Calculation of aircraft collision probabilities

The Problem of evaluating the relative effectiveness of various air traffic control systems can be formulated as that of comparing their levels of safety at any fixed capacity. In the research presented here, a new mathematical model of this problem is developed in which aircraft collision probabilities are related to the control concept through certain parameters that statistically describe the uncontrolled (or nominal) traffic pattern and the performance of the selected control system. The performance parameters considered describe the abilities of the system to monitor the airspace, predict conflicts, generate commands, and execute avoidance maneuvers; and can be used to model many control structures, both ground-based and airborne. The analysis performed is thus an extension and synthesis of previous work in which the important characteristics of each control function are identified and related to the probability of collision. The use of the proposed model is illustrated by applying it to a parametric evaluation of several different control concepts of current interest. Specifically, and for a traffic pattern in which all aircraft are nominally flying with constant velocities and in which avoidance maneuvers are limited to straight, steady climbs or dives, collision probabilities are calculated and compared for: blind flying (no control), the see and be seen concept, PPI´s and ground controllers, airborne pilot warning indicators, and collision detection and avoidance systems based on the TAU criterion. Methods for extending these results to curvilinear flight paths with lateral avoidance maneuvers and more general control concepts are briefly discussed.