Optimal 4-D Aircraft Trajectories in a Contrail-sensitive Environment

Aircraft induced contrails present an important source and a growing concern for climate change in aviation. This paper develops a methodology to determine optimal flight trajectories that minimize the total flying cost in a dynamic, contrail-sensitive environment. The total flying costs consist of costs due to fuel burn, crew, passenger travel time, CO₂ emission, and contrail formation. By constructing a multi-layer hexagonal grid structure to represent the airspace, we formulate the single aircraft trajectory optimization problem as a binary integer program that allows for flight altitude and heading adjustment, and contrail information update. Various cost factors are quantified, in particular the one corresponding to aviation-generated contrails, using the Global Warming Potential concept. Computational analyses show that optimal trajectories depend critically upon the time horizon choice for calculating the CO₂ climate impact. Shifting flights to periods with low contrail effect is not justified, given the limited benefit but potentially large passenger schedule delay cost increase. The analyses are further extended to determining the optimal trajectories for multiple flights using a successive optimization procedure.