DYSON SPHERE ECONOMICS
What habitat size achieves maximum economy of scale?

Habitable planets are in short supply. Futurists imagine a time when trillions of humans will live and work in gigantic orbital habitats. When considering a single habiat in isolation, one tends to assume that bigger is better, and more efficient. However, with multiple habitats the crucial expense is cost of inter-habitat shipping. Here we show that by choosing habitats of fixed radius, a Dyson swarm can achieve near-zero cost trade.

THE GRAVITY TARIFF

Exporting mass from any gravitational frame (a planet) is expensive.

At present, every kilogram launched from Earth to reasonably high orbit has a $20,000 shipping fee. For a habitat to engage in relatively free trade with Earth, launch costs would need to drop by a factor of 1000. Even a hypothetical space elevator offers a factor of 100 at best, and cargo throughput per elevator is extremely limited.

THE SPIN TARIFF

Importing mass into any spinning frame (a rotating habitat) is expensive.

Any space habitat that houses human activity must spin to provide artificial gravity for its occupants. See our survey of spinning habitat designs.

Of course, entering a spinning object is potentially very difficult, and dangerous. Futurists suggest that all people and cargo pass through a hub located at or near the top or bottom of the central axis. There are two cases.

Suppose the hub is stationary. The immediate problem becomes how to create a gigantic, rotating air lock that permits ingress and egress from the rotating frame. This is a massive technical hurdle.

Suppose the hub rotates. Docking spacecraft requires both to be in precisely the same frame of motion. Any inbound craft must therefore match the spin of the central axis. Even when not rotating, docking takes hours of careful maneuvering, and any minor rocket malfunction during the process can be fatal. Docking while matching spin is a massive technical hurdle.

Even if the airlock and docking issues could be solved, throughput is too low.

Suppose a habitat has a population of 100,000 people, much like South Bend, Indiana. Imagine if all vehicles picking up or dropping off people and cargo in all of South Bend had to share a limited number of parking spaces. Specifically, two parking spaces, one on each side of the axis. This is an unsolvable logistics nightmare. An axial hub simply cannot be the only means of ingress and egress for any sizable habitat.

AVOIDING THE TARIFFS

In space, every kilogram that changes frames comes at extreme cost and effort. The only way to avoid these costs is to keep mass from changing frames, so that it can be conserved (reused) as much as possible without penalty. This leaves two choices.

One option is to build gigantic, multi-purpose habitats, so large that trade between them is not a priorty, as each can contain its own industrial recycling and reprocessing facilities. This is a particularly daunting task. No city on Earth is even close to self sufficient. The scale would have to be immense.

The other option is to build smaller, special-purpose habitats, which diversify and specialize in function to form a proper economy. However, to do this these habitats must be able to exchange cargo (including waste) with extreme efficiency. Is this possible?

EXCHANGE OF MASS WITHOUT FRAME CHANGE

If we commit to spinning habitats of simliar diameter, they can exchange cargo without it ever leaving its spinning frame. This is possible by using passive docking at the outer rim.

In 1974 Gerard K. O'Neill himself suggested:

"engineless vehicles can unlock from the outer surface of one [habitat] move in free flight with the tangential velocity... and lock on to the other [habitat] at zero relative velocity."

This rim-to-rim transport between spinning habitats can be a passive process. One needs no pilot, no thrust, and no energy expenditure. Any assortment of similarly-sized rotating habitats can use rim-to-rim transfer to exchange passengers and cargo much like data packets in a network. The base cost of shipping from one habitat to another now scales by volume rather than mass or distance.

This method is efficient, scalable, and orders of magnitude less complicated than axial-docking based commerce.

SIZE MATTERS

On Earth, when one needs to commute, do errands, or ship cargo, one uses a transport system (car, bus, train, or boat) to get to and from the next town. In space, the next town over is simply in another spinning habitat. With rim-to-rim transport available, populated habitats need not be megastructures the size of cities or continents. In practice they need not be any larger than a walkable small town.

At these smaller scales habitats can instead zone themselves, and specialize to perform those functions that maximize their efficiency. Residential, resorts, amusement parks, retail, entertainment, agriculture, forest parks, nature preserves, agriculture, aquaculture, heavy manufacturing, medical services, recycling, and waste treatment can each be isolated in their own habitats.

For human comfort, habitats need to spin at most once per minute. To achieve 1g this implies a radius of at least 900 meters. Further, sustainable habitats should not require active stabilization to prevent catastropic tumbling. This implies a maximum thickness of 1/3 the radius.

Consider a torus of radius 1km. The outer rim of this habitat spins at 100m/s (225mph); a reasonable, manageable speed. From this rim one can use tangential capture and release to freely exchange passengers and cargo with other habitats of the same size. Habitats of this scale can be safely parked 20km apart, which makes transit time between adjacent habitats a mere 4 minutes.

Suppose the torus is 330m thick. Inside it the flat "land" area at 1g is 2.0km² (500 acres) and the average distance between two points is 1.6km (1mi). Upon taking into account multiple inner rings (decks) each a genorous 60m (200ft) in height, and ranging down to ½ g, the total livable space rises to 15km² (over 5.0mi²). This is plenty of room for a very comfortable, walkable town with 5,000 to 50,000 full time residents.

CONCLUSION

Maximum comfort and economic efficiency of rotating space habitats is achieved at a 1km radius. At this scale, the interior is the size of a walkable small town, and exhange of passengers and cargo between habitats becomes a cheap, routine, and easily automated process. From the standpoint of human comfort, construction time, and operating costs, larger habitats are simply a needless complication. As such, a the 1km radius torus is the ideal cornerstone for an efficient, diversified Dyson swarm economy.