Secondary mission optimization.

When a launch vehicle has performance capability in excess of that required for a primary mission, the excess propellant may be used to improve the performance for a secondary or abort mission. A variational treatment of optimal branched trajectories is summarized and a technique is developed for using excess performance capability in the most efficient way so as to maintain the ability to achieve a primary mission and improve the performance of the secondary mission if abort occurs. Numerical solutions are given for a launch vehicle closely resembling the Saturn V. These solutions demonstrate the advantages of using this ap- proach as well as its feasibility from a numerical analysis point of view. OMPLETE mission planning must include a secondary or abort mission to be performed in the event the primary mission cannot be completed. When the launch-vehicle capa- bility exceeds that required for the primary mission, the excess propellant may be used to shape the primary mission trajectory so that the performance of a secondary mission is improved. This paper presents a variational technique which maximizes the secondary mission performance subject to the primary mission constraints. Although the technique presented is applicable to a wide variety of problems such as dual maneuvering rendezvous and multiple payload missions, the concept is demonstrated most easily via the secondary mission application. The secondary mission-optimization problem can be stated more precisely with the aid of Fig. 1. The trajectory is divided into three parts called branches. The first branch (arc OB) represents the path of the first stage of the vehicle. The arc BP repre- sents the path of the last stage and point P is the orbit for the primary mission. If no failure occurs, the vehicle will travel along the path OBP. If the last stage has some malfunction at ignition or if, for some other reason, the primary mission is unobtainable at point B, the vehicle travels along arc BS with less than nominal thrust to achieve a secondary mission at point S. As an example, in the Apollo mission if the S-IVB failed to ignite, service module propulsion could be used on arc BS. The particular point B is chosen as the most critical point of the trajectory (due to separation, ignition, etc.). Other critical points and their associated branches could be included as long as the number of branches is kept reasonably small. The arc OOP represents the usual optimal trajectory for the primary mission with no secondary considerations and arc CS is a conventional optimal trajectory from the staging point C to the secondary orbit. The trajectory optimization consists of jointly shaping the three branches, called a branched trajectory, such that the primary mission constraints at point P are satisfied and some performance criterion is extremized at point S. The necessary conditions to perform this task are presented and applied to two illustrative examples. The problems differ in that they consider two separate measures of performance. First, a specific orbit is chosen for the secondary mission and the