Next, we scale the solar radiation pressure results (from the bicycle-wheel SPS calculations in Section 8.1 and the area projected to the sun by an inflatable sphere SPS). The maximum radiation-pressure force on an inflatable sphere SPS is about 17.7 N. The maximum combined forces on an inflatable sphere SPS are therefore about 22 N for terrestrial materials and 34 N for lunar materials. The total surface area of the inflatable sphere is 4k (925)2 — 1.1 x 107 m2. This means that the maximum combined stresses for terrestrial and lunar inflatables respectively are about 2 x IO*6 N/m2 and 3 x 10*6 N/m2. The required gas pressures to support terrestrial material and lunar material inflatable SPS’s respectively, are therefore about 4 x IO*6 N/m2 and 6 x IO-6 N/m2. These pressures are next substituted into the above equation m — 45,000 P. The inflatable sphere SPS constructed of terrestrial materials requires an interior gas mass of about 0.2 kg. An identical SPS constructed from lunar materials requires an interior gas mass of about 0.3 kg. Total gas mass required to compensate for diffusion through SPS walls: As discussed in Refs. 25 and 26, gas diffusion through an inflatable spacecraft's walls is a complicated function of wall and gas materials, temperature, and pressure. Rather than attempting here to solve this complex problem analytically, we argue by analogy with Quasat, a European proposal for an inflatable radio telescope in a 20,000 km orbit19. Quasat was designed to carry 1.6 kg of nitrogen gas to maintain inflation at a pressure of 10 Pa (1 Pa = 1 N/m2 — 10"5 atm). This high pressure is required to maintain the observatory-grade optical figure of the Quasat radio antenna. Quasat can be approximated by a sphere with a diameter of 10 m. The approximate volume of the Quasat inflatable orbiting radio antenna is therefore about 500 m3. Substituting into the Ideal Gas Law for the Quasat volume, 245 degrees Kelvin, and nitrogen gas, we find that about 0.069 kg of nitrogen is within Quasat at any one time. Therefore, the ratio of total gas mass to the mass of gas within the inflatable structure at any one time is 23. But Quasat has a design lifetime of 5 years and a SPS must operate for about 30 years. Thus, the minimum ratio of total gas mass to mass within the inflatable structure for our inflatable SPS is about 140. The inflatable SPS constructed from terrestrial materials must carry at least 30 kg of nitrogen gas. If constructed of lunar materials, this SPS must carry at least 42 kg of nitrogen gas.
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