Method for Calculating Aircraft Flight Trajectories in Presence of Winds

This paper presents a practical method to compute the four-dimensional flight trajectories of aircraft in the presence of winds. The proposed method consisted of numerically integrating the aircraft equations of motion over different segments that compose a typical commercial flight profile. For this purpose, the aircraft vertical trajectory was divided into seven typical flight segments: unrestricted climb at constant airspeed, restricted climb at constant airspeed, climb/level-off acceleration, level flight at constant airspeed, unrestricted descent at constant airspeed, restricted descent at constant airspeed, and descent/level-off deceleration. For each segment, detailed algorithms were designed to solve and then integrate the equations of motion using an Euler scheme. The lateral trajectory, on the other hand, was constructed by connecting a series of waypoints with straight and turn segments. The method was applied and validated on the well-known Cessna Citation X business jet, for which a qualified research aircraft flight simulator (RAFS) was available. A total of 130 tests were carried out with the RAFS over a wide range of operational conditions. The comparison results showed that the trajectory data predicted by the algorithms matched the trajectory data obtained from the RAFS with less than 5% relative errors.