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Fuel-Optimal Retrothrusted Soft Landing Through an Atmosphere

Author: Juncosa, M. L.
Corporate Author: RAND Corporation
Corporate Report Number: R-515-PR
Date of Publication: 1970-12
Pages: 33
Contract: F44620-67-C-0045
Project: Project RAND
AD Number: AD0718405

A simple analysis of the problem of achieving a soft landing for airdrop by fitting the payload with retrorockets, and a direct iterative numerical procedure for determining the switch-on point for minimal fuel consumption, in terms of either time or altitude. Through appropriate reversals of sign, the formulas may also be used for ascent trajectories of full-thrust, vertically boosted rockets where the assumption of a constant gravity field is acceptable. Since the unretrothrusted portion of the descent is identical with free fall, the dynamical equations are integrable in closed forms. For a constant atmosphere, closed form analytic solution is also obtained for the retrothrusted descent. For an exponentially varying atmosphere, however, one cannot escape a numerical integration of the dynamical equations.

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