Building a Generation Ship: The SFV Exodus

[Strato Incendus]

Alright, time to get started on what I joined this forum for a few days ago: Checking the plausibility of the worldbuilding for my story about a generation ship. Specifically, one with falling birth rates - on its slide into totalitarianism as a result. ;)
The main character is a 24-year-old pharmacist, responsible for, among others, the contraceptives on board. So she is right at the centre of the conflict when the commander starts infringing on people's individual freedoms to guarantee the survival of the species as a whole.
Eventually, the crew faces a similarly grim choice as in "The 100", namely "Survival - at what cost?" Is the survival of the human species (not even so much of individual human beings, since some of them are sent on dangerous missions and thus "sacrificed" for the "greater good") worth sacrificing even the most personal freedoms? Or are those freedoms worth so much that the crew would choose to preserve them, even if it comes at the risk of going extinct?

So much for the premise. As I just said, I am mainly here to test the plausibility of the world building. Naturally, 90% of this is restricted to the generation ship itself. But some of it extends to what happens back in the Sol system, as well as on the planet that is the ship's target destination.

For quick overview, I start out with some stats:

Ship Name: SFV Exodus (Solar Federation Vessel)
Target destination: Teegarden b (12.5 light years from Earth, renamed "Demeter" within story)
Speed: 10% light speed
by constant acceleration, making for a 125-year-long journey (at least according to plan)
Launch: 1st January 2375 --> expected arrival: 2500
Shape: elongated and thin like a pencil, with five rings for artificial gravity rotating around a "central pipe"
Crew size: 500 - 1,000 people
Rings, from front to back:
- public ring
- lab ring
- habitat ring
- factory ring
- farming ring
The crew starts out with 500 people, i.e., 250 couples. Since there are a little less than 200 nations on Earth right now, and the project founders literally wanted to get "all of humanity on board" with this endeavour, they selected at least one couple from every nation on Earth (both for cultural and genetic reasons). And then, a few countries could send several couples to get to 500.
500 people is a number I have seen reported repeatedly to avoid inbreeding on generation ships. The lowest number I found that might still work is 98 people (=49 couples), but that seems beyond optimistic to me.
Assuming those 500 founding crew members all have two children each to keep the population stable (at least Generation Zero are all volunteers), once those children are born, the crew size quickly jumps to 1,000, and should stay roughly in that ball park.

When it comes to the length of the ship, this is dependent on the required distance between the rings - assuming I would want to work with those five rings, rather than a continuous cylinder. I find the rings an easier structure to work with in terms of having dedicated sections for different purposes, easy to understand for the reader. Also, the rings show more clearly "hey, I have though about artificial gravity via rotation" than one long continuous cylinder. The cylinder structure in turn would look "smoother" from the outside.
Either way, I need a within-story explanation for the choice of rings vs. cylinder. Currently, this is just about the mass that needs to be propelled:

The ring diameter seems to be pretty much a given: Everywhere I checked, I keep coming back to a minimum radius of 225 metres being required to simulate Earth-like gravity (without having the ring rotate so fast that it would cause nausea among the crew members). So that is a diameter of at least 450 metres. As far as I could tell, though, a slightly larger diameter would not necessarily be a problem.
So I just made it a little easier for myself here and rounded the inner diameter of the rings up to 500 metres.

If I were to use a cylinder structure, that would mean the inner diameter of the cylinder would be 500 metres, with an according amount of mass required for the hull. By reducing the cylinder to five separate rings, rotating around a much thinner central axis, I should consequently save a lot of mass - not just in terms of production costs, but also in terms of all the matter that needs to be accelerated to 10% light speed.
But depending on what distance I might need between the rings, a cylinder might still be more mass-efficient if the ship ends up shorter overall as a result.
The study by Marine et al. (2019) examining some possible measurements of a potential generation ship suggests a cylinder structure with a length of 320 metres. Meanwhile, if I put the same distance in between every two rings as the inner diameter of a ring (500 metres every time), factoring in that I still need a cockpit / bridge section at the front and some exhaust pipes, I could see the Exodus be as long as some Star Destroyers in Star Wars (up to 3 kilometres; SW has both shorter and much longer ones).
Before I go further into the details and write a wall of text (because I have a habit of doing so ^^), here are my two most crucial questions right now, for which I cannot seem to find an answer anywhere - despite how frequent depictions of spaceships with rotating rings have become in recent years, as more and more people became aware of this necessity:

1) On a ship with several rings, how far would these have to be apart from each other (if they all rotate around the same central axis)? Because that is going to determine the minimum length of the "pencil"-shaped ship.
2) How thick should the central axis be (called the "central pipe" in my setting) around which the rings are rotating?

The answers ro these two questions will inform how much space I have on the ship overall, and thereby influence most of the secondary decisions.

As far as my layman understanding of this form of artificial gravity goes, there should never be any gravity inside this central pipe.
Which is why, close to the climax of the story, I have some people battle in the central pipe, flying around freely while shooting their weapons.
This is only one of several instances where it is vital to determine how much space they have in that central section, both in terms of length and diameter. So that I know how much I can have the characters move around during the fight.

(Of course, damaging the ship hull with weapons from the inside would be a pretty terrible idea, which is why I came up with a gun that only affects organic matter while leaving inorganic matter unharmed. Thinking back, I probably got this from one of the episodes of the animated Spider-Man series from the 1990s: There they developed a laser which can be set up in such a way that it conversely leaves organic matter unharmed, while only damaging inorganic matter - like a metal wall. Or Dr. Octopus's tentacles.)Finally, the speed of the ship, and the travel duration, could still be varied a little. The main character's generation is number five, but her parents are Generation Three. (Much like baby boomers are the parents of millennials, but there's still Gen X in between.)

In part two, however, I need to find a way to get this colossal ship up to (=close to) light speed.
So that in part III of the trilogy, the characters who arrive at the planet are still those you came to care about in part I - not their distant offspring the reader has no emotional connection to. :)

More about the choice of target destinations next time - as well as about the reason why the Exodus left Earth in the first place... ;)

 

[jedishrfu]

You should investigate the Rama books by Arthur C Clarke, the RingWorld books by Larry Niven, or the Dyson sphere design for good dimensions for your generation ship.

https://en.wikipedia.org/wiki/Rendezvous_with_Rama

The resulting images reveal that Rama is a perfect cylinder, 20 kilometres (12 mi) in diameter and 50 kilometres (31 mi) long, and almost completely featureless, making this humankind's first encounter with an alien spacecraft .

 

[Rive]

Kim Stanley Robinson: Aurora is also a good reference (well, up to ~ half of the book). However, this one may be a party killer since the ship there is quite like the one described here.

once those children are born, the crew size quickly jumps to 1,000, and should stay roughly in that ball park.

That won't do. Assuming a 70 years life expectancy you will get at least three generations parallel, not just two. The crew size will be lot (!) larger.

Rings, from front to back:

Mixed (and: redundant) functionality would make more sense. So, in case something happens with one ring you wont' lose all lab capacity, for example.

As far as my layman understanding of this form of artificial gravity goes, there should never be any gravity inside this central pipe.

That's true, as long as there is no propulsion. But in acceleration/deceleration phase that 'pipe' will bear the forces required to accelerate all the rings. It has to be quite sturdy.

 

[Filip Larsen]

Shape: elongated and thin like a pencil, with five rings for artificial gravity rotating around a "central pipe"

Let me address that a bit.

Free rotation of pencil-shaped mass distributions (i.e. rotation around the minor axis of the principle of moment) are rotationally unstable. Without any active control (e.g. ejection of reaction mass) and giving enough time the structure will end up tumble end-over-end instead. If you want to cater for this fact in your world building you either need to use some active control (doesn't sound feasible on a generation ship), or design the ship so it does not have a pencil-shaped mass distribution.

As an example consider a hollow cylinder of length $h$ with the bulk of its near-constant density mass between radii $r_1$ and $r_2$ rotating along its symmetry axis (an O'Niell cylinder), then for the rotation to be stable you have to have $h^2 < 3(r_1^2+r_2^2)$. This sets a limit on how long the "pencil" can be.

Later: Since you are aiming for a set of rings it may very well be such a structure can be made much longer (at least geometrically) than a cylinder without getting unstable rotation, assuming a rigid coupling between the rings. If the couplings are only semi-rigid I am not sure if this in itself extend or reduce the critical length of the structure before it becomes unstable. My intuition is fairly sure that if the length of such a structure is above the critical length, then the being semi-rigid means more rotational energy sinks will be present thus speeding up the departure from pure rotation.

Assuming rigid couplings it could be a fun exercise to try calculate the critical length of a stack of rings.

 

[Ibix]

Speed: 10% light speed
by constant acceleration, making for a 125-year-long journey (at least according to plan)

That doesn't sound like constant acceleration. That sounds like a short burst of high acceleration at both ends and constant speed in between. Also bear in mind that at 0.1c a one milligram rock strikes like 100kg of TNT. A 100g rock is a getting into Hiroshima bomb ranges. There aren't many such floating around, but even one is fatal and you'll never detect something so small early enough to evade. You need some kind of deflector or other handwave.

 

[256bits]

Free rotation of pencil-shaped mass distributions (i.e. rotation around the minor axis of the principle of moment) are rotationally unstable. Without any active control (e.g. ejection of reaction mass) and giving enough time the structure will end up tumble end-over-end instead

Might be why some are 'revolting'. The thing flipped end to end which caused confusion and temporary chaos and discussions on what to do next. Some think conspiracy, sabotage of the missions, ensuing trust issues with the leaders and there you have it. Tyranny and insurrection. Just due to a minor calculation not being done prior.

 

[Strato Incendus]

Great, thanks a lot for your fast and many replies! :)

The resulting images reveal that Rama is a perfect cylinder, 20 kilometres (12 mi) in diameter and 50 kilometres (31 mi) long, and almost completely featureless, making this humankind's first encounter with an alien spacecraft .

Okay, that seems huge - especially compared to the measurements suggested in the study by Marine et al. (2019), which was a mere 320 metres.
While it is of course always helpful to be aware of what other authors have done, at least in the fantasy genre, I have been observing a trend of many authors taking their "research" regarding what is technically possible not from history, but from what other authors did. That way, many ended up perpetuating the incorrect use of terms like "longsword", or about the weight of chain mail, etc.
So when it comes to the length of the ship, I would certainly prioritise the calculations suggested in this thread more highly than what has been done in other stories before. Me bringing up the Star Destroyers was more to show that ship lengths of several kilometres are not unheard of in sci-fi. That does not mean I necessarily want the ship to be that large. In fact, smaller is probably more plausible for most readers (if only in terms of what building such a ship must cost).

What is crucial here are the minimum measurements: Like the minimum radius of the ring / cylinder to produce artificial gravity without requiring too fast rotation; the minimum surface area required to house 500 to 1,000, potentially 1,500 people and feed them all.

Aside from those logistical questions, the main reason for making the ship larger is psychological: You want to avoid confining too many people in too tight a space. And I am not even talking about overpopulation here yet. Rather, considering the rat- and mouse utopia experiments by Calhoun (Universe 25), where the populations went extent without ever coming close to the carrying capacity of the enclosure.

Of course, the larger we make the ship, the more pressing the questions become: Why not add even more people? Why not make the cylinder even larger and turn it into a permanent residence, without the need to find a new planet at all?
At that point we would be talking about an O'Neill Cylinder as a permanent habitat. That is a premise I find interesting in and of itself - specifically, for a different story (or very late sequel to this current one), set close to the end of the universe.
But for the time being, in order for the premise of a generation ship to work, colonising a different planet still needs to be considered worthwhile - meaning, offer a superior quality of life - compared to staying on the ship for all eternity.

Kim Stanley Robinson: Aurora is also a good reference (well, up to ~ half of the book). However, this one may be a party killer since the ship there is quite like the one described here.

Thanks for the tip! ;) The Tau Ceti system is indeed one of the "alternative candidates". It was brought to my attention by Isaac Arthur's fictional generation ship "Unity", including the idea of sending two ships there, and then having one travel onwards to 82 G. Eridani (which is 20 light years from Earth, but only 8 further ones from Tau Ceti). Such plans are indeed also ventilated at one point in my story: If the mission of the Exodus to Teegarden b proves successful, further generation ships will be launched to Tau Ceti, 82 G. Eridani, and Trappist-1. The last one is 40 light years away, so clearly the most ambitious goal.

For the Exodus, I went with Teegarden b because of its high Earth-Similarity Index. I am aware it is most likely tidally locked, but it should still be possible for such a planet to have a magnetic field, thanks to tidal heating (even though magnetic fields may be more common with rotating objects?).
I am also wondering whether it would need to have a moon to be habitable. As far as I am aware, Earth probably would not be habitable without the moon, because it would be spinning too fast. But a tidally locked planet does not spin to begin with, so whether or not Teegarden b has a moon might not be that crucial after all. :)

That won't do. Assuming a 70 years life expectancy you will get at least three generations parallel, not just two. The crew size will be lot (!) larger.

You are absolutely right - here I forgot to tell you about another crucial piece of my worldbuilding: 70 years is in fact already pretty old for the crew members on the Exodus. This is one of the more cynical aspects of the setting, inspired by the Star-Trek episode "Half a Life":
Since most of the older generations are aware they will not live to see the ship's arrival at Teegarden b anyway, it is quite common for them to take the so-called "exit pill", a method of painlessly ending their lives at some point beyond the age of 60. (In "Half a Life", it has become a rigid tradition to do so on one's 60th birthday. As far as I remember the episode, it is the peer pressure and inflexibility of this tradition that is the main criticism of the story, not the possibility to do so per se, if it is indeed voluntary.) Of course, there is always the issue of "if everyone can do something, peer pressure will arise that everyone should do that something".

So given that this procedure is strictly voluntary, what might drive some of the elderly crew members to take this radical step? There are a couple of reasons:

Spoiler

First, there is no real way of retiring on this ship - people are expected to continue contributing to keeping the ship running. This is indeed not too far off from the way the first retirement programs were designed: When Bismarck set the retirement age in Germany in the 19th century, he picked an age that was only one year below people's average life expectancy back then. So there were hardly any "sunset years" - there was merely a single "sunset year".

Second, the world is small: After 60 years or more, there is nothing left on the ship that you have not seen before already. The main sources of purpose the individual crew members can find - aside from the continuation of the species - are their jobs. But since people also have successors in their jobs (usually apprentices of some kind), at some point they will render themselves redundant: Seeing how your apprentice outgrows you and overcomes "the master" can be humiliating. Eventually, the younger person will be faster, more efficient, while also gaining more and more experience in their job each day - the one thing the older "mentor" has more of.

When your children are grown up, your trainee starts outperforming you at your own job, and you know you will never live to see the ship's arrival anyway, many of the primary sources of meaning fall away. Now the main thing they have to look forward to are the ailments of old age.

It might feel radical for us here on Earth, especially now in modern times, with so many ways to keep ourselves busy well into our seventees and eightees. But on a ship like this, there is much less entertainment available: You live for your job and your children, and both start drifting away from you at some point, the older those children get. Even if one is not bothered by anything else, eventually, life in this small enclosure will simply become dull and boring. Add resource scarcity into this, and I can easily see some people over sixty living on a generation ship say: "You know what, I have done my part, had my two kids, served this ship all my life - the next generation can take over now and go on without me."

Mixed (and: redundant) functionality would make more sense. So, in case something happens with one ring you wont' lose all lab capacity, for example.

Yes, this is something I have been thinking about a lot - mainly about what is the lesser of two evils. What is more likely - that one ring would be destroyed entirely? Or that only the outer layers would get damaged, but on every ring?

If each of the five rings had one floor for farming, one for lab capacities, one for habitats etc., and the farms are always on the outermost deck, then damage to the ship could just as easily destroy all the farms. Of course, the main way of preventing this is varying the order of the same functionalities between rings. So on one ring, the farm would be on deck 3, elsewhere on deck 4, etc. But conversely, farming probably needs the most space (even when it is vertical farming), and the largest surface area will always be found on the outer decks, where the ring / cylinder circumference is longer.

In contrast, if I have a dedicated ring for each functionality, then damage to the outer parts of the ship (say, deck 5 gets damaged across the entire length) would still not eliminate a single functionality: The ship would continue with decks 1-4, while still having farms, habitats, a lab etc.

What type of architecture is more advantageous thus depends on what type of damage to the ship we would expect to be more likely: Damage to an entire ring, without harming any of the others? Or damage to an entire layer of the ship (probably the outer one)?
This is an open question; I have not come to a final decision on this yet. :) So please, feel free to speculate about this and make your suggestions!

That's true, as long as there is no propulsion. But in acceleration/deceleration phase that 'pipe' will bear the forces required to accelerate all the rings. It has to be quite sturdy.

Great point, I had not thought of this yet, thanks! :) I only had the intuitive feeling that the central pipe would probably have to be a lot thicker than I currently imagine it in the scenes that are set in there.
Any ideas for what you would consider "sturdy enough"? Is it possible to calculate this somehow?

As an example consider a hollow cylinder of length with the bulk of its near-constant density mass between radii and rotating along its symmetry axis (an O'Niell cylinder), then for the rotation to be stable you have to have . This sets a limit on how long the "pencil" can be.

Wow, thanks a lot! :) That was what I was hoping for. Just a question: If radius one is the inner radius of the rings / cylinder (250 metres in my case), what is radius two then? The outer radius of the rings (=on the outermost floor)? Or the radius of the central pipe?

That doesn't sound like constant acceleration. That sounds like a short burst of high acceleration at both ends and constant speed in between.

Okay, then I guess I was misinformed. My state of layman knowledge was that (assuming a sufficient energy source) it would be possible to accelerate to 10% light speed in a matter of a few weeks. I would not mind if the journey took a little longer, though. :) 125 years is still quite short.

Origially, I wanted to send the crew to just the closest exoplanet, Proxima b - using slow-enough propulsion for that journey to take 6300 years. But for one, that is more time than all the well-known parts of recorded history, and second, with what we know about Proxima b by now, it is unlikely to be habitable; if only for being hit by eruptions from its star regularly. Teegarden's star is a red dwarf, too, but a much calmer one in comparison.

Also bear in mind that at 0.1c a one milligram rock strikes like 100kg of TNT. A 100g rock is a getting into Hiroshima bomb ranges. There aren't many such floating around, but even one is fatal and you'll never detect something so small early enough to evade. You need some kind of deflector or other handwave.

I was aware of the danger of even minor collisions at such speeds in general - but thanks for providing some specific numbers on this! ;)

Here is the thing: At one point in the story I actually need a major accident to happen. And a collision was indeed the first thing I thought of. But even though it is going to be a major disaster for the crew, it can probably still just be a minor collision, like a graze wound to the ship. Otherwise, there is not just going to be a hull breach and some damage to the nuclear fusion reactor - there is not going to be anything left of the ship at all.
At several points in the story, I draw parallels between the Exodus and the Titanic. (The Exodus is deemed "unsinkable", since of course it cannot sink in space; both were transporting people on a way to a "new world"; then there is the theme of who sacrifices themselves to save the lives of others etc.) So a collision with something much smaller than an iceberg that still causes massive damage to the ship would not only be quite epic - it would make that comparison complete.

Specifically, it needs to be a problem that requires many strong hands to resolve, and a dangerous mission at that. The danger of the mission needs to be known in advance, so that aside from the security officers, only men are sent on that mission. Because the ship can more readily afford to lose some of them than of the women on board. And indeed, a good number of the young men who are forced to take part in this mission die in the process.

This is one of the catalysers for the commander to become more totalitarian in the measures she resorts to, in terms of childbirth, to restore the population on board to former numbers as quickly as humanly possible.

You need some kind of deflector or other handwave.

For the reason just stated, I want to be careful with such general protective measures, since they would deprive me of the opportunity to include a collision when I do need it, like in the context described above. Unless of course I then spontaneously go with the old Star-Trek solution of "the deflectors have failed"... :)
The only thing that never seems to fail in Star Trek (at least not on-camera, only mentioned for unseen decks) is the artificial gravity on board. Because that would have been more expensive to film. Luckily, that cannot happen that easily with rotating rings, once they are in motion.

Generally speaking, I think the main reason why Star Trek is still deemed more "science-y" than many other sci-fi stories is the core idea of the warp drive. All the other problems (artificial gravity, deflectors, cosmic radiation, hull breaches etc.) are usually handwaved away with some sort of "force field" or other electric solution.

Because of the radiation getting harder and harder the faster the ship travels, the Exodus actually does not have any windows - only a bunch of screens, and cameras on the outside. Basically, I did for every room what Star Trek has on the bridge: It still looks like a window from the inside most of the time. Except you can also have it show different things. Like for example, in the private quarters, have the screen simulate a sunrise in the morning. :) The crew will be happy for every little bit of normality they can retain from Earth.

Might be why some are 'revolting'. The thing flipped end to end which caused confusion and temporary chaos and discussions on what to do next.

Interesting premise! ;) But at this point it would take the story into a completely different direction. No, the main reason why they are revolting is the loss of personal freedoms, like bodily autonomy, in the name of the survival of the species.

(And no, this is not intended as a parable for measurements taken to halt pandemics - though I can already imagine some people will inevitably want to interpret it this way. That is why I explicitly state that this is not what the story is about.)

Rather, Neil deGrasse Tyson once said in an interview that with generation ships, we would have to be careful that they do not turn into "The Handmaid's Tale". That is basically what happens here (I even have the main character joke about putting on red dresses and white caps at one point). Except the commander is a woman herself, and her motivation is a little different than that of the rulers of Gilead. ;)

 

[Melbourne Guy]

If you are using spinning things to simulate gravity, @Strato Incendus, then spin calc is a helpful site. You'll likely find that generating a full gee requires a large torus or fast spinning torus. I've used both a torus - but at lower gravity - and a hollowed out asteroid - at a full gee - in my novels, but don't get lost in the physics; because if you get the emotional tone right, readers will forgive a lot of hand waving!

 

[jedishrfu]

As an aside on ship sizes, I found this video showing ship sizes for The Expanse.



The last ship is the generation ship Nauvoo with a length of 2070m

and this fan site that describes it as having a length of 2148m in The Expanse books:

https://expanse.fandom.com/wiki/Nauvoo_(Books)

and saving the best for last: an article from Universe today:

https://www.universetoday.com/14489...d another team of,for the sake of agriculture.

 

[Melbourne Guy]

and saving the best for last: an article from Universe today:

https://www.universetoday.com/14489...d another team of,for the sake of agriculture.

What I like about Marin's approach is the application of Monte Carlo modelling with two dozen parameters to estimate upper and lower bounds of the outcomes under consideration, @jedishrfu. It might not be right, but at least it's more robust than the usual wet finger in the air approach!

 

[jedishrfu]

These kinds of estimates fall under the Drake equation hastily created for an upcoming conference talk.

https://en.wikipedia.org/wiki/Drake_equation

a version of a Fermi paradox:

https://en.wikipedia.org/wiki/Fermi_problem

 

[DaveC426913]

Can I suggest that the ship would/should not be named Exodus.

Exodus is all about the past. It is a constant reminder of what is being left behind - never to be seen again. Some portion of the 1st generation of crew will get homesick, and a smaller portion will commit suicide, or even sabotage. Later generations will also be reminded of things past, and may forget why they're even on this mission. You do not want your crew's very life-giving world to evoke nostalgia and loss!

Earth is gone forever. This people's world is Demeter.

An appropriate name for any vessel should evoke thoughts and feelings about a bright and hopeful future.

 

[jedishrfu]

Some names come to mind:
- NewDawn
- Avalon
- BrightStar
- NextStop
- FortyTwo
- BlueSuedeShoes (1 for the money,2 for the show, 3 to get ready and 4 to go...)
- ...

 

[DaveC426913]

Ibn Battuta.
One of the most well-travelled explorers in pre modern history. Travelled a distance equal to 3 times around the Earth - in the 14th century. Travelled farther than most other famous travelers combined (Marco Polo included).

https://en.m.wikipedia.org/wiki/Ibn_Battuta

Has the advantage of not making the ship's name America-centric.

 

[Filip Larsen]

If radius one is the inner radius of the rings / cylinder (250 metres in my case), what is radius two then? The outer radius of the rings (=on the outermost floor)?

Yes, its the inner and outer radius of the cylinder/ring where the bulk of the mass is located. For example, assuming inner radius 250 m and outer 300 m (just to take some numbers), then a cylinder will become unstable at a length of around 670 m.

If we for the purpose of calculating the rotational stability of a ring structure assume it is like a hollow cylinder sliced up into $n$ slices each $b$ wide and then spaced $s$ apart (from center of one ring to the next) and attached rigidly to a central spindle, then it seems possible to get an expression for how many rings you can have before that structure becomes rotationally unstable around the spindle.

Let me add some equations so others have a chance to verify if they like. The two interesting moments of inertia for a cylinder is $$I_{C_z} = \frac{1}{2}m(r_1^2+r_2^2)$$ and $$I_{C_x}=\frac{1}{12}m (3(r_1^2+r_2^2)+h^2)$$ where $h$ is the length of the cylinder and $m$ the total mass. For a cylinder to be rotational stable around $z$ it requires that $I_{C_z} > I_{C_x}$, which gives the condition $$h^2 < 3(r_1^2+r_2^2)$$ which I mentioned earlier.

For a ring structure with an even number of rings and using $h = n b$, I end up with the moments of inertia to be $$I_{R_z} = I_{C_z}$$ and $$I_{R_x} = + \frac{1}{12}m (3(r_1^2+r_2^2)+b^2 + s^2 (n^2 - 1))$$ which means that for stable rotation around $z$ we must have $I_{R_z} >I_{R_x}$ or $$n^2 < \frac{3(r_1^2+r_2^2)-b^2}{s^2} + 1.$$ A similar expression should also be possible to derive for $n$ being odd.

With the numbers from before, i.e. $r_1 = 250 \,\mathrm{m}$, $r_2 = 300\,\mathrm{m}$ and choosing, say, $b=50\,\mathrm{m}$ and $s=100\,\mathrm{m}$ then I get that $n < 6.8$, that is $n=6$ should be stable, $n=7$ will probably will be unstable (since this is an equation for even $n$ we need the odd version to be sure) but $n=8$ surely will be unstable.

Note that all this assumes the whole structure is rigid, that is, all the rings are "locked" together. In the other end of the scale we would have that the rings are completely free from each other (ignoring any rocket thrust) which means they each rotate stable as a short cylinder given the expression for the cylinder. A practical ring structure will probably be in between those two extremes of rigidity, that is, some flexing or uncoupling is probably both unavoidable and perhaps even desirable, also to make the spindle more simple.

For instance, one could image that if each ring is mechanically attached to the spindle in such a way that it only absorb translatory forces from the spindle (i.e. rocket thrust) but not any torques and to large degree is free to rotate independently of the other rings, at least direction-wise, then each ring is more or less its own little cylinder and thus very stable in its rotation. This may of course introduce a lot of other engineering complications (like how to actually control the rotation direction of each ring) and design constraints but for a story it can perhaps also allow for more ways to introduce interesting plot twists (I am here considering how common it is in sci-fi to base plot twists on failing equipment ).

 

[BvU]

I did for every room what Star Trek has on the bridge: It still looks like a window from the inside most of the time.

Makes one wonder why they located the bridge on the center top of the dish -- where enemies aim their pot shots !

the main reason why Star Trek is still deemed more "science-y" than many other sci-fi stories is the core idea of the warp drive.

Isn't that the most un-sciency concoction of all ?

Anyway, I predict it's going to be a thick fat book you are going to come up with and wish you the best. I will read it for sure. Even if you let the moon break into pieces, sf readers have no problems, so don't worry about physicists

$\$

 

[DaveC426913]

For the reason just stated, I want to be careful with such general protective measures, since they would deprive me of the opportunity to include a collision when I do need it, like in the context described above. Unless of course I then spontaneously go with the old Star-Trek solution of "the deflectors have failed"... :)

You need to need to ensure your ship is plausibly defended. Making an interstellar ship that doesn't have a dust and meteoroid deflector will have your readers crying foul - it's such an obvious plot hole that that they will fault you the author.

The better idea is to have the design encompass all conceivable dangers - and then have a danger (or better yet, a confluence of dangers) happen that couldn't be accounted for.

 

[DaveC426913]

Question about the rotational stability issue:

Presumably, if at least one ring were counter-rotating, would that not mitigate the instability? The ship's length and number of counterrotating rings would be linked.

It seems to me, that the instability - and its clever solution - would be a cool addition to the book that no other author has considered.

 

[Rive]

Presumably, if at least one ring were counter-rotating, would that not mitigate the instability?

You can't do that without century lasting bearings and seals to retain the atmosphere. It's easier to have all the ship rotating as one solid body.

 

[DaveC426913]

You can't do that without century lasting bearings and seals to retain the atmosphere. It's easier to have all the ship rotating as one solid body.

Except that the author has established the core does not rotate.

 

[Rive]

Except that the author has established the core does not rotate.

I've certainly missed that. It's quite an engineering problem to make up those bearings for even just a decade (or so) acceleration with the rings already spinning. And that's just the bearings, not being airtight or anything...

 

[Melbourne Guy]

It seems to me, that the instability - and its clever solution - would be a cool addition to the book that no other author has considered.

Pretty sure I've read that solution before, @DaveC426913, and actually wrote that solution myself with a ship that has two counter rotating hubs, with the connecting zero gee tube the axle. One hub suffers catastrophic damage and doesn't that make a mess of things for the cast

But it reminds me, @Strato Incendus, you don't need external events like a foreign body strike to trigger a damage sequence. As noted above, just have a bearing seize and you've a dramatic and very impactful situation for the crew to respond to.

 

[Filip Larsen]

You can't do that without century lasting bearings and seals to retain the atmosphere.

I haven't read all the background details in this thread, but I imagine there are no direct need for air tight bearing and that the bearing itself perhaps was magnetic during normal operation, that is, the bearing has an outer ring attached to the crew ring and magnetically centered over an inner ring that is fixed to the spindle. I also understood it would be good for the story if the rings are a bit isolated crew-wise, so this means you could have to transfer from the spindle to the rotating ring by vacuum or a small ring-shaped airlock that sits coaxial with the bearing that can either be "docked" with the spindle or spun up to match ring rotation and "dock" with a spoke on that.

Btw, counter-rotating rings are a good idea for getting the initial rotation up (since it requires no reaction mass), or if the rings has to be spun up and down regularly, and it also allows more maneuverability of the structure as a whole at the expense of potentially higher torques transferred between the rings (through the spindle). However, for a generation ship it is perhaps less obvious what engineering benefit counter-rotating rings is supposed to bring. Flipping a generation ship at the half-way point is probably not going to be like flipping a "normal" rocket anyway, but perhaps more a question of moving the rocket engines around to thrust in a different direction, so counter-rotating rings would likely not bring any special benefit to solve the "flip problem".

 

[DaveC426913]

Pretty sure I've read that solution before, @DaveC426913, and actually wrote that solution myself with a ship that has two counter rotating hubs, with the connecting zero gee tube the axle. One hub suffers catastrophic damage and doesn't that make a mess of things for the cast

Still, I think it would make an awesome subplot in the story. I had never heard of this phenomenon until the video from the ISS with the T-handle wrench came out few years ago:



Is it even conceivable that the OP's engineers who built the prototype ring-ship won't have realized this was going to happen until it happened? You know, "we didn't think adding an 20metre observation cupola on the nose would make any difference, but it turned out that was just enough to destabilize the gyroscopic momentum of the rings, and the whole craft flipped end-on-end".

Now, having just said that...

But it reminds me, @Strato Incendus, you don't need external events like a foreign body strike to trigger a damage sequence. As noted above, just have a bearing seize and you've a dramatic and very impactful situation for the crew to respond to.

... a failure in design - without being precipitated by an external hazard - would call into question the competence of the engineers who built it. Such an should not be merely incidental to the story. It would need to be justified by the story.

 

[DaveC426913]

So, a question about this end-over-end instability phenom.

There's been some back-and-forth about whether the whole craft rotates or just the rings. The author wants just the rings to rotate, with the axial fuselage to remain in zero g.

Does that have any impact on the instability phenom? Will the end-over-end happen if the fuselage is not rotating?

^{[footnote: I have been using phenom as a contraction of phenomenon. I had no idea phenom is a word in its own right, with its own distinct definition.]}

 

[Filip Larsen]

Does that have any impact on the instability phenom? Will the end-over-end happen if the fuselage is not rotating?

The rotation of the spindle (or not) is not significant for stability, but what is significant is to what degree the spindle can and is allowed to transfer torques between the rings. At one extreme we have to fully rigid structure where the rings mechanically remain perpendicular to the spindle (imagine here the rings are welded to the spindle), meaning that any deviation from this position will be transferred as a torque through the spindle. At the other extreme we have that the spindle will only transfer translatory and pure in-ring rotational forces between discs (imagine the discs being welded to a long sequence of Cardan-like joints), meaning the rings are attached to the spindle via a bearing that does not transfer any deviation from being perpendicular to the spindle, at least not when its within some nominal angle range around being perpendicular.

The fully rigid structure can be expected to have a stability criterion more or less as mentioned earlier, to a precision that depends on how much of the total mass is in the rings. If the spindle has a significant fraction of the mass, especially near the ends, this will increase the moment of inertia around the X-axis much more than around the Z-axis, thus making the critical length even shorter.

The "fully" floppy structure on the other hand will not be unstable in this way since each ring will have isolated rotational dynamics, but it is hard to imagine that such a structure will not impose some interesting engineering problems that needs to be solved, like how the spindle and bearings can be made the able to transfer thrust and perhaps in-ring torques but not any out-of-ring torques, and how to ensure the set of rings are controlled not to collide with each other.

The author wants just the rings to rotate, with the axial fuselage to remain in zero g.

The spindle is more or less in near zero-g whether it rotates or not. If we have 1 g at the "bottom" of the rings and the spindle diameter is, say, 5% of the outer ring diameter, then there is max 5% g near the wall in the spindle. If the rings are not counter-rotating I miss a good argument for not also having the spindle rotate, especially if the rotation of each rings are mechanically tied to other rings. For the counter-rotating rings it makes much more sense to assume the spindle keeps a rotation that lies in between what the rings have, i.e. zero.

 

[DaveC426913]

The "fully" floppy structure on the other hand will not be unstable in this way since each ring will have isolated rotational dynamics, but it is hard to imagine that such a structure will not impose some interesting engineering problems that needs to be solved, like how the spindle and bearings can be made

The ship in KSR's Aurora had to deal with this.

The spindle is more or less in near zero-g whether it rotates or not. If we have 1 g at the "bottom" of the rings and the spindle diameter is, say, 5% of the outer ring diameter, then there is max 5% g near the wall in the spindle.

Yes. Though, for the author's 500m rings, that's a spindle diameter of only 25m. That's pretty ... spindly.
Surely it'll be at least 50m.

In 10%g, a human will weigh about 20 pounds.

The other thing to consider is that the air mass will rotate. The Coriolis Force will carry objects toward the outer wall.

For the counter-rotating rings it makes much more sense to assume the spindle keeps a rotation that lies in between what the rings have, i.e. zero.

No need to assume the rings are evenly distributed between rotating and counter-rotating.

If just a single counter-rotating ring is sufficient to stave off end-over-end flip for a fuselage of the required length, then it might only have one.

Regardless, you'd still want the fuselage to be non-rotating wrt the stars for logistical reasons such as astrogation.

 

[DaveC426913]

BTW, KSR's "Ship in Aurora did not have continuous rings. They were cylinders linked end-to end with sealable bulkheads.

There is a technical description of it here:
https://www.centauri-dreams.org/2015/08/14/a-science-critique-of-aurora-by-kim-stanley-robinson/

It is 10km long and 17km in diameter and housed ~2000 crew for a ~170 year journey.

This is an accurate proportional rendering I did of the Aurora ship.

Here is a detail of a cylinder and its funny gravity.
Each cylinder is 4km long and 1km in diameter.

 

[Filip Larsen]

No need to assume the rings are evenly distributed between rotating and counter-rotating.

I mainly "snap" to the idea that if a ship has counter-rotating rings anyway then having a total angular momentum near zero allows the options to spin all the rings down and up again without expending any reaction mass (only energy, though probably a lot of that). If the total angular momentum is not zero then that momentum has to be put in initially and the direction of angular momentum (and hence the rotation axis) will likely remain fixed during the remaining life of the structure.

Using half (or only some) counter-rotating rings to allow for a "longer" structure without it becoming rotationally unstable will, everything else being equal, require the spindle to transfer more forces, but I guess (without having the equations to prove it) that such a structure can have its rotational dynamics modeled as two counter rotating parts attached with a "rigid" rotation joint (or many such joints) that transfers all forces and torques except torque parallel with the rotation axis, and that this can be used to show that even if each part in isolation is too long to rotate stable then combining them "rigidly" will allow any internal flexing (which is what drives instabilities up) in either the two parts to cancel each other out keeping the combined structure stable. In principle, at least, and ignoring all other concerns. If used in a story, this probably means the joints will be an excellent part to introduce plot twisting mechanical problems in as they are effectively keeping the entire structure stable.

 

[Filip Larsen]

Here is a detail of a cylinder and its funny gravity.
Each cylinder is 4km long and 1km in diameter.

What is the reason for a linear crew cylinder? Air pressure? Why not slightly curved due to the structural load from the rotation? I assume, that at least the internal floors or levels are made to be perpendicular to the local "gravity" vector.

Interesting design, though. Perhaps I should put Aurora on my reading list for next vacation .

 

[Strato Incendus]

Wow, thanks a lot for your many replies! :) I hope my post does not get too long if I try to reply to as many of them as possible one-by-one:

If you are using spinning things to simulate gravity, @Strato Incendus, then spin calc is a helpful site.

Great tip, thanks a lot! :) I had not heard of this site yet. But that is a great way of ensuring, for example, that the rings will not only be able to simulate 1 g (like on Earth), but also 1.05 g (like on Teegarden b). So it makes sense not to go with the absolute minimum diameter the rings can have.

Yes, its the inner and outer radius of the cylinder/ring where the bulk of the mass is located. For example, assuming inner radius 250 m and outer 300 m (just to take some numbers), then a cylinder will become unstable at a length of around 670 m.

That said, I was not thinking of 250 m to 300 m, since the rings have a lot fewer decks. Having looked up the average ceiling thickness in buildings (0.2 m) and standard floor height (2.4 m), if I have 5 decks on a ring, that makes 2.6 m * 5 = 13 m ring thickness (vertically).
So if the inner diameter is 500 m (radius 250 m), the height of the rim gets added on both sides, too, making the outer diameter 526 m.

As far as the width of the corridors on the rings is concerned, I went with 32 m for the time being. I arrived there by imagining there should be quarters, or school classrooms etc. on both sides of the corridor, with the corridor in the middle still being wide enough to not just comfortably walk through, but also transport more bulky objects through. (Somehow all the furniture must have been brought onto the ship at one point, after all - even though most of it was probably assembled on board.)

So with a width of 32 m, the five rings would cover 32 m * 5 = 160 m of the total length of the ship. In other words, it needs to be at least 160 m long, but probably more, since we want at least some distance between the rings. Especially if some of them are supposed to rotate in opposite directions etc.

The spindle is more or less in near zero-g whether it rotates or not. If we have 1 g at the "bottom" of the rings and the spindle diameter is, say, 5% of the outer ring diameter, then there is max 5% g near the wall in the spindle. If the rings are not counter-rotating I miss a good argument for not also having the spindle rotate, especially if the rotation of each rings are mechanically tied to other rings. For the counter-rotating rings it makes much more sense to assume the spindle keeps a rotation that lies in between what the rings have, i.e. zero.

5% of the inner ring diameter, as someone else already said, would indeed just be 25 m for the diameter of the central pipe; 5% of the ouer ring diameter, given current measurements, would be 26.3 m.

I was assuming a diameter of 50 m minimum for the central spindle (=10% of the inner ring diameter)? Perhaps even 100 m (=20% of the inner ring diameter), if it needs to be a little more sturdy.

Given that this is high and wide enough to fit small buildings inside, I doubt the entire central pipe would just be one massive hollow tunnel; there would probably be several smaller sub-corridors within it.

My father also suggested the central pipe might be used as additional farming ground? There seem to have been some studies on crop growth in zero gravity. So far, I am only going with vertical farming on the eponymous ring, since that requires next to no soil.

Of course, this suggests a higher ceiling height for the decks on the farming ring. Since I have a little bit of leeway from my 250 m inner ring radius to the minimum of 225 m, I used this to extend the farming ring further inwards, i.e., shrink the inner diameter of the farming ring to the minimum of 450 m.

difference between outer and inner diameter = 526 m - 450 m = 76 m

Deck Height: 7.4 m
Ceiling Thickness: 0.2 m
5 decks a 7.4 m + 5 times a ceiling of 0.2 m = 5 x 7.4 m + 5 x 0.2 m = 37 m + 1 m = 38 m
38 m x 2 = 76 m (since the ring height gets added to the outer diameter on both ends)

Makes one wonder why they located the bridge on the center top of the dish -- where enemies aim their pot shots !

Yes, this is one of the most commonly observed plot holes (or rather: worldbuilding holes) in Star Trek in general. ;)

Isn't that the most un-sciency concoction of all ?

By that I just meant that the basic idea of the warp drive - traveling "faster than light" due to distorting space, rather than just "accelerating the ship beyond light speed somehow" - is more sound than any other FTL solution. I am not referring to the energy consumption this would require, nor to the issue of how to get into our out of a warp bubble if one manages to create one.

Anyway, I predict it's going to be a thick fat book you are going to come up with and wish you the best. I will read it for sure. Even if you let the moon break into pieces, sf readers have no problems, so don't worry about physicists

Oh wow, thanks for your interest! :) At this point, it feels a bit like premature praise, of course, but things like that certainly help keeping up one's motivation!

In terms of "SF readers have no problems", that is the point: Personally, I think they should. ;) At least a little more than they currently do. Our disbelief should not be suspended quite as readily as in fantasy, where magic and fairytale creatures are the default expectation.
Otherwise, readers and viewers might get their hopes up for technology that might never be feasible in the first place (like replicators and the means of creating artificial gravity in Star Trek). Similarly to how people got their hopes up too fast when it came to how quickly we would be able to unlock nuclear fusion as a power source.

There are other genres of fiction set in the future - like utopia or dystopia - that do not carry the implication that their scenarios are realistic from a technological standpoint (perhaps from a societal or political standpoint instead). For example, The Hunger Games never really discusses the technical details of the arena. There we are willing to suspend our disbelief more quickly - but we also accept that The Hunger Games is fiction, without the additional label "science" attached to it.

Can I suggest that the ship would/should not be named Exodus.

I hear your points. Ironically, they have given me a great reason why I should stick with the name Exodus more than ever now:

Spoiler

The catalyst that made me start writing this novel was discovering Abbie Emmons's writing advice on YouTube. I had watched other people from that community before (Jenna Moreci, Terrible Writing Advice, Hello Future Me etc.). But she focused specifically on the (supposed) "science" behind why some stories resonate with people an others do not. Also, she puts a lot more focus on thematic storytelling ("the truth you want to scream from the rooftops"), rather than just on characters and plot structure per se.

One of the crucial factors Emmons keeps coming back to is internal conflict. Usually, this refers to the internal conflict of characters. But in this case, there is internal conflict in the mission itself, too:
Most people intuitively realize one of the major ethical problems of a generation ship, namely that none of the crew members, aside from the very first generation, ever agreed to being part of this mission. The value that stands opposed to these considerations of individual freedom is that of survival. So at its most abstract level, the internal conflict of the mission is "survival vs. well-being and freedom" (similarly to The 100).

Then, the ship itself has an internal conflict, too: Indeed, most sci-fi stories seem to assume a fully globalised world, often one with a one-world government, usually related to the UN in some way. This notion however seems to contradict human nature, given that we evolved in small nomadic tribes of a few dozen to a hundred people. Humans are tribal creatures. The internal conflict of the ship itself is one of identity: "I am a member of the human species vs. I am the emissary of nation X."

Given what you said about the implications of the name, now that internal conflict becomes visible even in the name itself! Is the "Exodus" about what you leave behind? Or is it about the "Promised Planet" you are heading towards?

Even though it was the founders' ambition to have the crew on board transcend the past, they of course also want them to "export the past" (humanity and awareness of its history) to a new world. Since they selected at least one couple from each nation on Earth, that also means the lines between individual and national identity on board blurred. Even though every member of Generation Five has ancestors from many different countries on Earth, they still inherit the surname of one particular Generation-Zero couple.

And so, much like expats rediscover their place of origin, a lot of people on board delve into the past of what their specific ancestors used to live like. Among others, because this is a treasure entirely for themselves and their family - given that most of them are the only "representatives / emissary" of their country from Earth on the ship.

This subdivision is also plausible because, in contrast to many other sci-fi stories, there is no external enemy here from which the crew could set itself apart. Or rather, the only external enemy is the universe itself. An abstract threat, much like climate change - not one with a "humanoid face", like an alien species.

The "research" into their ancestors' past happens mainly via the ship's knowledge hub, called The Catalogue. Which is essentially nothing less than the entire storage of the Earth's internet in the year 2375 (when the Exodus departed from Earth). Do not ask me how many petrabytes of storage space that would require. But given how already the computer in Star Trek was able to play any music track at whim, or simulate any given place on the holodeck, that actually did not feel to far off from having an on-board internet - even though the story was written at a time when the internet did not even exist yet.

Holodecks, or my spin on them, are the other way people explore their heritage (with the simulations drawing from the data of the Catalogue, of course). In my case, rather than having a few huge holodecks on board that would constantly be booked out, every 2-bed quarter has two little closets (about the size of a shower, or a small sound-proof vocal booth), called VR chambers. These are not nearly as elaborate as holodecks - they mainly just simulate images and sound, not smell or touch. But at least everyone has one for themselves. If I can take on thing from Calhoun's mouse utopia experiments, it is that the need for privacy in a permanent enclosure as small as a spaceship is a factor that should not be underestimated.

Quite a few people on board even use such simulations to learn their ancestors' language. Of course, some languages are more useful on a ship like this than others: Everyone on board speaks English, naturally, but then there is for example a significant subset who also speak Russian. Or Spanish. Or Arabic. Or French. The only occasions when everyone gets to use their ancestors' language are of course within one's family (the most frequent application). And then when exchanging messages with one's distant relatives on Earth. Although the latter of course happens with a two-decade time delay, so that alone would definitely not make a language worth learning.

Has the advantage of not making the ship's name America-centric.

Actually, if anything the composition of the crew is already less America-centric, given that the starting conditions were just 1 couple from every sovereign country on Earth. That puts the US at a numbers "disadvantage", considering the share of people they make up worldwide, while geographical regions with a lot of smaller nations, like the Balkans in Europe, tend to be "over-represented".

That said, the US was among those countries that got to send several couples onto the ship. (With around 200 nations on Earth, having just one couple from each of them would amount to 400 people, but we need a starting crew of 500 people, i.e., 250 couples.) But they still do not make up nearly as much of the crew as most other sci-fi stories would have you expect.

Then again, I am not from the US myself.
Being the armchair traveler that I am, I know some nerd facts about a lot of different places on Earth, rather than having a lot of knowledge about one place in particular. So I can sprinkle that into the story.
The nice thing is: Even if I slightly misrepresent something here and there, that is still entirely plausible within the worldbuilding. Because no matter how often somebody in Generation Five references their ancestors: They themselves have spent their entire life on the ship. So they still know nothing more about their place of origin than what they could gather from the Catalogue. In other words: What they could research on the internet. Just like I did.

You need to need to ensure your ship is plausibly defended. Making an interstellar ship that doesn't have a dust and meteoroid deflector will have your readers crying foul - it's such an obvious plot hole that that they will fault you the author.

The better idea is to have the design encompass all conceivable dangers - and then have a danger (or better yet, a confluence of dangers) happen that couldn't be accounted for.

Going by Isaac Arthur's video "Interstellar Travel Challenges", a lot of these ideas seem to revolve around shooting down any space debris in front of the ship with sufficient prior notice. Of course, that is technically how the deflector in Star Trek works, too. It is just much more often framed as a "shield", which sounds like "yet another protective invisible barrier around the entire ship's hull", like in space battles. Whereas "shooting down the debris in front of you with a laser", even if that is actually what the deflector does, sounds more like a weapon.

The other idea that Isaac Arthur suggests in that video is sending a tiny sail ahead, similar to the solar sails that are being considered for Breakthrough Starshot. In the history of my story, between now and the departure of the generation ship, one of the Breakthrough Starshot missions indeed failed due to a collision of the unmanned probe with a speckle of dust at 15-20% of light speed, which utterly annihilated the probe. Because I can hardly see a light-weight probe like that being equipped with some kind of deflector.

Fictional history-wise, Breakthrough Starshot 2 was then successful at reaching Proxima b, however confirming that it is not habitable to humans - among others, because of Proxima Centauri's frequent eruptions that hit it at full force. Breakthrough Starshot 3 was then sent to Teegarden b and confirmed its habitability.

Indeed, I am using as many of these official mission terms as possible. For example, Venus has been colonised with HAVOC units (High-Altitude Venus Operational Concept), too. Naturally, some of these attempts at building cloud cities on Venus failed, too. And one ended in a major disaster with a lot of casualties. But nevertheless, humanity kept persisting. At one point in the story, the ship receives a bunch of messages from the Sol system (with a 10-year delay, of course, plus-minus half a year due to relativistic time delation). One of these messages comes from HAVOC-12 on the Southern hemisphere of Venus.

Still, I think it would make an awesome subplot in the story. I had never heard of this phenomenon until the video from the ISS with the T-handle wrench came out few years ago:

Talk about "show, don't tell". That was impressive to watch! :D No matter how my ship manages to solve this problem (I do like the idea of different rings rotating in opposite directions), I definitely need to bring this up at one point in the story now. If only so that I can dispel any concerns of the more informed sci-fi reader.

No need to assume the rings are evenly distributed between rotating and counter-rotating.

If just a single counter-rotating ring is sufficient to stave off end-over-end flip for a fuselage of the required length, then it might only have one.

If a single ring suffices, I might make the public ring (the one on the front) turn in the opposite direction as all the others. Or perhaps the farming ring, given that it extends further inwards as described above, and should therefore be much heavier than the other rings. Also, the farming ring is at the very rear end of the ship.

So if I have both the first and the last of the five rings rotate in opposite directions as the middle three rings (lab ring, habitat ring, factory ring), would that provide sufficient stability to prevent the ship from flipping around? ;)

Yes. Though, for the author's 500m rings, that's a spindle diameter of only 25m. That's pretty ... spindly.
Surely it'll be at least 50m.

In 10%g, a human will weigh about 20 pounds.

The other thing to consider is that the air mass will rotate. The Coriolis Force will carry objects toward the outer wall.

Regarding the diameter, see my thoughts above.

If the central spindle does rotate, indeed that would no longer make it a place with zero gravity - just too little gravity for humans. Which is why already now, people who spend the entire day working in the central pipe need to put in more time at the gym (2-2.5 hours per day, like on the ISS) than people who work on one of the five rings. I am not even sure how essential these long daily exercise routines would be for "ring personnel".

But even if it is not necessary in the same way as it is for ISS inhabitants right now, there are of course certain other reasons why, on a generation ship specifically, the commanders would want all of their crew to stay in shape. :D I already have my main character notice at one point that most people on the ship seem to go to the gym "for visual reasons first, for health reasons second".

Anyway: A rotating central pipe would make moving through it more akin to walking on the Moon (you would be even lighter, a little, but you certainly would not be able to float through the entire pipe without ever touching the wall).

Good thing you mention the Coriolis Force again here. :) But I assume that is something I would only get if I have the central pipe rotate indeed. So I cannot have my cake and eat it, too.
It would actually be advantageous to have something that helps people get back towards the walls of the central pipe (or its smaller sub-corridors), so that they can shimmy along some sort of handrail to get forward. I think the natural "floating speed" when moving through it would be pretty slow - and considering that the pipe will have to be anything between several hundred meters or even a few kilometres long, that would mean it takes quite a while to get from home to work, or from work to the canteen.

So the question is: Once you "take flight" within a zero-g central section, how do you get back to the wall? Especially if the pipe needs to have a thickness between 50 and 100 m minimum?
That sounds like another reason why the pipe should be subdivided into smaller corridors, so that you cannot get "lost floating in the middle" all that easily.

Also, I imagine the central pipe to have padded walls. In general, much like on a space station, everyone on the ship is obsessed with keeping things tied down / locked in place, so that no potentially lethal floating objects can occur.
This is of course especially relevant in the central pipe, where there is no gravity. But even on the rings with standard gravity, if the ship had to slow down "abruptly" (as fast as is reasonably possible from 10% light speed), that could turn anything into a lethal projectile, if I understand it correctly?

It is 10km long and 17km in diameter and housed ~2000 crew for a ~170 year journey.

Oh wow, and I thought my 3 kilometres for a crew of 500 to 1,500 people felt excessive. :) On the other hand, those 2000 probably have a much better quality of life.
However, that just goes to show again how other sci-fi authors can simply "make stuff up", like ships of an arbitrary length, O'Neill cylinders, Dyson spheres etc., without necessarily giving as much thought to how much mass would be required to build such a thing in the first place, and how fast you could propel it to reasonable interstellar speeds.

That is why I currently prefer Filip Larsen's method of actually calculating these measurements over taking too much guidance from what previous sci-fi authors have done. Unless we focus on specific sci-fi authors who are known to actually have calculated these measurements themselves, too (or asked somebody to calculate them for them :D ).

 

[DaveC426913]

So the question is: Once you "take flight" within a zero-g central section, how do you get back to the wall? Especially if the pipe needs to have a thickness between 50 and 100 m minimum?
That sounds like another reason why the pipe should be subdivided into smaller corridors, so that you cannot get "lost floating in the middle" all that easily.

I think that's the cart before horse. The pipe would be jam-packed with systems, equipment, machines and other functions - there would be no reason to have large open volumes without walls - it would be a criminal waste of precious space.

Oh wow, and I thought my 3 kilometres for a crew of 500 to 1,500 people felt excessive. :) On the other hand, those 2000 probably have a much better quality of life.
However, that just goes to show again how other sci-fi authors can simply "make stuff up", like ships of an arbitrary length, O'Neill cylinders, Dyson spheres etc., without necessarily giving as much thought to how much mass would be required to build such a thing in the first place, and how fast you could propel it to reasonable interstellar speeds.

KSR's story had a different premise than yours. A significant portion of the habitable area was actually wilderness. Few or no humans (except for hikers); lots of room for native critters to roam and live their best lives. The Ship was designed to preserve whole Earth ecosystems with as much fidelity as practical.

 

[Melbourne Guy]

Even if you let the moon break into pieces, sf readers have no problems, so don't worry about physicists

Are you referring to Seveneves by Neal Stephenson, @BvU? My goodness, that was a long, laborious novel

And @Strato Incendus, try not to get bogged down in the physics of your generation ship. It not only steals great chunks of writing time, but few readers will break out the slide rule to calculate that the force vector on your third exterior strut exceeds the structural integrity of the graphene you've used to make it. But they will put your novel down if the characters are unengaging, the plot tedious, and the writing style clunky. Your posts suggest that last aspect won't be an issue, but its easy to load up on technical detail and forget to flesh out the cast. I've done it myself and know that it pretty much always gets in the way of enjoying the story.

 

[Filip Larsen]

That said, I was not thinking of 250 m to 300 m, since the rings have a lot fewer decks.

That's OK, I was just using that as an example to illustrate the principle for one particular model of the rotation.

Assuming you still want to have an idea of what rotational stability to expect for a set of 5 spaced-out rings rigidly attached to a cylinder (i.e. everything rotating together as a solid object) with inner ring radius $r_1=225\,\mathrm{m}$, outer ring radius $r_2=263\,\mathrm{m}$, cylinder (spindle) radius $r_c=0.1r_2$, ring width $b=32\,\mathrm{m}$ and a relative "average" mass density between the rings and spindle construction at 1, then one can plot the moment of inertia around the desired axis (Z) relative to the moment of inertia around the undesired axis (X) as a function of the gap between the rings. As long as the ratio is above one you should be good. In the plot below that is the solid line with the ratio on the left Y-axis, so (assuming I didn't botch up my equations or spreadsheet too much) gaps less than 80m should be good. The dashed line is for total length with the value on the right Y-axis.

 

[Strato Incendus]

I think that's the cart before horse. The pipe would be jam-packed with systems, equipment, machines and other functions - there would be no reason to have large open volumes without walls - it would be a criminal waste of precious space.

Good point! As I said before, I would want more sub-corridors anyway, since it makes for a better chase / hide-and-seek during the mutiny. With just one massive pipe 100 metres in diameter, it is easy to evade the guards, and there would be nowhere to hide.

The only places where the pipe does reach its full 100-metre ceiling height now (i.e., the full diameter) is at the hub of the rings. If the hub sections in the pipe rotate, too, I guess this would create some small levels of gravity in those sections of the pipe? They are obviously rotating too slowly to create Earth-like gravity, given their diameter is only 100 metres. But a little gravity in the hub sections of the pipe would actually be helpful to get people towards the elevators - since those four elevators would be rotating around you while you are standing / floating in the central pipe at one of the ring hub. The elevators A-D then travel down the four spokes of each ring.

Here is what I imagine this to look like (just a non-proportional sketch I made in Photoshop Elements on a Public-Domain background):

KSR's story had a different premise than yours. A significant portion of the habitable area was actually wilderness. Few or no humans (except for hikers); lots of room for native critters to roam and live their best lives. The Ship was designed to preserve whole Earth ecosystems with as much fidelity as practical.

Ah yes, that is what I thought. In my case, there are neither any animals on board (the very first captain brought his dog along, but of course it died long before the plot starts), nor is there any traditional farmland: There are hydropons for vertical farming, and all the meat is grown in the lab (in-vitro meat).

And @Strato Incendus, try not to get bogged down in the physics of your generation ship. It not only steals great chunks of writing time, but few readers will break out the slide rule to calculate that the force vector on your third exterior strut exceeds the structural integrity of the graphene you've used to make it. But they will put your novel down if the characters are unengaging, the plot tedious, and the writing style clunky.

I fully agree - right now, I am just discussing what I consider the absolute basics, the bare necessities: I need to know how long my ship would reasonably be, how thick the central trunk etc., in order to even understand how much space I have to work with for all my scenes. It is far easier to decide this in advance, while a lot of the combat scenes are still rather vague in my mind, than to rewrite the whole thing because I made one conceptual mistake at the beginning.

In terms of characters, I think that is where my main worldbuilder disease shows: The premise "one couple from each country" really makes it tempting to keep adding in more and more people and connecting their personal motivations as an individual to at least fractions of their origin on Earth.
Sure, the more important thing is the depth of the main characters - which is why those were created differently: Namely, from the different ethical conflicts that could arise on a generation ship. (Basically, for every major ethical problem I see with the premise, I made one character or couple that has to deal with it somehow in their personal lives.) Of course, those main characters have specific places of origin on Earth, too, but the relevance of those is more in the background, compared to the side characters.

Sometimes I will just start working on a side character's profile, and suddenly I start getting more and more ideas for that specific character, expanding upon their personal motivation and history, until some of them turn into secondary main characters.

It was quite interesting to see which characters naturally emerged as more important as a result of this process - like "throwing a lot of ideas into a Campfire Pro file and seeing what sticks". In particular, in terms of originally unplanned side characters, I now have this security officer of Cambodian descent, and a deputy pilot with Somalian ancestry, both of whom draw their own historic analogies between what is happening on the ship and what has happened in their ancestors' homes back on Earth.

As of my ideas yesterday, the new chief engineer overseeing the nuclear-fusion reactor is a guy with ancestors from the Oceanic island nation Vanuatu, who chose this profession because, if it had not been for nuclear fusion, most likely his ancestors' home would have been swallowed by rising sea levels due to climate change. (His sister started working in the in-vitro meat lab for similar reasons.) Currently, in our present day, the climate-change-based threat especially for the islands in Oceania is of course still very much a real one - with Vanuatu being most affected. So it is not just a gimmick for the story, it does have real-world relevance.

That is just one example of how a character's ancestry can inform their decisions within the confines of this spaceship. Even though, as I said, of course neither of them has ever been to their ancestral home. But depending on which place on Earth someone still feels connected to, their ideals and and worries about where the ship's culture is headed vary.

As long as the ratio is above one you should be good. In the plot below that is the solid line with the ratio on the left Y-axis, so (assuming I didn't botch up my equations or spreadsheet too much) gaps less than 80m should be good. The dashed line is for total length with the value on the right Y-axis.

Great, thanks a lot again, especially for the making the graph! :) That is precisely the kind of guidance I was hoping for, to at least get into the right ball park with the ship measurements. Turns out I probably would have made the ship way too long otherwise.

Right now I would go with a between-ring distance of 60 metres each, then.

However, there is one thing I still have to factor in that I had not realized yet last time regarding the thickness of the rings:
The corridors on the inside are 32 m wide. Since I want the rings to dismantle and break down into their subsections A-D at the end, I need either the side walls or the ceilings to be thick enough to contain the door wings that seal off the entire corridor at that point.

If I hide the door in the ceiling / floor, even if it closes halfway from the top, halfway from the bottom, the same will be true for the floors above and below. Which would mean the ceiling thickness between each deck would have to be just as high as the ceiling height of the corridor itself. This seems like a bigger mess, because it would change the outer ring circumference, thereby the surface area on each deck etc.

If I hide the doors in the walls to the left and right, this means I need an additional 16 metres on each side so that the door can be flushed into the wall - and then when they come out during the dismantling process, together they will seal off the entire width of 32 metres.
I like this solution better, since it would also give me plenty of room left and right of the corridor for electricity and water pipes (which I need along the entire ring anyway). Water might even serve as an additional protection against radiation, I have heard from Isaac Arthur. But simply surrounding each ring with a wall of water on both sides sounds not only like a huge increase in overall mass, but also seems dangerous in case of an inward leak that could flood the entire corridor.
Then again, especially on the habitat ring, I need somewhere to store all the water for the bathrooms of the individual quarters. So perhaps the entire ring should be surrounded by water, and maybe the central pipe, too.
(Of course, arranged in such a way that it does not cross the electricity pathways).

Using just the inner thickness of the ring (which requires the same width for the hubs of the rotating sections in the central pipe), we would end up with 5 * 32 m + 4 * 60 m (between the rings) = 400 m minimum length for the entire ship. Those would just be from the first ring to the last, without a rear end (engine room / exhaust pipes etc.) and a bridge section / cockpit.
However, given the necessity for the additional 2 * 16 m walls on each ring, every ring has an outer thickness of 64 m. So that makes 5 * 64 m + 4 * 60 m = 560 m minimum overall ship length. And then, adding some additional length at the rear and front end (e.g., 100 m at the rear, 200 m at the front), I would end up with an overall ship length of 860 m.

Does 60 m inter-ring distance still work if I change B from 32 m to 64 m? As far as I understood, the graph you made is specifically for B = 32 m.