# Space station artifical gravity

1. Dec 14, 2007

### DaveC426913

I've got a [strike]great[/strike] good head for intuiting physics but no post-2ndary math.

How fast must a cylindrical space station rotate to produce a given g-equivalent?

Say we standarize the gravity at a reasonable 0.5g and the station at 100 feet diameter. And maybe another station at 1000 feet in diameter for comparison.

I've been toying with some of the fun effects you could have on such a station.

Playing a traditional ball game, or any kind of traditional sport for that matter would be extremely awkward. Throwing up-rotation would cause the ball to tank; throwing down-rotation could very well cause the ball to float around the entire station and hit you in the back of the head. Running would be worse; you'd either trip and fall on your face or you'd float and lose traction.

Also, kids would be a menace in the halls, always launching themselves into orbit.

Last edited: Dec 14, 2007
2. Dec 14, 2007

### mgb_phys

Force is just = r w^2 ( w in rad/s )
so 100ft diameter = 16m radius, 0.5g would be 0.5rad/s = 3.1 seconds / rotation

3. Dec 14, 2007

### DaveC426913

Hm. So at any given time, the occupants are moving at a speed of 100 ft/s. (300ft perimeter / 3.1 s). That's just over 60mph.

So, in fact, you could not launch yourself into "orbit". And only a good thrower could put a baseball into "orbit".

Actually, I don't understand your calculation. What is w? And how do you get from 16m / 0.5g to 3.1s?
(Also, I have edited line one of my OP.)

Does it get harder or easer in a larger station?

Last edited: Dec 14, 2007
4. Dec 14, 2007

### mgb_phys

w is omega - rotation velocity in rad/s (need to sort a problem with latex in opera)

F = m a = m r w^2, or w = sqrt( a/r )
With a = 0.5 g = 4.9m/s^2 and r = 100ft/2 = 15.24m
w = 0.56 rad/s, a full rotation is 2pi rad, so it takes 11s for a rotation.
(sorry must have got the last step the wrong way up )

So linear speed is 2 pi 15.2m in 11s = 8.5m/s = 19mph

ps. Was watching moonraker last night - they spin the space station to get artificial gravity (the commentary track says they copied it from 2001) but the don't walk on the EDGE of the spinning surface, gravity is along the axis of the station ie down = toward Earth - I imagine they have more artists and fewer scientists on staff than 2001.

Last edited: Dec 14, 2007
5. Dec 14, 2007

### DaveC426913

Huh! So you could launch yourself into "orbit"...

You know, now that I think about it, a lot of stories have got gravity and trajectories in rotating space stations all wrong.

For example, John Varley's Titan has it wrong. When Gabby fell from the core, she wouldn't be accelerating. She'd hit with the same radial speed she left the core with. Though it would be her horizontal speed that would get her.

Maybe I'd better read it again. I do remember that she had a very significant horizontal v. I don't recall if he indicated she was actually accelerating.

Last edited: Dec 14, 2007
6. Dec 14, 2007

### Shooting Star

Artificial gravity can be supplied by rotation, as long as you are still wrt the space station. As soon as you move, the Coriolis force comes into play, changing your direction.

In fact, if you are just at rest at a point in space, and the space station rotates about you, that can be viewed as the trajectory wrt the space station due to Coriolis force, if you do your calculations in the rotating frame.

7. Dec 15, 2007

### TVP45

And, at 100 feet (or anything small) the Coriolis forces are gonna do some bigtime Hallpikes on you. Oy and double oy!

8. Dec 15, 2007

### Shooting Star

I searched and searched for the term "Hallpikes", but couldn't find the meaning of the word, though it sounds impressive the way you've written it...

9. Dec 16, 2007

### TVP45

Oops. Sorry about that. I think that's called "stream of unconciousness" writing. A Hallpike (or sometimes called a Dix-Hallpike) is a movement where you quickly rotate your head to the side as you quickly lean back or forward. It sometimes produces projectile vomiting. If you want to check it out, look under otolaryngology terms on most medical sites.

10. Dec 16, 2007

### Shooting Star

Yes, whenever I searched, it gave me medical related links, which I didn't explore further.

I am trying to understand why you made that statement. For maintaining earth g as the centrifugal accn w^2*r, w must be high if r is Small.

But since Coriolis accn = 2 w X v', where v' is the velo wrt the moving frame, it would be greatest when v' is perp to w. If w is high because r is small, then it would do a great hallpike on the object.

Hallpike, hallpike...I must get the hang of how to use it. Some places it's given as hall pike.

11. Dec 16, 2007

### DaveC426913

I think he's saying that people would experience some serious disorientation in a rotating frame. Coriolis forces and gyroscopic forces and inner ear balance and all that.

12. Dec 16, 2007

### Shooting Star

Important point to note about pseudo froces

I forgot to mention one crucial point about the, uhh...hallpikes. Since these forces are inertial forces, they'll act on all points of a small body equally, like gravity. So, you won't really feel the hall-pikes. You'll be in free fall.

13. Dec 16, 2007

### TVP45

If you simply kept your head in the same orientation, you would feel nothing. But, if you knelt and then stood up, if you nodded yes to someone's question, if you turned suddenly to look out the window (porthole?), then you would generally feel the effect. The folks at Houston who do centrifuge work regularly see this.

Keep in mind you've got 3 angular accelerometers in each inner ear and, when they don't agree with either the visual input or proprioception, or (in some cases) somasensation, one of the responses of the body (this is thought by some to be a remnant of early flight response) is to empty the stomach.

Large r gives only a very tiny difference within the small range of motion of the human body.

14. Dec 16, 2007

### Shooting Star

That's why I immediately made the second post. If you are not touching anything, then you are simply weightless and no hall-pikes.

If you try to run along a radial path, oh yes, big time hall pikes or hall pukes. (I think -- haven't really calculated the differential force between, say, the head and the leg.

EDIT: This was posted before I saw TVP45's last post.

Last edited: Dec 16, 2007
15. Dec 16, 2007

### Shooting Star

Quite agree with you but afraid to nod...

Well, the severity of the symptoms would depend on the angle between w and v'. You know more of the details, it seems.

I can't get hallpike out of my mind.

16. Dec 16, 2007

### TVP45

Sorry to rambled off on a tangent. And, I didn't even explain it well; once I realized I had gone off, I didn't mention the otoliths which are really the culprit.

I have been following microgravity and artificial gravity for some years and just made a comment, without thinking, that others would not be expected to know. If you have any interest, you might Google Scott Wood, Owen Black, or Bernie Cohen and artificial gravity nausea. I think Scott Wood is probably the best guy; he's down at the centrifuge facility. I can never remember which sites permit linking and which don't, so I won't provide links. And, again, I probably answered far more than you were interested in.

17. Dec 16, 2007

### Shooting Star

>And, again, I probably answered far more than you were interested in.

I live partly for that. Thank you for bringing the details to my attention. I do understand the overall picture, but these small details are helping to make up a complete description.

In Clarke's "Rendezvous with Rama", a lot of funny stuff about the effects of Coriolis forces are there, but I never thought about these small details.

18. Dec 17, 2007

### wysard

Given that the Earth is rotating at about 1,000 mph and we don't "accidentally" launch into orbit I would have to say no. It's not about the speed, but the relative masses involved and the distance between thier respective center of gravity.

Little station, spin fast. Big station spin slow. BUT.. (Always there is a but...) Because a station is bigger, there is more strain on the trusses holding the circumfrence to the centre. It's a trade off of size versus materials. Where material=mass this becomes an issue. Not only for accelerating or decelerating the spin, but also just to get it into orbit to assemble in the first place.

As for putting Coriolis force? Unless the station is spinning very fast it is unlikely to lead to odd mental effects, just ones where physics seems to take a trip into right-angle land. While Sci-Fi occasionally blunders in this respect with the effects of one side going (arbitrarily) clockwise and the other the reverse leading to odd disorientation effects the human inner ear acts as a counterweight to the problem in humans. Otherwise every time an aircraft pilot did a barrel roll they would be rolling the dice.

19. Dec 18, 2007

### Shooting Star

Why is launching into orbit from earth being compared to launching into orbit from a rotating space station? What relationship is there between the two situations except the word "orbit"? What is meant by orbit around a rotating space station? The last question may please be answered by the people who seem to know a lot about it. Otherwise, I'm hallpiking, and more seriously, I'm curious.

20. Dec 18, 2007

### Staff: Mentor

I think that by "orbit" in the space station they are refering to the situation where, in the inertial frame where the center point of the station is at rest, the object is stationary and the space station is rotating around it. In such a situation, neglecting air resistance, the object would have a nice periodic circular path in the station's rest frame. Essentially an "indoors orbit".

Last edited: Dec 18, 2007