Landing domain analysis of shuttle re-entry vehicles

With increasing frequency in space shuttle operation, it is of interest to have more than one or two landing fields within the boundary of the reachable area of the reentry vehicle. This boundary, called the footprint, depends on the aerodynamic characteristics of the vehicle. It has been investigated previously but unfortunately was not completely constructed, especially the minimum range on the longitudinal axis and the left end portion of the footprint. In this paper, the previous work using the facilities of the continuation method and the multiple shooting method is extended, and a complete footprint is constucted. At first, the optimal trajectories are solved in the vertical plane and in the three-dimensional space to minimize the final range on the longitudinal axis, θ _{? min},. After comparison of the obtained minimum longitudinal ranges, we find that the three-dimensional optimal trajectory is the global optimal trajectory for θ _{? min},. With the application of the techniques of rotating the coordinates, based on this θ _{? min}, we obtain the complete footprint by the optimal lift and bank modulations for three-dimensional re–entry trajectories with lift constraint.