Abstract
A study of single-pass re-entry from escape speed and from circular satellite speed is made to determine the lift program for a hypersonic glider and the drag-modulation program for a nonlifting vehicle that minimize the heating of the vehicles within acceleration or range constraints. A new of numerical solution is used, similar to Kelley's method of gradients, that permits rapid convergence to the optimum lift program starting with an original good estimate. This avoids the twopoint boundary-value problem of the calculus-of-variations formulation, and is applicable to any optimum-programing problem. An acceleration-tolerance limit is introduced which describes the human pilot's capability to withstand acceleration more accurately than a simple acceleration limit. at tack program, must be determined in order to minimize the total heat and satisfy the desired terminal constraints. The straightforward approach to solving such complicated problems has not met with any significant success, despite the fact t ha t the formulation is clear.7 Recently Kelley and the present authors developed, almost simultaneously, a steepest descent technique which is capable of solving such complicated variational problems in a practical way using highspeed digital computers. This technique is presented in the next section and then it is applied to the two problems described above.
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