Rim Mass = 16 (fiber mass/16) 2n , where the multiplicative factor of 16 is due to the fact that the rim thickness is 4 times the fiber thickness and the rim mass/length is consequently 16 times greater than the fiber mass/length. The divisor of 16 is due to the fact that the rim is 2tc times the length of one fiber, not 16 fibers. The rim mass is therefore about 6.3 times the total fiber mass, or 0.35 kg for terrestrial, 2.4 kg for lunar basalt or fiberglass, and 24 kg for lunar glass ceramic. To calculate hub mass, we assume that the hub projects L/2 below the SPS and L/2 above the SPS. Assuming that the hub is constructed of material similar to lunar glass ceramic, and is a cylinder with a radius of 1 m, hub mass = 2000 k (I)2 L, where the factor 2000 is the (MKS) density of this material from Table 3. We next assume a hub length (L) of 10 cm. (This is justified below.) For such a hub length, the hub mass is about 630 kg. 8.3,1 Justification of a 10-cm Hub Length One source of SPS flex can be evaluated using Figure 4. Here, an SPS of radius (Rad) 1 km is in orbit R (42,000 km) from the Earth’s center (36,000 km above the Earth's surface). In this figure, the SPS is oriented directly towards the Earth. Parameter "h" represents the maximum flex caused as the SPS adjusts to the Earth's geodetic. We use a scientific calculator to first estimate length Z from R and Rad using the Pythagorean relationship. Parameter h is the difference between R and Z. A maximum length of h = 1.2 cm is obtained. Since L = 2h = 2.4 cm, a value of L = 10 cm is conservative by a factor of about 4. But for part of every orbital cycle, the SPS will be in darkness and its temperature may plummet from 245 K to near absolute zero. The coefficient of linear expansion of commercial glass is about 11 x 10‘6/K [Ref. 23]. Therefore, the maximum change in length of a 10-cm glass hub will be 0.03 cm. 8.4 Thruster Support for Bicycle Wheel SPS A bicycle wheel SPS will have to be slewed during the course of the day in order to track either the Earth or the sun (or both). Rotation about three axes (with a bit of
RkJQdWJsaXNoZXIy MTU5NjU0Mg==