An Approximate Optimal Maximum Range Guidance Scheme for Subsonic Unpowered Gliding Vehicles

Abstract

This study investigates the maximum gliding range problems of subsonic unpowered gliding vehicles and proposes an approximate optimal maximum range guidance scheme. First, the gliding flight path angle corresponding to constant dynamic pressure is derived. A lift-to-drag ratio<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:mi>L</mml:mi><mml:mo>/</mml:mo><mml:mi>D</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>inversely proportional to the dynamic pressure is then proven. On this basis, the calculation method of an optimal dynamic pressure (ODP) profile with a maximum<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>L</mml:mi><mml:mo>/</mml:mo><mml:mi>D</mml:mi></mml:math>throughout the flight is presented. A guidance scheme for tracking the ODP profile, which uses the flight path angle as control variable, is then designed. The maximum ranges of the unpowered gliding vehicle obtained by the proposed guidance scheme and pseudospectral method are compared. Results show that the guidance scheme provides an accurate approximation of the optimal results, and the errors are less than 2%. The proposed guidance scheme is easy to implement and is not influenced by wind compared with numerical schemes.