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I've been reading a few books lately, principally the Warhammer 40,000 descriptions of Earth and the Night's Dawn Trilogy, and it's got me wondering just how far down we could bury a planet under arcology type cities. I'm going to assume that artificial carbon allotropes are a viable and in fact widespread building material because we're already starting to be able to produce it with relative ease, and that our building techniques have progressed to nano-assembly.

Given that how far up can we build across the surface of the world?

Taking into account the compressive strength of bulk carbon in allotropic forms as a building material and the fact that there must be a basement level to take that compression somewhere at the bottom of everything and assuming that an unlimited supply of whatever raw materials we might need can be brought in. Economics are not an issue and with sufficiently shielded nano-assembly techniques depth is not an issues either, at least nothing short of 900km where natural diamonds are born.

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As high as mount Everest and more

Since buildings or skyscrappers are hollow the could climb even higher, the issue is that would need a base that strech as far as the mountain. I mean kilometers upon kilometers of base building to reach a stable building.

The limit is time itself, would you live in an apartment that takes 40 minutes only to comute to the exit of the buiding.

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    $\begingroup$ You would if you also worked, play, prayed, eat, and served in the same building. An Archology is a self-contained environment. $\endgroup$ – Andrew Neely Aug 22 '17 at 19:47
  • $\begingroup$ What Andrew said and you clearly don't understand the mechanics of mountain ranges, at all. $\endgroup$ – Ash Sep 5 '17 at 15:36
  • $\begingroup$ @Ash hahaha ok, sure. $\endgroup$ – Tridam Sep 5 '17 at 15:47
  • $\begingroup$ Sorry I come to this from an Earth Science background mountains are far more complex than people think they are. $\endgroup$ – Ash Sep 5 '17 at 15:53
  • $\begingroup$ Actually the most useful answer here, dammit I think I'm going to have to start over. Sorry that sounds way worse than it is intended to be it's a good simple answer with some thought behind it just without the science-y goodness I had hoped for when posing the question. I think I need to approach this from another direction altogether. $\endgroup$ – Ash Sep 5 '17 at 18:17
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So...yes diamond is hard. But it is a terrible building material.

Hardness is good for certain functions, tips for drill bits and saw blades being good examples.

Toughness on the other hand is the ability of a material to flex and not break, and on that scale diamond is not great.

This is why wood and steel make such great building materials. You can bend them 90 degrees and they will return to their previous shape (when properly prepared).

So given your pre-requisite that diamond be part of the solution I would say you are not going to get that far with diamond as a supporting material. Not sure what the height would be but its not going to be better than what we can do with steel today.

This article is a decent intro to differences in tough vs hard.

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  • $\begingroup$ Okay lets go away from diamond to bulk carbon allotropes and see where we can get to instead. $\endgroup$ – Ash Aug 22 '17 at 18:46
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You could, of course, go way out. I mean, WAY out.

As in space elevators.

Drop a cable down from a geostationary orbit, that is really, really strong.

Then attach modules to it, all the way up. The cable would be in tension, not compression. But it would take a very heavy counter-weight up in space.

Does this constitute a 'building'?

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A mechanical engineer could give you hard numbers, but here's an overview, ignoring what the building material is because that's just story construct. Call it Adamantium and a story will work as well.

(1) If your planet is wholly covered by buildings (e.g., Asmimov's world-city of Trantor), then the issue isn't as much about down toward the center of the planet, but circumfrentially around the perimiter of the planet. Think about an old fashioned Christmas ornament, one of the balls, nothing on the inside, glass(ish) on the outside. You can increase the thickness of the structure to the limits of the material itself and it won't impact the center. So (and here's the important part), so long as the entire world-city is designed properly from the "ground" up, the ground is basically irrelevant. How high can it go? That's an issue of the building materials themselves. If they'll allow it, outer space (which, from an engineering perspective, would require some better-than-average foundation tethering. Not to bear weight, but to keep the city spinning at the same rate as the planet. Or maybe the ramjets proposed by Larry Niven in "The Ringworld Engineers".).

(2) If your city isn't world-encompassing, then you need to worry about the ground the city is sitting on. If you assume (for the sake of argument) infinite material strength, then your buildings can only be as tall as the ground underneath can bear. Make the city heavy enough, and first the material under the city will be pushed aside, then the mantle it sits on will begin to subside (in other words, the city will sink). That's a serious limitation. A geologist might give you an idea of how much weight would be needed, but consider that the city of Venice, Italy is sinking. So it'll happen if you build large enough and high enough.

However it's worth pointing out that while the thought exercise is interesting, you're basically harvesting entire planets to obtain the building materials needed for this endeavor. It's like the idea of a Dyson sphere or the purported mega-structure in space. There may be perfectly rational energy reasons to build them... right up until you calculate the energy needed to actually gather and assemble the materials... and suddenly you understand no species in its right mind would ever build such a structure. No matter how efficient your engines, the cost will always be greater than the benefit. Especially when you realize the technology to do so presuposes interstellar travel and colonization. By the time you built it (or the city you're asking about) you would already have found easier and more cost-effective solutions to the problem.

But... it's fiction. Fiction is fun! Fiction lets you dream without the limitations of reality... which often results in the discovery that those limitations didn't actually exist.

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The question that this begs to be asked, of course, is 'Why do it?'

If you have the technology and money to build infinitely high from the earth, then why not start from scratch and build an infinitely large space station?

The advantages of such is that, building on earth, you have the problem of earth's mass creating a large gravitational pull with no contribution to 'inhabitable' area. If you start from scratch, the entire volume is inhabitable from the very center out, and all of the mass that results in a gravitational pull is structurally integrated into the design. Thus, stress is not directed all to the center, but is diffused throughout. This is the 'Christmas ornament' ball effect. The 'Death Star' in Starwars.

Of course, you can make the planet as big as you want, if it is one solid mass and not 'habitable' except for 'tunnels' throughout it. You just end up with a bigger planet.

If you use the 'Christmas bulb ornament' idea, why even encase the earth in the first place? Why not just encase a large volume of space?

What would the purpose of having an earth at the center be?

And, of course, there is the problem of materials. To build such a huge structure, one would need to use up the material in the earth to do so. That is, you would have to 'hollow out' the earth. This creates an interesting conundrum - gravity 'pulls' everything, not to the center, but to the center of gravity. If in building such a large construct, and you did so lopsidedly, you moved the center of gravity towards one side or the other. A person might actually be pulled 'up' from the center of what is now the earth, if the structure were really lop-sided. To ensure the center of the earth remained the center of gravity, the construction would have to be symmetrical.

And, of course, if the outer shell were rotated at a sufficient speed, the outer surface would attain escape velocity, and would 'pull' everything outwards, much like spinning a bucket of water around at a sufficient velocity causes it to pull the rope away from you (the concept of anchoring the other end of a space elevator). Thus, the structural design of the enclosure would be in tension, not compression.

But two more much more germane contributing arguments to the 'why?' question.

One is the effect that such a structure would have not just on the earth's rotation around itself, but of the earth's rotation around the sun, and the effect on the distance from the sun to the earth. Bringing in materials from off-planet means the total weight of the earth is increasing. That effects the total gravitational mass of the earth, and thus its rotational speed and velocity. With sufficient gravity, of course, the moon would eventually be pulled into the earth (if it were not completely consumed in the quest for construction materials).

Secondly, the velocity at the surface of a spinning ball increases for the same rotational speed, the further out you get. Eventually, with a large enough construction, either the earth would have to slow down in its rotation, or an object at the outer surface would be exceeding the escape velocity of the earth (the bucket-on-a-string example - at sufficient velocity of the bucket, if there is nothing holding the bucket to the earth, will 'escape' earth's gravity.

This, of course, begs another question be asked "How high up does a structure need to be built on earth, before the centrifugal force (speed) is sufficient to propel a standing human into space?'

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