# Would there be a “freefall zone” in the centre of a centrifugal artificial gravity?

In the novel Schismatrix, Bruce Sterling writes about people living on the inside of rotating cylinders (similar to Larry Niven's Ringworld and Iain M. Banks' Orbitals, but the atmosphere extends across the circumference of the cross section: they're long and narrow, not short and wide). He refers to a "free-fall" zone at their centre. Would this really exist?

• If you threw a ball "vertically" upward so that it reached a "height" greater than the world's radius, I believe it would still come "down", its trajectory appearing curved due to the Coriolis effect. Is that correct?

• If you entered such a world at the centre of the cylinders, would you float until you drifted toward an edge? If so, how would you then return to this floating state?

It's convenient to think about this in an inertial frame of reference. Imagine yourself floating in absolutely empty space, without any force acting on you.

Now add a rotating cylinder somewhere. Did anything change? If you ignore the mass of the cylinder (probably it's small) and atmosphere, there is no reason your floating state should change.

If the atmosphere rotates together with the cylinder (a reasonable assumption), you will feel no wind if you are in the center, and stronger wind if you are near the edge. The absence of wind is the only reason you could call it "floating zone" in the center, but not near the edges.

Now imagine a thrown ball (ignore the atmosphere for simplicity). It's moving in a straight line; if it passes through the center, it should reach a wall in future.

As for how you could return to the center if you are at the edge: you could climb a pole (or a rope, or the cylinder's wall at one of its ends) that reaches to the center. While climbing, you would feel a weak Coriolis force, but it would be small compared to the artificial gravity.

I have now realized that this description is incomplete without considering what the wind will do to you. Floating at the center is an unstable state. At any point except the center the wind will push you in the direction of cylinder's rotation, and if you are denser than air, you will tend to continue in a straight line, coming closer to the wall ("falling"). In your new position, the wind is stronger, and you will "fall" faster, so at the end you will crash into the wall.

The theory behind this is described in this Wikipedia article.

If your velocity is equal to the spinning cylinder you could float in any point inside the cylinder until you make physical contact with the spinning edge or any constructs spinning in the cylinder.

• Just to clarify: you mean "If your velocity is equal to the velocity of the center of the spinning cylinder [...]" I think. Right? – Floris Jan 6 '16 at 23:20
• True, in vacuum, but if it's a "habitat", then the cylinder will be filled with air, and the air will be rotating at the same speed as the cylinder. – Solomon Slow Jan 7 '16 at 14:19

If you entered such a world at the centre of the cylinders, would you float until >you drifted toward an edge? If so, how would you then return to this floating >state?

If you have a fast car you might be able to fly with it. Say the habitat has a radius $r$ and rotates with angular frequency $\omega$. The simulated gravitational acceleration felt by objects at the surface is then: $$a = \frac{v^2}{r} = \omega ^2 r$$ But if one drives in the direction counter to the rotation of the habitat at the speed equal to $v = r \omega$, this would remove the rotational effects, and so the car and its passengers would not experience the simulated gravity. After leaving the ground, however, the gravity would be quickly restored by the effect of wind, as others have pointed out.

Interestingly, this would work in a very similar way in a real gravitational field. Say we're on a spherical planet of the same radius as that of the habitat ($r$), whose gravitational field accelerates objects at its surface by the same amount that objects on the edge of the habitat are accelerated ($a$). In addition, the planet in this situation is not rotating. Then if one drives in the same car at the same speed $v$, then the car and its passengers become weightless (the car would be orbit in fact). Again, the effect of the wind would quickly reduce the relative velocity between the car and the surface, causing it to fall out of orbit.

In the planet scenario, driving in different directions does not change the effect. However, in a cylindrical habitat, if one goes in the direction perpendicular to the rotation, there is no effect at all. If one goes in the same direction as the rotation, the gravity becomes even stronger than before.