APPENDIX C: MASS AS A MEASURE OF STRUCTURAL COST
Structural mass is an important measure of the effort and resources required to build a habitat. To compare the masses required to construct different geometries two questions must be answered: How much mass is required to obtain a given amount of projected area? How much mass is needed to get a given habitable volume?
Formulas for the structural masses for several different geometries are given in table 4-7 both for stressed skin and for ribbed construction. It is convenient to represent the sphere as a limiting case of a cylinder with spherical endcaps. To do this the aspect ratio, $\lambda = L/R$, is defined. It is also convenient to express the minor radius of the torus in terms of an aspect ratio $\alpha = r/R$.
Mass Per Projected Area or Per Habitable Volume for Different Geometries
From the formulas in tables 4-6 and 4-7, the mass required for a piece of projected area in a given geometry can be calculated. These tables also permit the mass per unit habitable volume to be determined.
It is convenient to compare different geometries by taking the ratio of their masses per projected area. The ratio of the mass per projected area for a cylinder with spherical endcaps to the mass per projected area for a torus (where for simplicity only stressed skin construction is considered) is given by:
$\frac{(M/A){cyl}}{(M/A){tor}} = \frac{1}{2\alpha} \frac{\lambda + 2}{\lambda + 2\sqrt{\epsilon(2-\epsilon)}}$
which is independent of R and g and, therefore, of rotation rate.
Figure 4-19 is a graph of the variation of this ratio for several configurations. Where $\lambda = 0$, a torus and a sphere are compared; whereas for $\lambda = 10$, the four models C-1 to C-4 discussed by O'Neill (ref. 1) are compared to the corresponding toruses. In each case the internal load is taken to be 0.16 of the pressure of the atmosphere; the design figure in this study.
From tables 4-6 and 4-7 an expression can be derived for the ratio of the mass per habitable volume of a cylinder with spherical endcaps to the mass per habitable volume of a torus.
TABLE 4-7 — STRUCTURAL MASSES
| Geometry | Stressed Skin Mass | Ribbed Construction Mass | | :--- | :--- | :--- | | Torus | $2\pi R r^2 \rho \frac{g}{\sigma} (1 + \frac{3}{4}\alpha)$ | $2\pi R r^2 \rho \frac{g}{\sigma} (1 + \alpha)$ | | Sphere | $4\pi R^3 \rho \frac{g}{\sigma}$ | $6\pi R^3 \rho \frac{g}{\sigma}$ | | Cylinder | $2\pi R^2 L \rho \frac{g}{\sigma}$ | $3\pi R^2 L \rho \frac{g}{\sigma}$ |
Figure 4-19 — Mass per projected area and mass per habitable volume comparison for different geometries.
<!-- image -->APPENDIX D: THE PLASMA CORE SHIELD
Cosmic ray shielding is needed for all human habitats in space. The obvious solution is to use mass as shielding, but mass is expensive. Thus if a different means of radiation protection is possible and is compatible with the other requirements of a productive habitat, it should be used. Such a possibility is offered by the class of devices called "plasma radiation shields" (ref. 31). However, these devices are speculative.
A plasma core shield is a variant of the plasma radiation shield discussed in reference 31. Figure 4-20 shows a toroidal habitat with an "electron well" at the hub. Inside this well about $10^3$ C of electrons spiral along lines of magnetic force, and hold the metallic habitat at a positive potential of 15 billion volts. The enormous electrostatic potential repels the protons and other cosmic ray nuclei from the habitat, and cuts off the cosmic ray spectrum for energies below 7.5 GeV/nucleon (15 GeV for protons). With this cutoff the net radiation dose, including secondary production, is below the acceptable dose of 0.5 rem/yr.
The critical advantage of the plasma core shield over earlier plasma shields is that the fringing fields at the lips of the electron well keep the electrons electrostatically confined to the well's interior. Thus there are no electrons near the exterior surfaces of the habitat. This feature enormously simplifies construction, operations, and even theoretical analysis (e.g., the electron plasma in this device is cylindrically symmetric instead of toroidal). In essence this device is a "bolt-on" shield, since any metallic structure in electrostatic contact with the electron well is protected — provided it stays well within the last magnetic flux line which passes through the electron well but does not touch the well's metal sides (any line that does touch is "shorted out").
The shield is energized by operating a 10 GeV electron accelerator to shoot high energy electrons away from the habitat. Electrons form in the well when electrons from the solar plasma, attracted to the ever more positive habitat, are drawn along magnetic lines into the well. The main energy term in the system's energy budget is electrostatic energy, and this may exceed $10^{13}$ J of energy for a habitat sized like the Stanford torus (this energy is equal to 100 MW of power stored up over 1 day). This much energy could easily be transformed into penetrating radiations should a subsystem fail — for example, the magnetic cryogenic system. A safe procedure for dumping $10^{13}$ J of energy in a small fraction of a second is essential if the plasma core shield is to be usable.
One procedure is to accelerate positive ions away from the habitat. The electron cloud charge of $10^3$ C is only about 10 mmol of particles, thus 1 percent of a mole of hydrogen ionized outside the metal structure would be enough to neutralize the habitat once the habitat's electric field had accelerated the ions away. In effect, the "charge" account is balanced by absorbing the electrons contributed by the ions — now receding from the habitat at great speed. Of course the electrons in the well are affected by this rearrangement. As the well's fringing electric fields die away the well electrons repel themselves along the lines of magnetic flux — arranged not to touch the space habitat. Thus, in perhaps a millisecond, $10^{13}$ J and $10^3$ C of electrons are safely neutralized. Obviously some more work should be done to verify this possibility.
Figure 4-20 — Solenoid core plasma shield.
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Because a practical shield must remain in operation essentially 100 percent of the time, it must be possible to gain entrance or exit from the habitat at will — without turning off the shield. Since there are essentially no electrons external to the well this is not a difficult feat. It is only necessary to achieve varying levels of charge on objects being transferred from the habitat to the unshielded zone and back again. A device called a "shuttle shell" does this quite easily.
The shuttle shell is a Faraday cage equipped with electron/ion guns and a thruster unit. As the shuttle shell nears the habitat its electron gun bleeds off enough electrons (which go into the well) to equalize the potential between its cargo and the habitat. In reversing the operation the shuttle shell emits positive ions (which head for infinity) to neutralize its cargo. A subtlety of the shuttle shell's operation arises from the fact that like charges repel. Thus, a highly positive shuttle shell approaching a highly positive habitat feels a stiff "electric wind." To avoid excessive thrust requirements two shuttle shells might be used connected on either side of the docking port by cables which are winched in to draw the two shells to the dock, rather like cable cars.
Because the essential dynamic component of the plasma core shield is an electron plasma, plasma instabilities are to be expected. Experiments have shown that these can probably be controlled by varying the electron density as a function of radius. The real source of likely problems is the detailed systems engineering necessary to wed this device to a functioning habitat. Until extensive work is done to study all these ramifications the plasma core shield cannot be claimed as a practical solution to the radiation problem in space.
APPENDIX E: STRUCTURES BY VACUUM VAPOR FABRICATION
In making structures by vacuum vapor fabrication the goal is to create a uniform deposit of metal alloy with good mechanical properties. This should be accomplished with minimal equipment, labor, metal consumption, and environmental degradation. While a number of critical experiments must be performed, presently available information suggests that these goals may be attainable.
In physical vapor deposition of metals, most alloy systems show a full density, fine grained microstructure at a substrate temperature 0.3 times the melting point of the metal (ref. 32). As substrate temperature is increased, the grains become coarser, the yield strength decreases, and ductility increases. Because these properties correspond to those of rolled and annealed sheet, vapor deposited metals have been termed "a true engineering material" (ref. 33). Despite the fairly consistent behavior shown by many metals, experiments must be performed with the specific alloys that are of structural interest for space applications.
Given a metal deposit of adequate yield strength and ductility, uniformity becomes of concern. Irregularities in the substrate are replicated in the final metal surface; the problem is to ensure that non-uniform metal buildup (across steps and grooves, for instance) leaves metal with structural strength in the zone underlying the irregularity. This is aided by increased substrate temperature (to encourage migration of surface atoms), by a nearly perpendicular atomic flux (to discharge self-shadowing), and by use of an initially smooth substrate. Adequate uniformity seems possible with the above controls; if needed, however, there are several promising means of eliminating defects part way through metal buildup.
The equipment used in vacuum vapor fabrication can be very lightweight. It handles sunlight, thermal radiation, rarefied vapor, and an aluminum feed rod; forces on it are virtually nonexistent. The greatest mass in the system appears to be the solar furnace mirror area, which is directly proportional to energy consumption. This consumption is, in turn, driven by the efficiency of energy use (thermal radiation to heat of vaporization), efficiency of vapor use (aluminum vaporized to aluminum reaching substrate), and by the total quantity of aluminum deposited.
Ignoring efficiency factors, for a heat of vaporization of $1.1 \times 10^4$ J/g, a colony mass of 300 kt, a solar constant of 1.4 $kW/m^2$, and a fabrication time of 1 yr, the ideal mirror area is $7.4 \times 10^4$ $m^2$. An average flux deviation from perpendicular of 20° probably represents adequate collimation; with proper evaporator design the inefficiency of vapor use should be less than 2.5 (unused vapor is condensed and recycled); even a poor energy efficiency should keep the total inefficiency below a factor of 10. Allowing a full factor of 10, the mirror area is $7.4 \times 10^5$ $m^2$. At 100 $g/m^2$, this is 0.74 kt.
The remainder of the system includes refractory metal foil boxes for the actual solar furnace evaporation units, plastic film hoods to intercept scattered metal atoms, and a carefully made balloon in the shape of the desired structure. Including these masses, the total system is very likely less than 1.5 kt; if the fabrication time were extended over several years this mass would be less.
Because colony structures have rotational symmetry, the solar furnace evaporation units can cover different areas as the colony rotates beneath their beams. With proper arrangement, complex shapes and structures can be created, and the direct human labor required for fabrication is very small.
APPENDIX F: INTERIOR BUILDING MATERIALS AND COMPONENTS
Building materials and components must be developed for use inside the colony compatible with the selected modular framing system. The need is for light and strong floor deck elements, light and fireproof interior wall elements, light, fireproof, and acoustically treated exterior wall elements, and fireproof ceiling assemblies. All of these elements must be selected on the basis of their specific functional use, concern for safety against fire, smoke and human panic, and appropriateness to their relationship within the overall design context of the interior environment of the colony. The elements have been designed assuming the availability of sufficient amounts of aluminum that meets the necessary strength requirements of NASA report MSC-O1-542.² Also assumed available is a silicon-based fiberboard similar to terrestrial mineral fiber insulation board. The systems chosen are shown in table 4-8.