Rotating Space Station Numbers

Simulation Gravities Math Questions Further Reading VR

Throw:

Radius
Apparent G force	1 is earth like 9.8 m/s2
Rotational velocity (omega)
Edge velocity
Circumference	m
Width	meters
Inner Radius	meters
Shield density
Shield thickness
g stats
Head to foot g difference	...
g Walking spinward (1.5 m/s)	...
g Walking anti-spinward (1.5 m/s)	...
g Spinward when elevator up (5 m/s)	...
As:
Volume	...volume...
Total surface area	...surface area...
Ground surface area	...ground surface area...
Supportable population (with 1 layer, at 170 m2 per person)	...population...
Shield volume	...shield volume...
Mass	...mass...
Kinetic energy	...ke...

...Custom Station...

O'Neill Cylinders, illustration by Rick Guidice for NASA

Fun facts:

Mercury and Mars have approximately the same gravity, but Mercury is only 71% as wide as Mars!
The g values for the gas giants are at the top of the clouds. How you stay afloat is left as an exercise for the reader.
For the curious, the sun would be about 27.94 g at the surface. More numbers here.

Basic Math

Perceived fake gravity in a rotating space stations is:

A = ω2 * r
where ω is the station rotational velocity, and r is the radius.

If you are moving within that rotating station, you will experience an additional apparent force:

F = 2*m* (ω x v)
where:
   m is your mass,
   ω is the station's rotational velocity vector (the axis of rotation with length equal to rotational speed),
   v is your velocity vector in the rotating frame,
   x is cross product, thus making the resulting "force" perpendicular to both ω and v.

This basically means that if you are climbing up a ladder, you will feel as if you are pulled in the anti-spinward direction, and the reverse if you are climbing down a ladder, just as balls behave if you throw them up or down in the simulator above. You can read a much more detailed discussion of this in this paper by Theodore Hall.

Questions That Need Answers Right Now

In a rotating space station, would there be a constant wind on the surface? Specifically, how strong of a wind? Is there simulation software to run models on (maybe OpenFoam?) How will atmosphere move around within the station at different elevations? Will atmosphere tend to slow down the rotation over time? by how much? What conditions will cause clouds or rain? (last one something to do with dew point and moisture content in the air, answer would follow somewhat from a map of pressures at different elevations)
I assume hot air in a rotating space station would tend to float toward the center? Thus, if the (inner) surface is mostly around 60 to 70 degrees F, what can we say about the temperature at the middle in something like Kalpana One (a kind of squat cylinder)? What if sunlight were collected at the end caps, and reflected such that it is reemitted from a giant magic bar in the center. What would this do to the temperature and pressure at different elevations?
What is the math to compute the possible size of station based on material cohesion? What is the force of air pressure on the hull compared to force pulling hull apart due to rotation?

See for instance this wonderful summary of modern material strength on space station size. It also delves into atmosphere density gradients, and rough estimates for pressures due to atmosphere and non-structural components necessary for humans.
What is relationship between volume of compressed air vs. air at 1 atm? What kind of atmosphere and pressure can stations get away with?

As an example, a typical scuba tank compresses 80 cubic feet of air at 14.7 psi to .39 cubic feet at 3000 psi, and will last about an hour.

In general, one human per day breathes about .835 kg (.56 m^3 at 1 atm) of O2, breathes out .998 kg of CO2. The ISS interior uses 79% N, 21% O2 at 1 atm (14.7 psi). ISS eva uses 4.3 psi of pure O2. Suiting up for the eva means two hours and 20 minutes aclimatizing to the pure oxygen at lower pressure, which includes 10 minutes of high intensity exercise at the start of this "pre-breathe" process. See for instance this 2005 Nasa report about atmosphere in space stations and space suits.
What volume of cannister is necessary to reinflate a station of a given volume?

Going roughly by scuba tank ratios and for simplicity assuming constant density, compressed volume is .0049 of the original volume. So for example, Kalpana One with a volume of .06 km3, would require a spherical tank about 80 meters wide.
From 2 given masses, what is the stability and 3-D path of a typical lissajous orbit around various langrange points? How much does the multitude of bodies in the solar system affect the stability? How is this computed?
For something like Kalpana One, if light were collected at endcaps and redirected (fiber optics?) to a kind of central faux-sun, how would that light compare to natural sunlight on earth? Plants in general need (so I hear) reds for flowering, and blues for leafy growth. How much of this reflected light would be necessary to support a bunch of plants and adequate lighting on the inner surface? Human made lights necessary?
Is there some reason why L5 seems to be so popular for station placement, and not L4? Just the name? Some how easier to fly to from the involved bodies (ie from Earth to the l5 point of earth-moon system)?

No, not really.
Are relativistic effects all that relevant for calculating orbits around planets beyond Mercury? Is there some existing software with a C or some other programming api that can compute approximations for orbits? This would be for the purpose of creating realistic-ish orbital situations.

...need to investigate, for instance, the Gaia Sky! Will have to experiment. Seems to be able to show the orbit of the Gaia space observatory (launched 19 December 2013) orbiting around Earth-Moon L2, as well as a variety of other celestial objects. It is released under the MPL 2.0. Another open source project to examine is Celestia (GPL). One fabulous space toy is (the proprietary) Universe Sandbox, where you can set up various unlikely celestial configurations just to see what explodes.
Say an asteroid hits a station (size and speed dependent on what makes a good story). How does this affect station dynamics on a rotating station? What kinds of airspeed can be expected rushing out of a resulting hole? how feasible is it to still run around inside and set up machinery to patch (compared to movies that show catastrophic depressurization)? Would it make the station precess? would this wobble subside? (I have not tried building in Space Engineers)
In a large scale space habitat, as an ecosystem involving farming and oxygen generation, what can we say about its stability? Will it collapse due to being too much of a monoculture? Will it need substantial import of resources like soil bacteria, viable seeds, and wildlife?
Out in the void of space, are people going to be barbecued by all the radiation?

Yes. No. Maybe. There are two primary sources of radiation. One is our sun, the other is from cosmic rays. There are various mitigation techniques for either kind, like thick layers of water or other materials to stop radiation. If you are in low Earth orbit, near the equator, you might be protected by the Earth's magnetic field, and you won't have to build in massive amounts of shielding material. In any case, much work needs to be done on the long term effects of radiation, and ways to escape its terrible effects.
If you have a constantly spinning station, are the people inside just going to be throwing up all the time?

Opinion varies. A rough rule of thumb is 1 RPM is a decent maximum rotation rate, no matter what size of station you make. Most research on the subject involves experiments on Earth where a centrifuge spins with a rotation axis parallel to Earth's gravity. However in people's inner ears, gravity is not nullified, which complicates estimates of how much rotation people can tolerate, as people have to experience two orthogonal force vectors, resulting in a kind of perceived slanted "gravity" vector, rather than a single vector away from the axis of rotation. You can see an overview of rotational effects here.