Simulating gravity in a space ship via rotation

[Daniel Foreman]

Hi guys,

 

Another question I'm afraid.

 

Now obviously gravity is one of natures mysteries we don't understand it, and can't magically generate it's effects.

 

What I'm interested in centrifugal force and simulating gravity using that. From what I understand however, the size of the rotating section is quite important. If you have a small spinning ring, then the force at a persons head will be less then the force experienced at their feet. Making hard to move and disorientating.

 

What radius would a ring need to be to provide the feeling on earth gravity while avoiding the sensation of different levels at different heights of your body from the outer ring? At what point would it feel close enough to gravity to behave like gravity so that it is easy to move?

 

Or does the technique never allow easy movement under any circumstance?

[swansont]

The centripetal acceleration of a rotating object is v^2/r. So you want g = v^2/r (or w^2r, where w is the angular speed, in radians/sec)

 

r needs to be several times the height of a person to limit the gradient, as per your requirement. You would have to specify what that gradient is to know the minimum r. (e.g. if it's 1% over 2 meters, then r has to be 200 m)

 

One of the points of relativity is that you can't tell the difference between an acceleration and being stationary in a gravitational field. So it should feel like gravity as long as you are contacting the surface. If you jump, though, all bets are off.

[michel123456]

[swansont]

That's a clip of a special effect from a work of fiction. While it may be a plausible representation of the situation, there's no guarantee that it's an accurate one.

[Carrock]

According to NASA, this one is genuine.

 

[timo]

So it should feel like gravity as long as you are contacting the surface. If you jump, though, all bets are off.

Actually, I think that unless you jump very high/fast the feel should not be that different. Most importantly, you still come back to the floor (from an outside observer your jumping upwards looks like jumping up- and forwards in which case you hit the upwards-bent floor again at some point), and at a similar position as the one you started with (for an outside observer, the rotation of the circle largely compensates the displacement of the jumper).

[swansont]

Actually, I think that unless you jump very high/fast the feel should not be that different. Most importantly, you still come back to the floor (from an outside observer your jumping upwards looks like jumping up- and forwards in which case you hit the upwards-bent floor again at some point), and at a similar position as the one you started with (for an outside observer, the rotation of the circle largely compensates the displacement of the jumper).

 

This requires a more careful analysis. I think jumping would be different, partly because of the curvature of the floor, but mainly because you are no longer accelerating by virtue of contact with the floor. Someone jumping in earth's gravity follows a parabola and their speed changes with height. In this artificial environment your velocity will be a constant (as viewed from an inertial frame). So it's not at all obvious to me, from casual inspection, that it should be similar.

[Janus]

This requires a more careful analysis. I think jumping would be different, partly because of the curvature of the floor, but mainly because you are no longer accelerating by virtue of contact with the floor. Someone jumping in earth's gravity follows a parabola and their speed changes with height. In this artificial environment your velocity will be a constant (as viewed from an inertial frame). So it's not at all obvious to me, from casual inspection, that it should be similar.

It depends on the radius.

 

Start with a person jumping straight up (towards the axis of rotation) at a velocity that would get him to a 0.5m height on the Earth.

 

If the wheel is 100m in radius and turning at a speed that creates a centripetal acceleration on the inside "floor", then he will land some 13 cm from where he took off (as measured relative to the floor).

If we increase the radius of the wheel to 1000m, he lands ~4cm from where he took off, and with a 10,000 km radius he lands 1.3 cm away.

 

For someone standing on floor, he will appear to rise, slow down, stop, and fall back down vertically while curving a bit sideways.

[swansont]

It depends on the radius.

 

Start with a person jumping straight up (towards the axis of rotation) at a velocity that would get him to a 0.5m height on the Earth.

 

If the wheel is 100m in radius and turning at a speed that creates a centripetal acceleration on the inside "floor", then he will land some 13 cm from where he took off (as measured relative to the floor).

If we increase the radius of the wheel to 1000m, he lands ~4cm from where he took off, and with a 10,000 km radius he lands 1.3 cm away.

 

For someone standing on floor, he will appear to rise, slow down, stop, and fall back down vertically while curving a bit sideways.

 

If you jump straight up and don't land where you started, that's not like earth gravity. So, as you point out, you need to analyze it (which is what I was saying). Also, jumping forward (e.g. at 45º) with and against the direction of rotation would not yield symmetric results, which is another difference. And if you jumped with a large enough initial velocity you'd land on your head on the other side of the circle without having undergone any rotation of your body, yet another discrepancy.