Operational Requirements for a Collision Warning System

In this paper operational requirements are developed for a collision warning system under the assumption of airplanes moving in straight line paths at constant velocities. This assumption is believed to be reasonable during the on-route portion of an airplane's flight, but need not hold when airplanes are in a holding pattern around some airport. The problem is first reduced from a three dimensional problem to one of relative motion in a plane. Then, equations are derived which permit equipment resolution requirements to be established as a function of the radius of a safety sphere around an airplane, relative velocity, required warning range, and range at which first measurement is taken. Finally, with an eye toward minimizing computer storage and data handling, a statistic based on the difference between the first and last ordered statistics is considered, and the probability theory is derived to enable the computation of alarm and false alarm probabilities to be made.