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Humanity is in a late medieval stage, prior to the discovery of steam and combustion but quite knowledgable about metalwork . A country decides to build a large-ish city and 7 long chains leading to mountains, in the hope they may lift the city, a testament to their riches and people – and inevitable hubris, of course, as someone inevitably takes it down.

A few details:

  • There is a mountain range surrounding the valley the city is built in. The city has poured funding into huge half-kilometer chains reaching this distance.
  • The chains are not attached to the mountain-side; long holes (with spaces for housing and material transport) have been dug into the mountain side, with structural supports to ensure the chain isn't just attached to one place.
  • This design is replicated, albeit to a smaller extent, in the city, with about 50m between the hole the chain enters and where it's attached, again for redundancy.
  • The chains are literal chain-links, and can be of any thickness and material available to late-medieval society – neither cost nor scarcity are problems.
  • The chain-points in the mountains are of any height above 300m. Structural supports can be made in the mountains, but nothing can prop the city up from below.

Will it be possible to erect such a city on the valley floor and ultimately lift it, or is it an impossibility to lift something that large? How large, if at all, could such a city be before it is structurally unsafe?

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  • $\begingroup$ How much area does this city cover? How many buildings? How big is the average building? $\endgroup$ – Doug Warren Jul 31 '15 at 17:24
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    $\begingroup$ This is really a pure engineering question if I'm reading it right - is there an SE board for that? Might get better results there. $\endgroup$ – Dan Smolinske Jul 31 '15 at 17:26
  • $\begingroup$ @DougWarren That's part of the question – the largest size capable of being lifted. For simplicity's sake, I'd go with standard 2-storey buildings with a few below-'ground' and a rare few three- or four-storey buildings, all made of wood, stone or brick, whichever is easiest. $\endgroup$ – Mia yun Ruse Jul 31 '15 at 17:28
  • $\begingroup$ @DanSmolinske Aye, there is, but I'll wait an hour or so before reposting it there. Thanks for the heads-up – I'm not very good at placing my questions in the right places :p $\endgroup$ – Mia yun Ruse Jul 31 '15 at 17:31
  • $\begingroup$ Why not lift a foundation, and then build it. Or if you want a floating city, put it on a boat. $\endgroup$ – PyRulez Jul 31 '15 at 18:33
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No.

As the old adage goes, a chain is only as strong as its weakest link. It's clear that any single link in the chain must be able to support the entire force imparted from its portion of the city.

It'll be best to go with a studless chain, which reduces the weight per link at the cost of making the chain more difficult to handle. This is the largest one manufactured to date:

enter image description here

It was made to anchor the Schiehallion oil platform. It uses 14 of them to hold it in position. Note that this platform floats, it's not being held up by the chains, they just keep it from drifting.

That chain is rated for around 24,000 kN before breaking (for earth gravity that's about 2,447,318 kilograms. It has a mass of about 504 kilograms per meter. So the half a kilometer of chain alone would weigh 250,000 kg. If you hung the chain by the top link, that top link would experience 2,452 kN of force. It can support itself, so that's good. You have seven of them, so you have about 154,000 kN of force to divide among them if they are also supporting themselves.

The weight of the city would be hard to guess at, but looking at what we have left it's not going to be a very big one. 154,000 kN will be about 15 million kilograms in earth gravity. That might seem like a lot, but if you're using limestone or granite to build your city, you can only use about two olympic swimming pools worth, about 5300 cubic meters. Not a very impressive city. Not even a very impressive castle, of course, aside from the chains.

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    $\begingroup$ @AmiRuse Don't accept too quickly. I could have easily made an error in this calculation. $\endgroup$ – Samuel Jul 31 '15 at 19:03
  • $\begingroup$ A succinct answer with some hard numbers. Thank you very much – it's nice to know the limits of human technology sometimes! $\endgroup$ – Mia yun Ruse Jul 31 '15 at 19:06
  • $\begingroup$ I'm curious how many "regular" sized chains it would take to achieve the same effect as those seven. Could one just take the rating of one chain, subtract its own weight, and figure out how many it would take to have an excess of 154,000 kN? $\endgroup$ – DoubleDouble Jul 31 '15 at 19:45
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    $\begingroup$ @DoubleDouble Essentially. If you continue the process of making smaller and smaller links with more and more chains you will eventually something approaching steel wire. Which is the right direction for this kind of project, as that's how we build suspension bridges that can span just under 2 km. Lot's of redundancy and spreading of forces. $\endgroup$ – Samuel Jul 31 '15 at 20:31
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    $\begingroup$ @Samuel, you did make an error: you're assuming a vertical lift. For an angled load such as is needed to suspend a city between two mountains, the need to tension the chain reduces the load capacity further (IIRC, by the cosine of the angle). Once you factor that in, you'll be hard-pressed to levitate a small house. $\endgroup$ – Mark Jul 31 '15 at 23:23
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You would need chains quite a bit longer than half a km, or else you'd have to build in a valley even narrower than Yosemite (1.6 km wide on average, per Wikipedia).

Slightly better would be to use wire ropes: https://physics.stackexchange.com/questions/121233/which-is-stronger-wire-rope-or-chain as with suspension bridges - because that is effectivetly what you're proposing, a suspension bridge with buildings on it. Early 20th century technology can get you a bit over 1 km wide (e.g. Golden Gate Bridge at 1280 m), while some recent efforts span almost 2 km: https://en.wikipedia.org/wiki/List_of_longest_suspension_bridge_spans

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The scale for chains stretching half a kilometer while holding up a city would be a true wonder of even the modern world.

Medieval metallurgy would not even be capable making chains on that scale - probably looking at well into the 19th century for that kind of capability. Even with that kind of capacity, it is doubtful that wrought-iron would have the tensile strength to even hold its own weight suspended across half a kilometer.

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  • $\begingroup$ The Great Chain of Constantinople - used to block the harbor in times of war - was about 300 m long. However, it did not have to be terribly strong, as it was supported by floats. IIRC, it was made of wood. $\endgroup$ – jamesqf Aug 1 '15 at 1:27
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Looking at the geologic side of it, even with the strongest materials available today there would not be a chance of drilling such large and long tunnels into the mountain without self-collapsing due to the pressure of water and the weight of the sole rock.

Furthermore the surface rocks simply couldn't stand so much tension of an anchorage by many orders of magnitude. Also, even a small earthquake would amplify much more on a suspended structure and the anchorage points would produce such a huge increase in tension that even a stable structure in normal conditions couldn't stand the sudden increase of stress.

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Even if you could build it, living there might not be a good idea. The Tacoma Narrows Bridge collapse shows what happens when the wind gets under a suspended structure built before people understood that sort of thing. At best, it'd be like living on top of a jelly. At worst, the jelly would be living on top of you.

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