PARAMETERS OF HABITABILITY
In a rotating habitat in space three factors affect the area and volume
available for residence. Due to physiological considerations living and
sleeping are confined for a large portion of the day to a volume where
the change in pseudogravity, g, is less than some amount, 
g, which
experience must determine. The habitable volume is that volume where g/g
is less than or equal to some number which the study group calls the
habitability parameter, 
=
g/g. It is not inconceivable, for example,
that ways may be found to live safely and comfortably
through the entire range from 0 to 1 g. In that case
would equal 1,
and the entire volume of the space colony is habitable.
Projected Area
City planners and architects design human habitation in terms of the
surface area on which buildings may be constructed. In the kinds of
habitats discussed in this study, the curvature of surfaces on which
colonists might live is often pronounced. It seems reasonable to define
available surface area as the projection of area onto a plane
perpendicular to the direction of the pseudogravity. In a torus the
projected area is a strip through the diameter of the tube of the torus
(see fig. 4-17). If the minor radius is r and the
major radius is R. the
projected area for a torus is 
.
This is just 
the total skin area of a torus. Note that if the
torus is spun so that there is 1 g of pseudogravity at the outermost
surface, and if the aspect ratio, 
, is greater than the
habitability parameter, , the plane of projected area is outside the
habitable volume. For all the cases considered, 
, and the above
formula is sufficient.
For a rotating sphere the projected plane of usable area is the surface
of a cylinder inscribed in the sphere (see fig. 4-18). The surface of
this cylinder should not be more than R above the surface of the sphere.
The projected area then is
At = 0.29 this expression has a maximum
.
Consequently for
the expression for the maximum can be used. (Alternatively, for
smaller , the habitat might be spun to
produce 1 g at 
to maximize
the available area).
For a cylinder of radius R and length L the projected area is just the
surface area 
<.
Table 4-6 summarizes the expressions for projected area in different geometries.
Habitable Volume
Although projected area represents an important concept in conventional
architectural thinking, the available volume in the habitat may be more
relevant in specifying the apparent population density and the quality of
life. Habitable volume is defined as that volume in which the
pseudogravity does not vary more than the specified
amount, g, from the nominal value of g. Consequently, habitable
volume depends on g/g.
For a cylinder of length L and radius of rotation R. the habitable
volume is the annulus between R and (1 - R. In a sphere with a
pseudogravity no greater than 1 g on its surface, habitable volume is the
figure of revolution of the shaded area (as for the sphere in
fig.4-18)
In a torus with 1 g at its outermost circumference, habitable volume is the shaded area of the tube revolved around the axis of rotation. The formulas for these volumes are given in table 4-6.
TABLE 4-6 (gif format)
| Geometry | Projected area, Ap | Habitable volume, |
|---|---|---|
| Cylinder | |  |
| Sphere |  |  |
| Cylinder and spherical endcaps | +
|  |
| Torus |  |    < |
= g/gThe study group determined that a reasonable standard of projected area is 67 m^2/person. Also, a detailed inventory of structures and facilities required for individual and community life suggests that habitable volume should be about 1740 m^3/person. Consequently, a habitat, or a collection of habitats, suitable for a given population of 10,000 people, must provide an area of 670,000 m^2 and a volume of 17,400,000 m^3. These numbers determine the geometry in a fundamental way.
