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In this setting I'm brainstorming, a significant percentage of humans live not in planets or static habitats, but in massive ships that traverse the cosmos at ultrarelativistic speeds. As such, these ships must have everything required to sustain large permanent populations.

The design I'm thinking off is a series of rotating stanford toruses stacked on top of each other, like a pile of donuts, with the engines/propulsion at the bottom of the pile and the bridge at the top. Some of the toruses would be covered by high-density buildings like skyscrapers, while others would be fully dedicated to agriculture.

Assuming some ten toruses stacked on top of each other, what would be the maximum population these kind of ships could sustain? If that design doesn't work, what alternative designs could provide the highest population in a single ship?

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    $\begingroup$ Given that the Stanford Torus was apparently designed for 10,000 to 140,000 people, it's trivial to multiply by 10. So it's slightly unclear what you are asking - are you looking for whether there are limits on how far a Stanford Torus can be scaled up? (Hint: Can only be answered with current material technology knowledge, which has clearly been superseded if these ships are accelerating to relativistic speeds.) Might be better to pick the population size your story requires and see what the issues are rather than an open-ended question. $\endgroup$ Commented Jan 2, 2022 at 2:09
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    $\begingroup$ @BeyondDisbelief "H20 would rely on identifying ice from distant asteroids." Umm... what speed your starship moves relative to those asteroids? Because the "ice harvesting boat" will probably need to decelerate to capture the asteroid intact (as opposed to blow up itself and the asteroid) then accelerate back to catch with the main ship. As a mental exercise, imagine picking up a bottle from the side of a highway while driving a truck at 120km/h. $\endgroup$ Commented Jan 2, 2022 at 2:25
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    $\begingroup$ @BeyondDisbelief "I don't think thats an insurmountable problem?" Better check the benefit/cost balance, if you are using water constituents as ejection mass. One wouldn't want to discover that the cost of harvesting the water if greater than the amount of water that can be brought on board from the trip. $\endgroup$ Commented Jan 2, 2022 at 2:39
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    $\begingroup$ You're not stopping to mine if you're traveling at ultrarelativistic velocity. $\endgroup$ Commented Jan 2, 2022 at 2:59
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    $\begingroup$ @BeyondDisbelief at "ultrarelativistic speeds", it's...pretty bad, even without the rocket equation. Above 0.87c, your kinetic energy exceeds the energy equivalent of your rest mass, and that's not even particularly relativistic, with a Lorentz factor of only 2...it goes up steeply from there. In short, those "boats" will have to convert many times their final mass completely to energy in order to catch back up with the main ship. And applying that kind of energy in an "accelerator" without utterly destroying not only the boat but the atoms it's made of would be a neat trick... $\endgroup$ Commented Jan 2, 2022 at 3:19

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Having separate buildings in an inhabited torus is illogical. The inhabited torus should be a single vast building, unless you really want the image of separate buildings for some silly reason.

And food should not be grown in single level toruses. Instead the agricultural toruses should also be occupied by giant single buildings with many floors devoted to growing food using hydroponic or aeroponic methods. Or more likely the agricultural buildings would be vast machines to synthasize food from waste and other raw materials.

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