Computation of optimal Mars trajectories via combined chemical/electrical propulsion, Part 3: Compromise solutions

摘要

The success of the solar-electric ion engine powering the DS1 spacecraft has paved the way toward the use of low-thrust electrical engines in future planetary/interplanetary missions. Vis-a-vis a chemical engine, an electrical engine has a higher specific impulse, implying a possible decrease in propellant mass; however, the low-thrust aspect discourages the use of an electrical engine in the near-planet phases of a trip, since this might result in an increase in flight time. Therefore, a fundamental design problem is to find the best combination of chemical propulsion and electrical propulsion for a given mission, for example, a mission from Earth to Mars. With this in mind, this paper is the third of a series dealing with the optimization of Earth-Mars missions via the use of hybrid engines, namely the combination of high-thrust chemical engines for planetary flight and low-thrust electrical engines for interplanetary flight. We look at the deep-space interplanetary portion of the trajectory under rather idealized conditions. The two major performance indexes, the propellant mass and the flight time, are in conflict with one another for the following reason: any attempt at reducing the former causes an increase in the latter and vice versa. Therefore, it is natural to consider a compromise performance index involving the scaled values of the propellant mass and flight time weighted respectively by the compromise factor C and its complement 1 — C. We use the compromise factor as the parameter of the one-parameter family of compromise trajectories. Analyses carried out with the sequential gradient-restoration algorithm for optimal control problems lead to results which can be highlighted as follows. Thrust profile. Generally speaking, the thrust profile of the compromise trajectory includes three subarcs: the first subarc is characterized by maximum thrust in conjunction with positive (upward) thrust direction; the second subarc is characterized by zero thrust (coasting flight); the third subarc is characterized by maximum thrust in conjunction with negative (downward) thrust direction. Effect of the compromise factor. As the compromise factor increases, the propellant mass decreases and the flight time increases; correspondingly, the following changes in the thrust profile take place: (a) the time lengths of the first and third subarcs (powered phases) decrease slightly, meaning that thrust application occurs for shorter duration; also, the average value of the thrust direction in the first and third subarcs decreases, implying higher efficiency of thrust application wrt the spacecraft energy level; as a result, the total propellant mass decreases; (b) the time length of the second subarc (coasting) increases considerably, resulting in total time increase. Minimum time trajectory. If C = 0, the resulting minimum time trajectory has the following characteristics: (a) the time length of the coasting subarc reduces to zero and the three-subarc trajectory degenerates into a two-subarc trajectory; (b) maximum thrust is applied at all times and the thrust direction switches from upward to downward at midcourse. Minimum propellant mass trajectory. If C = 1, the resulting minimum propellant mass trajectory has the following characteristics: (a) the thrust magnitude has a bang-zero-bang profile; (b) for the powered subarcs, the thrust direction is tangent to the flight path at all times.