AbstractsMathematics

There has been almost fifteen years of political controversy surrounding changes to the rules and procedures by which aircraft conduct their flight within regional Australia. Decisions based on a predominately heuristic (rule of thumb) approach to design have had many adverse consequences for the integrity of the proximity warning function. A sound mathematical model is required to establish this function on a mature engineering foundation. To achieve this, the proximity warning function has been investigated as a hybrid-system. This approach recognises the dual nature of the design: that aircraft dynamics give rise to continuous mathematical models while the communication protocols controlling proximity require discrete mathematical approaches. The blending of each aspect has yielded a deeper insight into the operational limitations and failure modes of this function. The presentation of the thesis follows a design thread through the function. It begins with a description of existing standards and implementations. Risk models are then developed. The pilot interface is recognised as a primary design constraint. Mathematical models are then developed to describe the topology of flow, proximity dynamics, and the scheduling constraints associated with visual, voice, and data-link communications required by the proximity warning function. These analyses show that many aspects of design can be bounded by analytical formulae that bring new robustness to the design and resolve some of the misconceptions arising from the often inaccurate perceptions of present airspace operations. Failure modes, unaccounted for in existing designs are found to actually aggravate failure in the very situations in which the airspace design should be robust and should act to prevent collisions. In particular, there are divergences of performance between the demands required by the system design and the ability of the pilot to deliver such performances. In some cases, these failures may be traced to policy decisions such as service between Instrument Flight Rule and Visual Flight Rule category aircraft. On the basis of the conclusions of this research, a formal engineering review of the proximity warning function is required to assure the containment of the likelihood of mid-air collision for all future operations.