Rotating Spaceships

[Rossco]

Quick question for our space guys;

In lots of fiction/close to reality films including Stowaway, they depict rotating spaceships with each 'end' of the rotating ring being huge.
Is there a reason for this? (Other than it looks cool?) is it something to do with speed? i.e the smaller the ring the faster it has to turn to achieve the same G levels?

[KelvinZero]

Do you mean why is the radius large? There is evidence that a small radius would make people feel nauseous because the force would be different between head and toes, and there would be weird effects to you balance sense when you turn your head.

Here is a nice youtube clip that talks about the issues and makes a guess at how small a radius we could get away with:



(but generally speaking, the bigger, the more comfortably earthlike the sensation of gravity would be.. we don't know for certain what radius humans would readily adapt to)

[Rossco]

That's great, thanks for the reply, I'll have a watch of the video later.

My question was based on a video from SpaceXvision of their artificial gravity Starship concept, they show two sides extending out of each side of the Starship, which in principle is a fine idea, however they extend theirs out massively which then got me thinking if it would be that necessary or if just expanding it closer to the body would give the same result.

[daedalus1]

That's great, thanks for the reply, I'll have a watch of the video later.

My question was based on a video from SpaceXvision of their artificial gravity Starship concept, they show two sides extending out of each side of the Starship, which in principle is a fine idea, however they extend theirs out massively which then got me thinking if it would be that necessary or if just expanding it closer to the body would give the same result.

There is no need to rotate the spacecraft around its longitudinal axis thereby requiring large diameter. It can be tumbled end over end . As the spacecraft is probably already quite long there is no need for extra hardware.

[jbenton]

That's great, thanks for the reply, I'll have a watch of the video later.

My question was based on a video from SpaceXvision of their artificial gravity Starship concept, they show two sides extending out of each side of the Starship, which in principle is a fine idea, however they extend theirs out massively which then got me thinking if it would be that necessary or if just expanding it closer to the body would give the same result.

There is no need to rotate the spacecraft around its longitudinal axis thereby requiring large diameter. It can be tumbled end over end . As the spacecraft is probably already quite long there is no need for extra hardware.

I heard that there was an idea to have 2 Starships launch together, and have them dock (during the coast phase) from the aft end (which is designed to dock with a tanker anyways). That would give them twice the length for end over end tumbling.

[Rossco]

I think its the thought of having the whole thing tumble end over end is somewhat less elegant - forgetting of course, there is no 'up down forward or back' in space & the need for aerodynamics is also not required. 

[Paul451]

they depict rotating spaceships with each 'end' of the rotating ring being huge.
Is there a reason for this? (Other than it looks cool?) is it something to do with speed? i.e the smaller the ring the faster it has to turn to achieve the same G levels?

Yes. Centripetal acceleration is inversely proportional to radius, and proportional to the square of RPM. Ie, double the speed of rotation, you get four times the g-load. Halve the radius at the same RPM, you halve the g-load.

In addition, there was a lot of early research which said people couldn't adapt to higher rates of rotation. (There was also concern about having a large difference in g-levels between your head and feet.) So if you wanted higher g-loads, you would have to have a very large radius. For example, if you were limited to 1 RPM and wanted 1g, you needed a spacecraft more than a mile wide.

If you want to play with the numbers, there's an online calculator at: https://www.artificial-gravity.com/sw/SpinCalc/

Play with radius in units you're comfortable with (and remember it's radius not diameter), acceleration in "g" (Earth gravities) and angular velocity in rotations/minute (RPMs). Use different sizes, spins, etc, to see the relationships between size/spin/g-load. (Ignore the tangential velocity. Useful for catapults, but not relevant here.) The coloured indicators will also give you the "safety/comfort" according to the older research.

However, more recent research suggests people can adapt to extremely high RPMs, and that differences between head/feet aren't an issue. Throw in that we don't have any data of the lowest acceptable levels of gravity to avoid micro-gravity issues. It will likely turn out that the only thing limiting how small you can go is the physical space you need for the astronauts. But the maths of size/spin/g-load still applies.

[Rossco]

That's great info, thanks for the reply. Interesting stuff.

[Vultur]

However, more recent research suggests people can adapt to extremely high RPMs

That's really cool/promising! Do you have any links or names of papers?

[Paul451]

However, more recent research suggests people can adapt to extremely high RPMs

That's really cool/promising! Do you have any links or names of papers?

If you go to Spincalc, Ted discusses old vs new research in his sources section. You want Lackner and DiZio as your starting point. However, most of their work is on trying to "break" the vestibular system in order to figure out how it works, pure research. But some of their early stuff was directly related to spin-gravity. For example: https://www.researchgate.net/publication/8607002_Adaptation_to_rotating_artificial_gravity_environments (semi-paywalled.)

Abstract
A series of pioneering experiments on adaptation to rotating artificial gravity environments was conducted in the 1960s. The results of these experiments led to the general belief that humans with normal vestibular function would not be able to adapt to rotating environments with angular velocities above 3 or 4 rpm. By contrast, our recent work has shown that sensory-motor adaptation to 10 rpm can be achieved relatively easily and quickly if subjects make the same movement repeatedly. This repetition allows the nervous system to gauge how the Coriolis forces generated by movements in a rotating reference frame are deflecting movement paths and endpoints and to institute corrective adaptations. Independent mechanisms appear to underlie restoration of straight movement paths and of accurate movement endpoints. Control of head movements involves adaptation of vestibulo-collic and vestibulo-spinal mechanisms as well as adaptation to motor control of the head as an inertial mass. The vestibular adaptation has a long time constant and the motor adaptation a short one. Surprisingly, Coriolis forces generated by natural turning and reaching movements in our normal environment are typically larger than those elicited in rotating artificial gravity environments. They are not recognized as such because self-generated Coriolis forces during voluntary trunk rotation are perceptually transparent. After adaptation to a rotating environment is complete, the Coriolis forces generated by movements within it also become transparent and are not felt although they are still present.

I suspect the reason the early research got such different results (both from newer results and from each other, where the nausea limit could be as low as 1RPM or as high as 6RPM) is that they missed the importance of movement to retrain your brain. We also have a default assumption, which I've heard in many spin-gravity/rotating-spacestation threads, that we could tolerate higher RPMs if we limit head movement. We probably also limit head movement if we experience nausea, which compounds the variation between research.

The trick during training seems to be to reduce RPM below the point of nausea, then move around to adapt. Then increase the RPM to the new limit of nausea, move around again. Rinse-repeat until you reach the desired rate of spin. So the early research that produced higher limits, I suspect that when trying to find "the" limit, their testing protocol was to test at low RPM, have the test subject move their head/body around to test whether they were experiencing nausea, if not, they increased the RPMs to a higher level, repeated testing, increase/test, increase/test. Inadvertently, they were giving the test subjects increased tolerance. Whereas researchers who went straight to the target RPM, or tested at high RPM then dropped down until the subjects stopped feeling nauseous, the subjects didn't get a chance to develop increased tolerance.

[KelvinZero]

However, more recent research suggests people can adapt to extremely high RPMs

That's really cool/promising! Do you have any links or names of papers?

That youtube clip from David Kipping at Colombia University also seemed to be quite optimistic and includes a bunch of academic references in the text below it. I would guess anything claimed in the clip is justified in one of those references.

[Vultur]

If you go to Spincalc, Ted discusses old vs new research in his sources section. You want Lackner and DiZio as your starting point. However, most of their work is on trying to "break" the vestibular system in order to figure out how it works, pure research. But some of their early stuff was directly related to spin-gravity. For example: https://www.researchgate.net/publication/8607002_Adaptation_to_rotating_artificial_gravity_environments (semi-paywalled.)

Cool, thanks! That does look more promising than other numbers I've seen.

[Twark_Main]

Ignore the tangential velocity. Useful for catapults, but not relevant here.

The tangential velocity tells you how much delta-v the spacecraft needs to reserve for spin-up or spin-down. This is helpful for calculating the total mass penalty of the AG system, including fuel.

[Shevek23]

Another use of the tangential velocity--it is another way to calculate the radius needed for a given G effect.

The formula is pretty simple for this--A=(V^2)/R where A is acceleration, and V is this purportedly to be ignored "tangential velocity" and R is the radius. This means the square of V is radius times the G we want, so the square root of those two latter is V. We can also swap around to say R=(V^2)/A. All this is just another way to express the same thing as A=R*(Omega^2) where Omega is angular speed.

So say we decide that it darn well would bug us to have our head at half the G our feet are at, but we won't mind if it is just a 25 percent difference. So we want radius to be more than 4 anyway, and we want G to be 10 m/sec^2, a hair over Earth surface G. We know R and we know G, they multiply to 40 so we can see that V would be a bit over 6 m/sec. That means it is 1.5 radians per second, and there are 2Pi radians in the whole circle, so it cycles round every 4 seconds or so which means RPM is 15.

You ask me, that seems like a heck of a fast RPM to adapt to but maybe we can. Such a speed would give us a full G spinning a Starship on its long axis (which is not dynamically stable, we'd need to be tweaking it with reaction wheels or pulsing the reaction engines or it will tend to tumble, shimmying badly on the way to this).

Another example--believing as I do that people cannot adapt to continual low G and need to at least often be in full G in the long run, a Lunar surface colony could not sustain human life unless people get on some kind of centrifuge under a full G much of the time. Minimum size centrifuge is what we are talking about here mostly, but suppose we conservatively guess that say 100 m/sec is the maximum safe speed relative to the surface we can sustain safely--this is comparable to high speed trains in Japan or France OTL. That gives us V=100, thus V squared is 10,000, we want a full G (a hair less but 1/6 G at right angles adds very little per the Pythagorean addition we do here) about 10, so dividing that square by our desired full G we get 1 kilometer in radius--here's where we get 1 RPM, because now the speed is 1/10 radian per second, and it takes 2pi or a bit over 60 seconds to go around, hence roughly 1 RPM. This is what they thought was the maximum RPM in the old days.

Of course we could probably go a lot faster than 100 m/sec relative to the ground, using tricks like magnetic levitation and so on, which would lower the RPM and raise the circle radius. We can also figure on lower G than a full G if it turns out lower G's such as Lunar surface do us some good anyway--I do suspect it is better to spend months in space at lunar G than free fall!

Anyway the tangential velocity is a very useful thing to pay attention to in many circumstances and should not be dismissed, I find it a lot easier to work with the velocity/radius/acceleration relationship than angular speed/Radius/acceleration myself.

It also comes in handy in orbital mechanics.

[spacester]

A 100 m spin radius at 3 rpm will provide almost exactly 1.0 "gee" with a clear expectation that Coriolis effects will not be too difficult to adapt to by healthy humans.

Here's the formula:

G = [R * [(pi*rpm) / 30]^2] / 9.81
OR
R = (9.81 * G) / [(pi*rpm) / 30]^2

Where:
G = Decimal fraction of Earth gravity
R = Radius from center of rotation in meters
pi = 3.14159
rpm = revolutions per minute

Example:
R = 99.4 meters
rpm = 3
plug these in:
G = [99.4 * [(3.14519 * 3) / 30]^2] / 9.81
G = [99.4 * [.0986958]] / 9.81
G = 1.0000


My derivation:
The centripetal acceleration will be A = V^2 / R
where V is the tangential velocity
and R is the radius
And V = W * R
where W is the angular velocity (W = "Omega")
So A = (W*R)^2 / R
A = R * W^2
W can be confusing on the units, it's in radians per second and there are 2*pi radians in a revolution, so
rpm = (W radians/sec) (60 sec/min ) /(2*pi radians / rev)
rpm = (W * 30) / pi
W = ( pi * rpm) / 30
Substituting for W
A = R * [(pi * rpm) / 30 ] ^2
G = A / g
where g = 9.81 m / s^2 (Earth gravity)
So
G = [R * [(pi*rpm) / 30]^2] / 9.81

[Twark_Main]

Ignore the tangential velocity. Useful for catapults, but not relevant here.

The tangential velocity tells you how much delta-v the spacecraft needs to reserve for spin-up or spin-down. This is helpful for calculating the total mass penalty of the AG system, including fuel.

This also tells you how much fuel you need in your rescue jet-pack in case you fall off the station during an EVA. 

[spacester]

Quick question for our space guys;

In lots of fiction/close to reality films including Stowaway, they depict rotating spaceships with each 'end' of the rotating ring being huge.
Is there a reason for this? (Other than it looks cool?) is it something to do with speed? i.e the smaller the ring the faster it has to turn to achieve the same G levels?

Rotation is of course about creating spin-gravity for people and the design of an actual vessel to take our space faring game to the next level is all about the cleverness of the mass distribution.

Generally, you want to put your mass - the human habitat part - as far away from the center of rotation as you can. The first geometry that pops out is a dumbbell, two cylinders separated from each other by a relatively low mass connector.  So two spent rocket stages connected by a tether.

The simple dumbbell does not even make it to back of napkin design stage. Especially if you use a tether, you cannot control the dynamics. Pretty much a nightmare in that category.

So you go to a rigid truss, that improves the spin control. But where are you mounting the thrusters to force that control? And what about a central hub, good idea or bad idea?

So the dumbbell is replaced by more units at the spin radius, so say four cylinders connected by trusses.

Choosing the spin radius and rpm is a big part of the design concept. For me, I settled on R=100 m and 3.0 RPM a long time ago.

So at a diameter of 200 m, pre-starship spent rocket stages will be pretty far apart and lonely. How do you circulate crew between your four habs? You probably don't.

So how about a connected ring of spent stages? Now we are talking, it doesn't have to be A.C.Clarke's wheel to be awesome.

Enter Starship, and its massive capability to deliver huge payloads on a rapid schedule.

There is a lack of discussion on these forums about what can be done with hundreds of Starship payloads. Still too soon?

For me, it is not too soon to look at how to construct a huge human refuge for up to 1000 people. In fact I have done so.

Minimum mass: 115 payloads at 115 T each = 13225 T
Maximum mass: 150 payloads at 150 T per payload = 22500 T
Design mass: 20000 T (for propulsion calcs)
Central design goal: Provide excellent conditions for robust human health for hundreds of humans, with plants all over the place, various partial gravity apartments, terrific radiation shielding everywhere, abundant energy and water, galley-cooked food, all the hot showers and hot-tub soaks you want.
Design lifetime: 100 years
Ultimate operating orbit: Mars - eight to twelve years in LEO first, then Cis-Lunar, then go help the Martians

[Paul451]

Choosing the spin radius and rpm is a big part of the design concept. For me, I settled on R=100 m and 3.0 RPM a long time ago.

If you go to 4 RPM, you cut the radius to 56m. Nearly half. Go to 6 RPM, radius drops to 25m, just a quarter. Why "settle" on 3?

[Edit: Also, your design might suffer from the intermediate axis problem, depending on how heavy that extended core thing is.]

[spacester]

Choosing the spin radius and rpm is a big part of the design concept. For me, I settled on R=100 m and 3.0 RPM a long time ago.

If you go to 4 RPM, you cut the radius to 56m. Nearly half. Go to 6 RPM, radius drops to 25m, just a quarter. Why "settle" on 3?

[Edit: Also, your design might suffer from the intermediate axis problem, depending on how heavy that extended core thing is.]

5 rpm requires more adaptation. I want 98% of people to be able to deal with the Coriolis no big deal. I once again reviewed the info we have available, which is scanty, and I just think that at 3 rpm no apologies will be needed. The idea is to provide the ultimate safe haven for space travelers. Also, I admit I like the slick math at 3 rpm - radius in m/100 equals gee force. Smaller radius designs are perfectly valid, but this design is firm on that choice.

You are correct about the intermediate axis problem. Well done.

I liked this design a lot until I finally got to the point where I could calculate the moments of intertia, and the ratio of the non-spin moments over the spin axis moment came out higher than I wanted. I don't think it would actually flip without active control, but I want a more inherently stable spin state. Also, the central hub is mostly empty, and I do not want to give that up (movie studio revenue).

So I actually did some work on this project today for the first time in a long while.

Dynamically, the base design is expected to be excellent for just spinning in space and station keeping. But I want propulsion built in and the rocket equation is a bitch so I needed to add a bunch of propellant tanks. I had the prior tanks too far from the plane of the habitat ring. They now form circular arrays all the way out to 80 m radius. I think it looks better to the eye of a dynamicist.

18 m diameter Starship 2.0 to the rescue! I added 80 tanks from 8 launches providing 12,000 T and now I need to run the numbers to check my guess. If there is interest I will update.

[edzieba]

The simple dumbbell does not even make it to back of napkin design stage. Especially if you use a tether, you cannot control the dynamics. Pretty much a nightmare in that category.

I see this asserted pretty often, but without analysis to back it up. For example, see the attached papers on modelling the tether dynamics of the OEDIPUS-A experiment (where unexpected nutation was observed), and the subsequent OEDIPUS-C experiment that validated the model and confirmed stable spinning tether dynamics, using only design parameters to allow passive stability without active control.