For some time I’ve dreamed of towns where all the building is underground, and the surface is devoted to soil — gardens and parks — but with some exposed windows to the sky. Subterranean construction faces a number of objections, one of which is a concern that it will be dim and dark, due to a lack of natural light.
We can achieve natural lighting conditions in almost entirely underground construction, with populations at low-urban densities, despite agriculture sustainability.
You’re standing on a grassy, gently rolling hill, in the shade of a tree-sized sculpture, sort of shaped like a rotifer or sea lily, with a cap some five meters across and eight meters tall atop a three-meter-tall stalk that must be metal to support that much weight, although it looks like sandstone. The stalk is some 1.5m across, and the sandstone is warm to the touch if you put your arms around it. The cap is not vertical, and the stalk is not straight; it bends noticeably towards the southwest.
A flagstone path winds its way down the hill; a bit further down, it runs between some bamboo boxes containing raised-bed gardens, some filled with a mix of leafy deep green plants, leafy purple plants, and flowers, and tall stalks of corn, while others contain clearly recognizable onions mixed with staked-up tomatoes and eggplants. No other buildings are in sight, just gardens, hills, forests, and waterways, and a few other organically shaped sculptures.
You walk down the sunny flagstone path between the gardens to a narrow brook, only about a meter wide but flowing slowly along its meander. A stepping stone beckons you across, but you follow the flagstones along its bank. A mix of trees lines its other bank, none more than about three meters tall, because this is a new forest; it’s dominated by fast-growing pines that are culled once slower-growing fruit trees have been nurtured in their shade. A clump of four-meter-tall bamboo, some culms three centimeters across, is visible a bit upstream.
A few meters downstream, the brook splashes down a little cataract into a pond, some seven meters across. Through the water of the pond, you can see the pond bottom clearly. Among its algae, you can see a number of rocks on the bottom; although many are opaque, as one normally expects, some of them are round and shining, like ovoids of dark glass. By the side of the pond is a weeping willow. Trails of bubbles are coming up on part of the pond’s surface.
Another grassy hill is next to the pond; over its crest is visible a sort of wooden arch, standing alone, with what appears to be a large wooden snailshell atop it. The flagstone path curves around the hill. Rather than accepting the pond’s invitation to swim, you follow it past a pink granite boulder protruding from the side of the hill. There is a three-meter-wide circular door in the boulder. You touch it and enter, ducking slightly and closing the ponderous door behind you with little effort, due to its high-precision bearings. It seals tightly.
You are in a three-meter-wide corridor with an arched ceiling, sloping down into the hill and beyond. Although it’s not as blinding as the sunny meadow outside, it’s brightly illuminated from all sides; the walls have the appearance of stained-glass windows, a brilliant glow from within illuminating the deep blues and reds that form the images on their surface.
The air in the corridor smells fresh, despite the apparent hermetic seal on the door and lack of noticeable draft inside.
You walk down the mild slope of the corridor, past a door labeled STAIRS near the entrance, past some 24 meters of the luminous murals, around a bit of a curve, past some benches, to a grouping of three large doors at the end of the corridor, two made from laminated bamboo and one apparently a dark-stained hardwood. The top of your head is now a bit lower than the threshold of the door through which you entered. You knock on the door of your host.
They open the door to welcome you. You enter, noticing that the door is quite a bit heavier than you would expect a laminated bamboo door to be.
The apartment is nearly circular, some 11 meters across, and as brightly illuminated and fresh-smelling as the corridor. It is nearly silent; the machine noises we often hear in conventional housing, from refrigerators, computers, air conditioners, etc., are completely absent. Also, there are no cars outside, and even if there were, the noise would not reach you underground. You hear only the sounds of your friend and yourself.
The walls here are white plaster, smoothly curving into the ceiling, rather than the luminous stained-glass look of the entry corridor. The upper parts of the walls and ceilings are illuminated by what seems to be sunlight, shining up at it from tiny alcoves in the walls. The ceilings are only three meters high, no higher than those of the corridor, because you are barely below ground at this point.
A 2-meter-wide round hole in the floor of the four-meter-across round room in the center of the apartment has a bamboo railing around it, providing a view to the four-meter-tall lower story. An archway on the outer edge of the apartment, near the door to the corridor, leads to a gently sloping two-meter-wide helical ramp curving around the perimeter of the apartment; after almost one and a half turns, this reaches the floor below, rendering the entire apartment wheelchair- accessible without elevators.
The total floor area of the apartment, not counting this outer helical ramp, is some 190m² (2045 sq ft); it is divided into ten rooms of different sizes, with different ceiling heights. The central downstairs room has a two-meter-wide hole in its four-meter-high ceiling leading to the three-meter-tall upstairs, for a total of over seven meters; while other parts of the downstairs have lofts for storage built over them, lowering the normally four-meter ceilings down to 2½ meters, and there are even a few alcoves where an adult cannot stand comfortably.
Different parts of the apartment are illuminated by different ways and to different degrees. Some parts have quartzite and agate protruding from the walls, brilliantly glowing from within; other parts have the ceilings flooded with sunlight; others have the stained-glass effect from the entry corridor.
There is another emergency-exit door labeled STAIRS in the lower story of the apartment, and also another mysterious door, which turns out to link to an on-demand electric very-light-rail system allowing you to travel to other nearby houses even when it’s snowing at speeds of 40 kph (11 m/s).
Brian Knight explains (confirmed by the Passive Solar Primer) that for passive winter solar heating of homes, you want 9–12% of the floor area of the house in south-facing windows, in the context of the 35° north latitude of Asheville, NC. “More than 12 percent puts the house at risk of overheating unless the design includes extra thermal mass,” he explains. This tells us that we can get enough natural light to make people happy with our architecture with only about 10%.
But that’s not 10% of the sunlight; that’s 10% of the floor area in the form of vertical south-facing windows. At 35° latitude, you’re only getting about sin(35°) ≈ 57% of that amount of sunlight, a bit more in summer, a lot less in winter. If you’re getting the light from windows facing the heavens instead of standard horizontal windows, you only need about 5.7% of the roof space to gather the necessary light. And that illumination will be stabler throughout the year.
Now, one thing you could do would be to try to do it with photovoltaic solar panels, and run electrical lights from them. The problem with this is that normal solar panels are only 16% efficient, and the luminous efficiency of a regular lightbulb is only 2%, a quartz-halogen bulb can reach 3.5%, compact fluorescents and LED lamps are typically about 10%, while sunlight is 13.6% (because only 37% of its light is within the visible band, and much of that is far from our photopic sensitivity peak). That means that every lumen of sunlight can only convert to about 16% × 10% / 13.6% ≈ 0.12 lumens of artificially generated light indoors. So instead of 5.7% of the roof space, you’d need about 48% of the roof space for solar panels for illumination alone, not leaving much space for anything else.
[Light pipes] (or light tubes, or lightguides) are like fiber optics, but thicker. Big ones can be silvered on the inside, like a thermos, and filled with air; small ones can be solid or water-filled. The light suffers a 4% Fresnel loss upon entry and upon exit, plus some absorption on the way down. (This absorption can be advantageous if you want to reduce infrared and ultraviolet in order to increase the illumination-to-heat and illumination-to-sunburn ratio; but ultraviolet absorption by Biosphere 2’s regular glass roof resulted in ecological problems within, so beware.)
Typical lightpipes can carry 70% to 90% of the sunlight fed into them for many meters. Optical concentration (imaging or nonimaging) can concentrate multiple square meters of sunlight into a lightpipe whose cross section is a fraction of a square meter.
So, supposing that you want to illuminate a 50m² subterranean apartment to conventional “natural lighting” levels. You can gather sunlight from a 50m² × 5.7% ÷ 80% ≈ 3.6m² area on the surface, stuff it through a 20cm-diameter 80% efficient lightpipe to carry it down to your apartment (leaving the infrared and ultraviolet up on the surface), and let the other 46.4m² of sunlight nourish your garden and park. Perhaps you can put the solar collector a couple of meters above the ground as a sort of artificial shade tree — the rotifer and snailshell sculptures mentioned in the introduction.
Needing 7.2% of your surface area (per underground story) is much better than needing 48% of it.
Illuminating the 190m² subterranean apartment in the illustration to this level will require shading almost 14m² at the surface. The rotifer sculpture mentioned at the beginning would have a mouth area of up to 19.6m²; the seven-meter-wide pond totals about 38.5m², and if the glass stones on its bottom cover 36% of the bottom, they would collect a similar amount of sunlight.
Nonimaging optics are limited to a concentration factor of C_max = n²/sin²θ, where n is the index of refraction at the absorbing aperture (1 if you’re doing it just via reflection) and θ is the maximum angle from the optical axis at which you’re gathering the light (the half-angle of the radiation cone apex). The rotifer sculpture might have a concentrating parabolic reflector of 2.2m radius at the mouth, concentrating down to a lightpipe throat of 75cm radius inside its sandstone-finish stem; that’s a concentration factor of 8.6, which limits it to collecting sunlight from no more than 20° off-axis, or a total of a 40° arc through the sky, unless you turn the rotifer to track the sun a bit, or feed multiple sculptures into the house, each covering part of the sky. Note that the tropics are almost 47° apart, so you’ll probably have to reorient the rotifer seasonally at least.
Note that if you can track the sun perfectly, the theoretical maximum without refraction is ≈1/sin²(0.54°), or about 11000 — about 11MW/m² or 1100W/cm².
You can trade off azimuthal field of view for elevational field of view for a given concentration, though; in the extreme of an east-west trough concentrating reflector, you could get the same 8.6-sun concentration by orienting the trough within 6.68° (or 6.68° - 0.54°, really) of coplanar to the plane of the sun’s nearly-planar apparent motion.
The apartment described in our introductory anecdote occupies some 133m² just below the surface, although it has considerably more floor area than that because of its two stories. It could host a fairly large number of people; it’s exceedingly spacious for just one or two people. It might become a bit of a pain to clean, in fact.
But the smallest number I’ve been able to convince myself of, for agricultural sustainability, is 50m² of cultivated area per person, using soybeans, dwarf corn, and ample soil amendments. In colder climates, even approaching this level of productivity requires greenhouses and similarly extreme measures. And if only some of the surface is gardened, in order to leave some of it for forests, brooks, and light collection, you need more space. And lower-labor agricultural systems like apple orchards are also lower productivity per hectare. (Mature tall-spindle apple orchards can yield 1000 bushels per acre per year; at 40 pounds per bushel and 52 kcal per 100g that’s 2331 kcal/m²/year (310mW/m²!) which is about ⅐ of the raw productivity of high-yielding conventional agricultural systems like corn. Supposedly netting and Tatura training can close most of the gap, but I’m skeptical, and anyway that moves the apples back into the high-maintenance intensively-cultivated category.)
Anyway, let’s say you need 100m² per person for gardening. Then 150m² per person gives you some space for meadows and forests and whatnot, too. That’s 6700 people per square kilometer; this compares reasonably to many current cities, such as Dalian at 7100, Rio de Janeiro at 6850, Bangkok at 6450, London at 5100, Athens at 5400, the Buenos Aires metropolitan area at 4950 (Buenos Aires proper is 14000), Moscow at 4900, Berlin at 3750, Accra at 3300, Quito at 3150, and Los Angeles at 2750.
The plan described in the introductory anecdote features a number of heavy doors that close tightly. The door to the outdoors is like this in order to facilitate indoor climate control, but the others are that way for fire-escape reasons: you need to be able to reach a fire escape that’s sealed off with a fire door without having to travel too far. So the door that appears to be laminated bamboo is actually a steel fire-door core with laminated-bamboo surfaces, so that fires or chemical releases inside one apartment don’t render the escape route for the others unviable.
I ran into a fascinating discussion of medieval sieges the other day; one of the discussants said:
There is usually a balance that prevents long long term sieges...a large population is capable of fully defending the walls and keeping the invaders out, but consume more resources and shorten the time that they can hide behind walls. A smaller force will consume less resources and hold out for longer, but they risk not being able to defend the walls fully due to lack of man power.
But of course a sufficiently large fortress doesn’t suffer from this problem, because its ratio of arable land to walls becomes arbitrarily large; and this happens sooner if productivity per acre is high. Leaving aside motte-and-bailey-type fortresses where the food is grown outside the fortress in the bailey, what’s the scale at which the lifestyle outlined in this scenario would become able to defend a hypothetical wall?
Suppose we need one defender per two meters of wall. Then a circle 300 meters across would have 942 m of wall around it, and also 471 × 150m² of land inside of it, and therefore be able to support 471 inhabitants, sufficient to defend that wall. 309 meters across would support 500 inhabitants.
This is a size sufficiently larger than Dunbar’s number that you would probably need some kind of official power structure within it.
In the example scenario, you have three apartments that access the surface through the same entry tunnel. In practice, you might want to cluster houses together more than that; there are great advantages to being able to borrow a hammer or some yeast from your neighbor without having to walk 100 meters, and in particular there are advantages to serendipitous meeting and chit-chat with neighbors. If you cluster groups of ten such apartments together, and figure two inhabitants per apartment, everybody’s gardens are a little further off (2000m², for the 100m² of gardens for 20 people, excluding parks, has a radius of 25 meters), but they’ll encounter each other much more often, and forests and ponds can be proportionally larger; and in the fortress case, you can go slightly motte-and-bailey and actually locate the parks for the outside the fortress walls, leaving only the arable land inside.
This allows you to reduce your 309-meter-across circle by about 30 meters: the 14 or so clusters around the outside shrink to 2000m² each, leaving the other 11 or so clusters in the middle with 3000m², for a total area of 61000m² and thus only 279 meters of diameter, or only 877 meters of outer wall.
I said there was an on-demand light rail. Specifically, what I have in mind is kind of like a horizontal elevator; a small capsule comes when you call it, and then takes you where you want to go, and is computer-controlled so it won’t hit other capsules and you don’t have to pay attention to driving it. Suppose, as above, that you have clusters of ten apartments containing 20 people, and your overall community is 309 meters across and 500 people, spread over a total of 25 stations. Each station, except the first, needs to be connected to at least one other station, and the stations are about 60 meters apart, so you need at least 1440 meters of tube. Say 1800 to be on the safe side, allowing for sidings and redundant loops. At an average of 5m/s you need 12 seconds to get to the next station and 60 seconds to get all the way across town. And you might have to wait 15 seconds for a spare capsule to come pick you up.
(Note that this 1800 is 3.6 meters per inhabitant, i.e. tiny in cost.)
The tube can be quite narrow. Suppose the capsules are designed to accommodate up to six people, two abreast, or one abreast if it’s a wheelchair; the cabin can be two meters wide, 1½ meters tall, and three meters long. The tube can be 2½ meters wide and 2 meters tall, so the 1800 meters of tube suggested above work out to 4500m², or 9m² or 18m³ per inhabitant.
Also, the capsules, rails, and power cables (or shafts, or whatever) can be fairly light. Six people weigh 600kg or less, normally; accelerating 600kg to 11m/s over 30m takes about 6 seconds, which means it’s about 1m/s² (a comfortable 0.1 gees), 600N, with a peak power of 6600W or a bit under 9 horsepower. Amazon sells a 1½-horsepower motor for pool water pumps for US$250 (the Hayward SPX2710Z1M); it weighs 27.7 pounds (12.6kg), so we can figure that a durable 9 horsepower would weigh 75kg and cost about US$1500. (Starter motors can be similar in power and weigh much less, but pool water pump motors are sold to run for hours continuously every day, not for a second or two a few times a month.)
So the whole capsule might weigh 800kg and need 12 horsepower of motors ( to hit its target speed. That’s ten kilowatts of electricity, which would be 21 amps at 480 volts — very easy to supply with no significant loss with a third rail. Given the short distances and the availability of rails, you could maybe even use 48 volts at 210 amps, eliminating the risk of electrical shock, although you could still get creamed by a capsule on its way through the station.
A single capsule would need 84 round trips (168 minutes) to transport the entire population from one extreme of the town to the other, so you might need some ten capsules in total, one for every 50 people; this would allow 12% of the population to be in transit at any given time, if necessary. That’s a total of US$30 worth of motor per person, and maybe another US$30 or US$100 worth of capsule construction.
I don’t know how heavy train rails need to be to support a 800-kilogram mini-train. Standard axle loads are 19.3 tonnes per axle running on rails that weigh about 44.6 kg/m; here we’re talking about 0.4 tonnes per axle, which (with linear extrapolation) would work on 0.92 kg/m rail, which is like a fifteenth of normal “light rail” rail. That would be a total of about 1700kg of steel for the system as a whole, or 3.4kg per inhabitant.
(In fact, you could go even chintzier: mountain bike tires are up to 57mm wide and can reasonably have a 15cm contact patch at 50 psi, so they can support up to 300kg each. Four wheels with mountain bike tires would work.)
If you were to scale a system like this one up, its 11m/s top speed would allow you to cross Buenos Aires, which is about 18km across at its widest point, in 27 minutes, plus half a minute to walk 30m to the nearest station and 10 seconds for a capsule to arrive. If you could double the top speed to 22m/s (79 km/h, 49mph; this would not require bigger motors, only accelerating for four times as long) then you could cut it to 14 minutes. Currently crossing Buenos Aires from Puente Saavedra to Villa Riachuelo in the bus takes 85 minutes on the 28 or 21 bus, which travel along the freeway. If you take the 76 and 150 through the city instead, it’s 109 minutes. And often you have to walk for hundreds of meters to reach the bus stop and wait there for tens of minutes.
Given the advantages of this kind of transportation system, which would cost US$95 of vehicle, 3.4kg of steel rail, and 18m³ of tunnel excavation per inhabitant even at the low urban density of 6700/km². As urban distances go down, the cost of rail and tunnel should go down proportionally. So having built such a system in Buenos Aires, with its 14000/km² population, would have been enormously useful.
Gordon Mohr suggests that you could recharge at subway stations instead of having a third rail. 60 seconds at 3kW is only 180kJ; at the 18kJ/kg of current supercapacitors, you’d only need 10kg or so of them. If you could recharge as you zipped through each station, you’d only need 6 seconds, or 18kJ. Amazon will sell you 2.7V 10F capacitors for US$2.84; they can store 36 J, so 18 J of capacity would cost you US$1420, comparable to the motor.