I am starting to write a short story that involves a space station with a wagon-wheel design for centrifugal gravity. I used this site, https://www.artificial-gravity.com/sw/SpinCalc/, and came up with a station with a circumference of 4800 feet, diameter of 1527 and a spin rate of 1.959RPM, which I have read will not cause motion sickness.

My question is, how would the curve of the station seem to a person walking inside? If you drew a straight line between two points 50 (or 100) feet apart, how much would the point in the middle be lower by? I just want to get a feel for what it would be like inside. I tried to figure out how to do the math, but I have no idea how to go about doing it.

If my math is correct, about every 13’ is 1 degree of arc. Depending on ceiling level, which determines field of view, I’d get the feeling of always walking up a slight incline. I don’t think the middle of the view would be “lower” as such as I am always at the lowest point. Forward and backwards curl up and away.

If you draw a 50-foot straight line, the point in the middle would be about 5 inches lower.
If you draw a 100-foot straight line, the point in the middle would be about 20 inches lower.
If you draw an x-foot straight line, the point in the middle would be about (2400/pi - sqrt((2400/pi)^2-(x/2)^2))*12 inches lower.

If you were in a cylindrical* hallway on the edge of the space station with an 8-foot ceiling and your eyes were 5’6" above the ground, you could see a spot on the ceiling 61’6" away from your eyes. You could then see a further 110’3" of floor. (Those are straight line distances, but the length along the floor or ceiling would be similar.) There would be a dip of about 2’3" between your feet and the furthest spot you could see.

Thanks for the replies. It’s just the info I needed. But I have another question, would an actual spaceship be possible with this method of mimicking gravity? Because there acceleration would cause a force pulling them in effect towards the back wall. What kind of acceleration would not be felt enough to be a problem?

The typical method for spaceships in fiction (The Discovery from 2001, for example) relied on accelerating with a non-spinning wheel, perpendicular to the direction of flight, which would be spun up once they were moving. I believe that Niven used a still-spinning model for a ship in his first Man-Kzin novel which used a laser as the engine; I don’t remember the acceleration, but it was pretty low.

One thing to consider is the minimization of materials per volume. Now a sphere is optimal but it makes the centrifugal artificial gravity messy. I’d go for a squat cylinder with a decent radius. It’s sort of the wagon wheel parameters with no materials used for the spokes and arms. Mass into orbit is a bitch.