MATHEMATICAL ASPECTS OF AIRCRAFT ENGINES RUNNING OPTIMIZATION FOR MINIMUM FUEL CONSUMPTION WHILE LANDING

Abstract

The consistency of the potential increase of fuel efficiency, based on aircraft maintenance optimization, is mathe- matically proved. The mathematical apparatus and a set mathematical model of aircraft spatial motion allow to analyze aircraft behavior on the stage before landing and to draw optimal flight path for minimum fuel consumption with fixed time.For effective problem solving the choice and realization of optimal flight paths are made. The algorithm for the problem of optimal civil aircraft flight control aimed at the most accurate realization of chosen soft path under limited time conditions is proposed. The optimization of the given process is made by solving a point-to-point boundary canonical sys- tem based on the Pontryagin maximum principle.The necessary initial data and conditions for the statement of problem are given. The mathematical model for the simplification of calculations is created and its equivalent representation is given by uniting problems of controls by thrust channels and the angle of attack as the thrust control function. The boundary-value problem is mathematically composed and the analytical apparatus of its solution is presented. Optimal aircraft landing paths reflecting the behavior of the angle of attack and thrust are constructed. The potential of this method is proved by the economic justifiability and its effectiveness, in particular the compar- ison of total aircraft fuel consumption on obtained optimal path to the classic path on which there are rectilinear sections what allowed to confirm the conclusion about the economical expedience and effectiveness of the method of aircraft con- stant landing while making flights.