Spin Gravity

One of the recurring problems of science fiction is how to create artificial gravity for our characters. In novels it's not such a big deal -- it's easy to write scenes showing they are in freefall the whole time. Movies have more problems, as freefall is very difficult to recreate convincingly on Earth (Tom Hanks actually took his entire crew up on the "Vomit Comet" to film parts of Apollo 13). Aside from that, we know that there are physical problems associated with long-duration exposure to freefall, so some kind of artificial gravity makes a lot of sense.

The easiest way (and only way, that we know of) to achieve this is by spinning the spacecraft or habitat on its axis. Centripetal acceleration will cause objects to be attracted to the outside of the spin (that is, radially, or perpendicular ot the spin axis). The amount of acceleration you get depends upon the radius of the rotation and the speed of the spin, specifically:

a = omega^2 * r

where omega is the rotation rate in radians/second (there are 2 * PI radians in one rotation) and r is the radius of spin in meters. The acceleration due to gravity is 9.81 m/sec^2, so, for example, a 21-meter radius and 5 revolutions per minute spin (2 * PI radians per 60 sec) yields a centripetal acceleration of approximately 0.6 g. If you want higher "gravity" either increase the spin rate or increase the size of your spin radius. As you move inward radially, the "gravity" decreases to the point where it is zero in the exact center.

But, alas, it's not quite that simple. There are two effects that we have to be concerned about. First of all, we cannot have a gravity gradient that is too large. Simply put, we can't have our crew feel significantly less gravity at their feet than they do at their heads. Not only is this physically disorienting, dropped objects would not only accelerate as they fall, the rate of acceleration would increase as well. Our reflexes are tuned to a constant force of gravity, so learning to deal with things in this environment would be difficult in the extreme. The formula for the gravity gradient is:

DeltaW / W = (Rb - Ra) / Rb

where DeltaW is the change in apparent weight, W is the weight, Ra is the initial radius, and Rb is the final radius. In practice, DeltaW needs to be less than 20% or so. All this means is that your habitat must be greater than about 7.5 m in radius. So, rotating your little Apollo capsule is not going to help you very much.

A much more serious problem is the Coriolis force. This force is felt by any object moving linearly (in a straight line) in a rotating system. If you've ever tried to walk straight on a rotating merry-go-round, then you've felt Coriolis force for yourself. The force also affects the fluid in the semicircular canals of the ear. This is why when you are rotating and turn your head rapidly, you become disoriented to the point of nausea. The magnitude of the force is given by:

F = 2 * omega *v

where v is the linear velocity of the moving object. So, the more slowly you move, the less Coriolis force you feel. Similarly, the slower your habitat rotates, the less force you feel. Since we have established that "gravity" depends upon both rotation rate and radius, and since we now know that rotation rate must be kept as slow as possible, this means we need to make our habitat radius as large as possible. Studies have shown that most people can adapt with minor difficulty to a rotation rate of 2 rpm, and almost no one experiences symptoms at 1 rpm or less. So, if we choose a fixed rotation rate of 1 rpm (omega = 0.105 rad/sec, omega^2 = 0.011 rad^2/sec^2), then the gravity we get is determined solely by the radius of the habitat. In order to get an artifical gravity of 1 g, we need a habitat 894 meters in radius. Basically, the ship is 18 football fields across! Needless to say, we can't build anything this huge anytime soon. If we can live with Martian gravity (0.3 g), however, we can get by with a third of this, or 268 meters in radius. That's still a really huge ship, but it's getting into the realm of reasonable. As a benchmark, a 100-meter radius habitat will produce about 0.11 g.

There are some other strange effects in a rotating habitat that could be put to good use in a story. If you are moving, the direction of your motion changes the gravity you feel:

• Moving outward forces you against the direction of rotation
• Moving inward forces you along the direction of rotation
• Moving in the same direction as the rotation increases the effective gravity you feel
• Moving against the rotation reduces the effective gravity you feel

So, by simply running in the direction of the spin, you get heavier! Run in the opposite direction and you get lighter! Pretty cool... A native could use these forces very effectively against an attacker who wasn't conditioned for them - a definite cool use of science that can drive a science fiction story.