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I want to design a realistic interstellar spaceship that uses centrifugal force for only the crew quarters. But while looking up for designs I found the most common ones are the torus or ring design.
The other is the modular design.
So which one is better for interstellar travel?
Modular designs are slightly easier to build, much easier to extend after being built, are much easier to isolate sections and allow you to have a pivot at the hub-end of each arm so the direction and strength of the artificial gravity can be maintained even under thrust.
Contiguous torus or cylindrical shapes will have weird effects at boost time and brake time, because the direction of gravity will not be "down" from the point of view of the contents. This isn't a problem for space stations, or spacecraft coasting, or even spacecraft on relatively short-haul flights with brief engine burns, but given that starships are likely to have exceedingly long boost and brake phases (possibly years) you want to design your gravity decks to handle that situation. There's a related question on this site that might be relevant (warning: it contains a long rambling answer by me): How fast can a ship with rotating habitats be accelerated?
If your starship is travelling reasonably quickly (by which I mean "could get to another star in under 100 years) you'll need a decent amount of forward shielding to protect your ship from collisions with interstellar dust, and reduce the radiation hazard of incoming particles. Shielding is dead mass, so really you want as little of it as possible. You therefore concentrate your shielding at the front of your ship (or habitation section) and have a loooong structure behind it. A cylindrical shape with a shielding endcap gives you much more volume for a given shielding area than a torus will. I found a nice paper on a segmented cylindrical starship design recently, and I seem to have lost it. Sorry :-(
Finally, do consider that frozen or dessicated meat cargo won't care about artificial gravity though, and will be easier to pack and shield.
In the absense of the segmented design I had hoped to share, consider instead the ISV Venture Star, the starship from Avatar.
Spun gravity section highlighted in red (modified image taken from Galaxy's spun gravity question linked above) currently folded up for thrust mode. The gravity section is tiny, it remains useful under high thrust, almost all of the payload is in unspun storage sections. Most of the rest of the design of the ship is pretty high quality too, with the slight exception of the mid-course flipover (which is suicide) and using rockets to brake instead of a magsail. That aside, this is an excellent starting point for any starship design question.
Lets have a quick look at the "continuous thrust" approach to providing artificial gravity, though.
It'll take you about 11 years, 285 days (from the point of view of an external observer) to fly to somewhere 10 light-years away at a continuous 1g and stop at your destination. At the turnaround point, you'll be travelling at about .987c, a Lorentz factor of ~6.16, and you'll have a kinetic energy of about 4.6x1017 joules per kilo of ship. A 100000 tonne starship requires an average engine power of about 2.5x1017 watts over its entire flight time, which is about 1.14 on the Kardashev scale.
Every nucleon you hit at that speed has about 6GeV of energy (compare with the ~2GeV of energy released when a nucleon and antinucleon annihilate), and you'll need shielding equivalent to several tens of metres of water per square metre of ship cross-section to keep all organic and electronic things safe. A 10m radius cylinder would therefore need at least 6000 tonnes of frontal water or ice shielding (realistically you'll want more more, especially if you have to handle mass loss over the journey!), not including shielding mass for galactic cosmic rays and for whatever drive system might be used.
The longer the distance flown, the worse this will get because the peak speeds will be that much higher.
Neither, because you don't want centrifugal gravity at all
There are two things that are important for interstellar travel;
1) Going really fast
2) Not hitting things
Dealing with these in order, your interstellar craft needs a constant thrust engine for the journey. Why? Because you're travelling very long distances, and if you have an 'always on' engine, even if the acceleration is low you'll still benefit from the compounding of velocity over interstellar distances by comparison to a normal chemical rocket that gives you very good acceleration over a short period. So what you want is a very efficient ion or plasma thrust engine that can achieve accelerations of between 4 to 10 m/s2 over years, preferably decades.
Why that specific range? Well, Earth's gravity accelerates us towards the core of the planet at around 9.8 m/s2 so that means that the acceleration range above would give you an acceleration range that would be between 0.4 and 1 earth gravities, meaning that your crew wouldn't need rotation to be comfortable, the ship would do it for them. Half way there, you just turn the ship 180o and keep thrusting - your engine is then slowing you back down but for the person on the ship, it's going to feel exactly the same and you don't even have to flip your furniture onto the ceiling.
As for not hitting things, any acceleration engine capable of such thrust levels for a sustained period is going to have you going really fast, especially around the mid point of the journey. Depending on where you're going, you may end up at some proportion of light speed, meaning that even interstellar dust is going to be a problem for you. How do you avoid it? Well, two ways; have a large shield in front of you of expendable matter, like an ice shield, and not making yourself a large target.
In point of fact, you want to have the lowest front profile possible so that you're not having to increase the size of your shield (and therefore your mass) any more than is necessary.
Ultimately, what that means is that your interstellar ship is going to look more like a lighthouse than a hamster wheel. Your crew is going to experience what feels like gravitational force from the constant thrust of the engine and you're not going to have anything protruding out the side of the ship if you can possibly avoid doing so.
Add to that the fact that having angular velocity means more moving parts, more maintenance, more that can go wrong on your journey, and it becomes clear that putting spinning sections on your ship is only making a rod for your back. It's just not what the ships are going to look like in the future, no matter how impressive the concept art may be.
Somewhat counterintuitively, I would suggest the issue isn't really the artificial gravity at all, but rather the protection of the spacecraft and systems from the effects of high energy radiation and impact with interstellar gas molecules and dust particles when travelling at high fractions of c.
The ship will need to be protected by various active or passive systems, which will likely lead to designs which may resemble the classic "ice cream cone".
Space isn't really like you expect
This can work either way: the protective mass (likely ice) will be packed in the "top" of the cone and the ship accelerated with the wide end forward. This will have the dual purpose of putting as much protective mass as possible forward and using the mass as a form of "wake shield", so the rest of the cone travels in a much harder vacuum than even interstellar space. The rotating torus or modules can be housed inside the cone, although due to size considerations they will need to be forward close to the protective mass to ensure the ring is large enough to achieve the desired amount of gravity at a low rotational speed.
Inverting the arrangement would then see the pointed end of the cone facing the direction of travel, and the cone itself would be made of ice, rock or some engineered composite material. The rotating part would then be shielded by the mass of the cone, and can be relatively larger since the cone can be extended to match the diameter needed. This would also permit a somewhat easier arrangement for active defence, a laser can be mounted along the axis of the cone to ionize offending particles, and a magnetic or electrostatic "mesh" can be placed along the outside of the cone to deflect the particles away. The advantage of this is the machinery can be packed in the cone without having to interfere with the rotating life support section, which is essentially towed along behind the cone.
Given the tyranny of the Rocket Equation ("every gram counts"), either arrangement would likely require some sort of beamed energy system to provide power external to the actual spaceship. The "point rearward" spaceship might actually resemble a pine cone, with hundreds of separate panels to capture the incoming energy or act as radiator panels
Space travel can be organic as well
Since to my way of thinking, simplicity should be the key, in either arrangement the life support section should be a torus fixed to the ship's structure itself (the entire ship them rotates around it's axis) to eliminate rotating joints and other possible points of failure. Variable gravity due to acceleration can be accounted for in design (if there is a constant acceleration, the "floor" can be tilted to reflect this), or the crew simply uses hand rails and other mobility aids if the periods of acceleration and deceleration are short. In very extreme cases, such as 1g acceleration, the rotation is simply stopped and the crew and equipment is oriented with "forward is up", while when not under acceleration the ship rotates and "outboard is down". Fittings are simply moved to match the prevailing vector of gravity.
Protection is the key. Even if the ship is postulated to have the crew in free fall for most of the voyage, the crew and life support compartment still needs to be protected from the effects of high energy radiation and the impact of gas molecules and dust particles.
As others have already pointed out, the rocket equation is brutal and the mission will dictate the spacecraft design. Even highly efficient fusion or antimatter drives don't perform well enough to make interstellar travel really convenient. Your only hope is to circumvent the rocket equation. Your best hope are concepts like Sail Beams, as they put the fuel and ejection mass back into your home system and away from the spacecraft. This means that the rocket equation no longer applies to you.
Beamriders need large, circular magnets to generate the magnetic fields which transfer the momentum from the sails plasma to the spacecraft. These possibly kilometer sized megastructures are where you would want to attach your infrastructure, optimally distributed around the rings. There are several options here, none of which seems superior. You could build a rotating ring on the in or outside of the magnetic ring and get a huge radius for free. A huge radius makes things a lot easier with spin gravity. A passenger liner might be best suited for such a setup. You could also use several small centrifuges, either rings or modules at an 90 degree angle to the main ring. This is probably better for cargo haulers and has the nice side effect that you can watch the relativistic kill missiles you use for propulsion fly through the vessel a few hundred meter from you if the craft is decelerating. If you are into that.
Comparing the two approaches I would say that the rotating ring probably has a few advantages over the distributed modules. Firstly it's size will make operating it slower possible and their size reduces the effects of tidal and coriolis forces. Furthermore, the great ring makes combing acceleration with spin gravity easier. Angeling the floor, possibly in an adjustable manner, will do the trick. The smaller habitats will constantly experience some shift in the strength and angle of gravity. This isn't great, but one would probably get used to is.
One other option to consider would be to use very small sleeping and working spaces which have gravity. Centrifuges must be large because of tidal and coriolis forces, but both are much less severe if one doesn't move. These centrifuges could have diameters significantly under 10 meters. You sleep in there and you do your desk job work in there. And you don't move.
As a side note, you will come across people who will claim that humans need exactly one G, 10 m/s^2, to be fine on a spacecraft. There is no scientific basis to this claim. We only know that 0G is bad for us and that 1G is survivable. We got no data for gravities in between. A lot of the effects of 0G are due to the total lack of gravity. Maybe even 0.1 G is perfectly healthy if one exercises enough. Maybe we truly can't survive outside a 1G environment. We simply don't know yet. But for your story assuming that low G is enough will make spacecraft design easier.
