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I'm not really sure what sort of factors would go into limiting the growth of a city, besides obvious geographical ones.

I can think of

  • Farmland requirements. If each person requires X acres to fed them, a city of 10,000,000 would require 10^6*X acres of arable land to sustain it.
  • Likewise, fresh water.
  • Sewage.

Given an Earth-like setting, with the same land/water surface area and actual agriculture-usable areas, how big could a city get, if unbounded by terrain?

For the purposes of this question, a city is an area of approximately 25,000 people/sq. mi (9,653 people/sq. km). This is taken from the approximate density of New York City, a reasonably dense city, compared to the world.

The city doesn't have to remain under one government, this question is about the sustainability of an urban growth pattern on a single planet. As such, all available resources come from the planet (with the exception of solar power, I suppose). No importing food from off-world.

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Most of the population lives in The City

If you had abundant energy and technology on the Earth and you are constrained to limit your resource usage to that of the Earth, the limit is at least greater than 7 billion people as you could simply put everyone in a single city and have all supplies shipped to that single city. With automation replacing all farmers, and other occupations that requires a physical presence today, everyone could live in that city. But without full automatization, farmers, miners, etc. that require a physical presence considerable distance away from the city, perhaps 10% of the population must live in the country.

The question then becomes how many people could Earth support with extensive use of hydroponic farming and artificial lighting, etc. - these technologies are currently used, they just do not dominate the market due to economics. Perhaps double or triple the current population is possible without breakthrough technology.

Since the most modern sewage plant can produce drinking water quality output, sewer and water is not going to be the ultimate bottleneck for city size and essentially all of the water can be recycled.

To get abundant energy with current technology able to support the entire population you need lots of nuclear power - renewables do not have the energy density to support such a city and you run into serious problems with wasted energy if you use seriously long transmission lines. Renewables will require significant numbers of maintenance people necessarily living in the country.


For a city of 7 billion people.

City Area: At NYC density, the area is 280,000 square miles. Slightly larger than Texas.

Sewage Plant Area 3,000 square miles (7125 times the area of Chicago's Stickney wastewater treatment plant that serves 2.4 million people).

Nuclear Power Area 60,000 square miles, 50 TW capacity (compared to 18 TW global energy use in all forms today) at 3. Cities are more efficient, but much of the world is in poverty. This is a lower-bound energy budget. 100 TW is more desirable

Renewable Power 1,500,000 square miles, 50 TW capacity -- this is simply impractical when you add in transmission losses and the material resources needed.

In reality, a better form of nuclear power would be very desirable for The City, but it would be possible with current technology, until you run out of uranium at least.


The land use for nuclear is based on current average usage. This could (and would) be reduced considerably if you had any serious intent of reducing land usage -- e.g., waste storage could grow vertically.

Thorium is more abundant than uranium and can actually be used in a CANDU reactor, so current nuclear tech level actually includes thorium, though a better reactor designed specifically for thorium would work much better. With reprocessing and breeding, the combined uranium and thorium reserves would last for thousands of years even if they supply the entire energy demand for the world. Breeding itself is probably best considered slightly future tech since it is only used commercially at 1 plant is Russia, arguably before the tech was ready for regular use.

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  • $\begingroup$ There's a limit based on transport, though - even if you have unlimited food outside the city, you can't feed an unlimited number of people concentrated in a space. As an extreme example, if food spoils in six months your city center can't be more than six months' travel from the farms. $\endgroup$ – user243 Dec 28 '15 at 0:23
  • $\begingroup$ @JonofAllTrades - Transportation technology is clearly able to transport food quickly today. We eat bananas from Hawaii, oranges from Brazil, etc. Did not say it would always be easy, just that it possible with current technology. $\endgroup$ – Gary Walker Dec 28 '15 at 0:45
  • $\begingroup$ Good background, but what is your actual answer in number of people? $\endgroup$ – Azor Ahai Dec 28 '15 at 1:54
  • $\begingroup$ Likely 14-21 billion for 2-3 times current population. It depends on how hard you push definition of current tech. This is based on no fudging of current tech level. Large scale hydroponic is not really a current tech (issues will certainly have to be worked out), but it would change the answer considerably. $\endgroup$ – Gary Walker Dec 28 '15 at 1:59
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Well, if you do things correctly, I'd say that you could theoretically have a city over all available land area on an earth like planet. Let me explain.

FOOD

"But wait!" I hear the errant commenter scream. "If the whole planet is a city, where are the farms!?" The straw commenter is right, of course. If you have all of the land area of a planet crowded out by a city, there is no land for farms.

Unless you incorporate the farms into the city.

You see, according to this answer, through the use of near future technology, it will be possible to feed about 49,210,000 people with a cubic kilometer of aeroponic farm building. If you have a few* of those around the place, food requirements are quite taken care of, without sacrificing much of the city's land area.**

*A lot

**The citizens will be on a steady diet of sweet potatoes. You never asked for variety.

ENERGY

I think it's actually possible to have this city running on nothing but renewable energy. The secret is hydrogen. Let me explain. Hydrogen can be produced by splitting water into its component parts, and its only byproduct if you use it as a fuel is water. The difficulty is finding the water. If you have easy desalination of mass quantities of water, like, say, coastal facilities utilizing a scaled up version of the Slingshot, which is actually present technology, you'd have water for power and water for drinking, all from the ocean! How does this translate into worldwide energy, though? Well, if you transport the hydrogen in liquid form in underground pipes, the pipes will actually be cold enough to support superconductors. Which means you could transport energy from your hydrogen power plants anywhere in the world with a pipeline with effectively zero loss, and it also covers water needs. The hydrogen could be supplemented by placing wind turbines on the roofs of skyscrapers, and the skyscrapers themselves being built with photovoltaic glass.

TRANSPORTATION

In keeping this as low emission a global city as possible, I'm thinking public Evacuated Tube Transport stations, a la Hyperloop, every few kilometers, with public bike docks outside of every Hyperloop station. You could also use airports, but those are costly space-wise, and you can't build one through a building.

So, to recap:

  • Vertical agriculture incorporated into the city

  • Desalination plants in coastal areas to extract fresh water from the sea

  • Hydrogen power base to take care of energy generation and transportation, supplemented with wind and maybe solar

  • Evacuated tube transport combined with bikes to create an efficient, environmentally-friendly transportation network

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  • $\begingroup$ "The difficulty is finding the water." Umm, no. The difficulty is the energy required to split the water into hydrogen and oxygen. Also, transporting hydrogen in liquid form would also require a huge amount of energy to reduce any hydrogen to the required low temperature. Where is all this energy going to come from? $\endgroup$ – adelphus Dec 28 '15 at 1:31
  • $\begingroup$ @adelphus True. These desalination plants could use energy gathered from wind and solar farms to split the water maybe? I know it's an energy loss, but it makes the hydrogen useful as a medium to facilitate superconducting, as well as a useful liquid fuel. I saw a thing about adiabatic expansion cooling gasses down, maybe an extreme version of that could be used to cool the hydrogen down with a low energy cost? $\endgroup$ – Desolationgame Dec 28 '15 at 1:43
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Our current cities have been grown haphazardly to meet the immediate needs of their builders at every stage of their growth. This has led to inherent inefficiencies in every aspect of each cities design. Efficient space, power and water usage, as well as adequate transportation and waste-disposal facilities have all taken a back seat to the millions of separate minds which have designed and created our biggest cities.

Alternatively, we can see our current cities as having been organically grown, with millions of subtle mutations made over time to address issues that never occurred to the original city planners. With that more humble mindset, it becomes obvious that detailed planning for extreme efficiency, prior to the arrival of the cities occupants, is a fools quest. No matter how well you plan out a city's infrastructure, the needs of its actual occupants will trump the planner's best intentions.

The best solution lies somewhere between the totalitarian rule of the planners and the total chaos of the occupants. To build a city for a billion people, layout both utilities and mass-transit grids, scaled for your desired population density, spread it out across 4000 square miles, then install a redundant copy of everything just to cover unexpected needs. Surround this infrastructure with 1.5 million square miles of farmland. No, better double that for redundancy sake. So let's say we turn Brazil into a farm and put our city in the middle.

Along the shorelines, install massive desalination systems and nuclear power plants. Some of the water will be used by the farms while the rest satiates the city's populace and meet's its waste disposal needs. Oops! I forgot to mention the waste disposal systems. Those go between the city and the farms so that grey water and biologic components can be easily used as fertilizer. That sort of surround the city with bad smells, but with a billion people living inside, this was never going to be a rose garden.

Now with all the infrastructure in place, we can let the populace free to figure out where they want to live, work and play. At this point, the city planners have done their best to give the mega city a chance to survive. Now it is up to the citizens to solve the problems that the planners missed.

Along the journey of crafting this answer, I have stumbled across some of the factors that might limit the size of a city on any earth like world. Assuming equivalent diameter and water/land ration (which resulted in 57 million square miles of land on a 200 million square mile surface) and placing all of that land as a single continent in a temperate zone, I estimate that the largest farm that an earth could ever host is (extremely optimistically) almost 57 million square miles in size. Since my 1 billion citizen city needed 3 million square miles of farm, that means that the biggest city that can ever exist on an earth type world with current technology levels, would host about 19 billion souls.

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Well, if you take the maximum carrying capacity of the Earth as fifty billion people, then the maximum city size is around forty-nine billion people. Presumably it would be located in Europe, Asia, and possibly Africa.

If you have trouble seeing how we get to fifty billion people, remember that we aren't limited to farms on land. Sea-based farms can also provide nutrition and do not require irrigation.

Another option is putting farms on top of the city. Build underground and leave the soil intact above.

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  • $\begingroup$ +1 for sea borne farms. I sincerely doubt we could move billions of people underground, for psychological reasons at the very least. $\endgroup$ – Azor Ahai Dec 28 '15 at 1:52
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user14837 almost got it. Food and water are not limiting factors. Energy is the problem, though. Hydrogen can transport energy, it's not an energy source, though. For that you'll need either fission or fusion if we can make it work. Those produce a lot of waste heat. All that heat will require even more power to run the air conditioners to keep civilization inhabitable. Eventually you reach the point the oceans boil--and then Earth goes the way of Venus. Surviving that with near-future tech is quite problematic.

Addressing Gary's comment about power:

A quick look shows lots of cities in the 60,000/mi^2 density. There are 57 million square miles of land. That's 3 trillion people. They're all industrialized so lets use US data instead of the world data. The world energy is 6x the US energy. We need to multiply by another x3 because of this. We are now up to 1,500x current levels. Your numbers give about .01 degrees for current use--x1,500 is 15 degrees. I'm not finding good data on the energy use of the indoor farming that will be needed but it's considerable. It's going to be well past those 15 degrees.

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  • $\begingroup$ If you do the math, for a 2 degree temperature rise, mankind would have to have over 4500 TW in fission/fusion heat generation, this would yield about 2000 - 2500 TW in electricity. Current usage is about 18 TW (in all forms, not just electricity). This is not a problem with current tech. $\endgroup$ – Gary Walker Dec 28 '15 at 0:51
  • $\begingroup$ You crank the population up to 3 trillion. Don't you think that there might be some other resource constraints that we might hit before having every square mile on the planet covered with a very dense city using current levels of technology? $\endgroup$ – Gary Walker Dec 28 '15 at 15:42
  • $\begingroup$ @GaryWalker It's possible there's some limit out there we couldn't cope with. I was addressing user14837's answer though--he was showing no limits, I pointed out one. $\endgroup$ – Loren Pechtel Dec 29 '15 at 3:10
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If the civilisation on the planet has spacefaring capabilities in order to transport waste off planet and food from other farming colonies, then there is theoretically no limit to the size of a city. Such a city would be known as an ecumenopolis.

One early example is that of Asimov's Trantor, which was supplied by 20 agricultural colony planets which supported Trantor's food requirements. The number given by Asimov (45 billion) appeared to be a mathematical order-of-magnitude error, as the density is nowhere close to that of a city, but the general city size is plausible.

If the constraints of a planet are lifted, then cities can theoretically exist on surfaces such as ringworlds or Dyson spheres which can have sizes vastly exceeding that of a planetary ecumenopolis. The sizes of such cities is only limited by the capacities of astroengineering that the civilisation possesses.

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  • $\begingroup$ This question was in fact inspired by Trantor and Coruscant. Please note, though, I've asked for near-modern technology, which I don't think includes the capability to ship food in from 20 agricultural planets. $\endgroup$ – Azor Ahai Dec 27 '15 at 8:30
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    $\begingroup$ @Azor-Ahai If you assume near modern technology, this question is pointless, since with near modern technology you get cities of maximum size ~20-50 million people each in the world right now. $\endgroup$ – March Ho Dec 27 '15 at 8:34
  • $\begingroup$ Fair enough, although my original intent was to ask a question about how big of a city could one planet support. I've edited the question to state that more clearly. $\endgroup$ – Azor Ahai Dec 27 '15 at 8:48

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