Method to Calculate Aircraft VNAV Trajectory Cost Using a Performance Database

Abstract

Vertical Navigation (VNAV) trajectory optimization has been identified as a means to reduce fuel consumption. Due to the computing power limitations of devices such as Flight Management Systems (FMSs), it is very desirable to implement a fast method for calculating trajectory cost using optimization algorithms. Conventional trajectory optimization methods solve a set of differential equations called the aircraft equations of motions to find the optimal flight profile. Many FMSs do not use these equations, but rather a set of lookup tables with experimental, or pre-calculated data, called a Performance Database (PDB). This paper proposes a method to calculate a full trajectory flight cost using a PDB. The trajectory to be calculated is composed of climb, acceleration, cruise, descent and deceleration flight phases. The influence of the crossover altitude during climb and step climbs in cruise were considered for these calculations. Since the PDB is a set of discrete data, Lagrange linear interpolations were performed within the PDB to calculate the required values. Given 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 for two aircraft; one with an aerodynamic model in FlightSIM, software developed by Presagis, and the other using the trajectory generated by the reference FMS.