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The city of Sanctury has been holding back the volcanic apocalypse for 174 years, and has grown to 60,000 people. The question is, if everything needed for life is grown within the city, how many people can it fit per square mile?

Technology level is early industrial, the apocalypse occurring circa 1850, with a mix of magic and technology.

Gunpowder exists, but a crossbow is still considered more effective.

There is a monorail which operates on the principles of steam power but is controlled remotely by magic.

Volcanic ash and scavenged brick serves as an aggregate, allowing very strong construction, and tall buildings.

How densely would people have to live for the city to grow everything it needs?

Bearing in mind that over the last 174 years, people have had little to do but worry about food and might discover some advanced agricultural techniques long before they would otherwise.

speciesUnknown
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    In a temperate climate with decent arable land one hectare can feed about 4 or 5 people; that makes 400 to 500 people per square kilometer, or 1000 to 1250 people per square mile. For 60000 people you need 100 to 150 square kilometers or 40 to 60 square miles. That's agricultural land; the actual city is extra. Your people may also want to have some pasture land (to grow some cattle to get leather, glue etc.), some wooded land (to get timber for construction), some quarries (to get stone), and so on. – AlexP Nov 23 '17 at 21:47
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    You might consider dropping the magic solution for this question. Magic can do anything, like cram 60,000 peple into a quarter-mile square having a magically high tower and room to spare on the property for a shrubbery. If you remove the magic requirement, we're limited by the building heights of the time. And please pick a year, "early industrial" encompasses 6-story to 30-story buildings. Otherwise, the question may be deemed too broad. – JBH Nov 23 '17 at 21:51
  • Thanks, this is a good response, why don't you make it an answer? – speciesUnknown Nov 23 '17 at 21:52
  • Because this was written off in a minute, I don't have time to look for references. Note that the answer refers to traditional agriculture, without artificial fertilizers and motor-driven equipment. With modern tech you can extract at least two or three times more calories from the same area. – AlexP Nov 23 '17 at 21:59
  • @ AlexP: You're perhaps looking at the absolute best case there, as modern tech will probably exhaust the soil in a century or so. And how are 60K people going to produce modern tech? Bottom line: Absent magic or sufficiently advanced technology that synthesizes food, a city can't be self-sufficient. An area that's sparsely populated enough to produce food for everyone who lives there has to be rural. – jamesqf Nov 24 '17 at 03:46
  • @jamesqf Modern agricultural tech is actually less damaging to the soil than 19th century tech. For example, deep seeding disturbs the soil very little compared to ploughing, and mulching stubble adds organics to the soil, in contrast to burning that removes them. – pojo-guy Nov 24 '17 at 04:43
  • @pojo-guy: 1) So what percent of farming uses these modern techniques? 2) Less damaging than 19th century techniques does not mean undamaging. 3) Neither one changes the bottom line. Food production is limited (upper bound) by surface area * insolation * efficiency of photosynthesis. 1 watt-hr = 0.86 food calories. Insolation is typically 750 w/m^2, for a generous 12 hours per day. Wikipedia gives photosynthesis an efficiency of 3-6%, so a max of ~460 calories/m^2. But much of that is indigestable plant matter - roots, stems, cellulose &c. – jamesqf Nov 24 '17 at 05:50
  • @jamessqf Modern farming achieves much higher density and better yields than 19th century and earlier (roughly 6x more calories per acre). See http://mathscinotes.com/2017/01/calorie-per-acre-improvements-in-staple-crops-over-time/ – pojo-guy Nov 24 '17 at 05:59
  • @pojo-guy: (Continued) Wikipedia (again) gives ~0.25% to 0.5% of sunlight converted to usable food, so about 40 usable calories per m^2 per day. So unless my mental arithmetic dropped a decimal point somewhere, under the most optimistic conditions you need about 50-100 m^2 of growing area per person. – jamesqf Nov 24 '17 at 06:04
  • @ pojo-guy: Ever hear of conservation of energy? I don't care how modern your farming techniques are, you can't get more food calories out than you have solar calories in. And if you've heard of thermodynamics as well, you'll know that in reality you'll get less. – jamesqf Nov 24 '17 at 06:06
  • @jamesqf for the purposes of food, you can only count the edible portions of the plants. 3-4 acres per person is more realistic, with no room for contingencies. Using pre-1940 technologies, you are talking about 15 acres per adult – pojo-guy Nov 24 '17 at 06:08
  • @jamesqf Modern farming in USA is built on recuperating from the harmful methods of the 19th century that depleted the soils and led to the dustbowl years and widespread famine. A well run modern farm improves the soil conditions year after year, within the bounds of what the farmers know to check. That doesn't mean there arent serious challenges still. For example, farmers who are dependent on ground water for irrigation are discovering that the salinity of their wells are harming their soil over time and are having to figure out how to desalinate the soil. – pojo-guy Nov 24 '17 at 06:19
  • Let us continue this discussion in chat. – pojo-guy Nov 24 '17 at 06:45

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From a comment chain that got too long and should have been an answer (thanks @jamesqf for the conversation):

Using 21st century sustainable industrial farming practices, you will need 4 acres of land per person to keep people fed. If fresh surface water is used for irrigation, the farms should remain productive for a very long time.

Since modern industrial farming is built on recovery from the bad practices of the 19th century that led to the dustbowl years and widespread famine, it follows that adherence to the practices improves the soils year after year within the parameters of the indicators that the farmer knows to check and manage.

The caveat of "what the farmer knows to check and manage" is crucial. For example, one of the challenges faced by farms that are dependent on well water for irrigation is the trace amounts of salt in the well water build up in the soil over time and poison the land. 21st century agriculture is struggling now with the question of how to economically desalinate soil at scale.

If pre-1940 practices are followed, you can expect to require 15 acres of land per person, with the caveat that the soils will be depleted within 150 years +/-, and the city will be forced to either acquire more land or develop farming practices analogous to 20th century industrial farming.

This allows no buffer for contingencies (disease, pests, accidents).

My town is home to about 50,000 people, and covers 31.67 square miles. It is not incredibly densely populated, but if it were more densely populated I would not want to live here.

So, using 21st century level industrial farming, a marginally self sustaining city of 60,000 people will require 375 square miles (a square 19.4 miles to a side) of farmland plus 32 square miles of living and working space. 407 square miles

Using 19th century farming practices, a marginally self sustaining city of 60,000 people will require 1406 square miles of farmland plus 32 square miles of living and working space. 1438 square miles

Keep in mind that this is marginally sustainable - a bad crop year would wipe out your city, so you would want to double this and have other plans in place for contingency.

pojo-guy
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    Good answer based on realistic farming, and an important point about bad years, which might be more common due to the intensive cropping of a small space. (North Korea for an example?) But for the folks who'll say "Oh, but we'll use hydroponics/aeroponics/vertical farming/whatever", there's still that hard upper limit where you can't produce more food calories than you have solar watts coming in. – jamesqf Nov 24 '17 at 18:05
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    Take the "behind the seeds" tour at epcot in Disney world. The greenhouse curators can tell you about all of the problems with hydroponics and aerponics as they supply Disney's on site restaurants . – pojo-guy Nov 24 '17 at 18:10
  • Coming from experience, your estimated number of acres per person to keep fed appears higher than necessary. There are plenty of entire families who grow a large portion of their own food, and I know some personally who grow more than 50% of what they eat, on much less land than that. I have done vegetable gardening personally as well. I don't know what the land requirement is to sustain a person, but I know it is less than 4 acres. And that's using pre-1940* practices*. – Loduwijk Feb 08 '18 at 20:53
  • Don't forget farmland includes animal products - milk, beef, pork, chicken. Pre 1940, it was not unusual for meat products to be obtained largely by hunting. Today hunting is relatively constrained as compared to the 1940s (or even the 1970's). – pojo-guy Feb 08 '18 at 21:03
  • @pojo-guy You are right, I wasn't thinking about the cows. Still, check out the answer at https://worldbuilding.stackexchange.com/a/42712 My sister does food and chickens, their entire property (mostly unused) is an acre and a half; I think they provide about a quarter of their diet during the warm season (about 1/3 the year) for 6 people, and could easily expand the garden to several times its size. And they give some of their food away as well. It is so annoying that nobody has a good estimate on land area to sustain a person; the estimates are all over the place, albeit understandably. – Loduwijk Feb 08 '18 at 21:33
  • The estimates are all over the place because there is so much variation in land fertility and climate. That estimate might be overly generous in a fertile area like southern Arkansas, but completely unreasonable in northern Arizona. These are national averages for the USA. – pojo-guy Feb 08 '18 at 21:38
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What you describe sounds quite different from traditional self-sufficient rural towns, and clearly doesn't match our modern tightly-interdependent cities. You might be able to draw content from the concept of the arcology.

Arcology, a portmanteau of "architecture" and "ecology", is a field of creating architectural design principles for very densely populated, ecologically low-impact human habitats.

The concept has been primarily popularized, and the term itself coined, by architect Paolo Soleri. It also appears in science fiction. Authors such as Peter Hamilton in Neutronium Alchemist or Paolo Bacigalupi in The Water Knife explicitly use arcologies as part of their scenarios. Arcologies are often portrayed in science fiction as self-contained or economically self-sufficient.

Paolo Soleri has a beautiful book full of his visionary cities. None have been produced, of course. He was far more of a visionary than an actual architect, but he did analyze the density of his cities. Generally speaking, they attain 300-350 people per acre. That's 192,000 to 224,000 people per square mile. Of course, he dug deep to create 3 dimensional cities, so you'll have to take that into account. However, his goal was generally to try to be self-sustaining, so with his designs I assume there's enough space for food in such a city.

I'd certainly take that as an upper bound, but using 1950's technology, Soleri thought it was attainable.

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Cort Ammon
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  • OP asks specifically with concerns about the food for all these people. Technically, you could fit more than 300 people per acre if we discount the food. You could house thousands in that space if you go vertical, millions per square mile. But you cannot feed even 100 people with 1 acre. Since you are not addressing food, your answer is correct. But OP says "The question is, if everything needed for life is grown within the city, how many people can it fit per square mile?" and reiterates at end saying "How densely would people have to live for the city to grow everything it needs?" – Loduwijk Feb 08 '18 at 21:14