In the future Air Traffic Management (ATM) implementations based on 4D trajectories, both the ATM problems (safe separation, sequencing for the best runway utilization) and the flight management problems (best fuel efficiency) may be solved together using a multidisciplinary optimization of all aircraft 4D trajectories. The paper presents advancements on 4D navigation based on an objective function for the optimization process, which effectively models the total costs and risks of air navigation. The resulted gate-to-gate 4D trajectories generated by a dynamic model flight simulator for the specific type of aircraft with the individual initial Flight Management System data are "flyable", and they present the best cost-risks trade-offs. The paper also reveals results on some simulated experiments using genetic algorithms to minimize the objective function presented. Nomenclature C = c o s t C D = coefficient of drag 1 Associate Professor, Faculty of Aerospace Engineering, otp@brainbond.ro, Member AIAA. 2 Associate Professor, Faculty of Aerospace Engineering, constantinescu_ce@yahoo.com 3 Researcher, irina.stefanescu@rosa.ro

In the aftermath of the disappearance of the Malaysian 370 (MH370) flight in March 2014, new positioning methods were employed to establish the search area. In the absence of all other positioning technologies (Transponder, Radio communications, Radar), these innovative methods are based on the handshake signals between an INMARSAT satellite and the satellite transceiver on board the aircraft. The log of these signals was made public in order for the scientific community to engage in solving the mystery of the MH370 trajectory. The log indicates the delay between the interrogation and response signals, as well as the relative velocity indications, based on the shift of the carrier frequency due to the Doppler-Fizeau effect. This paper puts forward an original, independent and accurate positioning method and allows the calculation of the MH370 trajectory considering the wind vector field that day, the accurate satellite orbit and an accurate model of the Earth (the WGS-84 ellipsoid).

The paper reviews the optimisation methods of the flight trajectory for airliners. In contrast to maritime navigation, where the shortest route (the orthodrome) is preferred, in air navigation, the brachistochrone is the optimal flight trajectory on the sphere or on the ellipsoid, considering the wind vector field (maximising the tail wind and minimising the head wind over the duration of the flight). The major impact of the wind on the flight trajectory results from the possible significant velocity at the normal cruise flight levels, which could reach 200 kts, or 40% of the aircraft true airspeed (TAS). Brachistochrone is independent of the flight performance optimisation (range versus speed), as computed by the flight management system. Whichever cost index (CI) is selected (and consequently, the cruise Mach number), the brachistochrone is the minimum time of flight trajectory at that target Mach number. In cruise flight, the minimum time of flight is also equivalent to the minimum fuel consumption. It concerns just the wind velocity field. All these qualify the brachistochrone as the greenest trajectory, the most fuel and emissions efficient solution relative to the atmosphere. The paper classifies the brachistochrone problems (2D, 3D and 4D brachistochrones, with or without flexible time of departure). Some numerical examples are provided. The overall optimal 4D trajectory considers many aspects, including safety, by minimisation of total costs and risks of the 4D trajectory.

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