טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentDruckmann Erez
SubjectOptimal In-Flight Trajectory Modifications for Ballistic
Missiles and Free Rockets
DepartmentDepartment of Applied Mathematics
Supervisor Professor Yoseph Ben-Asher


Abstract

The research deals with exo-atmospheric trajectory modifications of ballistic missiles, which rapidly take place in order to hit a specific target. The problem presumes a missile which is launched towards a fictitious target, and changes its trajectory during flight (by a single impulse) in order to reach the planned one. Such a maneuver can harden on interception of the threat, due to the rapid change of the initial trajectory.

The single impulse exo-atmospheric trajectory modification can be optimized by an appropriate selection of the initial range (i.e. fictitious target) and the point of transfer along the initial trajectory. The present research deals with the optimization of a weighted cost function that takes into consideration the propellant needed for the maneuver (represented by the change of velocity) and the remaining time of flight after the maneuver, representing the reaction time of the interceptor.

Closed-form analytic expressions are developed and the optimization is performed using exhaustive search techniques. Numerical results are presented for Minimum Energy, depressed and lofted trajectories, and also compared to the more general case in which drag is also acting on the re-entry vehicle.

Among the results of the research: development of an analytic method for finding the most efficient transfer point along the trajectory; emphasis of the differences among the physical behaviors of inter-continental, long-range and short-range ballistic missiles; emphasis of the efficiency of depressed trajectories over minimum-energy ones; examination of the shape of the trajectory in order to maximize efficiency. The expressions and results are developed in a general method, which can be simply modified in order to be used also as a tool for developing interceptors for ballistic missile defense.