# How fast can a ship with rotating habitats be accelerated?

Alright so I'm not really a physics person by any stretch so forgive me if I butcher some physics jargon on this post.

So I'm making this hard sci-fi interstellar ship with a rotating habitat that can house its crew as the usual trope we all see. So I thought it would be powered by fusion rockets and matter/anti-matter hybrid engines allowing it to reach approximately 60% lightspeed travel in space. So I already figured that out but there's one thing that is actually bothering me a bit.

Can a ship with a rotating habitat be stable as it travels space that fast for years? And I know there's no wind in space which would be a threat to its stabilization but let me show you an example.

The ISV Venture Star (Avatar)

So in universe, The ISV Venture Star was the second transport ship developed by the RDA that transports a thousand crew the fictional planet of Pandora in the Alpha Centauri system.

A hybrid engine itself, it uses solar sails to travel from Earth to Pandora with the capacity to travel 0.7 or 70% lightspeed.

The ship is approximately 1,646m long & 330 m wide.

So I figured that this was a very great hard sci-fi design indeed and one of the best. But there was one thing that I didn't notice until a friend told me.

So in the beginning of the film the habitat section was completely in rotation and functional. But it turns out that the Venture Star was a sleeper ship.

The majority of the crew is kept in stasis for the duration of the flight and that these modules are actually folded parallel to the ship when everything is under thrust.

Then I started thinking, If we accelerate a ship at at those tremendous speeds similar to the Venture Stars capabilities, Is it actually possible for a ship with a rotating habitat to do so? I mean, would it have an effect on the habitation's stability and the people inside it?

And the Venture Star was not really a rotating torus as it was just two sections linked by a passage.

But what about a ship like this:

or this

Can ships with large rotating torus habitats be safely accelerated at tremendous speeds? Or is there actually a limit to how fast these ships should travel to safely navigate in a stable manner in interstellar space?

If so, how can it affect the Coriolis effect on-board if it were to travel that fast and the physical problems it would cause for the ship.

This was just something I'm wondering so I just want to hear from people who are physics savvy on what they have to say about this.

• You've got quite a few questions in there; some of them unrelated to each other ("Is it safe to accelerate a ship like this to those speeds?" is a very different issue to "could a ship with a big centrifuge be accelerated to high speeds?"). I'm happy to roll out some answers, but it is likely to be a bit of a wall'o'text! – Starfish Prime Jun 23 at 8:11
• Welcome to worldbuilding. Your question has some loose ends.What do you mean with accelerating to 60% to 70% range? I know it is a jargon one hear in many sci fi stories, but nobody is tasked with answering questions there. Then, we enforce a 1 question per post policy, you have more than one. Last but not least, you are asking those questions for a couple of configurations. This makes the post too broad. Please take the tour and visit the help center to understand what we expect from a good question, then rework your post to fit our standards. – L.Dutch Jun 23 at 8:34
• I would recommend trimming out the background about Avatar (which, as you note, has a completely different ship design anyhow) and focus on your base question of whether sustained high speeds would have any drawbacks on a ship with centrifugal gravity. – Cadence Jun 23 at 9:02
• You might read "Rendezvous with Rama" by Arthur C Clarke. At one point they describe certain features of the interior of the cylindrical world they are exploring as showing a maximum limit for acceleration and maneuverability of the craft (and this is not the engines they are describing). – StephenG Jun 23 at 9:41
• The speed of the ship is irrelevant. Only the acceleration has any impact on the structural integrity of the ship: on a long enough flight, you can accelerate slowly to your maximum velocity without increasing the duration of the voyage by all that much. – Adrian Hall Jun 23 at 14:23

Can a ship with a rotating habitat be stable as it travels space that fast for years?

The speed it travels at is irrelevant. The stability is important, but quite unrelated... the interesting gyroscopic effects of rotating bits of spacecraft applies just as much to starships as "stationary" habitats. It is in the nature of starships that you will need enormous engines (or other devices to provide thrust, like a photon sail) and enormous shields and huge reaction mass tanks (for rockets) and supplies and all the rest... this works to your advantage, because the rotating part of the ship can be relatively light and small compared to the rest which will help with stability. Combined with reaction wheels and reaction control thrusters, your ship should be stable enough.

If we accelerate a ship at at those tremendous speeds similar to the Venture Stars capabilities

Pedantry alert: you don't "accelerate at a tremendous speed". Acceleration is the rate of change of speed. If relativity is to be believed (and evidence suggests that we probably should believe in it) one inertial reference frame is pretty much like another. So from here on, I'll ignore speed (almost) entirely, and concentrate on acceleration because that's all that matters.

I believe that the Venture Star was designed to be accelerated at 1.5g, which is an impressive figure. At that rate, you don't need your spun gravity... you'd just turn it off. Given that modern day engineering is capable of making structures that can withstand 1G of acceleration for extended periods of time, having your spun sections cope with 1.5G should be no problem, especially if you parked them ahead of time. Which is of course exactly what the Venture Star did.

Can ships with large rotating torus habitats be safely accelerated at tremendous speeds?

You've got three quite separate issues.

1. Are the support structures capable of standing up to the main engine thrust, even when the rotating sections are parked? I'm going to assume "yes", because having a ship that falls to bits when you press the go button is a bit embarassing.

2. Are the bearings up to snuff?

That's harder to say. With the engines switched off, the forces on your bearings are largely radial. Turn them on though, and now the hub is being pushed forwards and the outside will naturally want to lag a bit. You now have to use thrust bearings instead of simple bearings, which will increase the complexities of the engineering somewhat.

3. What happens to the direction of artificial gravity when the engines turn on?

It'll start pointing backwards, is what will happen to it, because the contents of the spun sections will be experiencing acceleration due to both centrifugal and engine thrust forces, and those vectors will add up and point somewhere other than straight towards the stern or straight away from the axis.

Here's a couple of helpful diagrams shamelessly stolen from Project Rho's informative page on spun artificial gravity, which you seem to have visited before but might be worth you revisiting:

If you're prepared to park your rotating sections before lighting up your engines (which for a toroidal gravity deck simply means reducing its rotating to zero rather than folding it up too) you can avoid these problems, but if you want to combine both forces (eg. because you have low thrust and you run your engines for a long time) you'll want to have intermediate, angled positions so that your artificial gravity vector always seems to point down.

Here's a nice example of acceleration due to gravity (indistinguishable from thrust due to your engines) combined with centrifugal forces:

(also demonstrating that we are capable of making suitable bearings capable of withstanding forces as strong as 1G of thrust, though making it work for years in a vacuum is left as an exercise for the reader). Note the outward movement, with hinge points at the top of each tether. Youtube link for a slightly more exciting ride.

Take home message: a torus is great if you're not accelerating, that's why they appear on lots of habitat designs. A starship will necessarily have long periods of acceleration, which makes its use inconvenient during those times. The ratio of thrusting to coasting will inform your design. A torus might be best for very long coasting flights.

Or is there actually a limit to how fast these ships should travel to safely navigate in a stable manner in interstellar space?

Your speed limits in space have little to do with your artificial gravity.

Firstly, you're very sharply limited by your drive technology. For a rocket, even a super high tech beam core antimatter rocket like the Venture Star, you are limited by your exhaust velocity. For a beam core antimatter rocket, that exhaust velocity is about 30% of the speed of light (for reasons I'm not entirely certain about; the pions coming out of an annihilation reaction are travelling at .94c, but the quoted pratical exhaust velocity figures for beam core rocket designs are lower than that, eg have a look at the Robert Frisbee's excellent paper How to build and antimatter rocket for interstallar missions which goes into some detail on the issues and performance of antimatter-driven rockets).

Your ship's delta-V, $$\Delta V$$, is the maximum change in velocity it can perform. If you carry all your fuel and reaction mass with you and travel at modest speeds, this is constrained by $$\Delta V = V_e \log_e(R)$$ where $$V_e$$ is your exhaust velocity, $$\log_e$$ is the natural logarithm function and $$R$$ is the ratio of the fully-fuelled mass of your ship to the unfuelled mass.

Important Note By "modest" I mean "not too close to lighspeed". As your Lorentz factor creeps up (and by .6c it is a non-ignorable 1.25) the less you can make use of simple equations (as Hypnosifl helpfully pointed out). Similarly, when you're using a rocket where a substantial amount of the stuff going out the back simply turns into photons and departs unhelpfully, you can't just use the regular equation. The highly complex and ugly relativistic antimatter rocket equation is available in Frisbee's paper, if you're feeling brave. For simplicity, and to give you a rough idea of what you're up against, I'm ignoring it. Just remember that the numbers I'm giving below are hugely over-optimistic, and real figures will be much, much worse.

Now, that said: If you want your $$\Delta V$$ to equal your $$V_e$$, you need a mass ratio of $$e$$ (or about 2.72). To add anothe $$V_e$$ metres per second to your $$\Delta V$$, you need to multiply your mass ratio by $$e$$. If you want to get to 60% of lightspeed and your $$V_e$$ is 30% of lightspeed, you need a mass ratio of about $$e^2$$ or 7.4. To get back down from .6c to 0 again, you'll need a total $$\Delta V$$ of 1.2c and hence a mass ratio of $$e^4$$ or 55. For a 10000 tonne starship, that means you need more than a quarter of a million tonnes of antimatter on board, and good luck with that.

Take home message: Rockets are terrible for interstellar travel. There's a good reason the Venture Star used a laser sail for boosting (though I prefer sailbeam designs). You should probably use a magnetic braking sail too.

The second issue is shielding. You'll note that the Venture Star diagram you've shared has a massive stack of plates marked "debris shielding". I won't go into the details of shielding a ship trucking along at a decent percentage of the speed of light, but it is hard and the damage it will take will be punishing. Lose that shielding and you're dead. Your speed is therefore limited by how much shielding you can get your engines to push. Centrifuges won't come into it.

Oh, and a third potential issue:

safely navigate

Navigating starships is tricky, because working out which way you have to go isn't entirely trivial. Once you've solved that issue, you light up your big rocket (or other boost mechanism) and away you go... you don't need to do much steering on the way.

In the case of spun sections, that's very important. Off-axis accelerations, such as those caused by rotating the ship, will have all sorts of very unpleasant effects and will definitely put large and uneven loads on your bearings. Turn off the rotation before turning!

(also, partial turns at high speeds are a terrible idea, because you'll get high-velocity crud slipping past your shield and wrecking your ship. don't turn at high speeds. interstellar flying should be in straight lines.)

If so, how can it affect the Coriolis effect on-board if it were to travel that fast and the physical problems it would cause for the ship.

Important note: the artificial gravity is provided by the centrifugal force, not by the coriolis force. The former affects all objects in a rotating frame, the latter only affects objects which have a velocity vector relative to that frame (eg. a person walking around in your hab section, or a dropped object, etc).

So long as you're thrusting along the rotation axis of your gravity decks, and so long as your bearings are strong enough to withstand the force of the engine thrust and the stresses of your rotating sections, you'll be just fine.

• Great answer, but one little issue--the equation you give for delta-v as a function of the fully fueled/payload mass ratio and exhaust velocity is the classical one, if you get up to a significant fraction of light speed you have to use a slightly different equation for a relativistic rocket, delta-v = c * tanh((v_e/c)*ln(R)). Some calculations for the mass ratio for an ideal relativistic rocket with exhaust velocity c can be found here. – Hypnosifl Jun 23 at 20:06
• @Hypnosifl that's a reasonable point; the lorentz factor at .6c is 1.25, and I was kinda handwaving it away (because its boring until you get to .86c *cough*) and probably shouldn't. – Starfish Prime Jun 23 at 20:07
• @Hypnosifl its actually even worse than that for beam-core rockets like the OP is considering, because you get weird effects with mass being lost without imparting useful reaction force. There is a relativistic equation for antimatter rockets, but it is horrible so I'm choosing to ignore it ;-) – Starfish Prime Jun 23 at 20:33
• Doesn't that just mean lowering the effective exhaust velocity in the relativistic rocket equation, rather than needing a different equation? Or are you talking about an equation for the effective exhaust velocity? – Hypnosifl Jun 23 at 20:38
• Looking at the derivation, I think the V in that equation may have a different meaning from the "effective exhaust velocity" in the standard relativistic rocket equation--he seems to assume a certain fraction of the fuel exits parallel to direction of travel with velocity V and a certain fraction exits orthogonally (or is otherwise wasted) and therefore not considered to contribute to the ship's acceleration at all, whereas normally v_eff takes into account that all exhaust particles don't move parallel to travel direction. So his equation is probably equiv. to normal rocket eq. with v_eff. – Hypnosifl Jun 23 at 21:59

If you have ships capable of reaching .6 c, rotating habitats are not only unnecessary, they're counterproductive. Your main concern isn't getting 1 g acceleration to keep the crew from getting sick from weightlessness, it's getting only 1 g to keep them from turning into the new paint job. Accelerating at about 1 g, it would take about 200 days to get to 60% c and it would take the same amount of time to slow down for rendezvous with the target. What you would want to do is constant 1 g acceleration for half of the journey and constant 1 g deceleration the rest of the way. That's as fast as you can go anyway and it also coincidentally completely solves the micro-gravity problem.

Edit: To answer the question directly, considering the only purpose of a rotating habitat is to keep the human passengers healthy, about 3 g would be a hard upper limit. Sustaining those kinds of forces for a period of days or more might be possible. Any more and there's no way the hearts of the passengers could pump blood up from their legs. The technology currently exists to build bearing that could take that kind of beating so whatever the passengers can survive, so will the habitats.

• A rocket that can do a 1G brachistochrone to another star is so astonishingly unbelievably difficult to make that it makes a mere beam-core antimatter ship with a rotating gravity section seem positively easy. – Starfish Prime Jun 23 at 14:28
• If you can do close to 1 g, like .5 g or .2 g even, you can probably do 1 g with optimizations and a bit of suspension of disbelief, this is all very theoretical anyways. If you're off by orders of magnitude, how do you even get to .6 c within a human's lifetime? That's my thought process anyway. – Sac_Winged_Bat Jun 23 at 14:33
• No, you can't just do 1g if you can do .1g. A tenfold increase in rocket performance isn't an optimisation, its an engineering revolution! – Starfish Prime Jun 23 at 14:43
• I don't think this actually answers the question in any way. – Ash Jun 23 at 14:53
• I mean that the current estimations for very theoretical propulsion methods could feasibly, and for the purpose of fiction believably, be off by a factor of 10, much less by a 100 or more. – Sac_Winged_Bat Jun 23 at 14:55

The basic answer is "of course" but that answer comes with a caveat which is "if you're willing to take the time to do it" i.e. if you only accelerate at 1/1000th of a gee you can almost certainly leave your rotational sections running while you do so. It will take your ship a very long time to get up to a noticeable fraction of the speed of light but you will get there eventually.

If you want to boost up to 0.1c in the space of minutes or hours it's a different story; that kind of acceleration is going to be a brutal strain on the fabric of your ship already without having things like floating bearings in it's design let alone working.

Any acceleration that is a noticeable fraction of the pseudogravity being produced by the rotation will cause a decided "lean" in the net gravity felt by any inhabitant.

Precession is an issue that needs to be addressed at the design stage to ensure that ships don't "wobble" in their course.

• The effects of precession could be minimized by having two (or an even number) of counter-rotating rings. – Michael Seifert Jun 24 at 18:08
• @MichaelSeifert Yup that's one design solution, a simple counter spinning gyro could also work I believe it's an issue that needs to be addressed but it's not a major obstacle. – Ash Jun 24 at 18:23

For rotation, you need a bearing. For a section that size and operating that long I see no realisitc alternative except for an active magnetic / electric bearing. The benefits of this type over closest alternatives are:

1- low to negligible friction - less wear / decreased maintenance and risk of failure

2- gaps in front and back between rotor and outer race of the bearing are monitored by inductive sensors and compensated by the controller. This will counteract vibration before it increases destructively. With a bearing this size, that could amount to a non-trivial amount of power needed to stabilize the rotor.

That said - I think it would not be a great idea to keep this assembly rotating during acceleration / deceleration. As acceleration places load on the spaceframe, the bearing's rotor (and everything it is supporting) will be pushed back towards the engines likely overpowering its compensator. It would be grinding against the back of the race and given this size it would likely just shatter. I could see it having a "locked" position where some kind of caliper brakes immobilize the rotor and picks up the structural load. That means spinning down the torus before a hard burn - and spinning it back up to desired rpm once the burn is complete.

If it's easier acceleration like from a light sail or ion drive then as long as you're within the compensation range of the bearing you'd be ok.

• You do not need a bearing - the entire craft could rotate. – StephenG Jun 23 at 12:14
• If your only concern was the habitat modules, yes that is the simplest option. But there could be other mission critical systems like sensors that need to remain stable. Creator's call – Adam Coville Jun 23 at 12:33