Characterizing the Effects of a Vertical Time Threshold for a Class of Well-Clear Definitions
A fundamental requirement for the integration of unmanned aircraft into civil airspace is the capability of aircraft to remain well clear of each other and avoid collisions. This requirement has led to a broad recognition of the need for an unambiguous, formal definition of well clear. It is further recognized that any such definition must be interoperable with existing airborne collision avoidance systems (ACAS). A particular class of well-clear definitions uses logic checks of independent distance thresholds as well as independent time thresholds in the vertical and horizontal dimensions to determine if a well-clear violation is predicted to occur within a given time interval. Existing ACAS systems also use independent distance thresholds, however a common time threshold is used for the vertical and horizontal logic checks. The main contribution of this paper is the characterization of the effects of the decoupled vertical time threshold on a well-clear definition in terms of (1) time to well-clear violation, and (2) interoperability with existing ACAS. The paper provides governing equations for both metrics and includes simulation results to illustrate the relationships. In this paper, interoperability implies that the time of well-clear violation is strictly less than the time a resolution advisory is issued by ACAS. The encounter geometries under consideration in this paper are initially well clear and consist of constant-velocity trajectories resulting in near-mid-air collisions.