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In this paper we study the 4D trajectory planning problem in a contrail sensitive environment. We identify the control inputs that steer the aircraft from the initial fix to the final fix following a horizontal route of waypoints while performing step climbs and descents, in order to minimize the overall flying cost of fuel consumption, CO 2 emissions, passenger travel time, and persistent contrail formation. The optimal trajectory design problem is formulated as a multiphase mixed integer optimal control problem, which is converted into a mixed integer non-linear program by first making the unknown switching times part of the state, then applying a Hermite-Simpson direct collocation method, and finally introducing binary variables to model the decision making. We solve the mixed-integer nonlinear program using a branch-and-bound algorithm. The numerical results show the effectiveness of the approach.

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