Influence of drag force upon the shortest time trajectory of an aircraft

Abstract

The shortest time trajectory of an aircraft between two given locations is determined using a simple mathematical model. By taking into account the drag force (viscous friction force with the air), a problem of variational calculus is obtained which consists in determining two functions that minimize a functional, subject to a non-holonomic constraint. The trajectory is determined directly, by numerical integration of Euler equations with multipliers. Three types of drag forces were considered: constant, linear and quadratic. The results are verified through comparison to the values obtained from numerical minimization of the involved functional approximate forms.

Keywords

• extremal of a functional
• non-holonomic constraint
• constant drag
• linear drag
• quadratic drag
• brachistochrone