Optimal thruster configurations for the GP-B spacecraft

Thruster locations and control schemes which make the most efficient use of the available propellant of a constant flow propulsion system are investigated. A set of three necessary and sufficient conditions are established for a thruster system to be optimal in the sense of maximizing the smallest magnitude force which can be generated by the thrusters. Analytical expressions are derived for the 'the envelope of least authority' which is defined as the smallest force magnitude versus moment magnitude which can be generated by any given thruster system. Several thruster configurations are proposed for the GP-B spacecraft and their performance is compared with respect to their envelopes of least authority. The results are applicable to any system composed of thrusters which saturate at some finite value.