You express concern to the operator of the mass catcher over the possible hazard of using high velocity pellets as propellant mass because they constitute artificial meteoroids. They are ejected with high velocity, not so high as to escape the Solar System, but sufficiently high to escape the Earth-Moon system and take up solar orbits. Typically, they will range inward as far as Venus and outward to Mars' orbit.
The operator's response is reassuring. He reminds you that the astronomer George Wetherill (ref. 21) studied the lifetimes of meteoroids in such orbits, or the times before collision with Earth. He found a mean lifetime of 10⁷ years. The Earth presents a surface area of 5 X 10⁸ km², while a colony's area is some 1 km² or less, and a spacecraft's area much less. Using a standard that no more than one impact from a pellet per square kilometer every 10 yr may be allowed, then 5 X 10¹⁴ pellets may be permitted to orbit the Sun following ejection. If each has a mass of 10 g, the allowed mass of ejected pellets is 5 X 10⁹ t. This is some 10,000 times the mass of pellets to be ejected in the course of carrying material for building the colony. He assures you that the rotary pellet launcher will be a useful propulsion system for many years, before the environmental effect of ejected pellets becomes noticeable in comparison to the effect of meteoroids naturally present in space.
HOME TO EARTH
It is now 2 months since you left Earth. In that time you have traveled over 750,000 km, you have another 386,000 to go to get home to Earth. You have seen a tiny community of 10,000 men and women crowded into the colony and in small bases on the Moon and at L2 separated by vast distances which are in turn dwarfed by the immensities of space. Homesickness is inevitable. It is time to leave the realms of the colonists. Their tasks and their will to do them are enormous, and only those people can be colonists who have a large capacity to work hard and long when, as soon happens, tedium replaces the initial excitement. You speculate that it will be mostly their children and grandchildren who will master space. The great mass of mankind will remain in the cradle of Earth; only a few will go into space.
You are fortunate to get a berth in one of the ships that brings supplies to the Moon and rotates personnel from the Moon base directly back to Earth. In the early years all the men and women of the base went straight back to Earth and so the personnel transporter was full to capacity. Now increasing numbers choose to spend their rotation time at L5 instead of on Earth and berths are available on the run to Earth. You wonder whether this seed of human society planted in such an unlikely environment will flourish, and settling back into your seat to read a terrestrial news magazine you conclude that only time will tell.
APPENDIX A: STRUCTURAL DESIGN CONCEPT FOR A SHELL STRUCTURE
A section from a symmetric structural shell transmitting only normal stresses in orthogonal directions may be designed either as a stressed skin or a rib system. The stressed skin is the most efficient in that the same material carries the stress in both directions and there is integral resistance to secondary torsional and bending loads. In addition, both fabrication and construction generally are simplified and problems with sealing joints, finishing, and maintenance are reduced.
For a rib system, such as shown in figure 5-22, each orthogonal set must entirely carry the membrane force (N₁ or N₂) in that direction. This increases the mass required to carry the membrane stresses by the factor (1 - σ₂) (where σ₁ > σ₂ and σ₁ and σ₂ refer to the membrane stresses in directions 1 and 2) plus the intermediate plates required to bridge between the ribs. Moreover, if the ribs are made of cable and are flexible there is no resistance to secondary torsion, bending, or buckling. There may, however, be some advantages in fabrication and construction to include some cables encased in the ribs.
The obvious requirement for any shell configuration is to avoid ribs whenever possible. Therefore, this design assumes a stressed skin structure except in the windows where the required ribs flare into the skin at the boundaries.
Design Formulas for Torus
For a stressed skin design of a torus the required skin thickness in the meridional and hoop directions, respectively, are given by the analogous equations for the cylinder and sphere.
Figure 5-22 — Shell structure rigid rib system.
<!-- image -->In general tₕ > tₘ for the range of values of interest in this design. For the Stanford Torus, p₀ = 51.7 kPa (7.5 lb/in.²), R = 830 m, and r = 65 m. (Note: Since angular velocity must be 1 rpm, then R + r ≅ 895 m. Furthermore, projected area 4πRr ≅ 650,000 m².) The structural material is assumed to be aluminum with ρ = 2.7 t/m³ and σ_w = 200 MPa (29,000 lb/in.²). The value used for P_g is 7.66 kPa (160 lb/ft²), which is 530,000 t of internal mass on a projected area of 678,000 m². For a tabulation of internal mass, see tables 5-2 and 5-3.
The thickness required to contain both atmospheric pressure and internal mass is determined by equation (2):
<!-- formula-not-decoded -->Considering atmospheric pressure only, equation (1) governs:
<!-- formula-not-decoded -->This represents a difference in cross-sectional area of 2πr(tₕ - tₘ) = 1.634 m². An efficient way to use the structural material might be to construct the shell with the minimum thickness needed to withstand the atmospheric pressure, and provide the additional required area in the form of hoops incorporated into the supporting substructure of the internal structures, as illustrated in figure 5-23 (next page).
The structural mass for a torus design with a stressed skin is determined by
<!-- formula-not-decoded -->On the other hand, if a completely ribbed system were used the structural mass would be
<!-- formula-not-decoded -->but tₕ must now be determined by
Since approximately 1/3 of the surface area consists of solars (the chevron windows), the mass of the standard torus is taken as 2/3 M_ss + 1/3 M_rib, which equals 156,000 t.
APPENDIX B: STRUCTURAL SYSTEM FOR HOUSING
The structural system consists of aluminum tube columns with a typical 4 X 6 m bay size. Beams are also aluminum, spaced at 2 m on center. Beams and columns have fixed connections to form rigid boxes, allowing them to span up to 6 m. Figure 5-24 shows this structural frame assembly and figure 5-25 details the beam and column connections.
Figure 5-23 — Torus structural cross section.
<!-- image -->Figure 5-25 (right) — Column and beam connection detail.
<!-- image -->Figure 5-24 — Structural frame assembly.
Image
Floor elements consist of 5-cm-thick aluminum honeycomb sandwich panel construction. Structural calculations for such a floor and beam system were developed for use in Skylab and as such have been assumed for use in the colony. The system allows dead load weights of less than 120 Pa (2.5 lb/ft²) and is capable of taking upwards of 12 kPa (250 lb/ft²) in live load (ref. 22). Walls could be a number of different materials. For sound isolation and for fire protection, a 10-cm-thick silicon cellular panel has been assumed. Ceiling construction, likewise a fire resistive construction, is also made from silicon fiberglass.
APPENDIX C: AGRICULTURE
The agricultural system is derived from standard nutritional requirements for adult men and women and for children. The space colony population is used to normalize these requirements to that of a "typical" person weighing 60 kg as shown in table 5-16. These requirements are met by an average daily diet which is shown in table 5-17(a) which also includes the caloric and nutritional values calculated for this diet. The nutritional requirements are met and an excess of protein is provided by a substantial margin. Vitamins and trace minerals are also available in excess quantities as shown in table 5-17(b). A more careful analysis of the colony's protein requirement could provide savings in meat requirements and, in turn, provide substantial savings in the required land area for plants.
The diet is treated as a daily average of all components as if each colonist ate a small portion of each foodstuff each day. In reality, of course, the colonists would eat a varied selection that over time averages to this diet. The individual components of the diet are chosen to provide adequate variety for both nutritional and psychological purposes. These components are meant to be representative of classes of foods and not specifically limited to these items. For example, pork could be considered as a feasible diet component with feed and area requirements intermediate between beef and rabbits. In addition, it should be explicitly stated that this diet represents typical American preferences and does not recognize ethnic or religious dietary preferences. It is reasonable to expect, however, that such preferences could be adopted if desired.
The meat in this diet dictates the requirement for a stable herd of animals for which the rates of birth and slaughter are equal. In effect, each colonist has 26 fish, 6.2 chickens, 2.8 rabbits and about 1/7 of a cow (see table 5-5). The plant diet for these animals plus that for humans then forms a total requirement for all plants as given in table 5-18. Food processing byproducts and silage are extensively used in satisfying the animal diet. Implicit in this derivation is allowance for yields in meat dressing and food processing, for moisture and silage content of the grains, and for the metabolic requirements of the various animals. These factors are given in table 5-19, parts A-J, along with the carbon, nitrogen, hydrogen, and oxygen elemental balance for each step in the food chain (refer to fig. 5-16). Sorghum is chosen as a principal component of the animal diet because it can be produced in excellent yield and because it provides a source of protein (11 percent) while also providing silage and sugar. Protein make-up for the animal diet is provided from soybean (34 percent) and from meat processing byproducts.
From the quantitative requirements for each plant component, total plant growing area requirements can be obtained based upon estimates of crop yields as presented in table 5-4.
The success of the colony's agricultural systems rests entirely upon the photosynthetic productivity. Crops were estimated assuming a yield double that of the world record for that crop, as shown in table 5-20. In addition, a factor of 1.1 improvement is obtained by shortening the growing season from 100 to 90 days. The record yield data come from harvests under good but not ideal or controlled growing conditions. Comparison of typical terrestrial and space colony growing conditions is presented in table 5-21. Including the shortened season, the net improvement is a factor of 2.2 which is further enhanced by harvesting 4 crops per year. Thus the farmer in a typical American midwestern farm who produces 100 bushels of corn per acre in a single season year would look with astonishment on the space colony farmer who produces 4164 bushels of corn from a single acre in his 4-season year. While this factor of 40 is substantial, it is believed to be credible since a portion of it is derived from year-round growing. Substantiation of crop yields is required and can be obtained through careful study under controlled conditions (and most of the research could be performed on Earth). The improvement that has already been achieved for certain vegetables in Abu Dhabi (ref. 5) is shown in table 5-22.