Optimizing the flight trajectory is a goal that will minimize fuel consumption and time related costs. Lateral Navigation (LNAV) has been investigated as part of identifying optimal trajectories. Winds and temperature have an important influence in the cost of a flight. Tail winds and low temperatures are desired, as both reduce flight costs. Implementing algorithms to locate where these favorable conditions exist close to the defined trajectory of a given flight will help to achieve optimal flight trajectories. These algorithms are to be implemented in an FMS using an aircraft model which is normally given in the form of a Performance Database (PDB). The approach given in this paper uses Dijsktra's algorithm. This method is part of the graph-search techniques. The search area is defined by discretizing the cruise trajectory and defining adjacent waypoints, forming a grid where the possible trajectories are created. The algorithm requires the aircraft's gross weight at the top of climb (TOC), the location of the top of descent (TOD), and the desired cruise speed and altitude. The related costs are calculated using the PDB's model for two different commercial aircraft at a constant altitude and at a constant indicated mach. To minimize the costs, the algorithm considers the fuel burned, the flight time and the cost index (CI). The temperature and winds in the trajectory are obtained from the Canadian weather forecast (Environment Canada). Wind influence is taken into account by adding it to the ground speed, based on its direction regarding the aircraft's trajectory heading. The effect of temperature is considered in the PDB. Generated trajectories are compared against the geodesic (or great circle) route.
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