Frequency of encounter of aircraft in a random horizontal field

Calculations were made of the frequency of encounter as a function of azimuth of encounter of a passing aircraft with the aircraft in a random planar horizontal field. All the field aircraft moved at a constant speed but in random directions. These calculations included the total frequency of encounter with the aircraft of the field and the frequency of encounter with those aircraft of the field which were encountered in the fore quadrant, in the lateral quadrants, and in the rear quadrant; the calculations were made for various speed ratios of the field aircraft and the passing aircraft.