Space station artifical gravity

[TVP45]

OK thanks. here's another related idea I've been struggling to have answered.

So far I've been speaking about the physics of a wheel (or a cylinder) to achieve 1G, but how about a sphere? Sure you could rotate it on it's axis to get your 1G at the equator, but could it also be twisted in another direction as it rotated so that no matter where you were on the inner surface you'd still be traveling at 412 fps, thus achieving 1G?

Impossible? Crazy?

It's not the linear speed that causes problems in humans; it's rotational accelerations that produce nausea, vertigo, ataxia, etc.
There is a strong response to rotational velocity, but that has a short time constant.

You could, in principle, spin about all three axes (or really as many as you want), but the acceleration would not be constant or only vertical and the effects would be startling (projectile vomiting). The multi-axis trainer at JSC is tolerable only because the person is at the center of the rotations.

 

[KontaktMan]

It's not the linear speed that causes problems in humans; it's rotational accelerations that produce nausea, vertigo, ataxia, etc.
There is a strong response to rotational velocity, but that has a short time constant.

You could, in principle, spin about all three axes (or really as many as you want), but the acceleration would not be constant or only vertical and the effects would be startling (projectile vomiting). The multi-axis trainer at JSC is tolerable only because the person is at the center of the rotations.

So, if I understand correctly, going 412fps (the example I brought up earlier for a 2 mile diameter wheel to provide 1G) isn't a problem, it's the rotation. And I would assume that the slower the rotation is the more tolerable the effect would be on a human being.

And taking that a step further, the larger the object is, the slower its rate of spin needs to be to provide 1G. Bigger is better, right?

Now getting back to the sphere idea you say that it is possible to spin it on several different axis simultaneiously but that the acceleration would not be constant.

Am I correct in interpreting this to mean then that a man standing on the inside of this sphere might sometimes be traveling say, 375fps then 400, then 420, or is it a matter of direction that would cause nausea? Since he would not only be rotating forward but shifting to the right (or left) simultaniously?

(This multi-axis idea seems to contradict Kdv's reply:

Impossible for a rigid sphere. For something non-rigid, it would onlybe possible for a very very short time until everything would rip apart. So, yes, it's crazy :-)

 

[Shooting Star]

So far I've been speaking about the physics of a wheel (or a cylinder) to achieve 1G, but how about a sphere? Sure you could rotate it on it's axis to get your 1G at the equator, but could it also be twisted in another direction as it rotated so that no matter where you were on the inner surface you'd still be traveling at 412 fps, thus achieving 1G?

I'm curious to know exactly what is the picture that you've got in your mind? You mean a rigid body, right?

 

[KontaktMan]

I'm curious to know exactly what is the picture that you've got in your mind? You mean a rigid body, right?

Yes. I have this concept for a Sci-Fi setting. The idea is that instead of a wheel or cylindrical space colony there could be a spherical one where you would get 1G simultaneously throughout the inner surface through some rotational pattern.

 

[Shooting Star]

Yes. I have this concept for a Sci-Fi setting. The idea is that instead of a wheel or cylindrical space colony there could be a spherical one where you would get 1G simultaneously throughout the inner surface through some rotational pattern.

Like what? Breaking it up into small strips parallel to the equator and letting them rotate so as to make the centrifugal acceleration be g on each? But you also insist that it's a rigid body...

Would you care to give a description?

 

[KontaktMan]

Like what? Breaking it up into small strips parallel to the equator and letting them rotate so as to make the centrifugal acceleration be g on each? But you also insist that it's a rigid body...

Would you care to give a description?

Hmm, that's an interesting idea, but no I pictured it as a rigid geodesic sphere.

 

[D H]

Hmm, that's an interesting idea, but no I pictured it as a rigid geodesic sphere.

Not possible. Suppose an object is undergoing uniform circular motion with angular velocity $\omega$ about some axis of rotation. If the distance between the axis of rotation and the object is $r$, the force needed to keep the object in uniform circular motion about that axis is [itex]r\omega^2[itex]. The angular velocity is constant for any point on any rigid body. The distance between the axis of rotation and a point on the body is only constant for a cylinder (without end caps) rotating about the cylinder axis.

 

[KontaktMan]

Not possible. Suppose an object is undergoing uniform circular motion with angular velocity $\omega$ about some axis of rotation. If the distance between the axis of rotation and the object is $r$, the force needed to keep the object in uniform circular motion about that axis is [itex]r\omega^2[itex]. The angular velocity is constant for any point on any rigid body. The distance between the axis of rotation and a point on the body is only constant for a cylinder (without end caps) rotating about the cylinder axis.

I'm not sure if you read my initial post claiming little physics knowledge, but I'm trying to educate myself, thanks to everyone here :-)

Some of these terms I've figured out, others I'm scratching my head.
What exactly is Omega?
And by angular velocity do you mean it's circular path?
In the original formula I discovered here G = (v^2 / r) / 32.2 what is the significance of the number 32.2? Where did it come from?

 

[Mentz114]

Hi KontaktMan :

talking about circular motion, omega ( $$\omega$$ ) is the angular velocity measured in radians per second. This is 2*pi times revs per second.

The number 32.2 looks like the acceleration due to gravity on the Earth measured in feet per sec per sec.

 

[KontaktMan]

Not possible. Suppose an object is undergoing uniform circular motion with angular velocity $\omega$ about some axis of rotation. If the distance between the axis of rotation and the object is $r$, the force needed to keep the object in uniform circular motion about that axis is [itex]r\omega^2[itex]. The angular velocity is constant for any point on any rigid body. The distance between the axis of rotation and a point on the body is only constant for a cylinder (without end caps) rotating about the cylinder axis.

Ok, revisiting this sphere concept I think that I now understand that it is only possible to create a contant G force by defining one axis, around which one equator revolves around.
Then how about a variable solution? If humans could handle it, what if the G forces were not constant but varied over a period of time? Over 1 revolution, or over many revolutions, whatever it would take.

Perhaps after completing a full revolution a new axis is defined, and on and on. A human then would go in and out of various G forces throughout his day. (I'm not saying it would be easy)

 

[DaveC426913]

Ok, revisiting this sphere concept I think that I now understand that it is only possible to create a contant G force by defining one axis, around which one equator revolves around.
Then how about a variable solution? If humans could handle it, what if the G forces were not constant but varied over a period of time? Over 1 revolution, or over many revolutions, whatever it would take.

Perhaps after completing a full revolution a new axis is defined, and on and on. A human then would go in and out of various G forces throughout his day. (I'm not saying it would be easy)

Sure. You'd have a cosmic-scale tilt-a-whirl. It would be little more use than entertainment.

 

[D H]

The acceleration felt inside a sphere rotating at a constant rate depends on the distance from the rotation axis. The axis will pass through two radially opposite points on the sphere. A human located at one these points (I'll call them the north and south pole) would feel no acceleration. Zero g. A person standing on the equator would feel the maximum acceleration. The person would lose apparent weight (how heavy the person feels) as they walked toward on of the poles. This concept has already been done in science fiction, multiple times.

Making the rotation rate non-constant is not a good idea. A rotating spherical object will keep rotating at a constant rate unless some external torque (e.g., rocket engines) act to change the rotation. A constant rotation rate is a better idea. Once the rotation is initiated, it won't take any extra energy to keep the motion going.

 

[KontaktMan]

Sure. You'd have a cosmic-scale tilt-a-whirl. It would be little more use than entertainment.

Well, after all, science-fiction serves a purpose in exploring far-out ideas :-)

So from your statement above it sounds like it's possible, only impractical in that it would feel like a amusement park ride.

What if the torque applied to the rotation (I hope this is an accurate description) is slight?
Say, a man is standing inside the equator of a sphere as it rotates around an axis and the sphere is given just enough torque to pull him out of that sweet spot just slightly each revolution so that it takes something like twelve hours to end up in a position where the axis was, now making him weightless, then back again over the next twelve hours to 1G again.

Or an even smaller torque making the transition happen over a week, a month?

 

[KontaktMan]

The acceleration felt inside a sphere rotating at a constant rate depends on the distance from the rotation axis. The axis will pass through two radially opposite points on the sphere. A human located at one these points (I'll call them the north and south pole) would feel no acceleration. Zero g. A person standing on the equator would feel the maximum acceleration. The person would lose apparent weight (how heavy the person feels) as they walked toward on of the poles. This concept has already been done in science fiction, multiple times.

Exactly why I would like to consider other options. (My favorite is the Rama series by Aurthur C. Clarke)

Making the rotation rate non-constant is not a good idea. A rotating spherical object will keep rotating at a constant rate unless some external torque (e.g., rocket engines) act to change the rotation. A constant rotation rate is a better idea. Once the rotation is initiated, it won't take any extra energy to keep the motion going.

Now, does adding torque to rotation make the rotation rate non-constant? I guess what I'm trying to say is, I'd really like to keep the rotation constant and add torque.

 

[wysard]

KontaktMan: Try using the following formula.

G = (w^2 * r) / 32.2

where:
G => Force in G's
w => Rotation speed in Radians Per Second
r => Radius

For your first problem for example
180 fps / 6283 ft ( 2*pi*r) / 2 * pi (radians) gives a "w" of about 0.182005

It becomes clear then that it is not the linear velocity, (ie: 180 fps or 412 fps [your v]) but the angular velocity (my "w") that is critical. Often people are misled by thinking a bigger "v" gives them a higher G regardless of the radius, but it is the ratio of the two that is the key factor.

If you spun your 2 mile space station at the same RPM (angular velocity) as the 2000 foot station you would create a force of almost 5 1/2 G !

 

[Shooting Star]

Exactly why I would like to consider other options. (My favorite is the Rama series by Aurthur C. Clarke)

One of my favourites too, as I've mentioned somewhere earlier in the thread. The stairs and the elevator has been discussed in great detail.

Now, does adding torque to rotation make the rotation rate non-constant? I guess what I'm trying to say is, I'd really like to keep the rotation constant and add torque.

You just cannot have the same centrifugal force at every point on the surface of a sphere. It doesn't matter in whatever way you rotate it, and then add some torque to it, and then paint it red or whatever. This has has been explained to you by several members, even using mathematics.

Can't you simply visualize it? Also, there will be instantaneous poles, where the Fc is zero, even if for an instant.

Stick to cylinders, as the Ramans did.

 

[wysard]

First off, I have to apologize to all. My browser cache was doing some very wonky things and as a result I was seeing posts from page 2 as the current page and responding. I realize that might mean that some posters noticed that my posts bore only a fleeting connection to the current part of the thread. (In other words I sounded a bit off my nut...lol) All is fixed now and I can see clearly (for now).

Second. DH, I understand what you were saying about constant angular rotation, what part I missed was if a hollow sphere rotates equally in all three dimensions simultaneously then the center of rotation "r" remains constant. As a result because "r" never changes wrt the inside surface there is no reason not to have a uniform force at the surface. Did I miss something? If you tumble an object in three dimensions the objects radius or location changes? (Not arguing, just scratching my head) That said, the corolis forces could be large indeed depending on the omega involved, so I wouldn't recommend say a running broadjump.

 

[Shooting Star]

Second. DH, I understand what you were saying about constant angular rotation, what part I missed was if a hollow sphere rotates equally in all three dimensions simultaneously then the center of rotation "r" remains constant. As a result because "r" never changes wrt the inside surface there is no reason not to have a uniform force at the surface. Did I miss something? If you tumble an object in three dimensions the objects radius or location changes? (Not arguing, just scratching my head) That said, the corolis forces could be large indeed depending on the omega involved, so I wouldn't recommend say a running broadjump.

There is always an instantaneous axis of rotation for a rigid body. The centrigual acceleration at a point at an instant will be given by $$\omega^2 R$$, where R is the distance of the point from the instantaneous axis. $\omega$ is not the same for different points, and hence centrigual acceleration will be different for different points.

Why do I have to invoke angular velocity etc to show that a sphere cannot rotate around infinite number of axes simultaneously?

 

[wysard]

There is always an instantaneous axis of rotation for a rigid body. The centrigual acceleration at a point at an instant will be given by $$\omega^2 R$$, where R is the distance of the point from the instantaneous axis. $\omega$ is not the same for different points, and hence centrigual acceleration will be different for different points.

So Omega is different for different points with the same "r" (because all of them share the same non-moving intersection of their axies) I am following this bit. My problem is with the

and hence centrigual acceleration will be different for different points

Which is only true if their are different instantaneous "r"s. Which there is not. Ergo centrifugal acceleration is the same at all points. Does "r" change magically somewhere on the sphere?

Why do I have to invoke angular velocity etc to show that a sphere cannot rotate around infinite number of axes simultaneously?

I don't know. I don't care about an infinite number. Three is sufficient given it is the number of dimensions required to describe a sphere. It's not like I want to tumble a tesseract you know.

Again, not arguing, just having trouble with observed external phenomena and seeing what you are driving at in this thought experiment about the inside of the sphere.

 

[KontaktMan]

You just cannot have the same centrifugal force at every point on the surface of a sphere. It doesn't matter in whatever way you rotate it, and then add some torque to it, and then paint it red or whatever. This has has been explained to you by several members, even using mathematics.

Yes, I appreciate the mathematics although I have a difficult time making sense of some of the calculations. Every message seems to introduce new terms for me to decipher. (Not your guys fault of course) I did a little searching and came across a couple of physics on-line glossaries I'm referencing to try and help me out.

You have to realize that yes, I'm out of my element here and is the reason I asked to have you 'bear with me' in my initial post. I really do appreciate all your replies. Thanks for letting me visit your forum.

Anyway, I believe I stated previously that I accept the fact that not every point on a sphere can have the same centrfugal force. What I'm trying to understand now are the effects created when you give torque to a rotating sphere.

As DaveC426913 said in a previous post "Sure. You'd have a cosmic-scale tilt-a-whirl. It would be little more use than entertainment."

OK, that's something I can picture. I kinda take that to mean, yeah, there would be various degrees of G's on your journey. That leads me to picture this: a man standing on the inside equator of a 2 mile sphere in a constant rotation to give him a feeling of 1G. A slight amount of torque is added, say only enough that it would take 24 hours for him to return to that exact coordinate in space.

What happens to him? How does he feel? Will he instantly feel something is wrong? Enough to induce nasea? Will the universe cease to exist? ;-)

Thanks

 

[wysard]

OK, that's something I can picture. I kinda take that to mean, yeah, there would be various degrees of G's on your journey. That leads me to picture this: a man standing on the inside equator of a 2 mile sphere in a constant rotation to give him a feeling of 1G. A slight amount of torque is added, say only enough that it would take 24 hours for him to return to that exact coordinate in space.

What happens to him? How does he feel? Will he instantly feel something is wrong? Enough to induce nasea? Will the universe cease to exist? ;-)

You need to be clearer here. Do you mean a momentary instananeous torque? Like a bump, or "twist"? All that would do is cause a momentary push, or stumble, but would change the effective "axis" of rotation. Or do you mean add a new small, but constant torque, and in what frame of reference is it applied?

 

[KontaktMan]

You need to be clearer here. Do you mean a momentary instananeous torque? Like a bump, or "twist"? All that would do is cause a momentary push, or stumble, but would change the effective "axis" of rotation. Or do you mean add a new small, but constant torque, and in what frame of reference is it applied?

No, not just a momentary bump but a small constant torque. Not sure what you asking in terms of frame of reference.

The best ways for me to describe what I envision is back to this scenerio:
A man standing on the inside equator of a 2 mile sphere in a constant rotation to give him a feeling of 1G. A slight amount of torque is added, say only enough that it would take 24 hours for him to return to that exact coordinate in space.

What I'm searching for here is a compromise. If you can't have 1G throughout the surface of the sphere simultaniously all the time then can you have a gradual change so that a human might go about his day with say 1G at noon, (time to get in a nice cardio workout), while the G forces gradually lose force until midnight when he'll be weightless. From there the G forces increase again until noon when the pattern repeats itself ad infinitum.

Or an even longer period (and smaller torque) such as a week or a month? Gravity for such a space colony would be a shared resource.

 

[wysard]

It would be easier for him to go west, young man, go west...

Really.

If the man stands at the bottom of the sphere when it is stationary and we then spin the sphere right side clockwise, like the man had to walk forward to stay at the bottom. But he doesn't move because we spin it fast enough that he experiences 1G all the time (so he doesn't notice from an external frame that half the time he is upside down) to lower the G force on the person all they have to do is move at right angles to the axis of rotation. No special torque needed.

EDIT:
Adding a new constant thrust to the sphere (preferably at right angles to the initial spin) doesn't momentarily alter the frame, but adds a constant lateral acceleration factor to the body. Effectively altering where "down" is by the margin of thrust. Not only that because it is not a "bump" that can alter the spin to give your 24 hour turn around time, the effect of a small constant thrust accelerates so that what might have taken 24 hours for the first cycle, will take less and less time to rotate on the axis of the new thrust and would require harmonic calculation to figure out when succeding revolutions will put the person back in the intial position.

 

[KontaktMan]

It would be easier for him to go west, young man, go west...

Really.

If the man stands at the bottom of the sphere when it is stationary and we then spin the sphere right side clockwise, like the man had to walk forward to stay at the bottom. But he doesn't move because we spin it fast enough that he experiences 1G all the time (so he doesn't notice from an external frame that half the time he is upside down) to lower the G force on the person all they have to do is move at right angles to the axis of rotation. No special torque needed.

Yes but if you had an apartment in such a colony there would be the haves and the have-nots. Those that have 1G, those that have less, and those on the poles that have none. That's why I was exploring an alternate method where no matter where you live on the inner surface of a sphere everyone would get their daily allowance of gravity. (Or weekly, or monthly, however long the determined cycle would be)

EDIT:
Adding a new constant thrust to the sphere (preferably at right angles to the initial spin) doesn't momentarily alter the frame, but adds a constant lateral acceleration factor to the body. Effectively altering where "down" is by the margin of thrust. Not only that because it is not a "bump" that can alter the spin to give your 24 hour turn around time, the effect of a small constant thrust accelerates so that what might have taken 24 hours for the first cycle, will take less and less time to rotate on the axis of the new thrust and would require harmonic calculation to figure out when succeding revolutions will put the person back in the intial position.

So, by "contant lateral acceleration you mean the torque, right? Well no then, I'm not suggesting that the torque accelerate. Once the sphere is given torque it should remain at that speed so that the entire cycle always remains the same. (24 hours, 1 week, etc.)

So, is what I'm suggesting possible?

 

[wysard]

I guess. If you imagine two spheres one inside the other separated roller bearings one with a motor attached. Now spin the sphere(s) up to speed. You have 1 G at the equator and 0 G at the poles. If you then turn on the motor so it will make the inner sphere turn 1 revolution in 24 hours it would work. The trick here is that from the motor's frame of reference, neither sphere is spinning because both of them and the motor are all spinning at the same rate. As a result when you turn the motor on, it creates a uniform torque (theoretically) causing the spheres to rotate in opposite directions. If the motor works at right angles to the primary axis of spin then in a given day an object on the inner sphere would experience a constantly changing gravity cycling in a sine wave motion from 0 to 1 G twice per day.

Question is, how would you get in, or out of the colony?


EDIT:
As an afterthought, to ensure there are no "dead" spots or places that do not get their fair share of G forces you need to ensure that the speeds of the spheres are at least relatively prime. For example if you start both spheres spinning at some RPM that is prime, and then engage the motor to turn at some other prime RPM times 2 ( assuming both spheres have the same mass and the stator and rotor are the same mass...that pesky equal and opposite reaction thing...) then you should be good to go. Less of course the "how do I get in or out?" bit.

 

[KontaktMan]

I guess. If you imagine two spheres one inside the other separated roller bearings one with a motor attached. Now spin the sphere(s) up to speed. You have 1 G at the equator and 0 G at the poles. If you then turn on the motor so it will make the inner sphere turn 1 revolution in 24 hours it would work. The trick here is that from the motor's frame of reference, neither sphere is spinning because both of them and the motor are all spinning at the same rate. As a result when you turn the motor on, it creates a uniform torque (theoretically) causing the spheres to rotate in opposite directions. If the motor works at right angles to the primary axis of spin then in a given day an object on the inner sphere would experience a constantly changing gravity cycling in a sine wave motion from 0 to 1 G twice per day.

Question is, how would you get in, or out of the colony?


EDIT:
As an afterthought, to ensure there are no "dead" spots or places that do not get their fair share of G forces you need to ensure that the speeds of the spheres are at least relatively prime. For example if you start both spheres spinning at some RPM that is prime, and then engage the motor to turn at some other prime RPM times 2 ( assuming both spheres have the same mass and the stator and rotor are the same mass...that pesky equal and opposite reaction thing...) then you should be good to go. Less of course the "how do I get in or out?" bit.

I admire your creative solution. This is all quite an elaborate design, one which I have a difficult time comprehending, but would it really take that much complexity?

Maybe it takes that harmonic calculation you mentioned in a previous post. Even in 1 rotating rigid sphere given torque, I would expect at some point a cycle to be established where the man (With 1G becuase he's initially standing at the equator) would return to the coordinates in space he started at. In that case does he return to feel 1G or does the introduction of torque forever take that force away?

 

[wysard]

It's not really all that elaborate, just two spheres one inside the other, like a box inside a box. And the advantages it offers in terms of ease of modelling forces involved and a real world ability to isolate, monitor and control the torque force you specified makes it hard to beat, although I'd love to hear any other ideas.

As to the reason for the concern for the harmonics is that while in your visualization we can make the man start at 1G, and by some torque, float down to near zero and back in a day, try this experiment. Close your eyes and imagine the sphere you want, and then put a torque on it. But imagine you don't know where the man is standing! Suddenly instead of a truly simple solution that fits just where you originally imagined the man, you must now create a solution that always works, no matter where the "mystery man" is standing on the inside of the sphere.

By the same token, if you don't know where the man is standing, imagine he started instead of at the equator, he started somewhere around the 45th parallel. If you make the torque an even divisor of the original rate of spin it is VERY easy to wind up with a scenario where the man NEVER gets to neither Zero, nor to One. Those are the "dead zones".