Some General Considerations
Because it is expedient, although not entirely justified, to treat the shielding which protects against the dangerous radiations of space separately from the choice of the geometry of the habitat's structure, that problem is left to a subsequent section. Subject to possible effects of the shielding, the choice of habitat geometry is determined by meeting the criteria of the previous chapter at minimum cost. In considering how different configurations may supply enough living space (670,000 m²) and how they meet the physiological and psychological needs of people in space, the following discussion uses the properties of materials outlined in appendix A. Throughout, aluminum is assumed as the principal structural material.
The Habitat Must Hold an Atmosphere
The simple fact that the habitat must contain an atmosphere greatly limits the possible forms. For economy in structural mass it is essential that large shells holding gas at some pressure must act as membranes in pure tension. There is, in turn, a direct relationship between the internal loading and the shape of the surface curve of such a membrane configuration. Also, when the major internal loads are pressure and spin-induced pseudogravity along the major radius of rotation, R, the possible membrane shapes must be doubly symmetric, closed shells of revolution (refs. 5,6).
Figure 4-1 — Subset of Cassini curves which, when revolved, generate possible geometries.
<!-- image -->The possible "smooth" shapes are the ones generated from the curves in figure 4-1. Four fundamental configurations arise:
- A sphere — by rotating curve 1 about either axis
- A cylinder — by rotating curve 2 about the z axis
- A torus — by rotating curve 3 about the r axis
- A dumbbell — by rotating curve 3 about the z axis
Neglecting secondary effects from variations in pseudogravity and localized bending stresses from discontinuities in deformations, the study group concluded that all possible membrane shapes, that is, any possible habitat, must be one of the four simple forms described above or some composite of them as shown in figure 4-2.
The desire to keep structural mass small favors small radii of curvature. As figure 4-3 shows, the wall thickness to contain a given pressure drops quickly with decreasing R. Of course, structural mass can also be reduced by lowering the pressure of the gas. Both possibilities turn out to be useful.
Figure 4-2 — Basic and composite shapes.
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Figure 4-3 — Shell thickness as a function of radius for spheres, cylinders, and toruses spinning to produce 1 g.
<!-- image -->A Rotating System With 1 g at Less Than 1 rpm
Rotation is the only feasible way to provide artificial gravity in space. Pseudogravity depends upon both rotation rate and radius of rotation, and figure 4-4 shows the lines of constant pseudogravity as functions of these two variables (ref. 7). On the graph are shown a number of rotating systems: C-1 through C-4 are the rotating cylinders proposed earlier (ref. 1) by O'Neill; T-1 is a torus and S-1 is a sphere described later in this chapter; Arthur C. Clarke's Rama (ref. 4) is shown, as are space stations of Gray (The Vivarium) (ref. 8), Von Braun (ref. 2), and Tsiolkovsky (ref. 9). Obviously only systems with radii of rotation greater than 895 m can lie on the line g = 1 below 1 rpm.
Thus, among the simple, basic shapes the torus is clearly superior in economy of structural mass.
An aluminum cylinder like C-3 would weigh about 42,300 kt and have a projected area of $55 \times 10^6$ m², enough to hold 800,000 people — rather than the 10,000 people of the design criteria. Similarly a sphere of radius 895 m would hold 75,000 people and weigh more than 3500 kt if made of aluminum.
A dumbbell shape has the advantage that the radius of curvature of the part holding the atmosphere can be made small while the radius of rotation remains large. However, in this configuration people could only live on the cross section of the spheres, and to hold 10,000 people with 670,000 m² of projected area the spheres would have to be 326.5 m in radius. Together they would weigh about 380 kt.
A torus also permits control of the radius that contains the atmosphere separately from the radius of rotation. Moreover, the torus can distribute its habitable area in a large ring. Consequently, the radius needed to enclose the 670,000 m² of projected area can be quite small, with a correspondingly small mass — about 150 kt for a torus of major radius 830 m and minor radius 65 m (where the mass of internal structure is neglected). The advantages of the torus compared to the sphere and cylinder are discussed further in appendices B and C which define some criteria and parameters useful for such comparisons. The important point is that for a given radius of rotation about four times more mass is required to provide a unit of projected area in a cylinder or a sphere than in a torus of small aspect ratio.
If minimum structural mass were the only concern, composite structures would be the choice. Twenty-five pairs of dumbbells would supply 670,000 m² with spheres 65 m in radius and a total mass of 72 kt. The spheres could be made smaller still and formed into a ring to make a beaded torus. Alternatively, the toruses themselves could be made with quite small minor radii and either stacked and connected together to form a kind of banded torus, or built separately to form a group of small, independent habitats.
However, as pointed out in the previous chapter, it is desirable to compensate for the artificial and crowded nature of the habitat by designing it to give a sense of spaciousness. Composite structures are rejected largely on architectural criteria of environmental perception. Not only would they be more difficult to build than the simpler shapes, but also their short lines of sight, little free volume and internal arrays of closely-spaced cables and supporting members would produce an oppressive ambience.
If the colony were composed of a number of small structures, there would be problems of communication and transport between them as well as the drawbacks of small scale. Nevertheless, as table 4-1 shows, multiple structures (and composite ones too) offer substantial savings in mass, and it might well be that some of their undesirable aspects could be reduced by clever design. It would be an attractive option to be able to build up a colony gradually out of smaller units rather than to start off with an initial large scale structure. The subject of multiple and composite structures is worthy of more consideration.
Figure 4-4 — Properties of rotating habitat systems.
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The various properties of possible configurations are summarized in table 4-1. The parameters show the mass requirements and indicate the degree of openness of the different structures. The single torus, although not the best design in many respects, seems to give the most desirable balance of qualities. Relative to the sphere and cylinder it is economical in its requirements for structural and atmospheric mass; relative to the composite structures it offers better esthetic and architectural properties. Because of its good habitability properties, large volume, a variety of possible internal arrangements, the possibility of incremental construction, a clear circulation pattern, access to zero gravity docks and recreation at the hub, agriculture as an integral part of the living area, and a clear visual horizon for orientation, the torus is adopted as the basic form of the habitat. The dimensions of this single torus are given in the first column of table 4-1.
SHIELDING
The need to shield humans adequately from the ionizing radiations of space imposed some significant design decisions. An ideal shield would bring the radiation dosage below 0.5 rem/yr cheaply and without impairing the contact of the colonists with their environment. However, after considering active shields which electromagnetically trap, repel or deflect the incident particles, and a passive shield which simply absorbs the particles in a thick layer of matter, the study group chose the passive shield for their design.
Active Shields
When a charged particle passes through a magnetic field, its path curves. Thus, as figure 4-5 shows, the proper configuration of magnetic field lines can form a shielded region which particles cannot enter. Since for a given magnetic field the curvature of the path of a particle is inversely proportional to its momentum, the region is shielded only against particles below a certain cutoff momentum or cutoff energy. Particles above this cutoff energy can still penetrate (ref. 10).
The problems of magnetic shielding become apparent when the cutoff energy has to be chosen. Protection against heavy ion cosmic rays, the so-called high-Z primaries (i.e. the iron nuclei and others mentioned in chapter 2) and most solar flares would be achieved with a cutoff of 0.5 GeV/nucleon. The difficulty is that most secondary particles are created from the primary flux above 2 GeV/nucleon which can penetrate the shield and generate secondaries in the mass of the shield itself. As a consequence a magnetic field around the torus with a cutoff of 0.5 GeV/nucleon and a structural mass of about 10 kt, corresponding to a thickness of matter of 0.5 t/m², would actually increase the exposure to about 20 rem/yr. Only the addition of shielding to an extent of 1.3 t/m² could reduce the dosage to a level equivalent to there being no secondary particle generation by shielding, that is, about 8 rem/yr. Furthermore, even then a specially heavily shielded shelter would be required as protection against secondaries produced by the strongest solar flares. The consequences of the production of secondary particles are shown in figure 4-6.
A cutoff of 10 or 15 GeV/nucleon would eliminate so many of the high energy particles that even with secondary production the dose would not be above 0.5 rem/yr. A shield of this capability would also protect against the effects of the strongest solar flares, and no shelter would be needed. The difficulty is that the structural mass required to resist the magnetic forces between superconducting coils precludes this design even for the most favorable geometry, namely, a torus.
Similarly, electric shielding by a static charge seems infeasible since a 10-billion-volt potential would be required for even moderate shielding. On the other hand, a charged plasma which sustains high electrical potential in the vicinity of the habitat is a more promising approach (ref. 11). However, means to develop such a plasma requires extensive research and technical development before a charged plasma might be considered for design. Some further details of this approach are given in appendix D.
Figure 4-5 — Magnetic shield around a torus.
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Figure 4-6 — Magnetic shielding parameters — torus: R = 900 m; r = 60 m. This figure plots the structural mass of a magnetic cosmic ray shield as well as the annual radiation dose versus the shield's cutoff energy. The dose is derived from a rough calculation which includes spectrum cutoff, nuclear attenuation, secondary particle production, and self-shielding (50 g/cm² from body tissue and local mass concentrations). The dose calculated is probably uncertain by a factor of two. The essential reason why the dose declines so slowly with cutoff energy above 3 GeV is that the spectrum cutoff factor is cancelled, largely by secondary production in the shield's structural mass.
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