Time-Minimal Aircraft Trajectory in the Presence of Unsteady Wind by Shape Optimization

Consideration of wind effect in airline operations has become crucial for saving travel time, maximizing operational efficiency, and reducing fuel consumption. In this paper, we propose a new approach to solve the time-minimal trajectory problem by formulating it as a shape optimization problem, accounting for unsteady wind conditions. Unlike traditional methods, our approach works on parameterized trajectory in a continuous spatio-temporal domain, which does not require a discretization in the two-dimensional domain. Furthermore, the approach also simplifies the cost function evaluation, with only one co-dimension along the trajectory. Hence, our approach guarantees continuity of flight states, and is independent of network (also referred to as a mesh or a grid in the literature) quality and constraints. Through a suite of simulations and case studies, we demonstrate the effectiveness of our approach in reducing travel time for various flight types, including long-haul, medium-haul, and short-haul flights. The obtained optimized trajectory is shown to achieve a balance between headwind avoidance and distance minimization, leading to a time-minimal solution. A statistical analysis is performed on three popular flight sectors, HKG-LHR, HKG-ICN, and HKG-TPE, to validate the effectiveness of the developed algorithm in reducing flight time, using flight information extracted from real airline operations. Optimized trajectories are then compared with those from Quick Access Recorder (QAR) data shared by Cathay Pacific Airways. Our findings offer practical implications for airlines seeking to enhance operational efficiency and reduce environmental impact.