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Proceedings Paper

Trajectory Optimization Of Earth-Launched Interceptors At Supercircular Speeds
Author(s): R M Howe; E G Gilbert; Ping Lu; N X Vinh
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Paper Abstract

An alternative to satellite-based kinetic energy weapons for intercepting ballistic missiles early in their trajectories is the use of earth-based hyper-velocity rockets. Simple calculations show that with existing solid-propellant technology, rockets can be accelerated to more than twice circular-orbit speeds with mass ratios of several thousand to one. For intercept distances ranging from 2000 to 5000 miles this translates into flight times of between 4 and 10 minutes. This permits interception of hostile ballistic missiles during their ascent trajectory when vulnerability remains high. The use of miniature guided warheads in the defensive weapon reduces the interceptor takeoff weight to within reasonable bounds. Parameters to be optimized include the mass ratios and thrusting time for each stage, the coasting time between powered stages, and the parameters used to represent the time history of angle of attack. A quasi-Newton minimization algorithm is utilized with penalty functions to implement the terminal constraints, as well as any other constraints. The necessary gradients are computed numerically using finite differences. The multiple stage trajectories are calculated many thousands of times faster than real time using an AD 100 multiprocessor computer. A VAX host computer implements the optimization algorithm and inputs new parameters to the multiprocessor for each successive trajectory run. In this way the total required time for an overall trajectory optimization consisting of several thousand trajectories is reduced from several hours to several minutes.

Paper Details

Date Published: 9 May 1988
PDF: 8 pages
Proc. SPIE 0872, Propulsion, (9 May 1988); doi: 10.1117/12.943743
Show Author Affiliations
R M Howe, The University of Michigan (United States)
E G Gilbert, The University of Michigan (United States)
Ping Lu, The University of Michigan (United States)
N X Vinh, The University of Michigan (United States)

Published in SPIE Proceedings Vol. 0872:
Joseph Flanagan, Editor(s)

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