Devil in the Details
I had occasion recently to return to some freshman-level physics. As the player most concerned about technical details in my role-playing group, and as the most scientifically literate, I’ve inherited from the GM much of the responsibility for designing the spaceship we’ll use to hop from planet to planet in our science fiction adventures. One of the questions raised in the process is: what substitute for gravity will we use?
We have several options, well anchored in the literature, but most of them suffer from associated problems. Living in freefall sounds fun, but it’s uncomfortable and even unhealthy over the long run, and wouldn’t fit the mental image of science fiction ship life—made unshakeable by television shows and movies shot on sets with gravity. Traveling under constant acceleration is expensive; the fuel costs are enormous, and it’s unlikely that the fastest, shortest, or most fuel-efficient path connecting point A to point B will match a constant-acceleration trip at 1g. Turning on an “artificial gravity field” inside the ship is about as convenient as it gets. Unfortunately, it’s also pure science fantasy, which isn’t the brand of science fiction we’re aiming for.
Bearing these shortcomings in mind, I naturally gravitated towards spinning the crew quarters about a central axis, replacing gravity with centripetal force—not a perfect match, but close enough for daily life. Sitting on the outer ring, you’d feel something akin to gravity pulling you outward, like a weight swung around on a string. Climbing “up” toward the axial tube connecting to other parts of the ship, this force would decrease until you are once again “weightless”—that is, in freefall—at the center. This method is simple, low-tech, and cheap. It doesn’t require complicated explanations, and doesn’t require scientific fudging.
That is, until you look at the numbers. Fool that I am, I calculated the spin we’d need, and got an answer I didn’t like. According to classical mechanics, a equals v squared over r for a point spinning about an axis, where a is the acceleration, v is the angular velocity, and r is the radius at which it turns. Put another way, v is the square root of a times r. We have a; that’s the Earth gravity we hope to mimic, 9.8 meters per second squared. We have an approximate r; that’s half the width of the crew quarters. Since we’re presuming a very generous space about the size of a two-story house for a crew of 6, that’s about 8 meters after shifting things around to a single-story disk. At these values, v is just under 9 meters per second, or twenty miles an hour, for those who prefer English units. You can wiggle these values around a bit by settling for a lower centripetal force, or by spreading the quarters farther out and paying for the lost space, but it doesn’t help much.
Twenty miles an hour is a problem. For one thing, if you stand up, your head moves in a smaller circle, resulting in less acceleration, less “gravity.” How much less? A 1.75 meter tall person would feel earth gravity at his feet, but only 78% of earth gravity at his head. That’s a big difference, enough to feel it, and enough to get disoriented. Another problem is trying to travel through the door from the axis to the revolving quarters. If that door is at a meter radius from the center, it zips by at 2.5 miles per hour, the speed of a brisk walk. Passing through would be risking your life; lose your footing, and the revolving door frame, backed by the mass of the entire crew quarters, pinches you right in half, or chops off stray appendages.
Suddenly, mimicking gravity with a rotating section looks a lot less attractive. The technique only works with much larger spaceships, with a very large r, where the outer ring spins faster, but the inner ring, where the revolving door of death is set, spins slower, like the axle of a large wheel turns slower than the axle of a small wheel, for a given ground speed.
Now, using the theoretical phenomena while ignoring the actual calculations measuring those phenomena is an old and respected tradition in science fiction. Ships in the books accelerate at rates that would, in reality, turn the occupants to jelly. Computers solve problems which would, in reality, require astronomical calculation times. Medicines delivered at the last possible instant before fatality would, in reality, leave a person pretty messed up, instead of instantly cured. I could similarly ignore the hard facts of math behind rotating ship parts. But I won’t. Dave is counting on me for some technical honesty, so I’ll provide it. Besides, the best of sci fi starts with the technical assumptions. Sometimes, playing fair with those assumptions causes a story to evaporate. But other times, you just get a different story. And that, too, is an old and respected tradition in science fiction.