MODELLING AN AIRCRAFT MAXIMUM ENDURANCE HORIZONTAL FLIGHT FOR AIR TRIALS

Abstract

The paper considers theoretical preparation for the aircraft pre-air-trial. The construction of some mathematical models of a horizontal flight is based upon the material system of variable mass motion. Optimal speed of horizontal flight is obtained as a function of variable mass. This speed is a solution (extremal) of the objective functional of the flying apparatus horizontal flight endurance. The solution delivers maximal value to the objective functional. The main significant assumptions made at the problem setting are: the rate of the aircraft horizontal flight speed change is negligibly small, flying object engines thrust has the horizontal component only, the dependence between aerodynamic coefficients is simplified in approximation with a quadratic parabola; the data used in simulation are abstract, although plausible. It was shown that in spite of the speed changes during the studied flight, the rate of that change plays an unimportant role for the considered case; therefore, such supposition of the rate neglecting is properly grounded. The derived equations allow taking into account the rate when it is the matter of importance. Since the presented study is the simplified one, the obtained results could be considered as some reference values to be tested and possibly approached to.