A fast vertical trajectory prediction method for air traffic management, and relevant ATM system

The invention concerns a method and system for the prediction of aircrafts vertical trajectory, in particular for Air Traffic Management, comprising the following flight calculation modules: Take-off; Climb; Cruise; Descent; and Landing, corresponding to the relevant flight phases, wherein: the calculation of the predicted aircraft trajectory is effected by using a set of TEM equations comprising, as output variables, the vertical rate of climb or descent, the true air speed, the energy share factor, the thrust and the drag, the mass of the aircraft modeled as point-mass, and comprising, as inpu variables, the Mach number depending on true air speed and temperature and altitude, the gravity acceleration, and the fuel flow, and the flight path angle; the calculation of the predicted aircraft trajectory for Cruise phase, wherein only the mass is varying, is performed by using the following analytical solution to said set of TEM equations.