are incapable of producing sufficient torques and angular momentum for SPS applications. Figure 2.4-8 lists representative values of torques and angular momentum required to control the POP axis of SPS. Angular momentum of 108 - 109 newton-meter-seconds or more are required. Figure 2.4-9 shows the capabilities of existing devices. All the data plotted are for reaction wheels and momentum wheels. Control moment gyros with an angular momentum of as much as 6100 newton-meter-seconds exist but are not plotted. Extrapolation from the existing wheels indicates that high capacity wheels can meet SPS requirements for masses on the order of 2600 to 5400 kg. Since the extrapolation is over 5 to 6 orders of magnitude these estimates must be considered soft unless they can be independently verified. Consider that the momentum wheel is well approximated by a circular hoop. This corresponds to the mass of an actual wheel being concentrated at the rim. Centrifugal loads are carried in the hoop as hoop stresses. Large amounts of angular momentum can be stored in a lightweight hoop of large diameter. The fundamental trade is diameter versus mass. Figure 2.4-10 illustrates the wheel requirements to store angular momentum of the order required by SPS. The angular momentum is that available at the stress limit of the wheel. As an example, 10$ newton-meter-seconds of angular momentum can be produced by an aluminum wheel 200 m in diameter with a rim mass of 4500 kg. Such a wheel is very light compared to a thruster system of equivalent capability. The question posed is how to design a wheel of this size. As a point design, a reaction wheel was conceptualized to meet SPS POP axis requirements. A spoked wheel was chosen since it is a stiff structure with the mass concentrated at the rim. Furthermore, it can sustain high torque loads. Figure 2.4-11 illustrates the resulting design. The outer hexagonal ring is part of the structure of the reference SPS. A wheel diameter of 700 m was chosen to fit the available opening. The wheel is mounted to the vehicle by a second set of spokes that position the wheel and transmit torques from the wheel to the vehicle. Torques are provided by a pair of symmetrically located electric motors that torque the hub of the wheel. It's anticipated that such a large wheel would be fabricated with the same type of beam makers used to fabricate the basic vehicle structure. The total estimated mass includes 5000 kg in the rim and 1000 kg for the remaining components. This wheel falls only slightly above the extrapolated line of Figure 2.4-9. From this analysis, large lightweight momentum wheels to meet SPS requirements appear potentially feasible. Free Oscillations The usual gravity gradient stabilized satellite is intended to be stationary with respect to an earth-fixed reference system. This orientation is not suitable for SPS since the solar arrays must track the sun. The question then arises, can a satellite be passively "stabilized" with respect to an inertial reference? Stabilized, in this case, must be interpreted to mean that small amplitude oscillations are permissable but no long term rotation is permitted.
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