9. Trajectory

Section III is focused on flight trajectory planning, execution, and monitoring, building on the air navigation fundamentals and air navigation systems presented in the previous sections. This chapter presents flight trajectories with their mathematical models and algorithms: direct-to trajectory, loxodrome or rhumb line, and orthodrome or great circle route, calculated by spherical trigonometry, haversine, and rotations methods. As the most efficient air navigation method, the brachistochrone is presented further. Instrument flight procedures, area navigation (RNAV) and performance-based navigation (PBN)/required navigation performance (RNP) trajectories are presented next as less efficient but very safe flight trajectories.