APPENDIX A. TRADEOFFS OF LOW-COST ANTENNAS SURFACES VERSUS HIGH EFFICIENCY WAVEGUIDES The solar power satellite utilized high efficiency slotted waveguides for the antenna radiating surface. A 96.5% microwave transmission efficiency, together with a capability for handling high powers, were significant advantages for the waveguides. For the lunar antenna, however, slotted waveguides would cost $35.6 billion (1977 dollars) because of the 200-fold increase in the quantity of waveguide surface required (two antennas, each with an area 100 times larger than the SPS antenna). Thus lower cost, reduced efficiency radiating surfaces should be considered for lunar antennas. One possibility is a steel, open mesh, parabolic antenna fed by a single power conversion tube. While such low-cost alternatives are attractive, the associated reduction in antenna transmission efficiency produces elevated costs in other portions of the LPS system. A 10% efficiency reduction for instance would require $3.3 billion of additional power collection expenditures as shown below to maintain a 5GW output. Nevertheless, significant savings for the overall LPS system might result if wire mesh radiators can be installed at a unit price well below that of waveguide radiators. This appendix considers two aspects of the tradeoffs involved: (1) the impact on LPS system costs arising from reduced antenna efficiency, and (2) derivation of an optimum radiator cost to transmission efficiency relationships to minimize LPS costs. (1) LPS System Cost Impacts Due to Antenna Efficiency Losses The electricity rate for a power plant (mills per kWH) may be expressed as: Use of a lower efficiency antenna normally would act to reduce delivered plant capacity. This effect could cause rate increases out-weighing a partial savings in system costs. A more economically feasible way for using wire mesh radiators is to increase the lunar transmitted power to make up for lost efficiency. This is the approach considered in this cost trade-offs study. It should be cautioned however, that excess power lost to sidelobes and diffuse scattering could pose certain environmental hazards for a high-powered LPS system. Cost increases required to provide additional LPS transmitted power may be gauged from the itemized costing data in Table 1. Each item is assumed to increase in cost in proportion to system scaling factors such as antenna size, rectenna size, and transmitted power as indicated (1,5). Costs increasing in direct proportion to transmitted power include all solar array components ($9,337.6 million), antenna klystrons, thermal control, power conductors, switch gears, converters and replacement klystrons ($7,539.7 million), and PLVs and POTVs for transportation ($6,000.0 million). In addition, 1/2 of LEO and solar array construction costs ($318.5 million) increase with power. Other LPS cost categories are assumed independent of transmitted power. Total LPS system cost hence may be written: System Costs = 60 + 0! + 1.053 Cr (A-3) Co — power independent costs ($73,796.2 million) C, — costs increasing with transit power ($24,090.3 million including growth) Cr— antenna radiator costs ($35,600.0 million for waveguides) A 5.3% factor has been added into the costs of solar array and antenna hardware to include a 17% growth allowance less amortization. Utilization of wire mesh radiators in place of waveguides would cause power dependent costs to increase in inverse proportion to antenna efficiency (EJ:
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