In this paper, the optimal free flight trajectory to avoid conflict in air traffic management (ATM) is investigated. The mathematic expression of this problem is derived based on the relative motion parameters and the safe separation condition of the planes. The energy of maneuver has been taken as the objective function, which is simplified by considering two-legged maneuver specified with a waypoint and making the resolution of maneuver not only shorter travel distance, but also less speed variation. The constrains taken in to account include separation condition, constant speed and constant heading, the relation between the turn time related to the waypoint and the relative motion parameters. The optimal strategy is solved by the determined optimal model.
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