One of the principal axes in the quest for improved aircraft operations, oriented towards attaining the future environmental and economic standards such as fuel consumption and air pollutant emission reduction is the development of flight trajectory optimization algorithms for the Flight Management System. This paper provides a comparative presentation of the algorithms developed and results obtained, at LARCASE, with the purpose of determining an optimized vertical flight trajectory for a given flight plan. The approach considered in the construction of the optimized vertical trajectory navigation plan (VNAV) was purely geometric. The optimization objectives were represented by the minimization of the number of vertical (climb, level-flight or descent) profile segments composing the VNAV trajectory, and the employment of climb and descent trajectories whose gradients are equal, or closest to a specified value which accounts for the aircraft's performances and flying conditions.

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This paper presents a new method for the geometrical construction of an optimal vertical flight plan associated to a provided lateral flight plan defined as a succession of waypoints characterized by their along-the-track distance relative to the first waypoint and their constraints. The principal objective of the proposed method is the minimization of the total number of vertical flight plan segments, whose slope values closest match the values set for their corresponding flight phase and altitude. The main advantage of the proposed method is that it constructs the optimized vertical flight plan employing faster—and less-intensive computations than methods based solely on aircraft performance models. Also, the proposed algorithm has the advantage of generating ground-fixed predicted vertical flight plans which, when flown, are less sensitive to varying wind conditions, thus, smaller trajectory deviations than those computed using solely the model-based algorithms. Two implementations corresponding to different trade-offs between conflicting preferred gradient and minimal segment length constraints were compared. The results show that a vertical flight path segment’s construction and resulting configuration is dependent on the configuration of the vertical flight plan segments that precede it. The results also show that for a majority of the test cases, the resulting flight plans computed using the two implementations were identical. Moreover, even when the flight plans were not completely identical, many of the corresponding segments were identical.