There have been floating cities in fantasy stories for ages. From Hyrule to Urth to Malazan, a fantasy world as imagined today is not really complete without some airborne structures slowly drifting over the landscape. A massive, mountain-sized citadel suspended in mid-air can also be a breath-taking visual element in the hands of a skillful artist, like these three:
My aim in this article is to try to visualize what a real cloud city would look like, either on Earth or on another planet with an atmosphere (like Venus for example), while staying within the known limits of physics and material science.
That means no antigravity, tractor beams, unobtanium, or anything else indistinguishable from magic. This still leaves us with many forms of physical lift and thrust; most of which do consume energy to keep a mass airborne. The only physical form of lift which does not require continuous power, and is therefore perfect for continuous suspension in mid-air, is buoyancy.
What exactly is buoyancy? A scientific description of it will usually include Archimedes’ Principle (with the famous shout “eureka!”), and give mathematical formulas for calculating the force in different scenarios [e.g. this page from NASA: https://www.grc.nasa.gov/www/k-12/WindTunnel/Activities/buoy_Archimedes.html].
For an aspiring architect wishing to design structures that float in mid-air, there is a simpler, more practical way to define buoyancy:
(1) The density of a (neutrally) buoyant body is equal to its surroundings.
In other words, for a Cloud City to stay aloft by buoyancy alone, its total average density must be the same as the air that surrounds it. If you determine the total mass of your Cloud City, you also determine its total volume at a given altitude and air pressure, and vice versa.
The art of making buoyant structures that carry things that are denser than air (like people, plants and water), is to attach them somehow to materials and shapes that are lighter than the surrounding air. If you can attach your denser-than-air components to lighter-than-air components so that their sum averages out to exactly-as-dense-as-air, the total package becomes neutrally buoyant.
This art of attaching heavier things and lighter things to each other gives the designer freedom to use any materials available, but rule (1) remains as a system-level constraint in any design. As long as you keep the total volume/mass ratio constant, you can distribute the mass of your city as you like, leading to the rule of thumb corollary of (1):
(2) Buoyancy = weight distribution.
In 1670, long before the first manned flight, Francesco Lana of Brescia published the design for his aerial ship. In his design, the lighter-than-air elements were large air-tight spheres with all air pumped out. These vacuum spheres were most likely inspired by Magdeburg hemispheres, an invention by Otto von Guericke demonstrated in 1654.
This type of “vacuum airship” has never been demonstrated at scale, because no existing materials have the sufficient strength-to-mass characteristics to form stable vacuum containers that are lighter than air. [We are however living in the golden age of material science, with new materials being engineered constantly. Vacuum airships are not completely ruled out as a possibility yet.]
All buoyant airships that have been built and flown have been based on “lifting gases”, like helium. Due to the thermodynamic nature of gases, the denseness of a volume filled with gas at a given pressure is closely related to the molar weight of its constituents. Hydrogen and helium, the first elements of the periodic table, have the smallest molar weight [molecular hydrogen, atomic helium], thus they are the gases with most lifting power; in other words their natural densities at a given pressure are the smallest of all known gases.
I will not go into details about the evolution of buoyant air vehicles here. Those interested can read about their history in many books, like the profusely illustrated Travels In Space: A History of Aerial Navigation by F. Seton Valentine and F. L. Tomlinson (Hurst and Blackett, London 1902) [readable e.g. via archive.org]
Even though heavier-than-air vehicles have pretty much conquered the commercial airspace since the mid-1900s, there are still fans of lighter-than-air airships. Here is one futuristic concept illustration for an “aerial cruiseship”:
As estimated by Dan Grossman at airships.net, the mass of the water in the pool alone would require a ship 4,5 times the size of Hindenburg to lift. [And from the snowiness of the peaks in the background the thing must be kilometers above sea level, requiring an even bigger volume to compensate for the thinner air!]
Another problem with the DS-2020 concept image is that the massive pool is on top of the ship, apparently above the helium gas bags. This puts the whole ship in an unstable configuration, with its center of weight (marked with a red cross) above its center of buoyancy (marked with a blue cross). Without some massive active stabilization system, the whole ship would capsize as soon as it lifts off. (Which isn’t necessarily a bad thing; for my money I would much prefer to swim in a glass-bottom pool over vast scenery than in a conventional one.)
Remembering rule of thumb (2), buoyancy is about mass distribution. In all real airships so far the mass distribution has always been asymmetric, leaving the ship with a center of buoyancy and a center of weight separated by some distance. These kinds of asymmetric bodies have a preferred stable orientation, with their center of weight directly below their center of buoyancy.
The natural orientation of the two centers can be utilized in blimps to control attitude. Here is a simplified sketch animation of a blimp shifting its center of buoyancy back and forth using its ballonets, causing a pitching motion since the center of weight is not moving:
[Pitch control can of course be accomplished by moving the center of gravity also; in fact this was the method used in early airships like the first Zeppelin. Ballonets are a more lightweight technique for the purpose, and they are anyway needed in non-rigid or semi-rigid ships, to maintain their shape at different altitudes.]
The location of the centers of buoyancy and gravity in a buoyant body is a result of mass distribution. I have used density diagrams that are helpful in approximating the location of the centers. The center of buoyancy is the geometric center of the whitest areas, which are less dense than air (the gray background). Conversely, the center of weight is the center of areas that are darker/denser than the background/air.
[In theory it is also possible to form a buoyant body where the centers of buoyancy and gravity are collocated. Such designs would not have any stable orientation, so they would just rotate around their centers like soap bubbles in air.]
Another very common, but ultimately unrealistic, design is to make a cloud city flat and wide, like it was floating on top of water. A wide design was suggested by milliner E. Petin already around 1850:
The four wide and flat parts around the mid-height of the balloons are not awnings or roofs, they were meant as control surfaces: if they were slanted when ascending or descending, they were supposed to transfer part of the vertical momentum into horizontal travel. The Petin ship was never built at full scale (or not allowed by the authorities to be unmoored according to some reports), so how the ship would have moved in air remains guesswork.
Surface marine ships can have a metacenter, meaning that they can be stable even when their center of gravity is above their center of buoyancy. [This also is the case for example when you lie on top of an air mattress in a pool.] But an airship is not a surface ship; it is totally immersed in air and cannot use any surface effects. It is in error to think that spreading the mass of a cloud city wide like in a surface ship would make it more stable.
The atmosphere of Venus is naturally more dense than that of Earth, so it is possible to build Venus airborne cloud cities where the breathing air also works as a lifting gas. Combining the functions of a space as both living and lifting makes flatter, wider designs possible, but that is not necessarily a good thing for stability. Here is an exaggerated animation of what happens in a wide cloud city design when movement of mass occurs:
Because the centers are so close together, even a slight shift in the center of gravity tilts the whole structure with a keen angle.
The dome design is possible to improve by increasing the distance between the force centers, for example by making the dome taller and lowering as much mass as possible under the decks, to work as a counterweight. Similar movements now cause smaller tilt angles:
For best stability, the structure could be equipped with an automatic stabilizing mechanism, shifting the counterweight to keep the center of gravity always aligned:
The Sultan of the Clouds is a 2011 science fiction novella by Geoffrey A. Landis, set in a future Venus cloud colony. Landis is also a scientist, and has advocated Venus cloud-tops as the most suitable location for human colonization in the Solar system. Here are some cover illustrations for the award-winning novella:
Hypatia, the cloud city where the story takes place, consists of many kilometer-wide geodetic domes. The breathable air that also serves as lifting gas, is contained by millions of millimeter-thin polycarbonate plates joined together on a graphite-based frame.
Although it may not be clear from the illustrations, the text also mentions a counterweight under the city, “a rock the size of Gibraltar”, so the design should have the correct stable orientation from having asymmetric force centers. [No mention is made how stability is maintained when people and goods move around.]
Even though the transparent domes of Hypatia are made of millions of individual panels, its denizens are not worried about its stability:
“Here, you know, there is no pressure difference between the atmosphere outside and the lifesphere inside; if there is a break, the gas equilibrates through the gap only very slowly. Even if we had a thousand broken panels, it would take weeks for the city to sink to the irrecoverable depths.”
This may be the case if the breaches are all at the same height and there is no wind. But what about if there are simultaneous breaches at the top and the bottom of the dome? Like hollowing out an egg, Venus atmosphere would flow in from the bottom hole at the same rate that breathing air would flow out from the top hole, pressure staying constant the whole time.
Here is the (again, very exaggerated) animation of a catastrophic failure, starting with a mechanical failure in stabilization, followed by simultaneous breaches at opposite ends of the dome:
It should also be noted that a dome that contains the main buoyant part of the city is not resting on top of the ground, like geodetic domes on Earth. Once it is filled with a lifting gas, the dome is pulling the rest of the city up, with a force equal to the full weight of the rest of the city.
Here is the Venus poster from NASA JPL “Visions of the Future”. The design is of course very stylized, but the conical underpart of the city would make a more sturdy housing for the counterweight, with multiple A-frames. The counterweight could even be made of something useful for the function of the city, that is just located low for stability.
The first known (by me at least) proposal for a Venus floating city is this design from 1971 by Russian engineer and science fiction writer Sergei Zhitomirsky. There is no counterweight as such, just separation of machinery and equipment to different levels, but the tallness of the dome contributes to stability by raising the center of buoyancy.
[Zhitomirsky also mentions the possibility of using helium-oxygen mixture instead of nitrogen-oxygen air as lifting gas. Such heliox-mixtures would theoretically work as lifting gases in Earth atmosphere as well, if the dome is large enough. So far I am not aware of anyone ever attempting to fly inside a heliox balloon on Earth.]
While these large domes are stylish and futuristic, real cities are usually grown naturally, part by part. If that growth happens in mid-air (as it needs must on Venus), maintaining rule (1) the whole time can be tricky.
Water life can be a source of inspiration for buoyant designs that grow. Some marine mollusca, like nautilus and spirula, have buoyant air chambers inside their hard shells. As the creature grows in size and mass, it adds new chambers one by one into its shell, creating a beautiful self-similar geometry.
Beautiful as they are, the designs of buoyant sea life may not be possible to translate directly to buoyant air structures: Because the natural density difference between life and air is more drastic than the density difference between life and water, buoyant elements in aerial structures need to be much larger in relative volume.
So what is the answer to my question, what would a real cloud city look like? Well, like cities on the ground, there is no single design that all must follow. From the images in this article, the painting “New World Coming” by J Otto Szatmari is to me perhaps the most realistic, with its vertical shape and the obvious gravity of the mass suspended from multiple balloons. More of his paintings are visible here: https://jotto.artstation.com/