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Abstract-Trajectory optimization is a crucial process during the planning phase of a spacecraft landing mission. Once a trajectory is determined, guidance algorithms are created to guide the vehicle along the given trajectory. Because fuel mass is a major driver of the total vehicle mass, and thus mission cost, the objective of most guidance algorithms is to minimize the required fuel consumption. Most of the existing algorithms are termed as "near-optimal" regarding fuel expenditure. The question arises as to how close to optimal are these guidance algorithms. To answer this question, numerical trajectory optimization techniques are often required. With the emergence of improved processing power and the application of new methods, more direct approaches may be employed to achieve high accuracy without the associated difficulties in computation or pre-existing knowledge of the solution. An example of such an approach is DIDO optimization. This technique is applied in the current research to find these minimum fuel optimal trajectories.
Abstract-Trajectory optimization is a crucial process during the planning phase of a spacecraft landing mission. Once a trajectory is determined, guidance algorithms are created to guide the vehicle along the given trajectory. Because fuel mass is a major driver of the total vehicle mass, and thus mission cost, the objective of most guidance algorithms is to minimize the required fuel consumption. Most of the existing algorithms are termed as "near-optimal" regarding fuel expenditure. The question arises as to how close to optimal are these guidance algorithms. To answer this question, numerical trajectory optimization techniques are often required. With the emergence of improved processing power and the application of new methods, more direct approaches may be employed to achieve high accuracy without the associated difficulties in computation or pre-existing knowledge of the solution. An example of such an approach is DIDO optimization. This technique is applied in the current research to find these minimum fuel optimal trajectories.
Dynamic performance of Surveyor's vernier engine is shown for operation on propellants saturated with dissolved helium. An analytical dynamic engine model is developed for use in evaluating spacecraft control system performance through analog computer simulations of actual missions. Teflon propellant bladders are sufficiently permeable to allow the propellant to become saturated with helium pressurization gas before terminal descent. The major effect of dissolved gas on engine dynamic performance is attributed to helium released from solution in the oxidizer circuit between the throttle valve and injector. At the lowthrust end of the throttling range the pressure downstream of the throttle valve is much lower than the supply pressure because of the greatly decreased pressure drop across the fixed area injector and decreased chamber pressure. This creates the existence of a two-phase compressible mixture that in turn is responsible for large engine dynamic response lags. Theoretical and experimental engine phase lag, gain attenuation, and step response, along with helium solubility in the propellants for various pressures and temperature conditions are presented. The engine utilizes monohydrate of monomethyl-hydrazine and mixed oxides of nitrogen as propellants and is throttleable over a nominal thrust range of 30 to 104 Ib. Nomenclature= effective injector area and nozzle throat area, respectively c* = characteristic velocity f s = ratio of helium and vapor mass to oxidizer mass fh -ratio of helium mass to oxidizer mass F, F = thrust and nominal value, respectively F c , Fco •= thrust command and its amplitude, respectively g =--gravitational constant K a -gain attenuation defined by Eq. (24) Ki, . . . 6, and 14), respectively Mh, M g = mass of He and He plus vapor, respectively Mo, Mv = mass of oxidizer and oxidizer vapor, respectively Mf, M m , Mo = mass flow rate of fuel, medium, and oxidizer, _ __ _ respectively Mf, MO, Mt -fuel, oxidizer, and total flow rate, at nominal operating level, respectively P, P = pressure and nominal operating value, respectively
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