How Can Kalpana One Be Expanded to Accommodate 3 Million Inhabitants?

[cbrons]

These questions are about a fictional space station in my novel. Just a little background, the station itself is modeled on an expanded version of the “Kalpana One” proposal (pdf here if interested) which was developed by the American Institute of Aeronautics and Astronautics.

The Kalpana One is a cylinder with:

Radius (R) 250m

Length (L) 325m

Angular Velocity (Ω) 2.0 revolutions/minute

Centripetal Acceleration (A) 1.0 G

Population ~3,000 people

Question 1 – Can you offer a suggestion on how to increase the dimensions to facilitate a population that is roughly 1,000x bigger – for a final population of about 3 million? Having the final length and radius will help me develop a layout of all the important settings.

I’ve found calculators (such as http://www.artificial-gravity.com/sw/SpinCalc/SpinCalc.htm) but they don't seem to allow me to calculate expansions in length and radius alone while keeping the needed variables constant. And I am assuming I can’t get away with just multiplying the radius, length, population, etc. by the same value. I just don’t have the level of mathematical understanding here to really know what figures might seem plausible or at the very least (my true goal here) not seem completely ridiculous to a reader.

Question 2 (now this will seem like a very dumb question, I apologize) – Would a station of this size (both the original and increased size) have to orbit a planet? Or could it theoretically be placed at an appropriate length from a star on its own? In my novel, this station is in a foreign star system (not in our solar system). In this regard (not in direct orbit around a planet or planetoid), it is similar to the Citadel from Mass Effect.

From the .pdf on Kalpana One: “Although the design is not orbit-specific and is intended to be replicated many times, and expanded, the first Kalpana One orbital settlement may be built in an equatorial Low Earth Orbit (LEO) at an altitude of approximately 600 km or so; high enough to avoid rapid entry into the Earth’s atmosphere and minimize reboost requirements, but low enough for the van Allen Belts to provide radiation protection to reduce shielding mass.”

Unfortunately, I again do not have the physics and mathematical background to know all the variables that might or might not make such a thing plausible.

 

[Danger]

I'm just going to hit a couple of your questions, because I'm really not in a position at the moment to deal with this. It can definitely occupy an orbit of its own, independent of any planet. That would be inefficient, though, if that planet has resources. Closer makes for easier transport.
Also, if the planet happens to be Earth-like, you would benefit from the protection of its magnetic field from both solar efflux and cosmic rays. That would seriously cut down on the amount of shielding you would have to build in.

 

[Bandersnatch]

And I am assuming I can’t get away with just multiplying the radius, length, population, etc. by the same value. I just don’t have the level of mathematical understanding here to really know what figures might seem plausible or at the very least (my true goal here) not seem completely ridiculous to a reader.

To an extent, you can. The basic station has got about 160 square metres of habitable space per individual.
The surface area of the cilinder walls is $2\pi R*L$, so doubling the length doubles the population capacity, and doubling the radius increases capacity by approximately 6-fold(two times pi). You could have a 325 km long station with the original radius, or one with the original length and 80km diametre. Or anything else that has total area of its sides 1000 times larger than the original.
I suspect the only issues are of material strength and stability. Somebody else would have to chime in with a better understanding of the subject.