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On some far-distant waterworld, the entire human race has been moved to vast city-ships that endlessly traverse the global ocean. Assuming an unlimited supply of fuel, how large could such a floating arcology possibly get while still being able to move itself, and what propulsion methods could it even use if it got to the size of an island?

Edit: So apparently so long as I can get the city to float, it can move under its own power, regardless of size. The planet in question is effectively an Earth clone, with stronger tidal forces (meaning a larger/closer moon) but no substantial difference in surface gravity or atmospheric pressure and composition. The ocean would have salinity roughly akin to that of Earth's oceans, and would thus be substantially shallower.

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    $\begingroup$ Hello Paranoid, thanks for asking your first question on Worldbuilding. I'd like to point out that so long as the technology exists to allow something to float, it can be moved. It might not move quickly or turn easily... but propulsion isn't the problem. Think about it this way. If you could make enough Gerald R. Ford aircraft carriers to set them side-by-side, linking them together, they'd all float and you could move the lot of them and even turn them. The real problems are (at least) two-fold. (a) the ocean moves/heaves at different rates in different locations (*continued*) $\endgroup$ – JBH Apr 21 at 6:03
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    $\begingroup$ ...that means your construction must either be honking rigid or permit a lot of flexibility, otherwise the "island" will rip itself apart from the unequal pressures. That's a material science problem. And (b) the ocean is not uniformly deep. That means that your size is intrinsically limited by wherever you can put the draft necessary to bear the weight of the construction. As you can see, propulsion isn't the issue. Or, at least, it isn't the first issue. $\endgroup$ – JBH Apr 21 at 6:06
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    $\begingroup$ Not a duplicate, but related worldbuilding.stackexchange.com/questions/147564/… $\endgroup$ – KerrAvon2055 Apr 21 at 6:10
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    $\begingroup$ @JBH The container ship that ran aground in the Suez Canal was much bigger than the Gerald L. Ford aircraft carrier. In fact, there are many ships bigger then this carrier, and more are being made every month. In point of fact, you could put the Gerald R. Ford on the deck of the Ever Given and still have room for cargo. $\endgroup$ – Justin Thyme the Second Apr 21 at 23:59
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    $\begingroup$ @JustinThymetheSecond That's true. I used the GRF only because it's a recognizable example. You could string fishing boats and so long as the cables used to hold them together were strong enough, they'd basically work (although "ships" that short would likely be flipped forward and over with wave/storm action). You did a better job of pointing out the "where in the ocean" problem than I did when you mentioned displacement. Thanks. $\endgroup$ – JBH Apr 22 at 16:39
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Near limitless

An arcology doesn't require to be physically linked objects. That means it can be a group or groups of ships, sometimes connected to each other. As each boat has their own propulsion, you're basically limited by the slowest in speed and turning, assuming no assistance is given. The size of free floating conglomerates of ships could be defined as limitless. You probably would hit some unexpected maximum at a certain point, like the propulsion would heat up the water significantly or individual transport between boats would become an impractical mess, but it would be at a huge size.

If you want it to be a connected whole it needs to have flexibility in mind. A piece of A4 paper is strong. A piece of paper identical to A4, except it covers a square kilometer would rip itself apart quite quickly with a stray wind. The larger the size, the higher relative stresses become. A more nautical example are boats themselves. When moored at a marina or against other boats there are no rigid fixings. The boats are allowed to move up, down and a bit sideways/font/back. Otherwise incremental damages would break the ship, and rigid supports would easily break.

On the ocean you'll have waves and wind aplenty, making it imperative to have flexible supports. These flexible supports would make each boat basically independent of the rest, but maximise the range they can float off. It is likely you can still make some transportation on these flexible supports (ziplines as an example). It would still be a good idea to be able to unfasten the ships from each other.

You would end up with a lot of boats. Again, with each of the boats having propulsion moving shouldn't be a problem. Turning however is mostly determined by the speed of the ships on the outside. They have to move much faster than boats in the middle, so turning ratio's are reduced. It would be more logical that the boats don't have a direction they would face and the propulsion would pick a different direction, or that each boat individually can turn on the spot. That way not the whole flotilla has to turn for a new direction.

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Just ask Santa

Photo of North Pole

Let's look at the largest floating objects in the real world for inspiration. Googling "largest floating object" turns up links to the Prelude FLNG. Yawn. Think BIGGER! Santa Clause operates an entire city on the North Pole (technically the arctic ice cap). That's a lot of land area for him to manufacture the world's toys. According to NOAA, "Unlike Antarctica, there’s no land at the North Pole. Instead it’s all ice that’s floating on top of the Arctic Ocean." So if you had the technology and if your world has a large enough ocean, you could build a ship of a similar size (5.5 million square miles).

If you want something that's easier for the captain to maneuver in your world's rough seas, you could model the size of your ship on Iceberg B-15 (shown below), which was much more mobile than the North Pole. Even though it's a lot smaller than the North Pole, you'd still have room for a city on the smaller ship. B-15 was about 4,000 square miles, compared the Manhattan, which packs 1.6 million people into 23 square miles.

Iceberg B-15

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    $\begingroup$ On a different world, you probably could move the Arctic ice cap around (issues of mechanical strength aside). On Earth, the problem is that it wouldn't fit between Greenland and Europe, and would certainly run aground when it hits Iceland. $\endgroup$ – jamesqf Apr 21 at 16:17
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    $\begingroup$ There were actually very serious studies in making ships out of ice. popularmechanics.com/science/a4101/4313387 $\endgroup$ – Justin Thyme the Second Apr 22 at 18:33
  • $\begingroup$ @JustinThymetheSecond whoa that's neat! $\endgroup$ – Andrew Brēza Apr 22 at 19:26
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    $\begingroup$ For further reading on the topic atlasobscura.com/articles/… $\endgroup$ – Justin Thyme the Second Apr 22 at 21:24

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