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Different formulations of the fuel optimization problem for multiple burn trajectories are considered. It is shown that certain customary idealizing assumptions lead to an ill-posed optimization problem for which no solution exists. Several ways are discussed for avoiding such difficulties by more realistic problem statements. An iterative solution of the boundary value problem is presented together with efficient coast arc computations, the right end conditions for various orbital missions, and some test results.

A survey of wind tunnel research facilities in the United States is presented. The inventory includes all subsonic, transonic, and hypersonic wind tunnels operated by governmental and private organizations. Each wind tunnel is described with respect to size, mechanical operation, construction, testing capabilities, and operating costs. Facility performance data are presented in charts and tables.

An inventory of test facilities for conducting acceleration, environmental, impact, structural shock, load, heat, vibration, and noise tests is presented. The facility is identified with a description of the equipment, the testing capabilities, and cost of operation. Performance data for the facility are presented in charts and tables.

The inventory covers free jet and direct connect altitude cells, sea level static thrust stands, sea level test cells with ram air, and propulsion wind tunnels. Free jet altitude cells and propulsion wind tunnels are used for evaluation of complete inlet-engine-exhaust nozzle propulsion systems under simulated flight conditions. These facilities are similar in principal of operation and differ primarily in test section concept. The propulsion wind tunnel provides a closed test section and restrains the flow around the test specimen while the free jet is allowed to expand freely. A chamber of large diameter about the free jet is provided in which desired operating pressure levels may be maintained. Sea level test cells with ram air provide controlled, conditioned air directly to the engine face for performance evaluation at low altitude flight conditions. Direct connect altitude cells provide a means of performance evaluation at simulated conditions of Mach number and altitude with air supplied to the flight altitude conditions. Sea level static thrust stands simply provide an instrumented engine mounting for measuring thrust at zero airspeed. While all of these facilities are used for integrated engine testing, a few provide engine component test capability.

Phase modulator with tuned variable length electrical lines including coupling and varactor diode circuits

Atmospheric ascent optimal trajectories for medium to high lift drag ratio space shuttle type rocket vehicles

Digital computer program SWITCH for trajectory optimization of multiple-burn vacuum rocket flights

Shooting method for real time optimization of multiple burn rocket flights, presenting analysis, algorithm and test results

Iterative solution of boundary value problem for rapid optimization of multiple-burn rocket flights

Repetitive in-flight calculation of optimal rocket guidance using algorithm method for solving boundary value problem

Generalized indirect method solving two-point boundary value problems for rapid optimal trajectory computation

A new formulation for soft-constraint trajectory optimization is presented as a real-time optimal feedback guidance method for multiburn orbital maneuvers. Control is always chosen to minimize burn time plus a quadratic penalty for end condition errors, weighted so that early in the mission (when controllability is greatest) terminal errors are held negligible. Eventually, as controllability diminishes, the method partially relaxes but effectively still compensates perturbations in whatever subspace remains controllable. Although the soft-constraint concept is well-known in optimal control, the present formulation is novel in addressing the loss of controllability inherent in multiple burn orbital maneuvers. Moreover the necessary conditions usually obtained from a Bolza formulation are modified in this case so that the fully hard constraint formulation is a numerically well behaved subcase. As a result convergence properties have been greatly improved.