(1) Column/Cable Configuration An alternative approach is to eliminate the torque. This can be done for the short-term torque by making Ix = Iz by adding counterweights. Counterweights are attractive for configurations such as the column/cable (figure IV-B-4-2) because they can be placed on existing structure with minimum penalty. The RCS and the maintenance station, in fact, can serve as part of the counterweight. The total counterweight mass required is shown in figure IV-B-4-3 for various height/width (b/a) ratios, assuming dimensions b and c are equal. A long, slender configuration requires less counterweight, but at the expense of additional bus weight along the outer edges of the array. A rough analysis indicates a weight-optimized b/a ratio of about 2.3. If this ratio is set at 2 to facilitate use of uniform segments in all columns, total counterweight mass is 1.07 x 10® kg. If RCS were used to counteract gravity gradient torque on the same configuration, peak thrust (total at both ends of the Z-axis column) would be 123 N, and the average thrust 78 N. At a specific impulse of 98,000 m/s, propellant requirements would be 25,200 kg per year, or 907,000 kg over 30 years with 20 percent allowance for tanks. Since all of this propellant need not be launched at the outset, counterweights appear advantageous only if a high specific impulse cannot be achieved, or if contamination considerations force propellant consumption to an absolute minimum. The long-term torque can be handled similarly by making all three moments of inertia equal. This can be accomplished by a suitable choice of the ratio b/a, which in effect uses the solar array itself to counterbalance the antennas. If the mass of each antenna is 8.125 x 10$ kg, the parameters used in the previous example require that b/a = 0.407. Referring to figure IV-B-4-4, it may be seen that the counterweight mass increases substantially for small b/a unless the column height is very large. However, interference with the microwave beam limits the height of the column in relation to dimension "b". If the southerly antenna is aimed at 40°N. latitude, the maximum value of c is 1.748b (see figure IV-B-4-5). Minimum counterweight mass for Ix = Iy = Iz is then 7.7 x 10® kg, an increase of 6.6 x 10® kg over that required for two- axis equalization. Such a penalty is not justifiable, and this concept was dropped. For the long-term torque, it is also possible to align the spacecraft principal axes with local vertical and the flight path, reducing the (sin 2e) term to zero. This is applicable to the long-term torque because the angle varies through a limited range (+23.5°), making it possible to maintain a reasonably good solar attitude. If the power output is proportional to the cosine of the angle of incidence, the maximum loss is 8.3 percent (at the solstices) and the annual average loss
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