the high content of carbon and water – the stuff of life. If one was nickel-iron then that, too, would have extra value. But all asteroids have great value once they’ve been captured into a stable Earth orbit, as all of them contain oxygen, silicon, magnesium, and iron.

Clearly, we don’t need to fight over these trillion-dollar resources. There are enough potentially valuable asteroids to share.

Recipe for a Space Habitat

To build permanent habitats for people to live in space will require several needs to be addressed:

• Living space providing adequate room plus radiation and meteor protection
• Gravity or its equivalent
• Oxygen to breathe
• Water to drink
• Food to eat
• Something profitable to justify life in space

Luckily, some of these are easily addressed, as certain asteroids have all the resources we need, including the majority of the asteroids in the belt – the carbonaceous chondrites.

STEP 1: Capture an asteroid into a useful orbit. The next great opportunity is the asteroid Apophis 99942, which will be in a location suitable for capture in 2029. See my post, Capturing Apophis for details. The good news is that Apophis contains 50 million tons of resources, including 10 million tons of iron, 15 million tons of oxygen,  12 million tons of magnesium, and perhaps 8 million tons of silicon. The bad news is that we presently believe that Apophis is an LL Chondrite, low in volatiles including water, carbon, and nitrogen, also relatively low in calcium, aluminum, and titanium. Available carbon is likely less than 0.2%, water less than 1%. Still, half of these values equates to 50,000 tons of carbon and a quarter-million tons of water.

How much water and carbon is needed? Studies of high-intensity farming techniques suggest that about a half-ton each of carbon and hydrogen are needed per person to grow crops for food and oxygen recycling. This is equivalent to about 3 tons of carbon dioxide and 5 tons of water, per person, much of which will be contained in the growing plants of our farms. Plants are, after all, carbohydrates. We also need significant amounts of nitrogen (for proteins), and phosphorus as well as various trace elements. But all of these are abundant in ordinary asteroids except carbon, hydrogen, and nitrogen. The most common asteroids, carbonaceous chondrites, contain these volatiles in abundance.

Still, it is clear that even a dry rock like Apophis contains enough raw materials to support as many as 50,000 people.

STEP 2: Establish a temporary beachhead. An empty shuttle tank works great.

An empty Space Shuttle SLWT External Fuel Tank has a hydrogen tank 8.4m by 29.5m (97x27’), and an oxygen tank 16.6m by 8.4m (54x27’); these function nicely as pressurized crew quarters. If the hydrogen tank is converted to recycling (growing plants and recycling wastes), its 1493 cubic meter volume could support about 36 people who reside in the oxygen tank volume (553 m^3), or about 15 cubic meters per person (2x2.5x3m).

You bury the tank for radiation and meteor protection. Five meters of regolith gives about the same protection as Earth sea level; we could get by with three meters on top.

STEP 3: Mine the asteroid and use a solar furnace (or other techniques) to smelt it into useful metals and free oxygen. Also, the first gases emitted when you heat up the regolith are CO2 and H2O. Save them. And note that all the leftover slag is extremely valuable as radiation shielding for the habitat we want to build, so don’t throw it away, either.

To yield enough water and carbon dioxide to grow food for one person, you’d need to process only 50 tons of ore from a carbonaceous chondrite like the Murcheson meteor, but more like 500 tons if Apophis is truly an LL chondrite. You’ll get a little excess carbon which lets you make steel instead of just iron. 100 tons of steel.  As a bi-product, you’ll end up with perhaps 25 tons of oxygen, which you’ll want to save, also. This is a good use for a few more empty shuttle external fuel tanks. We’ll be using oxygen as fuel, I suspect, in VASIMR type thrusters powered by solar energy.

STEP 4: Establish a farm in that empty hydrogen tank (or in several of them as the colony grows). My estimates of needed space are based upon 64 square meters per person of crop area, using high-intensity techniques, and using LED light sources. I also assume hydroponic techniques instead of soil, because it’s easier to recycle the root mass. We won’t use soil (even if it’s free and abundant) until we have a huge surplus of carbon and water to waste.

Note that we need to feed extra CO2 to the growing crops – humans don’t produce enough to grow everything we need, because of the small fraction of plant material that is edible. We’ll even be burning the dried crop residue to create CO2, or turning it into coke (carbon) to improve the efficiency of iron production.

STEP 5: Start building Solar Power Satellites. You’ve got the steel, and all the magnesium you could want, plus more than enough silicon. A square kilometer array of solar panels or collectors intercepts a gigawatt, yielding a net 200 megawatts to Earth. But why stop at a gigawatt? You’re building in outer space where it is simple to build large structures.

A circular array with a 1.6km radius would yield 4 gigawatts of power to be beamed to Earth from geosync orbit. Each generates $1B per year in wholesale electricity (at $.03/kwh). With no energy costs – just maintenance.

The steel & other raw materials for each one consumes about 1% of Apophis’ regolith. By the time you’ve built 50 of them, your revenue is $50 billion a year, and you’ve only consumed half of Apophis.

STEP 6: While you are building Solar Power Satellites in one factory, you can be building a large, permanent, self-sustaining habitat in another. Many designs have been proposed, and I, personally, like a rhombic triacontahedron. It is constructed from 30 identical rhombic steel plates. A simpler design (but more difficult to build) is a cylinder. Both would be spun for gravity.

For radiation and meteor shielding, you need about the same mass of shield as the Earth provides us: 10 tons per square meter. That’s about 5 meters of regolith, or 3 meters of slag (which is nice and dense). I realized that this much mass, spinning at one G along the periphery of a sphere (which is close to a rhombic triacontahedron) exerts an outward force entirely equivalent to a pressure vessel, whose characteristics are well known. To contain a force of 15 tons per square meter (3 tons of which is air pressure), a spherical pressure vessel 100 meters in radius only needs to be about an inch thick, masses about 25,000 tons of steel.

The limiting factor for population is likely to be heat dissipation. Using very high efficiency LED light sources to grow our food, and minimizing all wasted energy interior to the structure, we need about 20 square meters of cooling area per person (assuming passive cooling – the only safe kind). Thus, a 100 meter radius habitat, spinning at 3rpm for 1 G, has sufficient area for a population of about 6,000 people. It takes about 4 tons of steel per person to build the pressure vessel. Since the area per person is constant (20 square meters), and the amount of shielding per unit area is constant (10 tons per square meter), each person needs 200 tons of shielding. Thus the habitat for 6,000 people requires a 25,000 ton steel pressure vessel, plus probably that much again for internal structures, plus 1,200,000 tons of shield mass. This is 2.5% of Apophis – we could build 20 of these with the half left over from building 50 solar power satellites.

Spinning at 3rpm is too fast, you say? If the radius of our vessel is increased to 225 meters (yielding 1 gravity with a 2 rpm spin), our pressure vessel needs to be 5.6 cm (2.25 inches) thick, and requires nearly 300,000 tons of steel. But it now is large enough to support a population of over 30,000 people. And its construction consumes 12.5% of Apophis. Yes, we can still build 4 of these: one in Apophis orbit, one above geosync as the ideal place to maintain those solar power satellites, and I’m sure we can find places to stash the other two. How about L4 and L5?

Sorry, but if you want to spin at 1 rpm (radius of 890 meters), it takes all of 2 Apophis-size asteroids to provide the needed raw materials and would have living space to support about 500,000 people. But it takes more steel per person the larger you build it – there is no economy of scale, as larger and larger pressure vessels take more and more steel per unit area (and thus per person). But as long as we are doing the math, if you raise the radius to 4 kilometers, your steel shell must be a full meter thick, and itself provides all the shield you need.