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This question is inspired by Mortal Engines, but I imagine something more feasible. The original question I wanted to ask was "How to keep a city in the air?", but I figured out there is another problem - I don't know how big, and heavy, it needs to be.

As to why - tax-free zone, poor housing situation on land, etc. are among many great reasons to have a town not connected to a specific territory, but instead to put it in the air or over international waters. Recent AI limitations that made companies plan to put tens of thousands of GPUs on international waters, even if it is just an elaborate hoax, are yet another good idea to build worlds around.

Was it ever estimated how much mass per X amount of citizens is needed? If there are ready-made analysis available, I'll consider them valid answers. If there are not, here is what I want:

  • 2000 people because that's the lowest limit of what can be considered a town where I live. Also, this sounds like a good number.
  • Single family apartments in "houses" that consist of up to a dozen apartments.
  • Water, electricity and municipal heat grids.
  • Sewage system with water reclamation, to minimize supply lines.
  • Public areas, even if minimal ones, because Kowloon showed us that such paces will happen.
  • Places of employment (offices, workshops, etc.) for at least 80% of working age population.
  • Basic education and healthcare.
  • Supplies for at least a month of operation without resupply.
  • Transportation (walkways, lifts, etc.)
  • I want it to feel like a town / city, not a big ship.
  • External income should come from businesses that are heavily regulated elsewhere, like biological research, AI research, diamond and luxury goods trade with countries under international sanctions, etc., and from being a headquarters of companies with multi-million dollar incomes.

What I don't want to calculate yet is:

  • Growing their own food.
  • System to keep it in the air, afloat or whatever.
  • Propulsion.
  • Electricity production.
  • Basically anything that wouldn't be in a traditional city.
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    $\begingroup$ I am grossly unqualified to write an answer, but as a quick-and-dirty guesstimation I believe that a the 50,000 tons displacement of a medium-sized cruise ship capable of carrying some 2,000 guests would be a very optimistic lower bound. Regular buildings are very much heavier than naval construction, with a pretty flimsy American-style single-family house weighing some 70 tonnes, so total 35,000 tonnes just for the houses; then add roads, work spaces, shops, power generation... $\endgroup$
    – AlexP
    Nov 15, 2023 at 0:16
  • $\begingroup$ @AlexP I agree with the lower bound, but I want people to live there, so they need to have homes, not cabins. I don't need it to be real buildings, but I do need them to feel real in everyday use. $\endgroup$
    – Mołot
    Nov 15, 2023 at 0:18
  • $\begingroup$ One other point: What their main industries are will have a very significant impact on weight. a 2,000 person village is not going to have enough people to have a truly diverse workforce e.g. there's not going to be one of every industry. And the reason this is important is different industries have different weight requirements. Consider the weight of a Lead Smelting plant vs a beauty salon. $\endgroup$ Nov 15, 2023 at 1:23
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    $\begingroup$ We need more information on the purpose of the town, which will inform demographics etc. While some people will be employed keeping the town running, what are the rest doing to bring money in? If the main industry is a call centre for multinational clients, the workplace requirements will be very different vs a factory manufacturing tractors. Or is it a retirement village? The demographics plus distance (travel time/cost) to a major city will also affect health service requirements. $\endgroup$ Nov 15, 2023 at 1:23
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    $\begingroup$ For 2000 people you don't need an actual "city", just a big building. 2000 people is basically a small high school with all its personnel. $\endgroup$
    – Stef
    Nov 15, 2023 at 9:38

5 Answers 5

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Let's establish some upper and lower bounds.

The ISS is a self-contained ultra-lightweight city for 7 people. Wikipedia tells me it weighs 450 tonnes. So for 2000 on a super-ISS we can extrapolate to 128,571 tonnes.

The tiangong space station has a crew of 6 and a estimated mass of 100 tonnes, so we can extrapolate to 33,333 tonnes.

Now these are very optimistic. Linear scaling of mass may work in space where you don't have to worry about gravity, but here on Earth most things follow the square cube law. Also, these are engineered to be launched into space at astronomical prices. A earth-bound-city is likely constructed of inferior materials. Either way, your city is almost certainly going to weigh more than 30,000 tonnes.

Cruise ships run in at 170,000 tonnes for 2000 people, so heavier still.

For reference, this is heavier than the Bagger288, the heaviest land vehicle which weighs in at only 13,500 tonnes.


So what about an upper bound? For this let's just lift an existing city in it's entirety, dirt and all.

The township of Methven, New Zealand has an estimated population of 2010 people, and wikipedia has it listed at an area of 4.18km2, or ~2000m x 2000m. So let's scoop it up. Let's be generous and take all it's land as well, to a depth of 20m. This ensures we get all the infrastructure and peoples basements. We now have some 80 million cubic meters of (mostly) dirt. A quick google suggests 1.5 tonnes per cubic meter for a total estimated mass of 120 million tonnes.

So there we go, your town if constructed of aerospace grade materials with super-cramped living conditions, could weigh in the tens-of-thousands of tonnes. Or if you picked up and moved an actual village it would be in the hundreds of millions of tonnes.


Side note:

I want people to live there, so they need to have homes, not cabins.

People adapt to what they live in. Many many people live in apartment blocks rather than suburbia. I have no doubt that future people who live in space stations would feel uncomfortable in a modern family suburban home just due to how much free space it has and how many openable windows it has! I definitely got used to living in a single-room apartment that measured only a couple meters square, and here in NZ, due to the building regulations, many people live in 'tiny homes' of under 30m2.

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    $\begingroup$ +1 for using cruisers and other real life examples of movable "cities" $\endgroup$
    – Pere
    Nov 15, 2023 at 21:54
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    $\begingroup$ +1 for Methven, NZ. Does Snow on the ground affect the weight ? $\endgroup$
    – Criggie
    Nov 16, 2023 at 1:46
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    $\begingroup$ @Criggie: for a few days each year.... But that does raise questions about the impact of rain. The density of dirt can vary by almost 50% based on moisture content. 1.2 - 2 tonnes per cubic meter. So that could put the upper bound even higher. $\endgroup$
    – sdfgeoff
    Nov 16, 2023 at 11:07
  • $\begingroup$ The space station-based lower bounds here seem rather pessimistic. Scaling up requirements from a small population to a much larger one is usually seriously sublinear, especially when starting very small — larger populations allow many more economies of scale. $\endgroup$ Nov 16, 2023 at 11:52
  • $\begingroup$ I read in the book Scale most human cities scale with a 15% efficiency increase per doubling for communal/shared infrastructure (such as streets or energy stations). $\endgroup$ Nov 18, 2023 at 0:18
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200,000 tons.

Can be reduced to ~25,000 tons for a traditional Japanese town with minimal facilities.

Good news: your question is actually answerable scientifically! When building cities today, one has to hire a geologist to determine if the bedrock can take its weight. So there's a lot of ready-to-go estimates.

Not so good news: since they have to hire a geologist to determine if the bedrock can take a city's weight, traditional urban construction is generally too heavy to be supported in the air.

This paper includes such an estimate for NYC: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022EF003465

Exact figures:

Live load requirements vary for different intended uses, from single family homes (0.48 kN/m2) to office buildings (2.4 kN/m2), up to heavy manufacturing facilities (11.97 kN/m2).
Flooring dead loads range from 0.1 to 3.5 kN/m2. Reinforced concrete ... 2.0 kN/m2 value for dead loads. The calculated cumulative mass of the buildings in New York City is 7.64 · 10^11 kg (1.68 trillion pounds), which is distributed over a 778.2 km2 area.

Averaging a neat ~1,000 kg/m2 or 100,000 kg per person. For a city of 2,000, that is 200,000,000 kg. This is based on the actual city of New York.

Can it be lighter?

Live loads are the useful stuff, like people and items inside a home. Dead loads are building weight itself. So, a lightweight, suburban style environment can have a lower density, but never less than 60 kg/m2. This would be extremely light construction. Think single-story Japanese homes with Shoji paper walls.

Let's assume you need at least 100 m2/person - this includes streets, yards, plus floor area, and would represent a twice denser than average suburban construction of 0.1 acre per family of 4. That gives just 6,000 kg/person to support. At that weight, the live load for a city of 2,000 could fit into just 12,000 tons.

However, the 12,000 ton estimate doesn't include anything except the living spaces. Everyone would have to work from home and get stuff delivered by Amazon drones from somewhere else. Doubling it sounds like a conservative minimum.

It's possible to go even lighter, but not realistic. Note that Shoji homes will not stand up to the rigors of flight, even at a relatively low altitude. The support and protective structures will take a lot more mass.

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Cloud Nine is the name Buckminster Fuller gave to his proposed airborne habitats created from giant geodesic spheres, which might be made to levitate by slightly heating the air inside above the ambient temperature.1

Geodesic spheres (structures of triangular components arranged to make a sphere) become stronger as they become bigger, because of how they distribute stress over their surfaces. As a sphere gets bigger, the volume it encloses grows much faster than the mass of the enclosing structure itself. Fuller suggested that the mass of a mile-wide geodesic sphere would be negligible compared to the mass of the air trapped within it. He suggested that if the air inside such a sphere were heated even by one degree higher than the ambient temperature of its surroundings, the sphere could become airborne. He calculated that such a balloon could lift a considerable mass, and hence that 'mini-cities' or airborne towns of thousands of people could be built in this way.

A Cloud Nine could be tethered, or free-floating, or maneuverable so that it could migrate in response to climatic and environmental conditions, such as providing emergency shelters.2

https://en.wikipedia.org/wiki/Cloud_Nine_(sphere)

https://books.google.com/books?id=iOhrizYNIjQC&q=cloud+nine+tensegrity+sphere&pg=RA2-PA190#v=snippet&q=cloud%20nine%20tensegrity%20sphere&f=false

See answers to this question:

Can Cloud Nine be built?

What you need is to find some calculations relating to hypothetical "Cloud Nine" structures.

One problem I see with "cloud nine" structures is their spherical shape. If one loses lift due to leaks or something, and descends to the ground all its weight will be held up by a small section of the bottom which probably won't be strong enough and will probably break.

Landing in water would enable it to submerge a large proportion of its volume and then float supported by water over a larger area, less likely to break the sphere. But water pressure increases rapidly with depth. If a mile wide sphere extends hundreds or thousands of feet below the waterline, the water pressure might break the lower sections of the sphere.

I also wonder what would keep a sphere from tipping over and floating upside down in the air, while the people all plummet to their deaths.

So perhaps the floating city would be designed as two hemispheres side by side instead of one full sphere. Maybe the living spaces of the city could be in a series of large but relatively small hemispheres arranged around the perimeter of a giant geodesic sphere for lift.

For maximum surface area within a giant sphere, the floor area should be a circle at the "equator" of the sphere. If the buildings are tall, that will put more weight in the upper half of the sphere and make it more likely to be top heavy and tip over.

Perhaps the buildings would all be one story above the "ground", with multiple stories of basements below the "ground", and with water storage in tanks below the "ground" level, etc. Thus the lower hemisphere may be heaver than the upper hemisphere to avoid tipping.

How would the "ground", a circular disc a mile in diameter, be supported? By cables from above, like a suspension bridge, or by supports from below? Either way should add a lot of weight to the town, which might make it too heavy to float.

Possibly There could be a relatively smaller circular area of "ground" right above the bottom of the sphere, and the tops of the buildings would support another and slightly wider layer of "ground" above it, and the buildings on the second layer could support a third, somewhat wider, layer of "ground", and so on.

And the highest levels of "round" might be ring shaped, going around the perimeter of the sphere and with open spaces in their centers. Each ring would have a greater diameter than the ring below it.

Thus the layout of the floating city would somewhat resemble that of Hell in Dante's Inferno, a set of concentric rings which get narrower and narrower at lower levels. The levels would be connected by ramps and elevators.

Or the layout of the floating city could be said to somewhat resemble the layout of A.E. Van Vogt's spaceship the Space Beagle, or the Death Star in Star Wars, except that most of the floating city would be empty space with the "decks" or "ground" filling only only small part of the total volume of the sphere.

To save weight, parts of a floating city, whether a "cloud nine" type geodesic sphere or some other type of design, might be made of aerogels.

Aerogels are a class of synthetic porous ultralight material derived from a gel, in which the liquid component for the gel has been replaced with a gas, without significant collapse of the gel structure.1 The result is a solid with extremely low density2 and extremely low thermal conductivity. Aerogels can be made from a variety of chemical compounds.4 Silica aerogels feel like fragile expanded polystyrene to the touch, while some polymer-based aerogels feel like rigid foams.

Despite the name, aerogels are solid, rigid, and dry materials that do not resemble a gel in their physical properties: the name comes from the fact that they are made from gels. Pressing softly on an aerogel typically does not leave even a minor mark; pressing more firmly will leave a permanent depression. Pressing extremely firmly will cause a catastrophic breakdown in the sparse structure, causing it to shatter like glass (a property known as friability), although more modern variations do not suffer from this. Despite the fact that it is prone to shattering, it is very strong structurally. Its impressive load-bearing abilities are due to the dendritic microstructure, in which spherical particles of average size 2–5 nm are fused together into clusters. These clusters form a three-dimensional highly porous structure of almost fractal chains, with pores just under 100 nm. The average size and density of the pores can be controlled during the manufacturing process.

https://en.wikipedia.org/wiki/Aerogel

So in a world where aerogels are cheap and plentiful, and where people build floating cities, aerogels would naturally be used to build the parts of a floating city which they were most suited for, to reduce the weight.

For example, I can imagine that aerogels might be useful for most of the parts in a building, so that the buildings in the floating town might be mostly made of aerogels.

And if the buildings in the floating city are mostly made of aerogels that would greatly reduce the total weight of buildings to be calculated.

Aerogel balloons have been suggested, Air filled aerogels are very light, but heavier than air. But if an aerogel could hold a vacuum, it would be lighter than air, and thus a solid but vacuum enclosing aerogel could be a lighter than air balloon, and maybe make a floating city.

https://discover.lanl.gov/publications/1663/2021-august/lighter-than-air/

Since aerogels are very strong, and also quite transparent, they could also be used for fake floating cities. Aerogel columns could support a city far above the ground. if someone could manage the lighting so that the columns couldn't be seen, it would look like the city was floating in the air, held in place by fake tethers to the ground.

So a conman might claim that the city was temporarily tethered in place, and that after it was settled by his customers, it would be set free to float in the wind.

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    $\begingroup$ "what would keep a sphere from tipping over" - easy, as with all things that are buoyant, having a mass center below buoyancy center would not let the object to tip over. With airborne stuff it's pretty easy, as air is already above the ground, both in and out the sphere, with water - not that easy, but structures can be still built so that attempts to tip the sphere while maintaining buoyancy equilibrium would cause its mass center to be raised, forcing it to tilt back. $\endgroup$
    – Vesper
    Nov 16, 2023 at 8:37
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    $\begingroup$ Interestingly, the original designs for the Cloud Nine structure were based on being a mile-across skeleton of titanium or aluminium, with plastic panelling to close it up. The overall structure functions as a hot-air-balloon, using the thermal mass of the town inside instead of a burner. If the air inside the structure is more than a few degrees above the ambient temperature, the structure will be self-supporting. Like a lot of megastructures, it's technically feasible, but really hard to build. $\endgroup$
    – Ruadhan
    Nov 16, 2023 at 17:10
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I remembered an older question where the OP asked for the energy output of a city falling from 10km. To answer that, I found an estimate of the mass of New York City. With the estimate I also found the methods used to get the numbers.

Here is the original article with the estimate and methods.

It has some interesting pieces of info, for example on street mass:

Streets average 63 feet in width, sidewalks about 15 feet. Asphalt (streets) and concrete (sidewalks) each weigh a little over two tons per cubic yard, and each street needs at least three inches of asphalt on top.

Once you figure out how many km of street your city has, you can calculate volumes and plug in the densities.

And for buildings:

For buildings over 30 stories, use 3,000 tons per floor. Buildings under 30, use 200.

You still need to figure mass for people (a fixed number in your case), pets, vehicles, food etc. you havenin the city, and then estimate masses for those too. The article in the link has some ideas for that.

I really don't have a number on top of my mind, but I hope the ideas above help you figure out some realistic mass. Next thing I would do is finding one or more towns with about 2,000 people living in them, and then trying to figure how many houses, streets, vehicles etc. they have in them. One place that comes to place is Westlake, in Alberta, Canada. It had a population of 2,040 people in 2021 and you can see it in Stree View in Google Maps.

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  • $\begingroup$ Why are buildings over 30 stories 15x heavier per floor? And what about buildings that are exactly 30 floors? (Also, what's magical about 30?) $\endgroup$
    – Michael
    Nov 16, 2023 at 15:35
  • $\begingroup$ @Michael in respective order: more foundation and supports needed, I don't know, and that is 12 less than 42. $\endgroup$ Nov 16, 2023 at 17:25
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    $\begingroup$ My first thought was that maybe it was near the transition at which wood gives way to steel supports, but apparently it is a lot lower than that, although I fell down the rabbit hole which is current efforts to introduce wood framing to taller structures, but the record currently is only around 18 floors, apparently. $\endgroup$
    – Michael
    Nov 17, 2023 at 12:19
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5000 tons

A lot of the questions assume just taking either a land-based city or an ocean-going ship and lifting it in the air. However, literally nobody would do that unless they had a way to lift things up in the air which didn't depend on weight (eg: neutralizing gravity). The better reference point is aerospace designs. Space stations like the ISS are not a great reference though, for different reasons: they include (very heavy) life support systems which you wouldn't need in the atmosphere, and (also very heavy) power systems. Here you're probably going to handle both life support and power separately, you're looking for just the living spaces and everything in them.

Let's start with a modern large airplane: Airbus A380. Usable area in the interior: 550 square meters. Max payload: 84 tons. Max passengers: 853 (very cramped of course). Empty weight: 285 tons, max takeoff weight: 575 tons, fuel capacity 253 tons. The engines are about 25 tons, not sure how much the wings are (probably pretty substantial, ~half of the total weight?). So a structure built in the same way as an Airbus would have roughly 1-3 tons of structure per ton of payload, and 0.25-0.5 tons of structure per square meter.

Now the payload: obviously people themselves (2000 x 0.1 tons each = 200 tons). Furniture? appliances? a lot of that stuff would again be optimized for weight; foamed plastics, foamed metals, carbon fiber. People routinely go backpacking with a load < 20% of their body weight, and sometimes as little as 5 kg (ultralight). Let's be a bit generous and give a total weight budget for a longer term habitat roughly equal to body weight (also 0.1 tons each = 200 tons). So we're looking at ~400 tons total payload. Applying the ratio above would also give 400-1200 tons structure to keep that in.

How about floor space? Average living space in Tokyo is 20 square meters per person (and for many people less than 10). The minimum recommended under very cramped living conditions is around 5. Take 2000 x 5 square meters = 10000 square meters x 0.25 - 0.5 tons per square meter = 2500-5000 tons of structure. So it seems the required weight of the structure is driven more by the floor space, less by the payload weight.

Now, the big reason why the Airbus is not a good model: it is meant to go fast, almost at the speed of sound: Mach 0.89. This puts huge dynamic loads on the structure, which is designed for a lot of worst-case scenarios (flying through heavy turbulence at max speed). I think slow-flying big planes, and especially dirigibles, are built a lot lighter. Ideally you'd want to get specs for a dirigible (just the gondola, not the total including the gas bag), and do the same kind of analysis. Those specs are a lot harder to find, but eg the Hindenburg was about 118 tons empty and had around 700 square meters usable space on the passenger decks; however the vast majority of the weight was in the hull, I doubt the passenger space accounted for more than 1/10th of the total weight; the horizontal cross-section area of the whole gas bag was >5000 square meters. So an airship would probably be a lot closer to 0.01-0.02 tons of structure per square meter of deck space.

I think ultimately you'd end up designing quite a lot more extra space, but in a much lighter (airship-like) structure: ie you'd end up with 20-50 square meters per person or even more, but still close to 5000 tons of structure total. If you're okay with a cramped feel, the practical lower limit is likely 600 tons structure + 400 tons payload.

Bonus: You may want to have some large but extremely light inflatable parts of the structure ("balconies", "observation decks", "bouncy castles") which can only be used in good weather / low wind conditions; they would get deflated/reeled in if the winds are high.

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