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. 417). 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. 418). 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 46 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.418)
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 46.
TABLE 46 (gif format)
Geometry  Projected area, Ap 
Habitable volume, 

Cylinder  
Sphere  
Cylinder and spherical endcaps 
+ 

Torus  < 
The 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.