Hence, any savings realized by reducing Cr are partially offset by increased power expenditures. If antenna efficiency were to fall to 48% for example (E„ = .48), the cost of LPS power equipment would be doubled to $48.2 billion. A high precision wire mesh antenna for the LPS might provide 85% antenna efficiency and cost approximately $3.56 billion (1/10 of waveguide antenna). Extra power-related costs would then total $326 billion allowing a resultant savings of $30 billion in waveguide expenditures. Clearly, open mesh antenna systems should be considered a valuable alternative for the LPS. (2) An Optimal Tradeoff Between Surface Radiator Cost and Antenna Efficiency By constructing a hypothetical functional relationship between microwave radiation cost (Cr) and antenna efficiency (E,f an appropriate point of operation providing minimal electricity cost can be found. An LPS antenna system using waveguide radiators (96.5% efficiency) has been shown to cost some $35,000 million for a 157 km2 area. Parabolic open mesh reflectors would make possible significant surface cost savings, costing perhaps 1/10 as much as waveguides ($3,560 million). Mesh antennas, however, are limited by energy losses due to non-specular reflection I2R mesh absorbtion, and parabolic surface distortions, and thus might achieve a maximum efficiency around 85%. Lunar systems using high efficiency waveguides (Cr = $35,600 million, Ea = 96.5%) and precision open mesh reflectors (Cr = $3,560 million, Ea = 85%) may be taken to represent two points from a continuous range of surface radiator costs and resulting antenna efficiencies. A suitable curve quantifying the trade-off between radiator cost and antenna efficiency is the generalized hyperbolic function: where the unspecified parameters A and B are found by substitution of the two known E„ and Cr points stated above into this equation, giving: A = .9797 (theoretical maximum achievable efficiency) B = $543.3 million The resulting antenna efficiency curve is shown in Fig. A-l. For actual LPS antennas, the continuity between mesh radiators (efficiencies less than 85%) and high efficiency waveguides is doubtful. Moderate cost efficiencies in the range 85-95% might be achieved by using a hybrid of the two approaches. An optimal point of operation for the lunar antenna system must provide both moderate surface radiator costs and high antenna efficiency since these factors enter directly into the LPS cost equations A-2 and A-4. Electricity cost may be rewritten: Using the functional expression for Ea derived in Equation A-5, allows the electricity rate equation to be minimized by setting the partial derivative with respect to Cr equal to zero. As expected, this optimization procedure yields a point of operation with relatively high antenna efficiency but considerably reduced microwave radiator costs. These numerical results should be taken to give only a rough indication of the trade-off relationship between £'„and Cr, since both the hypothetical point value assumed for open-mesh radiators and the presumed hyperbolic efficiency curve are not known with great certainty. The optimal trade-off results do, however, confirm the general findings of part (1). Any reduced cost antenna surface must attain propagation efficiency on the order of 85% in order to be cost effective.
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