Methodology for Vertical-Navigation Flight-Trajectory Cost Calculation Using a Performance Database

Abstract

Trajectory optimization has been identified as an important way to reduce flight costs and polluting emissions. Due to the power capacity limitations in airborne devices such as the flight management system, a fast method should be implemented to calculate the full trajectory cost. Many flight management systems use a set of lookup tables with experimental data for each flight phase, and they are called performance databases. In this paper, the trajectory flight cost is calculated using a performance database instead of using classical equations of motion. The trajectory to be calculated is composed of climb, acceleration, cruise, descent, and deceleration. The influence of the crossover altitude during climb and descent, as well as step climbs in cruise, was considered. Lagrange linear interpolations were performed within the performance database discrete values to calculate the required values. By providing a takeoff weight, the initial and final coordinates, and the desired flight plan, the trajectory model provides the top-of-climb coordinates, the top-of-descent coordinates, the fuel burned, and the flight time needed to follow the given flight plan. The accuracy of the trajectory costs calculated with the proposed method was validated with an aerodynamic model in FlightSIM®, which is software developed by Presagis®, and with the trajectory cost given by the flight management system benchmark of reference. Results showed that, for the same reference trajectories and for the same inputs, the cost computed by the method proposed in this paper is close to the costs provided by FlightSIM and by the flight management system benchmark or reference.