Azimuth homing in a planar uniform wind

Abstract

The planar trajectory of an azimuth homing gliding system maneuvering through a uniform wind field is presented. The kinematics of the motion is discussed generating two first-order differential equations which are separated producing an expression involving only position coordinates. A change of variables is introduced and exact solutions obtained by direct integration. The resulting trajectories fall into two categories classified according to their target-seeking or orbital characteristics. Flight paths in the target-seeking domain are shown to be convergent when the system has a wind penetration capability. The family of target-orbiti ng solutions are shown to produce trajectories which are captured about the target in elliptic spirals. Launch criteria are established from the time solution which takes the form of an ellipse for all categories of azimuth homing. The definition of a release path as the locus of points from which the flight time necessary to reach the target is constant, follows from this result. Nomenclature LID — lift to drag ratio t = time U = horizontal component of total airspeed vector u = \U\, horizontal airspeed V = system total airspeed vector a = radial offset angle W = wind or field velocity w = I W I, wind or field speed x = horizontal space coordinate fixed to earth y = horizontal space coordinate perpendicular to x and fixed to earth z = vertical space coordinate perpendicular to the x-y plane r = magnitude of the radius vector in polar coordinates 6 — angular position in polar coordinates X = u/w wind penetration parameter Subscript