What is the best number of habitats in a cluster

On 8/30/06, Darren wrote:
(...)
> A couple of definitions first, I refer to a single line of habitats arranged
> in a framework as a 1D structure, to get from the habitat at one end of the
> line to the one at the other end of the line you have to go through all the
> ones in between (I am assuming a framework holding the habitats and an
> internal transport system along the framework). A 2D structure would be like
> a chess board, a framework in a grid with habitats locked in the frame. A 3D
> structure would be like a cube or some other solid shape with the habitats
> located at the junction of the grid, a 10 X 10 X 10 grid would hold 1000
> habitats.

I have also thought about 3D clusters, but I found the following problems:

- Collecting solar energy would be more difficult in such a structure.
The habitats inside the cube would be mostly in shadow, and therefore
you would have to increase - 2D-wise - the surface of solar collectors
in the outside and build power lines to supply the internal habitats.
Either that or use nukes or some other energy source.

- Even worse, there would be difficulties in heat dissipation.
Internal habitats would irradiate their heat on the surface of the
external ones. In the end you would have to put some "air
conditioning" system in the grid itself to transfer heat (probably
using some efficient mechanism like convection) from the inside to the
outside.

So if I were to design a cluster, I would stick to 2D and 1D designs.

(...)
> The question is how large can a cluster of habitats get before you would be
> better starting a second cluster? Is there an optimum size for a cluster of
> habitats after which you start to lose efficiency? Ignoring things like how
> strong the frame can be, where are you going to get the mass and assuming
> they do not need to be in direct sunlight, you have some other power source,
> could you have a cluster with a million habitats or how about a billion?
> What are the limits?
(...)

It depends on the cosmic neighborhood and geometry.

I guess 3D clusters (dismissing the energy supply and heat dissipation
problems) probably can grow to the size of dwarf planets - many
hundreds of kilometers in side - until the gravity of the structure
itself starts to put too much stress on it. And I think that the
better design for such a planet-sized cluster would be a sphere of
concentric geodesic grids, creating and following quite natural
spherical equipotential surfaces of gravity.

2D clusters are basically limited by the gravity gradient in its
orbit. So a 2D cluster in GEO probably can't grow more than a few
hundred kilometers until the gravity field of Earth and the orbital
forces starts to bend it. On the other hand, I would think that a 2D
cluster freely orbiting the Sun somewhere in the habitable zone could
grow to thousands, perhaps tens of thousands of kilometers without any
problematic bending.

As for a ring 1D cluster, its maximum length is the circumference of its orbit.