The Calculation of Aircraft Collision Probabilities

Abstract

The basic limitation on air traffic compression, from the safety point of view, is the increased risk of collision due to reduced separations. In order to evolve new procedures, and eventually a fully automatic system, it is desirable to have a means of calculating the collision probability for any prescribed flight paths. This paper extends the statistical-probabilistic method of collision probability calculation, which has been limited to parallel, straight line flight paths, to arbitrary flight paths and vehicle shapes. The general formula is specialized to the cases of large relative velocity, nonzero relative velocity, zero relative velocity, and spherical collision surface. The formulas are applied to independent curved landing approaches to parallel runways.

A Quantitatively Derived NMAC Analog for Smaller Unmanned Aircraft Systems Based on Unmitigated Collision Risk

“…For simplicity, a MAC was assumed if the sum of the wingspans was greater than the minimum horizontal separation at closest point of approach and if the sum of the heights was greater than the vertical separation at closest point of approach Shared experimental assumptions included that aircraft are represented as volumes, each occupying a bounded, closed region of space and that aircraft position is a differentiable function of time. These shared assumptions aligned with Bellantoni [56] when they calculated aircraft collision probabilities. The volume assumption did not align with Kochenderfer et al [5], who used wireframe models of aircraft to estimate P(MAC | NMAC).…”

The Evaluation of Aircraft Collision Probabilities at Intersecting Air Routes

“…in the oceanic or off-shore areas, are operating in a non-radar environment, and thus are not monitored by a controller. (7) It is assumed that no external information concerning position errors of the aircraft can be obtained to prompt the pilot's corrective action.…”

“…In both studies by Reich 1 and Bellantoni 7 the aircraft collision probability over a given distance or, equivalently, duration of flight is approximated by the expected (average) number of collisions to occur therein. This implies that over the length of the flight considered a pair of aircraft are allowed to continue after colliding with each other for the first time, and additional crashes during the remainder of the flight are regarded as new separate incidents.…”

“…This paper first states assumptions of an analytical model and provides a useful insight into a general expression of aircraft mid-air collision probability advocated by both Reich 1 and Bellantoni. 7 The discussion NO. I…”

“…Analysis of collision probabilities at intersecting air routes typical in off-shore and continental areas, however, has not been fully explored to date. The only direct reference available on this subject appears to be the work by Bellantoni,7 in which a collision problem was formulated in the three-dimensional space and was apt to deal with airport terminal landing or take-off situations. For circumstances where horizontal linear air routes intersect one another at preassigned positions, the analysis provided by Bellantoni needs to be simplified and refashioned for use in extensive applications.…”