Colonizing the galaxy by slow boating reality check

Question

Humans like to explore and seem to have an almost instinctual need to expand. After spreading throughout the solar system and even into the Oort Cloud they decided that humanity should follow the robot probes out into the galaxy.

Without FTL, but having discovered a form of artificial gravity and having experience creating space habitats, they create a number of generation ships. These massive structures are initially given a population and crew of 30,000, with room to expand to 50,000, and each one has all the tools and manufacturing capabilities to make more generation ships and space habitats, along with the ability to terraform a planet.

Strapping on a few large meteors with ice, minerals and other things they may need in an emergency, these ships slowly make their way to the nearest solar system. Slow being a little less than half the speed of light, thanks to getting a very large boost as they start their journey.

Once there, they get to work making comfortable habitats for the now increased and cramped population using the resources of the system. They spend several decades there, creating a working system of habitats and making any repairs that are needed on the generation ships. After a century or two, the generation ships, possibly a few new ones as well, get crewed by people who want to travel and move onto the next solar system to do the same thing all over again. Eventually the fleet splits into two and each one does the same thing, eventually splitting again, and again and again.

If they find a planet that looks like it can be terraformed, a planet with no life, or only the most basic of bacteria which is wiped out, they get to work making the planet livable for the people who want to have a sky over their head. Any planet with multicellular life is carefully studied by probes, but left otherwise alone because the risk of contamination, allergies, etc, are too great for the ships, and terraforming them will destroy the ecosystem.

Is this a realistic way to colonize and explore the universe?

Answer 1

Slow being a little less than half the speed of light, thanks to getting a very large boost as they start their journey.

Slow down there!

literally.

At that speed it's not really a generation ship since you can get to many other stars within the original crews lifetime.

And there are hazards to going that fast.

Lets assume the ship is, say, 10X the mass of the worlds largest supertanker, that's very conservative for the numbers you talk about but it's a number to work with.

How do you slow down at all?

At 0.5 c that ship would have 7.197×10^25 joules of kinetic energy you'd need to get rid of if you want to slow down.

That's about 1800 times as much energy as the energy from entire worlds fossile fuel reserves. You need some kind of fuel and some plan for slowing down.

Hitting things in your path

If there's something the size and mass of a sugar cube in your path it hits the front of your ship with the energy of the nuclear bomb dropped on Hiroshima with all the energy pretty well focused to rip through any sane quantity of armor.

And that's not the only problem.

The atoms between the stars

using the figures for a cold neutral interstellar medium from wikipedia: 20—50 atoms/cm3

So let's go with 25 atoms/cm3

25000000 atoms per cubic meter.

Lets imagine the ship is a nice neat cylinder. We can treat the volume of space that the ship passes through as a cylinder with a cross section equal to that of the front of the ship.

Now lets look at how much it hits while traveling, say, 10 light years.

Treat it as a cylinder 10 light years long with the diameter of the ship, again, lets guesstimate that the ship has a radius of 100 meters.

This lets us estimate the total number of (almost all hydrogen) atoms in the path of the ship, lets assume they all hit and there's no shockwave effects:

946073047258080000000 π m^3 (cubic meters)

Multiply by 25000000 atoms per cubic meter.

mass of (946073047258080000000 * π *25000000 ) hydrogen atoms = 124.4 kilograms

so over the course of 10 light years it will impact with 124.4 kg kilograms of gas atoms. For simplicity I'm assuming all hydrogen.

Those atoms are hitting at .5c so the front of your ship (assuming it's a big round shield with radius 100m).

kinetic energy of 124.4 kilograms at .5c is 1.73×10^18 joules

I'm going to ignore time dilation because it's hard and I need to maintain my sanity.

so at .5 C it takes us 20 years to travel those 10 light years

So lets convert that into the energy of the gas hitting the front of the ship each hour.

1/24 (1/365 (1/20×1.73×10^18 J (joules))) = 9.8748×10^12 joules/h = 2.743 GW h (gigawatt hours) per hour

has to cope with 2.743 GW hours worth of energy hitting it every hour. It's like having a large nuclear power plant at the front of your ship producing heat. you have no way of getting rid of that much heat with your ship in a vacuum and it will be melting your heat shield.

So just slow down

It's really common for writers to throw around large fractions of light speed but without magitech shields there's massive practical problems with going that fast at all. At those speeds the fine mist of interstellar gas is enough to cook an astronaut to death just from being outside the ship unshielded and enough to destroy any shielding made of matter within a short time.

Since your ships are generation ships anyway you almost certainly want to slow your ships down to something sane like 0.05 C (or probably even lower if your crew want to continue to live)

At least then you have some chance of stopping and some chance of surviving if you hit some grains of sand in deep space.

EDIT:

Putting more ice or rock on the front of the ship does not help.

Lets imagine that we put a cylinder of solid ice 100 meters thick at the front of the ship as a shield.

it's an idea, I'll give you that, but lets work out how long it's likely to last at 0.5C ....

cylinder | radius 100 meters, height 100 meters = 3.14159×10^6 cubic meters

That's 3,141,590 cubic meters of ice, millions of cubic meters of ice.

Wolfram alpha gives a helpful table for this

Phase change energies for 3.14159×106 m3 of water from 25 °C:

 energy required to heat to boiling point | 9.85×10^11 kJ (kilojoules) 
 energy required to convert to vapor | 7.01×10^12 kJ (kilojoules) 
 energy required to heat to boiling point and convert to vapor | 8×10^12 kJ (kilojoules) 
 energy released from cooling to freezing point | 3.28×10^11 kJ (kilojoules) 
 energy released from converting to solid | 1.05×10^12 kJ (kilojoules) 
 energy released from cooling to freezing point and converting to solid | 1.38×10^12 kJ (kilojoules)

It's annoying that it calculates from 25 degrees C but the energy released from cooling and energy needed to heat can just be added together.

Practically speaking I'm being very very forgiving by assuming that the energy needed is the same as at sea level.

To melt that much ice we could need 1.05×10^15 J (joules)

To turn that much ice into steam we would need about 7.01×10^15 J (joules)

Unfortunately the front of our ship would be receiving 1.975×10^13 J (joules) every hour while traveling at 0.5 C from impacts with the fine mist of atoms in interstellar space.

From there's it's just a matter of multiplying.

it would shield you for a little while....

Within 5 days your 3 million cubic meters of ice has melted.

after 34 days your ice has all turned into steam.

But what if we use something stronger than ice!

Lets imagine that instead of 3 million cubic meters of ice we make that shield out of 3 million cubic meters of solid iron!

It takes 6.11×10^15 J to melt 3 million cubic meters of solid iron.

Within 26 days enough energy has hit the front of your ship to melt 3 million cubic meters of iron.

This is not exactly how long your shield will last, some energy will be radiated away, some will be lost to cooking your crew and iron may ablate in a less simplistic manner but it's a rough ballpark figure.

At 0.5 C shields are not enough. Asteroids traveling at 0.5 C would melt and turn into a gas in short order.

I cannot stress enough how poor natural intuition is when it comes to the rigors put on anything traveling at large fractions of the speed of light.

Answer 2

Is this a realistic way to colonize and explore the universe?

No.

Apart from problems with generational ships, which you'll find discussed on Worldbuilding SE in other questions, there is a fundamental flaw in the reasoning:

they get to work making the planet livable for the people who want to have a sky over their head

The people you have described have, for hundreds of generations, been a space-dwelling people. Planets may be interesting to you, but they're just grubby, messy places with restrictions like not having easy access to space (which is, in fact, home!) and gravity defined by something you can't change, whereas your ship-dwellers (presumably) have some form of pseudo-gravity but can also get to zero-gee (and maybe all points between) easily.

As they have and can manage resources without needing a planet, all they need rocks for is to build more homes (i.e. more ships). And they can get those rocks easily without bothering with dirt and bacteria-infested planets that they have to clean first.

Nope, they're going to expand all right, but they're going to do it in space.

Rocks? Who needs 'em. :-)

And if you have the tech to build generation ships like you describe, you have the tech to make them from (for example) asteroids. You have the tech to make a sky for yourself (and what a sky - something that's controlled and safe and familiar).

For you, the sky could well be that the world curves over your head in a giant cylinder. Actual sky as we know it would be unnerving - you've never seen it and for hundreds of generations no one has written a song with our version of the sky in it.

No, planets are, to a space dweller, completely pointless.

What would they do with planets?

Visit them.

Planets are nice places to park, maybe, giving you an interesting view and access to, well, nothing you don't already have in space for these guys. You can explore planets and maybe some people (the dedicated scientists or the crazy people) will want to stay down there for extended periods, but live there?!?!?!? No way!

And you've grown up used to the idea of living in a sealed, controlled environment with a stable population.

The biggest problem that ship will face is convincing anyone to get off!

Even if they reach a destination and need repairs, they'll find a way to do that from space, extracting materials from easier to access sources (small moons, asteroids, etc. ) and not by doing anything crazy like landing.

Every solar system is indeed an opportunity to expand, but you could do an awful lot of expansion in space without ever getting lumped on something as yucky as a planet.

These guys won't leave home and home is space.

The minority (and presumably there will be some weirdos like this) who want to live on a planet and become "pioneers" (imagine the derision that would be said with by people who travel anywhere they want in space!), might set up colonies, but these will be villages with bare essentials and just enough equipment to keep them going. You're not going to waste resources on these nutcases if you and your people have been thrifty and efficient space dwellers for a hundred generations.

Think about a hundred generations.

What were your ancestors doing and where and how did they live a hundred generations ago?

Do you know? Do you care? Would you consider their way of life anything you want now?

Your science (even in a generation ship) has advanced and it will be focused on the needs and desires of space dwellers. You won't even care about the intentions of the people who sent your ancient ancestors into space.

You're a space dweller. And proud of it!

No "Rock Clingers" on this ship. :-)

Answer 3

Is this a realistic way to colonize and explore the universe?

Sure it is, this is the same process used by Polynesians to colonise the Pacific Islands.

They had boats with everything they would need and would find a place, build. Then a few generations later when population pressure mounts they would split and some would go looking for another Island group.

Your idea is the same just scaled up.

Answer 4

Sure, everything seems fine.

Except ( and this is my Opinion )

If they find a planet that looks like it can be terraformed, a planet with no life, or only the most basic of bacteria which is wiped out, they get to work making the planet livable for the people who want to have a sky over their head.

Once you realize it will take hundreds of years, aboard a "generation" ship that is custom built to sustain the population for that time, you will realize that it's unlikely they would want to settle on a rock. Especially if they have to terraform it.

Often times the most efficient engines have very poor thrust to weight ratios. It's very possible to build an engine perfectly suited to travel in space that has no utility lifting weight out of a deep gravity well.

Given this, and the fact that they are now perfectly comfortable living in their "tin can" remember without FTL it's going to take dozens or hundreds of years to travel to even the closest stars. Even going to the nearest stars to earth will take (@0.5c) anywhere from 8-20 years depending on how fast you can accelerate.

After spending 20 years in a perfectly controlled environment why start over. There are no elements on a planet that are not more easily acquired in orbit (if all your infrastructure is in orbit). The only thing unique would be the life on that planet which may or may not be poisonous. Even if it's not, would you ruin the biosphere just to dig up metal you can get by the ton other places? At most you may want to observe and do research on this new life. See if it's compatible with your life, etc. This could take centuries and the risk ... well, you could introduce some virus or bacteria that wipes your whole population out.

In short, once you have generational ships, there is no reason to settle on a planet. In fact, it costs more energy to do so.

In more likelihood, they will set up an orbital habitat, with some production capability. Maybe drag an asteroid into orbit. And then send science teams down to the planet to research every so often.

Answer 5

In the early 1600's one hundred people settled in Jamestown. Those 100 people came form a population of 4 million UK subjects. If a colony ship has a population of 50,000, there are very poor odds that you would have enough people willing to start a colony on another planet.

But suppose the population of the Earth is eight billion people. Now you'd have a pool of 200,000 colonists. You select 50,000 of those people and put them on the generation ship in suspended animation. The generation ship is then crewed with 30,000 people to run and maintain the ship and watch over the sleeping colonists. This becomes a sleeper/seeder colony ship hybrid.

A potential dark twist on this idea is the Australia solution. If a person on the generation ship commits some terrible crime, instead of execution, that person is put into suspended animation, and dumped onto the colony world.

Note: My answer was based on the other answers where the colony ship takes decades to reach the next solar system.

Answer 6

Yes, except the part where you state

If they find a planet that looks like it can be terraformed, a planet with no life, or only the most basic of bacteria which is wiped out, they get to work making the planet livable for the people who want to have a sky over their head. Any planets with multicellular life is carefully studied by probes, but left otherwise alone because the risk of contamination, allergies, etc, are too great for the ships, and terraforming them will destroy the ecosystem.

Reasons:

1. Based on the reconstructed history of life on our planet, the stage which for you is OK to use is a small fraction of the total time where life is possible. This reduces the likelihood of ending on a planet, and people in cramped spaces get easily angry...

2. Based on the history of human colonization, efforts to preserve the hosting environment/populations arise centuries after the colonization has been made. Again, people in cramped spaces get easily angry, and anybody will have an hard time explaining 50000 people that they have to stay in their glass bubble surrounded by deep and hostile space a few more centuries for the sake of preserving the slimy pink mossy blob which covers that nice planet few hundreds kilometers away.

Answer 7

Is this a realistic way to colonize and explore the universe?

Yes

Considering the preconditions you have given, which basically say that you are not interested in technological problems at all, surely it is a realistic way!

It's your story. You have to find problems (like pointed out in many of the other answers, for example, "why would they want to live on a planet") and solve them for your version of humanity.

Solving those problems would be the point of interest of your novel.

E.g., the argument that people who have lived in space for 100 generations see no point to settle on a planet could be resolved this way: assume that the spaceship technology is barely fun enough to keep everyone from suiciding. No heroic extra-vehicular activities in race boats for fun; no action-packed alien missions, nothing of that sort. Just boringly slogging along. Maybe they don't regularly play with gravity, no "free fall sex" escapades or anything of that sort. Maybe there does not develop a sense of infinite freedom in space (which there is nothing of, for us, right now). They have no limitless space available to them personally, but just a clunky, degrading, half-lit, stale-air metal can in which they are constantly reminded of death on the other side of the wall.

Maybe, to make those generation ships work, they need very strict hierarchies/duties to keep them afloat at all; and part of the incentive to go down to the planet is that small, like-minded groups can go to vastly separated regions to do their own thing.

Maybe they bring along pictures/books/films of the earth which turn into some half-religious planet cult; being allowed to live on a planet could from the beginning be made out to be the highest climax of everyone's life.

Finally, think about how great of an adventure space is for us today; you can be pretty sure that lots of boys and girls fantasize of spending some time on even our limited versions of space travel/space stations. After 100 generations, maybe in your world, it is simply reversed - boys and girls are just bored to death by their spaceship and really looking forward to adventures on a planet.

And so on. Whatever reason anyone of us could think about to make it unlikely that your plan works, gives you a reason to make your story interesting.

Answer 8

Yes, it's realistic.

There are a few problems that many of the respondents have overlooked.

1. machines break.

These star ships might need to last thousands of years. Think of how worn down the pyramids are - these ships have to run for twice as long. Granted, there's no pesky atmosphere to deal with, but you've still got problems with lubrication, for example. After 5,000 years, your elevators might break down.

This would be no big deal in a community of billions, but even with sci-fi level fabrication and automation techniques, there will be some issues that cannot be fixed without a shipyard. If there's no ship yard, that means stopping and building one. Which leads us into the next problem:

2. 50,000 is not enough people for specialization of labor to work properly.

When they have to stop and fix something, they are going to have to check the wiki, and hope that the problem was something we anticipated 10,000 years ago. Even if every person on the ship works and studies, maybe they won't know how to fix the ship. Maybe they will have to build a new one. Could you build a new pyramid? What if you also had to build the crane you'd use to make the pyramid?

3. Dictator-ships.

Ships 'aint democracies. They have captains and strict rules - even cruise ships have big long lists of do's and don'ts. How long would you like to live on a cruise ship before you wanted off? What if you want 4 kids? Or what if you don't like the weird-ass religion that your ancestors made up on the journey? What if you've got some recessive gene that the captain has decided to purge?

To conclude: Only a tiny fraction of people ever get on colony ships, but when the time comes, they always get off.

Answer 9

The Journey In 2 Halves

We already have an 'artificial gravity' per your requirement, which also sets the time to arrival; acceleration at ~1g. For the first half of the journey you accelerate, then you turn it around and decelerate for the remainder. Per relativity, this will feel exactly like being in a 1g environment on a planet.

There is a neat derivation of the time to arrival via this mode for various destinations on this page, with the result that it would take no more than 30 years to get anywhere you have the data to bother exploring, even popping to the next galaxy.

Note that in the Earth frame it would take you a lot longer to get there, but time dilation being what it is, that doesn't matter to the skyfarer.

Generational attitudes, settlers and mariners

Some of the other answers assume people would prefer to stay in space, on the assumption they are there for many generations, and it's hard to get out of the gravity well and leave a planet if you land on it.

If it's just 1 generation then I suspect a large fraction of the population would be keen to start their life on the planet; these settlers would see the destination as their opportunity, mirroring those who journeyed to settle the Americas.

We generational mariners

But the gravity well is deep, so it would make sense for a number to remain on the ship in a wide orbit and pick a new location to head for. These mariners would never land, carrying on to the next planet. After a few generations there would be essentially some who had been on the ship for generations, had never wanted to settle on a planet. If they had a good stock of varied genetic material (e.g. a basic sperm bank) to maintain a decent gene pool, there is no real human limitation on this approach.

I would wonder, however, whether some such ships would stop bothering with planets. Perhaps there would be reverse-Moana figures who sought to revive the idea of settling when they discover the ship's origins.

Moon-miners

One reason not to just forever flit through the stars is the need for physical resources; reserves of water and minerals which can replenish the exploring ship. It would make sense to harvest some such resources at each system where a settler-division happens; either by sending the settlers down with a rocket which could return material, or more likely by mining smaller moons. This mining stage could easily take a number of years to construct the equipment, refine the material and return the extracts and equipment back to the ship. During this long goodbye, perhaps some of the mariners would change their mind and opt to settle.

Colonial control

A key part of the settlement of the Americas was the need to control the settlers; in this instance, the home planet would want to know the settlers weren't going to return to destroy them.

There is a tension here; on one hand the colony ship experiences less time than Earth; only decades could pass for them while centuries pass on Earth, so Earth can expect to have superior technology. But, this fact would make the settlers defensive; more people from Earth would likely arrive every few decades, bringing new technology, new diseases, new threats and new opportunities.

I think there is an argument for the possibility that the government licensing the explorers to leave Earth with such a ship would require that the settlers were compelled to plant some kind of doomsday device on their new planet to ensure their future cooperation, and obviate the need to impose an external threat.

The Overtakers

Consider a ship heading to its second destination planet; subjectively 50 years have passed, but from Earth's perspective several centuries have done. A more recent ship has overtaken the first, by not stopping at the first planet, and thus when the first ship arrives it finds the planet already settled by a century-old settlement.

Do they settle, but elsewhere on the planet? Or do they carry on to another planet where they could be even further behind?

Newer technologies would inevitably also permit later departures to arrive earlier; better g-suits, genomic adjustments, cryo, take your pick. What is the protocol? What are the rules, thousands of light-years into uncaring space?

The First Man For A Hundred Years

Earlier I mentioned an onboard sperm bank as an easy way to ensure a wide gene pool, which has an interesting side-effect: The more fertile men on board, the more the gene pool is narrowed (donor eggs would require a surrogate, so the men would most likely reproduce with the women on board). So the longer you plan to live in space, the fewer men you want on board on a purely pragmatic level. Potent men begin an immediate biological countdown.

This could easily lead in some instances to entirely female crews; where perhaps they have had to change destination a few times, and it is safer for the onboard society to just have female offspring for a while.

Eventually, perhaps, a boy would be born by accident or by design.

Alternatively, a larger male population could exist if the destination is assured but be required to leave on the landing raft, so that the onward exploration could continue unimpeded.

Dreamers

Some of the descendants of the settling ships would inevitably dream of the stars, of the people who continued on. With the passage of time some would build their own rockets and starships to follow the mariners, and with the joys of time dilation they could actually meet some of these historical figures, for whom proper time seeps only slowly into the margins of their existence.

Answer 10

There are a few realism flaws. First, 50% of the speed of light is insanely fast for a macroscopic object.

Second, taking only a few centuries to create new generation ships.

Slow them down to 1% or even 0.1% of the speed of light. Spend many 1000s of years expanding over a new system.

You'll still colonize the galaxy in the blink of a cosmic eye.

The current most practical form of interstellar colonization looks like star wisps -- ridiculously light von Neumann probes launched using a type-2 civilization's power output. Possibly coming to a stop using huge mirrors and lasers fired from the source system.

The huge investment and tiny payload (traveling at a very small fraction of c, as the interstellar medium is quite dense at fast speeds) then has to be able to replicate itself in the target system and industrialize it. It can carry data with it (uploaded consciousnesses possibly included, or entire biospheres of data) and when industrialization is well underway can deploy this data; or, if civilizations are sufficiently long-lived, it can build an antenna and get it beamed after the fact.

If it takes a probe 10 years to produce a duplicate and the probe weighs 2 grams, converting 0.01% of the solar system's mass into probes is 2E23 kg or E27 probes, which is 27/3*10 = 90 doublings, or just under 1 thousand years.

At that point, the system is going to be close to a type-2 civilization and would be capable of launching another star wisp at a small fraction of c.

It might also be able to catch a colony ship traveling at a small fraction of c.

A type 2 civilization has E26 watts of power. 1 year of output is E33 J.

At 1% C, kinetic energy is

$$E_k = mc^2(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}} -1)$$

$$E_k = mc^2(\frac{1}{\sqrt{1-0.01^2}} -1)$$

$$E_k = (.00005) mc^2$$

or 1 part in 20,000 of the mass-energy of the target.

This means we can speed up or stop 2E20 kg over a period of 1 year if we have 100% efficiency. Ceres is E21 kg.

So a type 2 civilization can launch something roughly the size of Ceres at 1% of the speed of light, and another type 2 civilization can stop it at the other side, assuming they can deliver the momentum over a distance of 1% of 1 light year.

5% of the speed of light makes this:

$$E_k = mc^2(\frac{1}{\sqrt{1-0.05^2}} -1)$$

$$E_k = (.00125) mc^2$$

30 times more energy for the same mass. It also makes the distance you have to project the energy 5 times further and hence 25 times harder (tyranny of inverse-square).

At 50% of the speed of light

$$E_k = mc^2(\frac{1}{\sqrt{1-0.5^2}} -1)$$

$$E_k = (.15) mc^2$$

120 times more energy than 5%, and 10 times further energy projection (which is 100 times harder).

---

The reason why the star wisp has to be as small as possible is that most of the mass you'll launch will be in the form of mirrors and lenses and light sails. You need to brake, which means you need momentum in the opposite direction. You shoot off lenses/and mirrors, then reflect light from your launch laser back onto the star wisp's light sail. These mirrors are pushed further out (and never stop), but you can get a tiny star wisp to stop with ridiculous energy expenditure over "short" interstellar distances.

Answer 11

getting a very large boost as they start their journey.

This is an issue. When travelling in space slowing down and speeding up are more or less the same problem. There is pretty much negligible friction to slow you down again. So if there is some special "boost" that it gets from its home system that put it over its maximum natural speed, how it going to stop?

It makes most sense to accelerate continuously for the first half of the journey, then decelerate for the second half.

Answer 12

Dr Bob Enzmann wrote extensively about this sort of thing. He is still around.look him up. Reasons for wanting off the ship: Vast open spaces. as Much population as you can handle. and the 2 word answer? Soylent Green!

Answer 13

Look at Larry Niven's Outsiders - they lived a little bit like this. There are technological issues as well as social issues with the whole concept, but most of them come from an extremely limited, anthropomorphic point of view. Just because humans, in our current state of development, could not maintain such a society, nor handle the technological challenges, does not make it an absolute impossibility. In fact, much good sci-fi comes from exactly that kind of projection. "IF" we were able to overcome such-and-such a technological or social obstacle, what would be the fallout?

Answer 14

You're real problem is between the statements "don't have FTL" and "do have artificial gravity." Real linear artificial gravity violates F=ma "equal and opposite reaction" and once you've done that, the speed of light changes from a speed limit to a curio. Chances are the next problem of getting all your energy back into a usable form when you hit The Big Red Stop Button (lever) will be solved too.

Answer 15

I would drop the notion that your technology includes artificial gravity (beyond spinning) and engines that can get you to half the speed of light. Which as many point out limits time for the generations and leads to the problem of hitting stuff.

I would assume that a spinning cylinder of a decent size with the interior designed to provide space, light and "nature" with the center axis being a source of light and "rain" and your vessel has decks below (outside of the inner space) that provide space for farming, then industrial tools, then storage and lastly the outermost deck would be flooded with water not only to protect the occupants from cosmic radiation, but also to make certain that the ship has enough water to make it across the vast expanse of interstellar space.

I would increase crew/passenger size to 100,000 with an expected expansion to 300,000. I would also consider that the on board time between stars is about the same as the remainder lifespan of a 20-something first generation person. 50 to 60 years seems reasonable thus you would have grandparents who remember green hills, blue skies and a horizon that bent down instead of up.

10% light speed tops makes a reasonable on board trip time. I'd go with something along ion engines, low thrust that continues for a very long time. Instead of turning the ship you would have thrusters that would point bow-ward at an angle, thus your deceleration time would need to be longer than your acceleration time. This way you can use both ice(s) plow/shield and a Bussard Ram Scoop collector to provide more fuel.

Ion thrusts are weak - 5.4 Newtons of thrust is the latest and most powerful ion engine. One can convert newtons to gravity... But I'm not doing it here. I can pretty much tell you that you would be pulling .01 g which would hardly be felt and the spinning craft would have a greater force on people than the continual thrust.

Your ship could get up to a decent velocity given lots of time, but a half the speed of light will bring way too many other technical questions to mind as previously explored.

300,000 colonist/terraformer/ship builders arriving in a stellar system is a good start. One could argue that the ship is feeling crowded by this time so passengers and crew would be hungry for more space. And humans are real good at making new humans so 20-40 years at this new star system, given enough space, humans could be at the half million mark plus.

They would need to stay in that system long enough to make enough humans to fill two ships... plus leave behind enough colonists to make a new world, make more ships - what ever direction they want. figure another three generations of time (say 60 years) and 1.5 kids per parent - magically the human population is at or slightly above one million. To give you an idea of how fast humans can make more humans, just look at population growth from 1900 (1 billion humans) to 2000 (7 billion humans).

So yes, your basic idea makes sense. Humans making more humans, the desire to find new fresh untouched worlds to explore. Perhaps groups of like minded people are off to make their own worlds by their own rules...

As for size. Rendezvous with Rama might be helpful. Not only with size, but with interior design to handle space travel.