In the scifi I am currently writing one of the central planets is a fully urbanized planet; that is, it is an ecumenopolis. I have my fair share of ideas on how to explain many of the logistical and ecological problems that such a setup brings, but I'm a bit stumped when it comes to estimating the population. It's definitely in the trillions, but beyond that I find it hard to estimate, the reason being that I can't find any reliable overviews of the ratio of zones in current cities. That is, the ratio of residential to commercial to agricultural to industrial development. Do we use twice as large an area for agricultural development versus residential? Three times much residential as agricultural? Half as much commercial? And so on. I'm specifically interested in the total amount of area (that is, not just the ground floor of a multi-story building but the total area of its floor), to get a good grip on just how much space we're using for various purposes. My planet would be covered with ca 1km tall buildings (on average) and, knowing how much space we use for industrial vs. commercial vs. agricultural vs. residential purposes. it should be easy to extrapolate (let's say, 30% is residential, then 300m of the the buildings would be used for residential purposes; with 10m floors that would be 30 floors, multiplied by the planet's area, divided by the average residential area one person occupies, to get a very rough estimate which is, in the very least, not off by orders of magnitude). Why not simply use, say, the population density of dense urban areas for reference? Well, areas such as Manhattan are, obviously, mostly commercial and residential. Its commercial areas takes more people than its residential area can provide (so a planet with that area would not have enough workers for its commercial areas by far), made up for by people working in the city living outside the city (to a certain degree doable on my planet). But then, what about all the industries that you need space for, and the agriculture needed to sustain all those residents? Obviously if you'd look at a dense urban area and include all the area needed to support it, the actual density would be far lower. You could stack it all vertically on Manhattan and you'd probably have a one-two kilometer high city with quite a lot more residents as well, but what's that population density look like? I can ultimately just handwave it all; there are many inhabitants living offworld, industrial and agricultural imports and such may alleviate space requirements fore those practices (or it's mostly selfsustained in which case the residential area is comparatively small) , so I can always say "it's got 15 trillion inhabitants" and then maybe a realistic number would be closer to 150 trillion or 1.5 trillion depending on how the logistics are solved ultimately, but it'd work. I've been reading about fictional ecumenopolises and serious looks at them usually gives estimates on 10-1000 trillion depending on various factors but there's also a lot of ifs and buts and unreliable factors concerning them, so, yeah, asking here in case new ideas or thoughts might provide some answers or at least better estimates.
Climate control systems (gas scrubbers, recyclers, weather manipulators), imports if needed, and mining of asteroids and moons in the system as a whole. There's various forms of (fairly large-scale) urban agriculture going on and, yes, there are oceans, though they are much smaller than on Earth. Form a purely ecological perspective the whole planet is a bit of a disaster but there's sufficient technology to at least sustain it for humans. Life support systems such as those mentioned (plus stuff like transport of food/water, waste recycling, maintenance, etc.) take up quite a lot of place. Note also that the planet itself is just one of close to a thousand inhabited planets which probably helps it sustain itself, isolated I don't see any way for a city-planet to be even remotely considerable. Regardless, my question was directed towards how to figure out the population of an ecumenopolis, specifically via figuring out how much area we use for various zones as of now and some extrapolation etc. I'm not particularly interested in debating the viability of it right now.
I'd start by working out how much land mass you have. Which would require knowing how much space was taken up by oceans. Hence the question.
Well, for agricultural, I think that you'd want to get a very rough calculation of food calories produced per acre per year, which tells you how many people you can feed with a specific area of land. A very quick Google gives me a chart with a range from 1.1 million calories per acre for beef, to 17 million calories per acre for potatoes. (However, I'm not sure if the beef number accounts for feeding the cows.) One could argue that future advances in plant breeding would increase that number, but on the other hand, those crops are irrigated; future advances in plant breeding might instead make it possible to grow a similar number of calories with less water and other inputs.
1000 billion people require approximately 2 quadrillion calories per day. You'd need approximately 117M acres of potatoes to feed that population for a day. At the low end of growing time, it takes 70 days for a potato to grow. So that acre could ideally produce 5 crops of potatoes per year, or 5 days of food for a trillion population. 70 x 117M = 8.19B acres to feed a population of 1T people potatoes for a year. This is roughly 1.2x the land mass of the US.
