Properties of a Real-Time Guidance method for Preventing a Collision

This paper studies a real-time coordination method for preventing a midair collision between two aircraft. The aircraft obey guidance laws in which the directions of the command accelerations are based on the predicted positions of the aircraft at closest approach if their velocity vectors were not to change. A general form of the magnitude of these accelerations is studied, but a simple aircraft model is used. The differential equations of motion have the form of Newtonian two-body dynamics, with some nonstandard complications. The equations are readily solved numerically, but a general mathematical description of the motion for all configurations is vital for this application. The description is quite complex, involving twisting and intertwining paths in three dimensions. It is proved that the motion always has some basic desirable features of evasion. The guidance implies a logical set of turning rules, which are more effective than the common rules of the air. If the aircraft are similar, the paths have various symmetries and congruencies and can be described fairly completely. In some cases, the paths are arcs of circles. Some exact solutions are given for planar motion. These provide control over minimum separation and accommodate limits on turn rates. There is a close connection with a cockpit display described recently, and so the results also support the effectiveness of the display.