Oberth cylinders ("oneills") for Imperial capitals


As far as I know it was Hans Oberth who first suggested¹ that an orbital habitat might consist of a hollow cylinder containing air and spinning on its axis to produce artificial gravity on the inside surface by the centrifugal effect. But these days, and in English, such structures are much better known as “O’Neill cylinders” after a proposal by Gerard K. O’Neill². O’Neill’s “Island Three” actually consists of two parallel and counter-rotating Oberth cylinders each with a a co-rotating set of mirrors, a linking framework, and a separate agriculture ring, but usage marches on. The structures that I am going to describe in the rest of this post are single cylinders without any windows, not instances of O’Neill’s actual proposal. Nevertheless I suppose that in Flat Black they are called “oneills”, not “oberths”.


There were orbital habitats in the Solar System, with permanent residents, in the century before the Destruction of Earth. But most of them were built in Earth orbit, and those were depopulated or destroyed in the destruction of Earth. The space habitats far enough from Earth to survive the radiation were mostly evacuated of the following decade and a half, the residents stripping the surviving space assets for everything salvageable and retreating by flinger to such colonies as seemed most likely to support space industries. That cannibalisation, and the ensuing centuries without maintenance, has left those habitats in poor condition: some have even been effectively destroyed. I’ll have to look at costings to see whether any of them are likely to have been built as oneills³.

A few of the most developed and prosperous colonies built orbital habitats during the Age of Isolation and the Age of Piracy, but these were very vulnerable to attack and to blockade during the Formation Wars, and most became un-viable and were evacuated and not maintained during the Formation Wars. Again, I’ll have to do some modelling before I decide whether any were oneills.

During the Formation Wars the personnel of the Eichberger Foundation⁴ lived in spaceships and in surviving orbital & asteroid habitats in Mayflower’s system. Theirs was very much a life in space, but they did not have resources to spare for building on a grandiose scale. Then for forty years after the Treaty of Luna came into effect the Empire concentrated its investible savings on building up its commercial space fleet and orbital operations. Only about 540 ADT did the Eichberger Foundation switch from intense re-investment and reveal that the Empire was immensely rich.

The [old] Capitol

The first oneill that the Empire built was the first Capitol, which was constructed in orbit around the ruins of Old Earth. The [old] Capitol housed a senate building, a paramount court building, a palace, administrative offices, accommodations etc. on a scale and in a setting that would awe visitors. As is supposed of the L’Enfant Plan for Washington D.C., the (old) Capitol was designed to create an overwhelming impression of grandeur and power, and to give the secretary-general and the president of the Imperial Council the biggest home-court advantage in the known universe.

The [old] Capitol was ready for occupation in 549 ADT.

Sectors and sector HQs

In 547 the Empire set up a system of sectors in the periphery. Twenty systems between about 105 and 120 light-years from the Capitol were established as reinforcement depots, to cut down the time it took for the Imperial missions in remote systems to send for and receive back-up. High commissioners were posted to these sector headquarters to supervise⁵ the resident commissioners in the several colonies of the sector and receive representations from the colonies’ governments, each SHQ became the seat of a fleet HQ of the Imperial Navy, a Divisional HQ of the Imperial marines, a sector court of appeals, divisions of the various assistance services receiving reports and allocating resources and personnel between colonies. An Imperial university was founded in each SHQ, besides a naval academy, an Imperial marines training base, and a bunch of reinforcement depots for this and that.

The Empire built an oneill to accommodate each SHQ; twenty of therm, named after great harbor and port cities on Old Earth. Like the [old] Capitol, they were built to overawe, but they were built later by a richer and more confident Empire that had the experience of building the [old] Capitol to work from.

The New Capitol

After 557 the Empire’s revenues from real estate development on new worlds started to augment its profits from the interstellar transport monopoly. Its operations became more expansive, intensive, and complex. A new generation of Imperials (including many recruits from the colonies) were less acculturated to living in confined habitats. The [old] Capitol became crowded. Furthermore, the prospect emerged that, starting in fifty years, the Senate was going to start steadily increasing in numbers as new worlds became independent colonies. And further still the scale of the [old] Capitol was no longer overwhelming visitors and senators, whose worlds were now more highly developed and who were now jaded by their experience of SHQs.

So a new capital was built, on a vast scale. The New Capitol is huge, stupefying in its scale, planned to accommodate expected expansion for centuries. It contains forests The capital was transferred to the New Capitol in 582, during the paralysis of the Establishment Crisis.

The Palatine

The Old Capitol was refitted and refurbished as a residential habitat for the Imperial family and headquarters of the Imperial Office, with an Imperial Marines Academy, Staff College, botanical garden, zoological park, historical, anthropological, technological, war, and art museums, and astonishing memorial to Old Earth.

Facilities and features in the Old Capitol are named, e.g. “The Palatine Elementary School”, “The Palatine Museum of Anthropology”, “The Palatine Zoological Park”, but the Palace is a structure in the New Capitol…. It’s official name is now perhaps “The Palatine Orbital Habitat”, but the facility is actually called “the Old Capital”.


The Empire has large orbital operations in several systems that are not part of the administrative framework described above.The are the economic and technological powerhouses that make up the Suite. Besides that such worlds as New Fujian, though passed over for SHQ locations because they are not far enough out into the periphery, have the industrial capacity to support a naval dockyard where their sector capitals (e.g. Metheglin) cannot.

These naturally require Imperial orbital habitats for significant populations. I have not estimated whether an oneill is more economic at the relevant scale than a collection of large stanfords.

¹ Neue Projekte für Raketen- und Raumfahrt, 1954

² The High Frontier: Human Colonies in Space, 1976

³ Rather than as “stanfords” (which seem likely to be cheaper except at very large scale), as habitat wheels attached to free-fall factories, refineries, orbital docks etc., or even as free-fall habitats.

⁴ And other survivors of the destruction of Mayflower, plus sympathisers who joined the cause.

⁵ But not co-ordinate, really. The isolation of colonies is such that there are few projects that require co-ordination of effort

It seems to me that the major choice is whether you go for this type of cylinder or torus, i.e. something assembled essentially from scratch to be just the shape you want it, or whether you go for Cole’s Bubbleworld (1964): core an asteroid, fill the centre with water, seal it up, spin it, heat it with solar mirrors until it melts and expands.

That latter, it seems to me, is the natural choice of a civilisation that’s “about” space more than it is about individual planets.

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What size are these Imperial capitals?

I have previously described one of the SHQs as three kilometres in internal diameter and nine kilometres long, but I’m not sure that that cuts the mustard. I’ve calculated that such a structure (spinning to provide 1 gee and one bar of air on the deck at standard laboratory temperature and pressure, and with ten tonnes per square kilometre of landscaping, buildings, under “ground” facilities, and contents) could be built out of 28 billion tonnes of mild steel, 4.8 billion tonnes of high-tensile steel, 600 million tonnes of aerospace-grade aluminium alloy, or 110 million tonnes of carbon-fibre-reinforced epoxy.

The problem with that isn’t really with capacity. I estimated in Gross demographics of Flat Black that in 606 ADT a typical SHQ would hold a population of half a million. With 85 km² of floor space (not including the lower reaches of the end-caps) that’s a population density slightly under 6,000 head per square kilometre (15,000 per square mile). That’s a truly urban sort of population density, but much less than Manhattan, Paris, or Barcelona. No, the question is whether such a structure is going to make the awesome impression that the designers will have wanted. It ought to, on anyone who comprehends a billion-tonne structure. But these things are have to work at a sub-conscious level, and I’m not confident that 85 km² and sight-lines no longer than about 9.5 kilometres is going to have the right effect on a visitor who might be used to flying over a metropolis the size of Los Angeles or Sydney.

So let’s consider the hundred square miles of the Federal District in the USA or Australia. 256 square kilometres. An oneill 16 km long and 5.1 km in diameter, with Earth-like conditions on the deck could be built of 2.6 billion tonnes of aerospace alloy or 420 million tonnes of carbon-fibre-reinforced epoxy. The SHQs would be urban but not crowded at 2,000 head of population per square kilometre. The Old Capitol will not have been truly outgrown — 3.3 million people in 256 km² would be the density of Barcelona, only starting feel overcrowded. I have a feeling that this is about the size I ought to be looking at. Perhaps the effect of awe didn’t work as intended,

So how big should the New Capitol be? Ten times the area of the Old Capitol seems barely adequate, though the floor area would be about the size of Rhode Island or Dorset. Ten times its length and width?

An oberth cylinder 51 kilometres wide and 160 kilometres long seems feasible with unidirectional-carbon-fibre-reinforced epoxy, but the hull would be 13 metres thick and mass 590 billion tonnes. Using a material based on long carbon nanotubes, on the other hand, might allow a structural hull less than half a metre thick and 25 billion tonnes in mass. It would be larger than Maryland or Vermont, larger than Burundi. That might be going overboard.

20 kilometres in diameter and 60 kilometres long? That’s feasible with reinforced polymers and would give 4,000 square kilometres of floor area. 3.3 million people could live there at a population density of 834 people per square kilometre: 13% Copenhagen and 87% wilderness.

I specified the Capital as a bubble-formed asteroid in early versions of the material, but now I don’t believe that the material is strong and light enough. One of my 3-kilometre-diameter one-gee habs would require a structural hull of 32 metres of mild steel,. Unrefined asteroidal nickel-iron (without careful alloying and without even the stony inclusions removed) would be just as dense and I think much weaker cracks and defects are a nightmare for tensile strength, I might be wrong about the strength, but I think such material would not be strong enough to support itself at any thickness. As for the more ambitious specifications I discussed above, hey aren’t feasible with high-tensile-strength steel or even with aircraft aluminium.

I built a little Oberth Cylinder calculator as an Excel workbook with no macros. Tell it the length and radius of your cylinder, the air pressure and centripetal acceleration you require on your habitation deck, the average molecular mass of your breathing mixture, the temperature of your atmosphere, and the mass-per-unit-area of the radiation shielding, armour, landscaping, and contents you want to instal. It will return the necessary angular speed and revolution rate, the minimum thickness and mass of the structural hull you would need, the equilibrium air pressure at the axis, and the mass of breathing air you’d need.

Some of the figures for tensile strengths of materials are dodgy. I’m sure I’m missing some important materials.

Hah, wait until you’re trying to work up a list of radiation blocking ratings for various materials. :slight_smile:

GURPS Vehicles Expansion 1 put 3 rpm as the maximum rotation speed for spin gravity for humans to tolerate it; I don’t know whether that’s backed up by research.

In NASA SP-428 O’Neill gives a figure of 3 RPM based on experiments with people in a rotating room, citing Billingham, J.: Physiological Parameters in Space Settlement Design. Third Princeton/ AIAA Conference on Space Manufacturing Facilities, Princeton, N.J., Paper 77-549, May 9-12,1977.

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Any feedback on the issue of scale?

The Old Capitol was built to awe in 549 ADT, but was outgrown by the residential needs of 1.7 million population and the administrative and ceremonial needs of the Senate, Paramount Court, and Imperial Council. And perhaps it wasn’t quite big enough to deliver the overwhelming impression intended. Is 10 kilometres long (excluding the end-caps) and 3.2 km wide the right size? What about 16 km by 5.1 km?

The SHQs were built about fifteen years later, with the experience of building the Old Capitol, and supported by an industry that was producing materials for rotorvators and orbital elevators. They are still adequate for the residential needs of about 320,000 Imperials and the administrative and ceremonial needs of an Imperial High Commissioner, a Sector Fleet HQ, a Divisional HQ, a Sector Court of Appeals etc. Should they be the same size as the old Capitol?

And the New Capitol. Built 33 years after the Old Capitol by a richer Empire with a more confident technology, with a view to (a) eventually accommodating perhaps ten million people, and (b) amply correcting the failure of the Old Capitol to give an overwhelming impression of power to the ruling classes of planets with GURPS TL 10 economies. How big? 40 kilometres long (excluding end-caps) and 13 wide? 60 km by 20 km?

Presumably these planets have their own space stations, and I think it takes more than “TL10” to determine how large and numerous those should be – which in turn will determine what is awe-inspiring.

Awe, to me, is the trick used in one of the Mobile Suit Gundam series: in this setting, most of humanity lives in O’Neill type cylinders. A faction takes a spare one of these, drains the air, substitutes CO₂, adds some partially-reflecting mirrors on the ends… you get the idea, effing huge laser.

Yes, but in 549 ADT only comparatively modest ones. The colonies lost their space assets and industries in the Formation Wars, ending in 495 ADT, and the Treaty of Luna meant Imperial inspections between the Kárman line and synchronous orbit and Imperial indirect jurisdiction beyond that.

Indirect jurisdiction? I think I’ve lost track of some features of the setting. In what sense in Imperial jurisdiction in, for example, interplanetary space “indirect”? What’s the direct jurisdiction with which it contrasts and in what sense is it “direct”? (Note that I’m not contesting the worldbuilding decisions; I’m just trying to get a better grasp of the terminology.)

I made another thread to answer @whswhs question.

You would also need to replace one end-cap with a window transparent to the appropriate wavelengths of IR, appropriately smooth and uniform. And as well as the CO₂ you’ll need about an equal quantity of N₂ and about four to five parts helium to each part of CO₂. You’ll also need a means of pumping the nitrogen with energy at the right wavelength and (most challenging, I think) a means of cooling the helium.

Let’s attack this from another direction.

The figure that O’Neill used in that NASA report that I cited above was that each person requires 157.1 square metres of deck for lifetime residence in a civilian habitat with recycling and agriculture. (SP 428, p.35). That’s 6,365 people per square kilometre, a shade fewer than Copenhagen or San Francisco, 30% the density of Paris. If the Old Capitol had more than 267 square kilometres of liveable space it would not yet be overcrowded. If the SHQ habitats had less than 51 square kilometres of liveable space they would already be over-occupied.

Suppose that the Old Capitol was built for a nice round 1,000,000 people, so that it is clearly insufficient for the 1.7 million current population of the New Capitol. The designers would have aimed for a deck area of 157 square kilometres. Supposing that the deck is as long as its circumference that suggests a cylinder 12.5 kilometres long (excluding the end-caps) and 4 km in diameter. Suppose further that the designers specified 10.0 m/s² pseudogravity, 100 kPa of breathing mixture at 29 g/mol, and ambient temperature of 290 K, with 10 tonnes per square metre for radiation shielding, armour, buildings, and landscaping and a safety factor of two on the strength of the structural hull.

That structure could be built of high-tensile steel, and if built of high strength aluminium alloy it could have a hull only 2.78 metres thick massing only 1.6 billion tonnes. Looking at “futuristic” materials, graphite-fibre-reinforced epoxide resin could do it 1.03 metres thick and 280 million tonnes. Diamond and pure oriented buckytubes are GURPS TL11 materials, and even buckytube-reinforced polymer sounds a bit speccy. Let’s suppose that a GURPS TL10 structural material could be five times the tensile strength of high-tensile steel (“nanocomposite” armour is five times as effective as steel) and about 1400 kg/m³. I calculate that that would suffice to build the habitat specified with a structural hull 0.48 metres thick and massing 140 million tonnes. “Nanocomposite” armour in GURS Spaceships is G$33,333 per tonne, so the structural hull of the Old Capitol might have cost something like G$4.67 trillion. That’s about ₢1.6 trillion, which is surprising affordable out of Imperial revenues, which even back then might have been in the region of ten times that, per year.

Then make the SHQ habitats 10 km long (plus end-caps) and 3.18 km in diameter for a nice round 100 km²: they’ll fit 637,000 people, which is okay for the 322,000 that the average SHQ calls for. Structural hulls 0.38m thick, 71 million tonnes of structure supporting up to a billion tonnes of fit-out and 100 million tonnes of breathing mixture. Cost about ₢789 billion each, or ₢16 trillion the set.

The when it comes time for the New Capitol, lash out on 1,000 square kilometres, enough for 6.37 million people at space-habitat densities, but cut the design load to 5 tonnes per square metre. Make the habitat 31.6 km long and 10.1 km across. That calls for a 1.8-billion-tonne structural hull consisting of 0.97 metres of nanocomposite and costing about twenty trillion crowns. Plus which five billion tonnes of fit-out and 3 billion tonnes of air.

(A 4,000-km² structure would cost about ₢178 trillion, and might be considered an extravagance.)

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If everyone is using the same units of measure, making a key statistic a round number of those units does indeed seem like an effective PR tactic.

(Agreed on the colony as laser thing; I think there were more complications, and as far as I recall it had been originally designed with covert conversion to this purpose in mind. The point is that it’s a qualitative distinction from previous weapons, and thus effectively terrifying.)

If we consider that what the structural hulls do is essentially to add artificial gravity (and air containment) to the “habitat” and “open space” systems constructed within them I suppose that you could say that in the Old Capitol artificial gravity masses 140 tonnes and costs ₢1.6 million per head of population, At, say, 3% real return amortisation is ₢ 48 thousand per person per year for the gravity bill. In the slightly smaller SHQ structures the artificial gravity masses 111 tonnes/person (capacity) and costs 12.4 million per person (capacity), or ₢ 37 thousand per annum for the gravity bill. And in the monstrous New Capitol the artificial gravity masses 283 tonnes and costs ₢ 3.14 million per head of population capacity, suggesting a gravity bill of ₢ 94,000 per person per year.

That’s a bit costly, the price of magnificence.

And radiation shielding.

That seems like quite a bit (assuming your credits are vaguely dollar-like). If this seems like a reasonable model of the premium for living in space – it’s probably larger, because an apartment block on a planet doesn’t ever need to withstand variable thrust or retain air against vacuum – then one has to ask how much of that is paid back in increased productivity and how much is Imperial “don’t mess with us” PR.

Crowns are quite a bit more than a dollar. They are supposed to be the price of a meal at McDonalds: Big Mac, regular fries, sundae, and regular coke. That’s about A$10 these days.

You can get the cost of gravity down by reducing the gravity to say 0.85 gee (median for inhabited worlds in Flat Black weighted by population), reducing the air pressure (to say 0.75 bar), raising the ambient temperature (to say 298°K) and reducing the radius of the habitats as much as possible (180m diameter brings you close to the 3 RPM limit), and leaving the habitats long and thin (to minimise the ration of end-cap mass to floor area). Then a “nanocomposite” structural hull need be only about 2 centimetres thick — 3.7 tonnes per possible resident, ₢41.4 thousand per possible resident, gravity bill ₢1,240 per person per year. But I’ll have to add radiation shielding.

I’m going to have to consider stronger high-tech materials such as S-glass fibre, and also look into GURPS Spaceships’ assumptions about the cost of materials.

The Imperial crown started out as an instance of ForeSight’s SVU (standard value unit). That is defined in ForeSight first and best edition as approximately the purchasing power in consumer goods of US$2.50 in 1985 “or the price fo a decent meal at McDonald’s, if such a thing is possible”.

Turning to the invaluable Measuring Worth currency converter I find that US$2.50 (1985) is something like

  • US$4.95 – US$5.70 today, depending on whether you favour the CPI or the GDP deflator.
  • £3.20 – £3.99, depending on whether you favour the RPI or the GDP deflator
  • A$9.60 – A$9.99, depending on whether you favour the CPI or the GDP deflator.
  • G$3.88 – G$4.39, assuming that the GURPS 4th ed. dollar is US$1.00 (2004).

Over a timespan like that it’s probably a reasonable thing to do, but even 24 years can be a long time. What is the correct cost in 1985 of “a private radio station that will play nearly any song ever recorded, on demand”?

(Apologies; this is a bit of a maggot of mine.)

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