Standarized Supramundane Habitat

Codex Cogitatum Index: 2018/02

GSD 42759.7424

Goal: Standarized areal density on supramundane habitat constructions.

Supramundane habitat is a delicate structure with active support structures, first introduced by Paul Birch. On top of the active support structure, is habitat area, often with landscaping and delicate geosphere ornaments. It is often complete with whole geosphere, hydrosphere, and atmosphere, usually with their accompanying biosphere.

The geosphere is composed of either hollow cubical network of silicate-walled rooms at a density of some 10 kgm^-3, or foamed silicate rock at 500 kgm^-3 to 750 kgm^-3 (typically 600 kgm^-3). The crust's highest peak is usually around 2 km from normal, and the deepest trench is around 2 km below sea level, which describes a range of about 4 km, with averaged thickness of 2 km. So areal density for foamed rock and/or hollow silicate-walled blocks are vastly different, therefore we would classify them into two types: Type A for hollow silicate-walled blocks at ~10 kgm^-3, and Type B for foamed silicate rock at a typical density of 600 kgm^-3. Then for average geosphere thickness of 2 km, its averaged geosphere areal density are:

Type A: 20,000 kgm^-2
Type B: 1,200,000 kgm^-2

Atop of the geosphere would be a soil layer of some 10 meters deep. This soil layer has a density of some 2,500 kgm^-3, so areal density of the soil layer is 25,000 kgm^-3.

Then about half of the surface would be covered with water body with an average depth of 1 km. Water density is 1,000 kgm^-3, therefore areal water density of surface water tables are 10^6 kgm^-3. However, only half of the surface is covered in water, therefore averaged areal density of water surface is 500,000 kgm^-3.

Atmosphere pressures ranges that majority of aucafidians would consider comfortable are above 1 bar (100 kPa) to below 2 bars (200 kPa). To simplify calculations, in a (yet to be digitized) essay I made on "Megastructures on Subralis," I explored that there are at least three common environmental standards known to aucafidians:

Standard Environment (SE), surface gravity of about 12.4 ms^-2 and a 2 bar (200 kPa) atmosphere.
Moderate Environment (SE), surface gravity of about 7.44 ms^-2 and a 2 bar (200 kPa) atmosphere.
Low-G Environment (LE), surface gravity of about 3.72 ms^-2 and a 1.3 bar (130 kPa) atmosphere.

The unit of pressure "Pascal" (Pa) is a unit of mass per unit area, that in SI Units is kgm^-2. Pressure is defined as the amount of force per unit area, and force is defined as mass multiplied by acceleration. Considering that areal density is unit mass per unit area, areal density of atmospheric body over a given atmospheric pressure under a body with a surface acceleration could be calculated with: Areal density = Pressure / surface acceleration. Areal density is in kgm^-2, pressure is in Pa, and surface acceleration is in ms^-2 respectively.

Then, the three common environmental configurations would have atmospheric areal densities as follows:

SE = 16,100 kgm^-2
ME= 26,900 kgm^-2
LE = 34,900 kgm^-2

For supporting orbital rings and associated supports (magnetic tracks of the orbital ring or mass stream, foundation bed of the toposphere, et cetera), it is usually about the same areal density as the geosphere + soil layer + hydrosphere + atmosphere masses combined, usually with about two-thirds of the support being the actual mass stream. So, to consider this we have to first compute average areal density of the geo-soil-hydro-atmo structure of all classes and configurations:

Type A:

SE = 561,000 kgm^-2
ME = 572,000 kgm^-2
LE = 580,000 kgm^-2

Type B:

SE = 1.74E6 kgm^-2
ME = 1.75E6 kgm^-2
LE = 1.76E6 kgm^-2

Then to get total areal density of this supramundane habitats, including its supporting mass streams, we doubles all of those values:

Structural areal densities of Type A Supramundane Habitats

SE = 1.12E6 kgm^-2
ME = 1.14E6 kgm^-2
LE = 1.16E6 kgm^-2

Structural areal densities of Type A Supramundane Habitats

SE = 3.48E6 kgm^-2
ME = 3.50E6 kgm^-2
LE = 3.52E6 kgm^-2

Interesting to note that, without atmospheres, areal density of geo-hydro-soil layers are:

Type A = 5.45E5 kgm^-2
Type B = 1.73E6 kgm^-2