Just how unrealistic is a hovering city?

Question

In my last question, we had some disagreement in the comments about the reality of a hovering city. However, that question wasn't about that.

This one is.

My civilization are building a giant hovering city to house people who have no home due to the massive overpopulation of the planet. It'll be about the size of London, 7 million people. With it comes all the industry, agriculture and other services a city needs to thrive.

I'm well aware, thanks to the comment thread there, that this city is unrealistic and would have some bad consequences. But just how unrealistic? What effects does it have on the planet's surface? Clearly, downwash is a problem, but how much?

Answer 1

Lots of the answers so far have focused on the economic reasons why a floating city is impossible. But what about physical reasons?

Aerodynamic Levitation

As a first approximation, we can treat the city as an air bearing. There are a couple formulas that we can take from an intro fluid flow class to calculate the amount of airflow required to hold us up, assuming incompressible laminar flow.

$$ \dot M \approx \frac{\pi b^3 \rho\sigma g}{3\mu} $$

Where $b$ is the distance in between our city and the ground, $\rho$ is air density and $\mu$ is viscosity, $\sigma$ is the load of our city and $g$ is gravity. Here are the values I assume:

• $g = 9.8~\text{m}/\text{s}^2$ (Earth standard gravity)
• $\rho = 1.225~\text{kg}/\text{m}^3$ and $\mu = 1.789\cdot 10^{-5}~\text{Pa}\cdot\text{s}$ (standard air at sea level)
• $\sigma = 1000~\text{kg}/\text{m}^2$ Assuming the average density of stuff (buildings, dirt, etc.) in the city is around the same as water, and if you flattened the city out it would be a meter high (this is a huge underestimate)
• $b = 1000~\text{ft}$ This is what my intuition tells me is a "reasonable" height, something like the spaceship in District 9.

We can plug in these values and we get:

$$ \dot M\approx 1.5\cdot 10^{15}~\text{t}/\text{s} $$

Yes, we need to move over a million billion tons of air per second to keep the city afloat, or enough to turn over the whole atmosphere in around three seconds. Now, this is obviously not going to be laminar flow anymore; we can calculate the air velocity at the edge of the city, assuming a diameter of $2R=45~\text{km}$:

$$ v = \frac{b^2\sigma g}{\mu R} = 20\cdot 10^{6}~\text{km}/\text{s} $$

This is obviously wrong, since it's 60 times greater than the speed of light. However, it does tell us that we can't levitate the city this way.

We can try another approximation, this time using actuator disk theory. It tells us that the amount of power required for the city to hover is given by:

$$ P \approx A\sqrt{\frac{\left(\sigma g\right)^3}{2\rho}} $$

Using the same values as before, we come up with a power of:

$$ P \approx 1000~\text{TW} $$

... which is 50 to 100 times current global energy consumption.

Even if we could circumvent these issues, we'd still have to apply a couple of psi to the ground below to support the weight of the city. This would certainly flatten any fields that city flies over, and if the force is applied in even a slightly unstructured way, this could easily flatten buildings. In addition, the ground itself could give way when you fly over another city: imagine doubling the weight of every building, and the settling that would occur.

Hydrostatic Levitation

We can get around the ground pressure problems by replacing the weight of the air that's already there; that is, floating the city with balloons. As a best-case scenario, I'll assume that the balloons are filled with vacuum.

To see how this works, imagine cutting out a disk-shaped slab of air and replacing it with a rigid shell. If the total weight of the shell is equal to the weight of the air removed, the forces on the surrounding air will be exactly the same, and the people on the ground won't feel any pressure.

I'll use the same figures as before for our calculation: a base height of $1000~\text{ft}$ and an average mass of $1000~\text{kg}/\text{m}^2$ (around $1.4~\text{psi}$, or $0.1~\text{atm}$). We can set up the following equation relating the mass of a section of the city and the mass of the air it displaces:

$$ m = \int \rho\ dV \\ \sigma A = \int \rho\ dz\ dA \\ \sigma = \int_{b}^{b+\Delta z}\rho\ dz $$

Using the US standard atmosphere, I get a value $\Delta z = 2900~\text{ft}$. If we using a lifting gas with density relative to air $\tilde\rho$, the equation becomes:

$$ \sigma = (1-\tilde\rho)\int_{b}^{b+\Delta z}\rho\ dz $$

For helium with $\tilde\rho=14~\%$, we get $\Delta z = 3400~\text{ft}$. Of course, this is only enough to keep you $1000~\text{ft}$ above sea level. If you want to float above the tallest building in the mile-high city (or get from one side of the US to the other) you need to have $\Delta z = 4000~\text{ft}$ high balloons.

Psuedoscience (Aside)

It looks like we need to ignore hard-science if we want to make this work. Personally I would have your city levitated with a variant of a reactionless drive. The common spaceborne sci-fi variant pushes on a gravitational well, so that momentum is conserved but no reaction mass is expended. If this is possible, it may also be possible to "latch on" directly to the gravity well of a planet. It would essentially be a floating solid foundation (although it would experience tidal motion due to the influence of the Sun and Moon). The energy requirements would be zero until the city moves, and when it does the required power can be made as small as desired by reducing speed (although the total amount of energy required to lift the city a given height is fixed by its weight).

Generic Problems

Whatever method you use, there are two more problems that I can foresee. First, your city will be a giant moving eclipse. Nobody wants an airship the size of Guam floating over their heads, even if it's just for a day: not cities, where there are lots of people to get angry; and certainly not in rural areas, where crops could be harmed by the lack of sunlight. Environmentalists will protest the disruption to the local ecosystem wherever you go.

Second, wind speeds increase rapidly with altitude, and temperature and pressure decrease; not to mention that low clouds would pass through the city like dense fog. Inhabitants of a floating city would experience worse weather than ground-dwellers at pretty much all times.

Thirdly, the city would likely be subject to electrostatic charging by the same mechanism that causes clouds to become charged. At the very best, the city itself would act as a lightning conduit during storms. At the worst, the city itself might generate a few small lightning strikes when first passing over a tall building. (Yet another reason to refuse passage to this power-hungry/regular-hungry darkness-bringer of a city.)

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Pretty much all these problems can be countered by floating close to sea level above somewhere with no people or plants. But in that case, they'd probably just drop it down the last 100 feet and float it on the ocean—much easier.

Answer 2

TL;DR:

In a hard fiction setting, hovering cities are a bad idea. Too much cost for too little benefit.

Reasoning:

Hovering cities are something really really hard to pull off without some extreme hand-waving.

Don't get me wrong. I love the idea of floating cities. In fact, on my works (I'm an RPG writer), I have several of them. Magically floating, of course, with the powers of applied Arcane Mysteries.

But hard-science hovering cities? That another beast entirely.

First of all, let's think about altitude. You can't have you city too far up on the sky, or people would suffocate. There is not enough oxygen up there to keep people alive comfortably. You have the option to encase it on a giant bubble, but that would be prone to disasters. So, let's keep it at a low altitude.

Anything that stays aloft need something to keep it aloft. You have a few options, but each one is unviable in some way.

• Jet engines are nice, but cause a massive amount of wind. One of the engines needed to put a Boeing in the air is enough to throw away a small car. To raise a city up in the sky, you need to direct this airflow to the ground, causing tornado-class winds that would wipe out life anywhere below the city.
• Propeller (helicopter-like) engines would simply not work. You would need a propeller so big that it would become impractical.
• Magnetic Levitation is nice, but you would need a magnet so massive that it would make the use of ferromagnetic metals anywhere near the city and IN the city impractical.
• Putting it in orbit would be... No, really. Just no.

Of course, there is no need to say that to put everything in the sky would use an absurd amount of energy. But let's not go that deep into the calculations. Jim2B already made some energy calculations in your other question that shows how this is impractical.

But let's suppose that your people developed some cost-efficient engine that works by some form of quantum-magic levitation. This already kills the "hard science" that you asked for in your other question. Let's hand-wave that.

Now you need to cope with the winds. So high above the ground, winds would be extreme. Your city would need several layers of protection to keep those winds at bay without destroying everything above it.

After you take care of that, now you have the issue of the buildings of your city. Normal sky-scrappers are ruled out. They need so much foundation that, unless you have a literal floating mountain flipped upside down, you wouldn't be able to provide enough. But let's hand-wave that, and suppose that you developed some sort of ultra-resistant carbon nano-tubes capable of providing the foundation you need to build something in your city.

Now we hit another problem that hovering cities face and land cities don't: water supplies. Unless you have some sort of futuristic water-recycling device, your city would always be on water shortage. You can't just tap in to the nearest river to keep you people well supplied.

Then you get to the sewers. You can't just throw away all that human waste by dropping it below - all the world bellow is covered by cities. So, you need to process it in-flight by some unknown process that happens really fast and doesn't exist yet. More hand-waving.

Then you need to take out the garbage that your people will produce. This falls on the same problem of the human waste - you need some unknown process to take care of it fast enough so you won't pile up the trash.

After that, you need food. London, and almost every other major city today, can't produce enough food to feed everyone that lives in it. You would need to buy food from people below, and this food would have a very high price. It's not cheap to send food to the skies.

If you solve the food problem, you have the money problem. How much would cost to live in that city? Everything is super expensive if compared with stuff on the surface, and that's because logistics alone would increase the prices a lot. The cheapest way to move stuff around is by the sea. Your city doesn't have any kind of harbour, so it will only be accessible by plane. Even a little can of soda must come to the city by plane. Just imagine the costs of that.

Finally, transportation. People won't be able to leave the city and come back easily. If you need good weather to do anything outside your city, it will rapidly become uninteresting as a business hub. London, and other major cities are major cities because they are the central hubs of civilization. They are rich, developed, and more importantly, accessible. A flying city is not accessible. At all.

That would destroy it's economy pretty fast. Factories would have problems getting their raw materials, people would have problems coming and going, commerce would suffer a big hit since people don't really need to go there to buy stuff (the rest of the world is a huge city)... so, economically, this city would be a total disaster.

Answer 3

The issue with a floating city is that it doesn't really accomplish anything that couldn't be done better using another approach, unless what you're trying to accomplish is simply 'be a hovering city'. This is mainly because of one simple reason: hovering is hard.

Hovering takes a ton of energy to do, especially for a city the size of London with commerce, industry, etc. In addition, it's going to require a bunch more energy to get all of your raw materials and resources from the ground up to the hovering city. All of this energy is expensive. In addition, you've got a massive engineering problem to solve in terms of how to make the city structurally stable and balanced (as well as capable of hovering) and a lot of material expenditure going into the workings of the hovering mechanism and the associated structure.

If you're out of land area and looking for a place to put a few more people, there are two options that would both be better than a hovering city: the ocean and in space. There's a ton of space in the ocean, and, assuming you build neutrally-buoyant structures, no major structural barriers stopping you from creating strings of buildings spanning its entire height. Your ocean dwellers won't be able to move vertically through the cities particularly quickly without getting the bends, but they'll survive and you can pack lots of people down there. Space platforms would be expensive to transport materials to, unless you're already bringing in materials from other planets, in which case they'd likely be commerce hubs for materials trading. Solar energy is plentiful and reliable in space and there aren't as many structural concerns for something in orbit since it need not support its own weight.

The only civilizations likely to build floating cities would be type-II civilizations with absurd amounts of cheap surplus energy, but these civilizations wouldn't be building them to reduce overpopulation, they'd be building them because they can. In a world in which most of the population is crammed either under the seas or onto orbital platforms, they'd also be a nice vacation spot or home for the wealthy, particularly if the surface of the planet is heavily polluted.

Answer 4

It isn't a traditional hovering city, but Buckminster Fuller said you could make spherical shells that would float like hot air balloons. The google terms would be "Buckminster Fuller Cloud Nine" or "tensegrity sphere". He was thinking of mile wide spheres (think two big geodesic domes joined together) and said a one degree temperature difference between the inside and outside would be sufficient to keep it airborne. The city population would be in the "thousands", so you'd need a flock of them to cover millions of people. And yes, he was thinking of flocks of them.

Answer 5

As already said it's a massive expense to get the city up there, keep it up there, and get people to and from them. This sort of energy is not cheap and is a tremendous limitation in it's own right. However, Everyone is already focusing on this issue, and you can always say A Wizard Did It there. Let's focus on the other implications....

There is maintenance issues with any solution, the things keeping your city in the air must be regularly attended and maintained, they will break down so your need duplicates and backup for the duplicates and your have to watch and maintain all of that. That's significant expense and man hours.

Then there is the fact that if your redundancy fails then everyone in your city dies horrible deaths. What happens when a hurricane hits your flying city? Can terrorists hold the whole city captive by threatening to pop a hole in your gigantic helium balloon floating you up? There is a significant danger of catastrophe, you need a good motivation to take this risk. Even if the city doesn't collapse to it's doom what happens when little billy goes chasing after his favorite ball and falls of the face of his earth?

There are also difficulties simply living that high up. The atmosphere drops the higher up you get, if your floating at any height your going to be dangerously cold and short of breath due to lack of oxygen. Your going to have more sun burns and mutation and skin cancer from lack of atmosphere protecting you from the sun's radiation. The winds will be so severe they could blow little billy off the face of the earth without him being stupid enough to chase after his ball. These factors depend on how high your floating, but you don't have to get too high before you start feeling them. The wind in particular will build up VERY fast, just stand on the top of a sky scrapper and see how hard it is to stand against the wind there. In fact the winds may be bad at skyscraper heights to make growing of crops and food quite difficult. Though it would at least give you some free wind energy if harnessed.

So there are major engineering hassles to making this happen, major inconveniences to living up there, and increased risk of falling to doom. What would motivate this to be worth while?

The usual answer is to increase land area but...that doesn't really work. If you float over an area your blocking out sun and rain from the area you block, messing with weather and animals (you would be amazed how fast their instincts would be screwed up by this). Nothing can live below you! You haven't significantly increased your land mass, you've simply transplanted it higher into the air, where it's harder to live.

Now if your floating city moved regularly this would be a little better. You would only block out light and water to a given area for as long as it took to move elsewhere, This would make it possible to live in the area your city floats over in theory. However, it will make it a horrible hassle whenever you float over them, one that could cause severe expense whenever you float over. Your have to be moving at high speeds to ensure you don't block out sun from any one location enough to ruin it; and high speed motion causes winds so great as to make your city uninhabitable.

Meanwhile if you look at livable land as land that can produce enough food you still haven't increased your habitable land by much. The crops growing anywhere you float over will lose light and thus grow less. Your only be able to grow as many crops on your floating city as you get sunlight, and all sunlight is 'stolen' from others, so effectively your crops only grow as much as crops below you suffered from your being above them (this isn't entirely true, there would be a slight gain but not much).

If you simply need living area for the sake of fitting people sky scrappers are a far more viable method. They suffer some of the height issues, being more expensive to make and requiring more immanence, but you fit people on multiple floors so you gain significantly more living space per square foot of land then your floating city provides, and it's inclosed and protected from elements and generally safer and easier then a floating city.

There is also politics issues. No one will want you to float over them because its does significant harm to them. How do you get people to agree to allow you to steal their light? How do you keep the government from ordering your city being downed? or worse from people declaring you an invading alien nation and unleashing war against you to save their most precious of natural resources, light. and yes light is that precious, it's the source of all other energy in the world, directly or indirectly, and must be preserved to survive.

Answer 6

This is based on Ratchet Freak's comment about gas air bags. I decided to do the math on that.

Taking some info from the answer in another question, I estimated the rough weight of a large city as 1 billion tons, or 2 trillion lbs.

Helium lift is roughly 60 lbs/1,000 cubit feet. Therefore to lift our city we need approximately:

33,333,333,333,333.3 cubit feet of helium, or 247.2 cubic miles.

Now obviously that's a lot of helium. But if our city is circular, with a radius of 15 miles, then it's area is 706.86 square miles. So if the entire city had helium bags over it a third of a mile tall, that lift would almost cancel out the weight of the city.

Alternatively, a circular ball of helium above the city with a radius of just under 4 miles would also do the trick, and might allow more sunlight.

As to realism, the first big problem is that the amount of helium we need is 2-3 orders of magnitude larger than the total helium left on Earth. Maybe if you have a convenient, close by gas giant you could mine it in huge quantities and set up your floating cities with this method, but I'm not sure how much that will really help. Probably still much easier to just build in space.

Answer 7

Now that you've found the secret, floating, magic stone to build your floating foundation with, let's see what comes next.

TL;DR

A circle of 28km diameter can fit your nice, compact urban and rural development, if you plan well.

Height - You probably don't want to go much higher than about 4km, as you start getting near the altitude of Everest Base Camp. This makes for a cold, windy city, and your annual Floatopolis Marathon event is going to be a tough one.

Buildings - Let's put a defensive ring of your tallest buildings around the exterior of the city, and inverse of most radial cities (like Brisbane, etc.). It will help, a very little bit, and offer nice real estate (think of the views). Centralize the one-off facilities (universities, sports arena, etc.), but distribute the others (healthcare, education, etc.).

Utilities - Consider a very (magical) long pipeway to bring utilities to the city, and a place to dispose stormwater, sewerage and trash. Although, London is aiming for zero waste to landfill by 2030. Power generation would be great from wind under and over (and through?) your city. Rainwater and air moisture can be captured and stored in cisterns. For all utilities, you will need lots and lots of recycling and clever thought.

Food - This is tough. You'll need vertical gardens, rooftop gardens, neighborhood gardens and tight groves for fruit. Greenhouses help if it's really cold up there. Urban chickens and small animals can help, but keep your industrial agriculture down-wind for sure.

Location - Since you can hover your city, you can place it anywhere that helps with the issue of temperatures and storms (climate). You may also consider having it follow the sun. Sunny and (relatively) warm all day and night.

Transport - You can save costs by not having motorized vehicles - except service vehicles - and compact urban development. For longer distance travel, I can hop on the Tube and get there in minutes: mind the gap!

Other Services - A city the size of London has major in-out services. I don't have source, but I imagine it to be tremendous. You will have to explain how in-house production and manufacturing prevents having hundreds of freight planes landing every hour.

Community Facilities: Education - Each government today has standards for Education, Health, and sometimes religious facilities. As an Urban Planner, I would suggest your 7 million people should have 1.4 million school-age population, so a thousand (large) schools. Try vertical schools. One major university can serve nicely.

Community Facilities: Healthcare - Again, just one urban planner's experience here, I recommend 7 hospitals (1:1million), and 230 clinics, which those can be inside/under residential or other buildings (or underground), but the hospitals have radioactive uses and waste, so keep them standalone.

Parks & Recreation - These may have to be rooftop for outdoor uses, but you can also easily house gyms, etc. in buildings. Build a lovely stadium for the Floatopolis Herons and for performance multi-use spaces.

Residential & Commercial - You'll need 2.8m residential units of various size totalling 420bn square meters, but stacked. Double that in office, and half that in retail Gross Floor Area. With compact urban development, total developed and undeveloped (parks/streets/etc.) urban GFA of 45,000,000m2 (that's your urban footprint) will work [source: I worked on a (much smaller), standalone urban development for a city of 100,000 people in the middle east, and used similar ratios]. Now add your farms and industry, so let's double your island's need to 90 million m2 footprint. If it is a square, lets go 10k x 9k, if it's a circle, the diameter is 28km or so.

Bonus - Dome your city, like the Houston idea.

Answer 8

Floating cities would only be cost-effective on planets with a much denser atmosphere than Earth, where your city could be of neutral buoyancy, using earth standard air as a lifting gas. An unstable surface would make this a more realistic possibility, and indeed this has been seriously considered by NASA for human colonies on Venus

Answer 9

I once saw a collection by Gary Larson (author of The Far Side) where he commented on the complaints he got about a particular cartoon: it depicted one mosquito wearing a dress and washing dishes in the kitchen, and another in a fedora and carrying a briefcase coming home and complaining about a long, hard day sucking blood. He got lots of letters complaining that it's the female mosquitos that suck blood, not the males. This amused him, because no one complained about mosquitos wearing clothing, living in houses, washing dishes, or carrying briefcases.

The point of that anecdote is: people have a very large capacity to suspend disbelief when you are consistent. Whatever handwavium technology or substance that you use to keep your city aloft will be far more believable if it's woven into the fabric of your society and world. How was it discovered/developed? Who prospered because of this, and who suffered (for instance, producers of now-obsolete technologies that were being displaced)? What mundane, everyday uses is this handwavium being put to throughout your world?

If it's fleshed out like this, rather than just being the-way-the-city-stays-up-don't-look-too-closely, then it's part of the basic premise of the story. Still not hard science, but even hard science fiction can let you get away with an implausible premise, as long as you've thought through the implications of what it means.

Answer 10

I think it's entirely practical if you're willing to change the premise slightly and make some assumptions about future technology.

Cities aren't built to house people, they're built for commerce. Historically this means building at a crossroads of some sort (a harbor, a trade route intersection, etc). If you want a reason to build a city in the sky, you need some commerce going skyward.

So, you don't hover the city, you hang it. It's the earth-side anchor for a cluster of space elevators going to a station in mid-level orbit. With a space industry of any decent size, the city becomes the most active transit hub on the planet. With that much money moving through the city, all of the other problems are solvable.

The big assumption here is that you need a material strong enough to build a space elevator. If you can explain that away, the rest is easy.

Answer 11

Apropos practicality, we should perhaps first consider the (now lost, alas!) work by the mad poet Navarth, "Castles in the Clouds and the Anxieties of Those Who Live Directly Below by Reason of Falling Objects and Wastes" :-)

The only way I can think to make a floating-in-air city actually float requires antigravity, and some handwaving. That is, your antigravity machine respects potential energy: put in the energy needed to lift an object to a certain height, and it stays at that height with no further expenditure of energy, exactly as if it was on solid ground.

Even if you can make a city float, you still have all the practical problems of food & water supply and waste disposal that a land-based city would have. Growing sufficient food requires a MUCH larger area than the actual city, as does capturing sufficient water. They're certainly not unsolveable: as a real-world example consider Las Vegas, which has to ship in basically all of its food and water from some distance away. It would seem, though, that it would be much more practical to address overpopulation by other means - e.g. contraceptives added to the water supplies of existing cities.

Really, the only reason I could see for such floating habitations wouldn't be as a disposal site for surplus population, but as luxury residences for the wealthy - quite literally castles in the clouds.

Answer 12

Buckminster Fuller calculated a large enough geodesic dome (or ball) could float as a hot air balloon due to the hot air trapped inside from solar heating, for kilometre diameter scales the carrying capacity can be quite significant.

Maybe tie a couple of those together?

Answer 13

If you have a material which has a super-super-super-high strength to weight ratio, then you can take a 'space elevator' or 'skyhook' approach:

1. Put a satellite into geostationary orbit

2. Spool out a cable of ultra-strong material from the satellite in each direction (one cable towards the Earth and one cable away from it).

3. Fix your city to the bottom of the cable, and fix your counterweight to the top of the cable.

Simple! As a bonus you can run elevators up and down the cable to get easy access to space.

NB:

• Floating city will need to be on the equator.

• Beware of the cable snapping (uncontrolled descent of up to 35,786 km of super-strong cable = not very good for the Earth's crust).

Answer 14

A bit like I mentioned in my answer on your other question, many power sources just add lots of weight to your city and produce little energy in comparison to the amount require to suspend a big city.

For every extra power source you add, you add weight, so you need more energy to support the weight, so you need more power sources..... it is vicious circle.

There is balance to be struck and it lies in the realms where you produce lots and lots of power. Perhaps best method would be by matter convertion.