Size for bubble-ring generation ship

Question

I've been thinking that the natural manner for interstellar dispersion of humanity with relatively hard science is with permanently habited nomadic generation ships. Instead of building a ship, going to a suitable system and abandoning the ship to colonize a planet model which comes with enough issues that it might be impractical, the generation ship in this model is the permanent home of its habitants.

Dispersion comes instead of the fact that it is both mobile and self-sufficient, so that it can move across interstellar space without any particular need for speed. A ship like this could use low thrust engines such as ion drives or, closer to stars, light sails. Since space has relatively low aerodynamic drag, a very low thrust would allow an orbit that is an expanding spiral that gradually leaves the system. So assuming that the generation ship is "permanent home" simplifies requirements a lot.

Even more so at the destination since it really causes no hardship if colonizing the planets is difficult or even impossible. The ship will simply restock its volatiles and materials needed for repairs and people will go on living in their home just as before.

To be self sustaining the ship would need to have redundant everything and capability to manufacture every component from raw materials gathered from asteroids, comets, or other micro-gravity objects. It would also need to be a fully self-contained ecosystem. And have the capability to rebuild the ecosystem if necessary.

Obviously such a ship would also have to be capable of building duplicates of itself. Indeed any reasonable planner would require demonstrated ability to self-replicate before risking interstellar space.

Thinking about a suitable solution for such a ship, I ended with a design similar to real life. A very large "bubble" with relatively thin skin and filled with water. The bubble would have all the space propulsion and navigation systems attached to it. Maybe "tugs" pulling the bubble with long cables? You want smaller spaceships for mining anyway, so dual purpose miner-tugs might be good.

Inside the bubble would be "rings"; large structures of the titular shape, each of which is a self-contained habitat with spin gravity. The "rings" would float freely in the water with perfectly ordinary water propulsion systems for moving around. The "rings" will each be fully self-sufficient with all the life support and manufacturing needed. But they could rely on other "rings" for redundancy and the "bubble" would take care of propulsion and protection from space hazards. So while each ring would have roughly the population and manufacturing capacity of a conventional generation ship they could be simpler and smaller.

When a ship self-replicates, they build a second "bubble" attached to their current one and move some of the "rings" to the new "bubble". They then move on and build new "rings" as required by population growth until the "bubble" starts becoming full and it is time to build a new "bubble".

Like I said this is similar to how life does it, so it should work fairly well. Such redundancy through self-replication should enable enough robustness to colonize even interstellar space, and thus eventually other systems, provided interstellar space has enough objects to support such nomadic ships. Which AFAIK we do not know one way or another.

Now to the actual questions:

How large should the "rings" be in both population and, approximately, physical size. Physical size only needs to be credible enough for verisimilitude since nobody actually knows how much space the needed life support and manufacturing capacity would take. We can't really build any yet after all. I am more concerned about ideas for optimal community size here.

**The optimal minimum and maximum numbers for "rings" in single "bubble". The minimum is the number needed to be robustly self-supporting, while the maximum must obviously be at least twice as much for self-replication to happen. But you probably would want some safety margin to allow population growth even when building a new "bubble" is impractical.

The size of the "bubble". This is obviously the physical size and mass of the "bubble" which would be pretty much the mass of the entire structure. Needs to fit the maximum number of "rings" and support enough photosynthetic algae to provide oxygen for the entire population. It will be much safer if it has an entire ecosystem up to fish since such diverse systems are more robust.

How much "skin" is needed to contain a bubble of water in space? The skin would get punctured by meteorites and radiation damage so it should be self-sealing and repairable. You can assume the outer layer is cold enough to be ice if that helps. What kind of pressure is necessary to maintain?

This is asking pretty much, but I am hoping for some useful ideas.

Answer 1

So to figure out size, you have to determine all the stuff that needs to go in it.

First, population.
On the low end, the minimum viable population could be around 180 people, and with the right breeding you could have enough diversity for 80 generations or 2000 years.
Other estimates say you wouldn't want less than 14,000 people, and as high as 44,000 people, because of disease, accidents, etc.

So lets say 10,000 people to start just to have a round number.
You need to feed them, so how much land do you need to feed one person?
Numbers I'm seeing say it takes about one acre to grow the food to raise a person. You might be able to get it lower with things like high capacity hydroponics, vat grown meat, raising fish in the bubble, etc, but you're going to want to have room for other things besides growing food.

How much of the ecology are you bringing along?
If you want to bring along plants and animals in different biomes for maximum diversity, then you'll need more land. If you are ok with bringing them along in another form, like printing out their DNA from stored patterns and growing them in artificial wombs, then you'd need less land.

Starting with the 10,000 acre number, which is a little less than 16 square miles (40km^2). Lets up that to 30 square miles for redundancy and room to grow.

You want it modular so that you can make more easily, or maybe even move them around, so lets say you make them from pods that have a square mile of space each. The pods are joined in groups of 10, like beads on a necklace, into rings with a 10 mile circumference. That's a diameter of a little over 3 miles.
At that size, you could have it spinning at only 0.43 rpms and still get 1g.

This would get you 3 rings, about a mile thick, and 3 miles across.
This gives you a pretty good idea of how large the bubble should be.

Next you have resources.
People need a lot of things that might not be available from asteroids and comets, and that would be lost over time by bonding with other elements, getting lost in the soil, etc. Some important elements might even bind to the metal of the inner hull. And once gone, there would be no way to get them back.
You could potentially make more using fusion, but if you discover that your great great great grandfather forgot to pack enough selenium 1000 years ago, making more is going to take almost magic level fusion technology.
Maybe if you happened to pack one of the reactors from SpaceChem, it would make things a lot better.

Salt buildup is going to be a headache too, but by using the water in your envelope you might be able to use it as a sink, so bringing salt water fish and desalinization equipment might be an option.

Society
So 500 years into a 2000 year voyage, and people who never saw Earth and who will never see the destination are starting to wonder what they're doing out there. They never asked to be on this voyage.
You might want to think about what to do about unrest and mutiny along the way.

Lastly is disease
Small things change a lot faster than us big things, especially in a closed environment. Your bacteria, fungus, viruses, and other things are going to be changing very fast, and so both you and your plants are going to be stewing in it. Having a strategy for wide spread crop failure because of a new blight is going to be important ahead of time. Same goes for human diseases.

Edit addressing comments:
First, disease. We kind of have a symbiotic relationship with bacteria, and if you sterilized us completely we'd die.
Plant's have a similar setup. Soil is a living thing, full of bacteria, small organisms, fungus and lots of other things. If you removed all that stuff, the plants wouldn't be able to grow.
You might be able to remove some of it, or create soil from scratch with only the stuff in it that you want, but even a little bit is enough to potentially cause issues down the line over centuries. It may be avoidable to some extent, with planning.

Society issues are a potential problem during times of hardship.
Not enough food, birth restrictions, leadership seems weak, something important breaks.
It may never be a problem, especially if it's the only think known, but any time you get a group that has more than one option, you'll have differences of opinion to deal with, which could lead to strife, which could lead to fighting...
It's worth at least planning for to some extent.

Resources... One of the parts with the question is that there is a chance that down the line there might be a split, where a second ship could be made. They could make all the parts for a new ship, but halving all the supplies on the ship would have to be planned very carefully. It would be one way to reduce population if it got to high and there was a world with enough resources to allow it.

It could be very low decks, or hydroponic stacks, or whatever. The gravity wouldn't be coming from mass like on a planet, since there is no way to get enough mass to make a difference. Instead you have a rings spinning to make centripetal force to simulate gravity. The larger the ring, the slower you can spin it and still get the gravity you want. A small ring needs to spin very fast, and the Coriolis effect can get pretty bad. Anything over 2 rpms could have adverse effects in the long term.
The further under 2 rpms, the easier it is on people, as a general rule.
The minimum size to keep at 1g and under 2 rpms is 223 meters in diameter.
If you want to play with different sized wheels, check this site out: http://www.artificial-gravity.com/sw/SpinCalc/

And really, all these are just ideas to consider.
If I missed anything, or misunderstood, let me know!

Edit 2: Further addressing
Disease
I get what you mean by sterilize now.
Yeah, you could sterilize a whole crop, though that would be slightly harder if you're growing in dirt as the disease could live there and infect the next crop. Maybe hydroponics so all the water can be stripped of nutrients and boiled. You could even have modular, self contained pods for them, keep things separated so if something does start you wouldn't lose the whole crop, just a pod.
BTW, this is what I mean about a hydroponics stack:

Also, prions are a disease that could develop spontaneously, as they are just misfolded proteins, which could happen from cosmic radiation.
There's no way to completely sterilize the ship when it's a set of biomes or while living things are on it. And destabilizing the micro-biome could be worse than leaving it be. Keeping things balanced might be a good goal.
Otherwise, yeah, start off as clean as possible and find ways to monitor things as you go along, in case something weird begins to develop.

Society
It probably would be more stable, especially with emphasis on having a mission.
So long as people don't lose sight of the vision.

Gravity
I understand what you meant now. Yes makes perfect sense.
If they are going somewhere to plant a colony, they might even want to match the local gravity so as to be used to it by the time they get there.
Also, you might be able to get rid of a ring by having an inner low g ring and an outer normal g ring on each torus. low g could be agriculture, manufacturing, etc.

Resources
So we're probably on the same page here...
So say each ring has the room and resources to support 5000 people.
You could have one bubble with 10000 and 2 rings, or two bubbles with 5000 and 1 ring each. If you split it up, and then after 100 years you decided to build a new ring in one of the bubbles, you'd have to find a planet or some other source of minerals to stock it.
That'll have to happen once in a while anyway, because no matter how closed the system is, there will be losses over time.
Vital minerals can bind to the walls of the ship as a kind of patina. You'd then have to recycle the panels to free those minerals.
It might not be a bad idea to have some kind of renewal plan in place; recycle each part of the ship over time, kind of like how our bodies replace every cell every 7 years (or something like that).

For an example of things that could go wrong on a generation ship, check out Aurora by Kim Stanley Robinson.
Not saying you should make that kind of story, but it might give you a couple ideas.

All the numbers just possible examples. You could go bigger or smaller easily enough.