# Artificial gravity by spinning?

1. Feb 12, 2013

### k!rl

Every time I see a SF pic which has some simulated gravity by spinning I can't imagine this actually working. The latest SF I watched (mission to mars) had a wide rotating cillinder somewhere in the middle of a much longer cillinder which formed the main ship.

Now imagine yourself moving from the front of the ship to the back of the ship, at some point you'd float through the spinning artificial gravity room. If you would float exactly through the center would you spin about your own axis? If you're floating a bit off center you would supposedly be swung to the outside of the cillinder?

What force would be responsible for this effect? How can the rotational force of the room be transferred to you if you're not touching anything?

I can imagine a simple earth based experiment by having a long hollow tube standing upright spinning around it's longtitudinal axis. If you'd drop a ball in there I don't think it would be swung out (sticking to the wall) before it actually hit the spinning bottom, which would finally transfer the rotational speed and swing it out?

2. Feb 12, 2013

### Whovian

The key seems to be making sure that anyone in the craft rotates with the wheel. Then, if the centripetal acceleration is 9.8 m/s^2, one can just use the equivalence principle to point out that this is locally indistinguishable from gravity.

So you sort of have a point, just a rotating disc isn't enough, something to make people rotate with the rotating disc is also necessary. If they're on the "floor" (the outside of the disc,) friction's enough to be responsible for this in most cases.

3. Feb 12, 2013

### VantagePoint72

It is only necessary for some force like friction to drag people along with the craft while it's spinning up from rest. Once it's rotating at a uniform rate, the only acceleration is centripetal. There is, by definition, no tangential component of acceleration for a uniformly rotating object and hence no need for a tangential force to keep any objects inside moving with the object. All that is needed is the centripetal normal force provided by the spacecraft's floor.

4. Feb 12, 2013

### VantagePoint72

No, you would not be pushed off to the outside of the spinning chamber. You are correct in saying you should float right through the spinning chamber as you passed from the main part of the spacecraft. However, if you then grabbed hold to something on the rotating cylinder so that you were pulled around with the chamber, then you immediately feel the fictitious centrifugal force seeming to push you down into the "floor".

Have you ever ridden one of those fairground rides that look like big spinning flying saucers? You start out strapped to the wall so that the harness can pull you around as the ride is tangentially accelerating from rest up to its operational speed. Once it reaches that speed, the harnesses are released and the only force you feel is the sensation of being pushed straight back against the wall. However, the operator sitting in his booth in the center of the ride is obviously unaffected by this.

5. Feb 12, 2013

### k!rl

So once you're spinning with it, would you keep spinning with it (no drag)?
Would it be safe to grab hold of the outer edge from a relative standstill (assuming the outer edge is spinning with a speed that equals 1g)?

What happens if you throw a ball up into the air to about the center of rotation? I'm guessing it would just come down normally into your hand again. Even if you threw it past the center of rotation? I'm guessing yes to the last one too, but it's a bit tricky somehow.

Finally, do you feel this is a realistic aproach for future spacecraft?

Thanks a bunch!

6. Feb 12, 2013

### QuantumPion

The rotation rate depends on the diameter, a large space station would be spinning pretty slowly so there would be no problem stepping off onto a non-rotating section.

The ball would appear to curve from your point of view, due to Coriolis force. However it would travel in a straight line to the other side from a fixed frame of reference.

Yes, but only for fairly large craft or space stations so that the differential force between your head and your feet is minimized. A small, rapidly rotating ring would be disorienting.

7. Feb 12, 2013

### k!rl

Thanks for the great little anim, however it's a bit confusing too because I'm not sure how the ball got to the center at the start of the movie.

Was it thrown up by someone sitting at -90 degree from the orange dot?
Or is it comming down aftersomebody at +90 degree from the orange dot threw it up?

8. Feb 13, 2013

### A.T.

The ball is shot from the center towards the dot.

Similar animation:

9. Feb 13, 2013

### CWatters

10. Feb 13, 2013

### davenn

11. Feb 13, 2013

### xAxis

No, it would fall ahead in the direction of rotation. For instance, if the ship rotates directly, it would fall to your righthand side.

12. Feb 13, 2013

### mrspeedybob

Agreed.
Take the following example...

Suppose you build a round rotating cylindrical space ship with an inside radius of 1000 m. Rotate it at a rate of 0.1 radian/sec in a counter-clockwise direction. Center it in a coordinate system where (0,0) is at the center axis of rotation. I am standing on the inside surface. At the exact time when my coordinates are (1000,0) I throw the ball toward the center at a rate of 100 m/s. The ball must travel in a straight line at constant velocity until it lands (newtons 1'st law). The components of the balls velocity are -100 m/s in the X direction and 100 m/s in the Y direction. It's easy to see that after 10 seconds the ball will contact the inside of the cylinder at coordinates (0,1000), ∏/2 radians counterclockwise from the position it was thrown from . During that 10 seconds the cylinder will have rotated 1 radian, which is less then ∏/2.

13. Feb 14, 2013

### k!rl

Thanks for clarifying everybody, seems sort of obvious in hindsight as always. Someday interstellar jue de buoles will be the favourite past time in the space resorts! =)

When the mass in such a gravity room is unevenly divided it may cause the spacecraft to wobble though.

14. Feb 14, 2013

### telecomguy

Here's an explanation that might assist in understanding.
A space station example starts at 26:22 in the video.

Last edited by a moderator: Sep 25, 2014
15. Feb 14, 2013

### Staff: Mentor

Right, and there might be some active control mechanism to keep the rotation stable.

If the station is not extremely large, all those effects from a position-dependent centrifugal force and coriolis force would be notable.

16. Feb 14, 2013

### k!rl

Thanks for the link telecomguy. I've seen some of Walter Lewins lectures before, I like his style!

17. Feb 15, 2013

### nalan

After 50 years of building things and programming I am retired and writing a science fiction book. I want to get things right but am having problems visualizing some of the effects of artificial gravity by spinning and the math and small examples have not helped. I have spent a few hours working the math in examples and getting numbers that don't mean much to me (see examples at the end).
My 'ship/space station' is an O'Neill colony large tube but bottle shaped. It is 50km long and 30km in diameter at the big end and 10km at the small end and rotates around the smaller axis, of course. It is filled with air, landscaped on the interior and has two rivers that curve around the interior DNA style from one end to the other.
My questions are:
1. What will be g at the small end if the ship rotates fast enough to create a 10 m/s equivalent centrifugal force at the big end? Will the g force be more or less at the small end? I think it will be less but I'm not sure and then, by how much less?
2. Will the Coriolis force be sufficient to drive the rivers flow? Which direction (small end to large end or the reverse) must they flow? (I will have them pumped in the opposite direction.) Or will the difference in g drive them from one end to the other?
3. Will the Coriolis force be sufficient to stir the interior atmosphere? Will the interior atmosphere float free of gravity and be stirred by the interior mountains and buildings to any degree? Would it build up momentum and start revolving with the structure?
4. If you jump from a large building in the interior would you float free until something turning around on a straight vector (to/from where) smacked you? Could you fly with wings in zero gravity up to the center where the sun tube burned off the glue and you hung there roasting slowly?
5. If people built buildings on the exterior of the tube the g force would be greater the farther the floor from the center of rotation; right? By how much, though? Would a 25 story building be crazy or would the g force just be a few tenths more and be barely felt?

(itex)R=1500^2m(\itex) radius at the big end
(itex)R=500^2m(\itex) radius at the small end
(itex)ω^2 1500 = 0.082 m/s(\itex) force of gravity on earth (rounded)
(itex)ω^2 500 = 0.14 m/s(\itex)
(itex)ω^2 = 0.3 rad(\itex) how fast a rotating frame of reference must rotate to simulate the force of gravity on earth.
(itex)T = 2∏/ω = 78.5 sec(\itex)
(itex)T = 2∏/ω = 44.8 sec(\itex)

--
Nick
"Age does not protect you from love. But love, to some extent, protects you from age." - Jeanne Moreau

18. Feb 16, 2013

### Staff: Mentor

For constant angular velocity ω, g-force is proportional to the radius r: $a=\omega^2 r$
Your "height" difference would be like a steep mountain, and air would be very thin at the small end.

The Coriolis force will give some deviation from a straight line - but you should reduce the "height" difference to get nicely flowing rivers.

"Down", towards the larger end.
Not the difference, the actual acceleration does this.
If you manage to get wind in some way, maybe. Otherwise, the whole air will follow the rotation of the cylinder without significant effects.
Only if you run at the velocity of the structure (as seen from outside), which is not likely for such a big cylinder. You would fall downwards, with some sidewards motion if the height is so large that it will kill you anyway (this happens on earth, too - for a free fall of ~100m, the deflection is of the order of 1cm if I remember correctly).
This is true on the inside, too. See my first paragraph how g-force changes with height.

19. Feb 16, 2013

### k!rl

In regards to question 4, if the building is sufficiently high and the cillinder sufficiently wide, meaby air resistance or drag could slow you down so much that you'd lose your speed and thus your "weight" before hitting the ground?

Especially when using wings, wich should function normally as far as I can tell, so long as there is air resistance.

Sound like an interesting story already nalan, inspired by icarus perhaps. Interesting questions too!

20. Feb 16, 2013

### Staff: Mentor

Air is dragged along with the cylinder. Air drag will make sure you end at the outer border of the cylinder.