Estimation of horizontal flight efficiency for air traffic management system

Optimal trajectory selection is one of the common navigation tasks. Air transportation considers horizontal and vertical flight efficiency. Different criteria of trajectory efficiency could be used in algorithms of flight planning: the shortest path, minimization of flight duration, and minimum costs. In air traffic management a portion of additional trajectory length to the shortest path is used as index of horizontal flight efficiency (HFE). In the paper, we study horizontal flight efficiency estimation based on area limited by airplane trajectory and grade circle line. HFE based on area could be useful to indicate the level of side deviation. Results of analysis indicate that a bigger area corresponds to bigger side deviations. Math models of HFE are given in the paper. Validation of considered models of HFE has been done with real trajectory data of particular flight connection, obtained by Automatic Dependent Surveillance-Broadcast technology. A flight connection with a highly inefficient trajectory due to closed airspace caused by the War in Ukraine is considered as an example.