How many people can my Spire world support?

Question

Alright so I have this big colony ship/artificial world and I need to figure out what kind of population it can support. I’ll cut right to the chase and give you the details.

• Length: About 1,000,000 miles long
• Diameter: 100 miles
• Circumference: 314 miles

Some more details, people live on the inside surface of the Spire, so if you were standing inside the Spire your feet would be pointing outward and your head would be pointed toward the center. The Spire is segmented into 500 mile long “units.” Each unit has 200 miles of food and water production, 100 miles of residential areas (which includes recreation), 100 miles of production, power generation, and administration, and 100 miles of waste processing, recycling, and a drone control center.

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You can assume that there is a perfect cylinder that is 1,000,000 miles long by 100 miles in diameter of useable space.

So given this amount of space and food production, what is the maximum amount of people this Spire could technically support?

Edit: The people living here have technology that’s early industrial level at best, renaissance technology for some, and some splinter groups are still at medieval levels. However, the Spire itself is far future advanced. We’re talking AI, programmable matter, easy antimatter generation, exotic matter, pretty much anything you can think of. The Spire takes care of the atmospheric conditions and weather so they are perfect for growing food, but the people are responsible for planting and harvesting.

Answer 1

This answer is a combination of relatively simple math and assumptions.

The main limiting factor in population is assumed to be food supply. One agricultural section is 200 miles long and 314 miles wide, which gives us 62,800 square miles, or 162,651.25 square kilometers.

Assumption #1: agricultural land utilization is 90%. The rest is occupied by buildings, roads and water bodies.

Arable land per section: 56,520 sq mi; 146,386.13 sq km; 36,172,800 acres

Assumption #2: one acre of land can support from 2 people (non-intensive methods) to 4 people (intensive preindustrial methods).

Assumption #3: all sections of the Spire are well-managed, which means that diseases, wars and waste are not significantly affecting population.

Number of people per section: 72,345,600 to 144,691,200

A 1,000,000 miles long spire means that we have 2,000 sections.

Total population: 144,691,200,000 to 289,382,400,000

Answer 2

Without Serious Handwaving, Zero

Such a world is not structurally stable. The theoretical largest possible structure of this nature using carbon nanotubes (10,000 km) is shorter than the diameter of the earth (~12,750 km). A spire of your proposed length would collapse under its own gravity into a molten sphere of carbon nanotubes in a horrifying catastrophe not unlike a mole of moles. I find it extremely implausible that even hyper-advanced material science is able to produce a material over 300x stronger than carbon fiber that can somehow resist the cosmic tendency for very large things to collapse into spheres. Gravity always wins.

This structure is long enough that it will basically behave like a giant uncooked noodle (maybe even a cooked noodle, depending on the material's ability to bend). A large enough imbalance of mass, particularly at either end, would send this structure careening out of control (I assume that gravity is simulated via rotation) and cause it to shatter into pieces or, at the very least, cause frequent severe earthquakes throughout most of the structure.

If somehow physically possible, there are still other problems.

There's also the issue of gravitational pull toward the center of the spire. The extreme ends of the spire will feel like steep mountains and potentially not be inhabitable as a result. The spire needs to apply antigravity at the extremes for this setting to work.

Transporting goods and data is a huge logistic problem. A message sent from one end of the spire to the other via light will take approximately 6 seconds (1,000,000 miles / 186,000 miles/second) to arrive. This doesn't take into account signal loss. Keep in mind that this distance is a little bit more than 2 round trips to the moon.

If you had some sort of magnetic transport system like the Bullet Train, you could achieve speeds of at least 125 MPH, probably a lot more by avoiding air resistance, but even a gain of a factor of 10 is going to come at massively higher energy costs and thermal output. If you somehow achieved a practical 100x speed gain (for 12,500 MPH), it would still take 80 hours to transport a good from one end of the spire to the other. Realistically, you're going to be stuck with much lower speeds for everyday use, effectively isolating the extreme ends of the spire from each other.

Spire units will need to be fairly self-sufficient and can only realistically trade within a dozen units or so. If each unit has its own sovereign government, chances are high there will be progressive tariffs at each unit along the way, limiting trade even further.

As far as population goes, 1 million * pi hundred = pi hundred million square miles. At 10 people per square mile on average, that gives you a total population of about pi billion people. Higher population densities are not out of the question, putting a theoretical limit somewhere around 30 billion people, possibly more.

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You wanted science-based, so I'm giving you hard reality. I suggest removing that tag if you intend to pursue this setting seriously.

Answer 3

We don't know exactly. But it's functionally unlimited.

The Earth is (roughly) a sphere whose radius is about 4K miles. Very roughly, we can compare the surface area of the Earth, to the surface area of this cylinder, for a workable estimate of how many people your vessel can support.

It won't be exact; people actually live in a volume, of course, but the two setups have an almost identical third dimension. Everyone living on the interior surface of the cylinder is very similar to everyone living on the exterior surface of the Earth. This is roughly a constant factor of (say) a third of a mile in height; it doesn't quite exactly cancel out, but close enough.

So the surface area of the Earth is ~ 197 million square miles. The surface area of your cylindrical vessel is A = 2πrh. (You can ignore the discs on each end; it works out to about a hundredth of a percent.) That end up being 314 million square miles.

Your vessel is about fifty percent bigger (by surface area) than the entire Earth. Interestingly, by volume, the Spire is a fortieth the Earth's size. This is because a sphere has optimal surface-area-to-volume ratio, and a cylinder gets further away from optimal as it gets more lopsided. The Spire is very lopsided.

We have not tested Earth's max supportable population limit

People have made grandiose predictions about the biosphere limit and so forth before. None of their dire prophesies of doom over an inability to grow enough food ever panned out. Certainly there must be some kind of limit imposed purely by how many people the Earth can support - but to date, societal pressures have been the constraining factor. If we wanted explosive population growth, we could restructure society in order to get it; we have other priorities.

TL;DR

The vessel is about 1.5x the size of Earth by surface area. A reasonable Fermi approximation for 'how many people can this vessel support' seems to be 'About half again as many as Earth can'.

But we don't actually know how many Earth can.

Answer 4

Just compare with earth. Earth has around 57 million square miles of land area. Your cylinder has 314 million square kilometers, about 6 times as many. Earth population in 1600 was around 0.5 billion, in 1800 around 1 billion. This gives you an estimate of 3 to 6 billion.

This is massively less than Alexanders answer because he assume perfect climate and soil conditions everywhere, whereas my estimate just uses average earth climate.