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Assume that the city is about 1-3 kilometers in diameter, built with relatively futuristic technology, and there are no plans to expand it further (If the need arises, they'll just build a second one).

What would better suit such a structure to be built from the engineering and resilience perspective - one large floating body, or a bunch of small interconnected but separated modules?

What I have in mind when I say "monolithic": A structure that looks more or less like a single object. It can have dampeners and soft links between parts if the city requires better flexibility of the structure, but visually it looks like one huge island-city thing, like Atlantis from SG:A: enter image description here

What I mean by modular: The city is more like a fleet of separate platforms that have some water between them, and are interconnected with bridges and anchors, like this: enter image description here

Especially considering the resistance to bad weather and storms. I have a hunch that a single large structure has the benefit of being just so huge and having great inertia, that any feasible waves short of a tsunami would be unable to affect it, so essentially it wouldn't rock at all even in storms, since even stormy sea's unevenness will be too small in scale compared to the city.

And if it turns out that a modular web of modules works better, what's the largest size you would want these modules to be?

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    $\begingroup$ Apart from the engineering perspective, a modular city is much more practical, as individual modules can be upgraded and changed to suit changing requirements and preferences. Think of any city in the world: there are constantly old buildings being refurbished or demolished, new ones being erected, changes to transportation, upgrades to utilities. No doubt this won't change in the future. $\endgroup$ – avid Dec 5 '20 at 23:10
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    $\begingroup$ Being able to fix your stuff isn't a modular design. Modular design is when the thing is made out of independent modules that can be easily swapped, added, removed and\or rearranged. $\endgroup$ – Darth Biomech Dec 6 '20 at 6:24
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Source: I've actually been employed to work on this very topic before.

Indeed if a floating structure is large compared to prevailing wavelengths it won't be rocked much by it, and there isn't much wave energy with wavelengths of many hundreds of meters. So rocking won't be your problem with a monolith of this size.

One problem with with a monolith is a not particularly intuitive one (that we usually don't think about because most of what we engineer is small compared to ocean wavelengths); wave reflection reaction forces. Objects that are big relative to a wave dont transmit, but reflect. The momentum imparted by a reflecting wave scales as the cube of the amplitude. For long wavelength high amplitude storm waves, the forces pushing you are really crazy, and no conceivable mooring system short of making this thing an island will keep it in place. Of course you could argue that's alright; have it be pushed around a bit by big storms, and have a form of dynamic positioning that keeps it where you want to be in the long term; but if this is to be a city where you'd want about 10x more space per person than a typical boat, and this thing is more than 10x less hydrodynamic than a typical boat (very generous), just staying in the same place against currents and winds is probably going to become quite an expensive affair. Putting it in a self-stabilizing location like an ocean gyre has been proposed; but there are many factors that dictate where you might want to place this, and this additional constraint isn't particularly welcome. Also if this gyre changes and your stability argument fails, there don't exist sufficient tugboats in the world to correct your error.

The simplest solution to all this: just go below the waves. Surface wave effects decay exponentially with depth. The static forces of going a few tens of meter below the water are an absolute walk in the park, compared to designing for the almost unbounded worse case scenarios on the surface. Also surface currents and obviously wind are much less of a concern here; though you will be displacing a lot more water per unit of usable volume, so the economics of dynamic positioning is still something you should keep an eye on. Also there are psychological issues; it just seems less appealing to live under water like that. You could imagine a system that sits on the surface most of the time when conditions are reasonable, but has the ability to flee under the waves when required though. Though the deck of a submarine typically also isn't that appealing of a hangout, so there are definitely open questions there.

If you want to be permanently on the surface, a loosely coupled fleet of elongated ship like shapes is a reasonable approach. They can orient their long dimension into the prevailing wave direction (typically there is such a thing; in cross-seas you are on your own w.r.t. comfort, but some geographies make them super rare) to get good stability most of the time, but are sufficiently hydrodynamic for dynamic positioning to be feasible. Probably you want a system of bridges/linkages between them; and maybe those could contribute some to stability in reasonable weather; but most likely you'd want to make that system retractable to prevent damage in worst case scenarios. If a single ship module was 1km long or so, it'd be so stable along the front/back axis that connecting them head to tail into multi-km structures would be relatively simple. (100-200m or so would be a very different story; that's right smack in the middle of the predominant wavelengths of big storms.) Longer structures have worse bending moments to contend with obviously; but that's a solvable engineering problem. If your ship gets longer, you need to make it higher to get good bending strength; and then also wider for roll stability reasons. So if the size of your module is say 1000x80x80 meters that's double the length and roughly 8x the volume of the largest ship ever built; big but not unthinkable, and still significantly modular compared to a totality of multiple square kilometers of area.

As alluded to above: linking floating objects together on the open ocean to withstand storm forces is an unsolved problem. Again, the maximum forces involved are insane. Even welding two halves of a boat together so it doesn't break in half in a storm isn't easy, so you can imagine how it is when you try and make it more complicated. Such linkages both need the range of motion to allow a multi-tens-of-meter wave to pass, and the ability to transmit insane forces. I am not saying impossible mind you, but how to actually engineer that system is to my knowledge an unsolved problem. Probably something involving huge hydraulic cylinders, with a very long stroke, but also the ability to output insane forces, would be required. I've never gotten deep enough into the details to figure out if its really feasible. If we are talking about a linkage this beefy, making it easily detachable sounds like a challenge if not impossible, so you really need to engineer it for worst case conditions.

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    $\begingroup$ Given your suggestion of going below the waves, would it be feasible to build a bulky foundation underwater, and then build raised platforms above the water line, so that the poles of those platforms are smaller than if the foundations themselves had been at surface level and thus less susceptible to the wave pushing? Would that negate a lot of the wave pushing while keeping your people above water? $\endgroup$ – Flater Dec 7 '20 at 10:55
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    $\begingroup$ What about an iceberg-like system where a good portion of the city is submerged while the rest is on the surface? Would that provide stability? (and "peace of mind" ;) ) How deep would the submerged part be? Actually several of the suggestions below seem to follow that approach. $\endgroup$ – stux Dec 7 '20 at 10:59
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    $\begingroup$ So, basically what you're saying is that Rapture is a good idea? $\endgroup$ – MBak Dec 7 '20 at 11:08
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    $\begingroup$ @Flater Sooo, connecting together floating oil rigs? (because - and I'm very far from an expert - that's exactly what this idea is :)) $\endgroup$ – mishan Dec 7 '20 at 11:23
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    $\begingroup$ @mishan: I assume oil rigs are still anchored to the sea bed, not sure if that's a requirement for this setup to work or if floating is still an option if you get the buoyancy right. $\endgroup$ – Flater Dec 7 '20 at 11:41
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The problem will be one of flexing forces which will only get bigger as the structure grows in size. Ultimately it would probably be better all round to have much smaller sized structures to counteract this.

One way partially around this would be to have some form of articulated linkage within the structure to help relieve stresses that would otherwise build up. For example see here at 4:24 mins: https://www.youtube.com/watch?v=J7xkdL0EdOA

This type of construction (and other variations on this theme) would enable much larger structures to be built. However I suggest that 1-3km might be too much even for this type of structure and it would be better to use this technology to build multiple medium sized structures possibly linked by universal couplings to allow relative motion as well as passenger travel between them.

edit: A lot of questions arise when you get more into the details. How important is it to be monolithic? How much money are you prepared to throw at it? How long does it need to last for? How much regular maintenance is acceptable? How much risk of destruction or damage is acceptable? How long is available to build it? Where does it need to be built?

Assuming it has to be monolithic and there are no constraints other than those imposed by nature, a very large structure such as you describe might be buildable. However it would be beyond the scope of existing structures so might encounter unexpected engineering challenges.

Versabouy has deliberately focused on “small” installations that are capable of being built in fabrication yards that can deal with 4000-5000 ton structures in order to appeal to a wider customer base. But some larger construction yards can deal with structures ten times this size or more.

Given sufficient time and money I’m reasonably confident that a versabouy like structure could be scaled up significantly perhaps 4-10 times. In addition I suspect that meter for meter a city might require less load than an oil platform, so fewer versabouys would be needed. But even with versabouys the platform is unlikely to be able to be safely extended to far beyond the 100-200m a side as a monolithic platform (versabouy currently supports a deck size of 250 x 500 feet with eight bouys.

This is because small differences in height will magnify across the deck causing tremendous stresses and strains. So some form of flexibility would still be needed. An additional layer of adjustment with sensors, couplings and pistons connecting to an upper deck might help but at huge additional complexity.

See also http://www.vbuoy.com/About_Versabuoy/whitepaper.html

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  • $\begingroup$ A very insightful video, thanks! So what would be a good size for such a platform? Around 400-600 meters? $\endgroup$ – Darth Biomech Dec 5 '20 at 16:22
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    $\begingroup$ 400-600m might be possible, but it is beyond known engineering at least as far as I am aware. It would probably need an additional layer of dynamically adjustable pistons, universal connectors and sensors to keep to top surface more or less flat and even. So lots of separate versabouy decks connected to a much larger over deck above by a lot of continuously adjusting supports (feasible perhaps, but practical who knows - check my answer I have added some additional information for your consideration). $\endgroup$ – Slarty Dec 5 '20 at 18:02
  • $\begingroup$ Ok, to answer questions 2/2: How much risk of destruction or damage is acceptable? As little as humanely possible. How long is available to build it? This part I will probably handwave away, since it needs to be done or nearly done in under 10 years and I understand that this isn't possible to build a high-tech city in just a decade. Where does it need to be built? ~in the ocean, duh~ on Earth, somewhere in the Atlantic; but part of the handwaving of speed is that originally the project was designed for oceanic planets in mind. $\endgroup$ – Darth Biomech Dec 5 '20 at 18:28
  • $\begingroup$ Ok, to answer questions 1/2: How important is it to be monolithic? It's desirable, since then it's easier to get it all in one frame (it's for a comic), but ultimately several platforms would be fine too. How much money are you prepared to throw at it? Not important for a story, so however is both needed and ends up being a non-absurd amount How long does it need to last for? In idea - several decades How much regular maintenance is acceptable? All of it? $\endgroup$ – Darth Biomech Dec 5 '20 at 18:40
  • $\begingroup$ I suggest that to keep the costs from spiraling into the absurd that you go with standard versabouy. It will still cost a huge amount I’m guessing it would probably end up as many tens of billions is that too absurd? If it's for a comic I would have thought that should work up fine and be well good enough to suspend disbelief. Especially as I see there have actually been plans for using such a system as an artificial island $\endgroup$ – Slarty Dec 5 '20 at 21:12
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A ring of 1-3km is pretty big. In any case, there is no such thing as a 1km long solid structure. Even if you, somehow, forge a 1km long "solid" iron boat, it will still bend like hell and eventually break apart. And I highly doubt you want to create the base for your city that way.

So since a large structure will act like it is made of smaller components anyways, you might as well build it that way. Not only does this greatly increase the amount of force the city can sustain, but it is also not stupid to do.

Look at modern ships, they are build to bend and follow the flow of water. At least to a certain extent. It is really not smart to build something with the intention of resisting every force. With this mindset, no skyscraper would be above 200 meters or so.

The same goes for your city. No matter how big it is, you only increase the area in which forces can act. So in a sense, the bigger you build it, the faster it will fail.

Thus the goal should be to build a city that deforms and doesn't resist the flow to a certain extent. This can easily be achieved by building the city with lots of small Interconnected platforms.

For your edit: The size of the tiles depends on what you want. I would guess that a hexagon-like shape would work pretty well with a radius of 100 Meters or so. Remember, the goal is not that the tiles start to deform. They should stay in their shape for the most part. So smaller is better.

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  • $\begingroup$ It seems that offshore oil platforms can be roughly 120 meters by 80 meters. But they sway, making connections a problem $\endgroup$ – Owen Reynolds Dec 5 '20 at 22:45
  • $\begingroup$ Ships are not build with significant flex. They are built with sufficient bending strength and stiffness to withstand worse case hogging and sagging moments. $\endgroup$ – Eelco Hoogendoorn Dec 6 '20 at 9:27
  • $\begingroup$ @OwenReynolds: Oil platforms are very tall (relative to being wide). Unless OP were building kilometer-high buildings, you wouldn't get that same sway. Also note that most connections for large infrastructure are not fully rigid to begin with, because you need to account for thermal expansion. Accounting for sway is the same, albeit a bit bigger. $\endgroup$ – Flater Dec 7 '20 at 11:42
  • $\begingroup$ @OwenReynolds A better analog might be an aircraft carrier, which are around 300 meters in length. They are often described as "floating cities". They are a combination of both models, of course, since every carrier has an escort fleet of smaller ships, which, while not directly connected, do frequently exchange personnel and equipment via boats and helicopters. One could imagine a civilian equivalent with some minor adjustments... $\endgroup$ – Darrel Hoffman Dec 7 '20 at 15:33
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Consider a typical offshore oil & gas rig. The amount of structure that is above the waterline may look unweildy and awkward, but it is kept very stable by the supporting section beneath the surface which is typically ballasted with concrete and maybe some additional saltwater ballast tanks. It's also usually anchored in place by long subsea steel cables to maintain position over a wellhead.

Offshore Oil Platform

I see this as a good starting point for a permanent offshore habitation. You'll need a desaliation plant for instance to make more freshwater and those ballast tanks could store potable water instead of seawater. You might have one auxilliary rig who'se entire purpose in fact is to process potable water and pump it via subsea pipelines to the main city module. Other auxiliary structures might include oil/ natural gas extraction, refinery and power generation. A typical offshore oil field can include lots of wellheads connected by subsea data / power cables and pipelines to one or several terminals. They don't have to physically touch each other to move materials back and forth.

offshore oil field diagram

So I think your city is doable. Either way, it's going to take a lot of divers, ROVs, helicopters, subsea cranes, boats and mainland support to keep this engineering marvel running.

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  • $\begingroup$ One major focus in the other answers is how unpredictably strong a wave might come. Your scenery appears to take place in calm water, where the water is shallow enough people to construct at the very bottom. $\endgroup$ – user80961 Dec 6 '20 at 15:10
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    $\begingroup$ Offshore oil rigs can typically handle rough seas and storms, but are they stable enough to be connected? A fleet of unconnected ones may be feasible, as long as there is enough distance between them where they don't crash into one another during storms. $\endgroup$ – Scott M. Stolz Dec 6 '20 at 18:24
  • $\begingroup$ It takes hurricane sea states to turn one of those rigs over. I would guess this is a sea-state 6 or 7 at least, cut to 1:30 to see how they handle. youtube.com/watch?v=tWbkcOcwoM0&ab_channel=TOXICPORTAL $\endgroup$ – Adam Coville Dec 7 '20 at 8:02
  • $\begingroup$ But as far as physically connecting them, above water? No I wouldn't want to do that. If you're going to have one huge one, it should be its own fixed structure with its own boom supports. You can save space though by offloading utility functions to other platforms further away connected by pipelining. $\endgroup$ – Adam Coville Dec 7 '20 at 8:04
  • $\begingroup$ @user80961: Oil rigs need to stay in place because they're supposed to stay above the oil deposit. Floating cities have no such constraint. The premise of a floating city inherently implies the ability to work out the buoyancy. Note also that the size of the wave required to cause notable issues grows as the installation itself grows, and the proposed city is significantly larger than an oil rig. $\endgroup$ – Flater Dec 7 '20 at 11:47
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This is possible if in the future people will discover a source of pretty much unlimited metal, namely iron.

A ship-like design that has like a hundred meters of solid iron as the city's base.

Here is an unrealistic scene that works perfectly in fiction stories:

enter image description here

I made an animation as give you a better insight at this future floating city:

enter image description here

I had to scale the gif way down, as the maximum size is 2MB. The link above provides the large animation.

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  • $\begingroup$ Damn, dude. That's fun. But I would hate to see what happens when a tsunami piles up against one of those walls... $\endgroup$ – Joanna Marietti Dec 6 '20 at 18:41
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    $\begingroup$ Solid iron in vicinity to sea water has the tendency to turn into quite less solid iron oxide... $\endgroup$ – mlk Dec 6 '20 at 19:35
  • $\begingroup$ thermal expansion will rip those wall apart fairly quickly. $\endgroup$ – John Dec 7 '20 at 2:24
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Monolithic and submersible.

Your floating city can be enclosed and duck beneath the waves, riding out bad weather at safe depth. It is self propelled and can move from place to place to provide the expertise of its residents and capabilities of its infrastructure to local populations.

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  • $\begingroup$ People will run out of oxygen that way. $\endgroup$ – user80961 Dec 6 '20 at 1:28
  • $\begingroup$ @user80961 Unless you have an internal biodome or another method that produces or stores oxygen for use. Also, even in a storm, you might be able to have part of it stick out of the water, at least enough to exchange air. They have figured out systems for space ships and submarines, so it is possible, although being this big, there certainly would be more engineering challenges. $\endgroup$ – Scott M. Stolz Dec 6 '20 at 18:20
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Modular is safer, a factory fire or explosion could sink your monolith.

The largest off-shore construction to date is the Prelude FLNG at 488 metres (1,601 ft) long and 74 metres (243 ft) wide, while the longest self-propelled vessel would be Knock Nevis oil tanker at 458m. There are aircraft carriers and passenger ships over 300m long.

So modules of say 500x100m should be quite feasible with only slightly better than current tech. That's more than big enough for a suburban housing block, sports or recreational complex, manufacturing plant, shopping mall, park, vegetable farm or orchard.

You would only need 60 modules to match your 1×3km monolith for surface area.

You could connect them using retractable bridges or tubes or just use boats (think Venice but with more waves).

You could even construct a circular reef say 1km out to act as breakwater, with gaps for your ocean-going vessels to get in and out

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See Savage's book "The Millennial Project" The first stage of this is "Aquarius"

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

https://tmp2.fandom.com/wiki/Aquarius

In a nutshell: Large floating cities, powered by the temperature difference between tropical and abyssal water.

Cities are fairly large -- about 10 km across, but a large outer fringe are hexagons several hundred meters each that act as 'farm land' and as energy absorption. Abyssal water is high in nutrients. It's discharged into the hexagons for fish farming. Other pads are black and act as solar energy aborbers to increase the temperature differential of the OTEC systems.

Ponds raise fish, shellfish.

Waste water is released creating a plume of plankton growth that fosters a local wild fish population.

Under side if hexagons are set up as artificial fish habitat.

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