טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentIlana Shapira
SubjectApproximated Analytical Solution for Optimal Range Glide
DepartmentDepartment of Aerospace Engineering
Supervisor Full Professor Ben-Asher Yoseph


Abstract

This thesis is about finding fast computable approximations for maximum ranges for gliders. These trajectories are characterized by boundary layers that depend on the initial and terminal conditions of the altitude, speed and path angle. All approximations are based on time-scale separation of the state variables, where the path-angle and speed are considered faster than the altitude and range. Open loop and closed loop trajectories are derived. The open loop trajectories fulfill the initial and final boundary conditions whereas the closed loop trajectories fulfill only the initial boundary conditions. The first approximation method is based on the Single Perturbation Theory, which leads to a double boundary layer structure having a single variable in each sub-layer. It is assumed that the path angle is faster than the speed. Open loop and closed loop trajectories are solved. The second approximation method is the Dichotomic Basis Method. It leads to an iterative algorithm that solves the boundary layer in an open loop form, assuming that the path angle and the speed change on a similar time scale. The approximated trajectories are compared to numerical, non-approximate ones and the conclusions are presented in terms of quantitative criteria for the applicability of each approximation. One possible application is for aircrafts that eject gliding missiles with specified final conditions and need to know the maximum gliding range in order to increase the stand-off.  A second possible application is for airplanes that undergo engine cut-off and the pilots need to know the maximum gliding range for safe landing.