Identifying Orthodromy and Loxodromy Segments in ADS-B Aircraft Trajectory Data

Abstract

Aircraft trajectories can often be interpreted in terms of two fundamental path types: orthodromies (great-circle routes, representing the shortest path on the globe) and loxodromies (constant track-angle paths). While great circles typically define the reality of intercontinental flight planning, operational constraints, such as waypoint routing and air traffic control instructions, mean that actual trajectories are composed of multiple segments, not always conforming neatly to one type or the other. Recognizing which segments correspond to orthodromies or loxodromies can provide semantic meaning to flight data, transforming raw positional information into interpretable patterns of pilot intent or controller intervention.

We present a method to automatically identify these trajectory segments without any prior knowledge about waypoints. The approach leverages map projections: with the Mercator projection, by construction, loxodromies appear as straight lines, while orthodromies do so in gnomonic projections. By detecting straight-line portions in these transformed trajectories, we can classify corresponding segments of the original flight path. This may enable the identification of even short segments, offering insights into flight planning and deconfliction manoeuvres—for example, detecting when an aircraft temporarily deviates from its planned orthodromic route under controller instruction. Using an open trajectories dataset where 13% of the total duration is labeled as deconfliction maneuvers, the identified loxodromies have a duration of 2% of the total duration while 39% of these 2% can be matched with deconfliction maneuvers, higher than the 13% prior.