Research Article
On the Kinematics of Vehicles Relevant to Conflict Detection and Resolution
Figure 4
The distance of closest approach is a unique minimum in the case of constant velocities when the trajectories are straight lines described in uniform motion. The distance of closest approach in this case is calculated most simply by choosing a Cartesian reference frame moving with the velocity of the second vehicle, so that it stays at the origin for all time. The OX axis is taken through the initial position of the first vehicle, at a distance . The trajectory of the first vehicle is a straight line in the direction of the relative velocity making an angle with the x-axis. The distance of the closest approach is thus (33). The distance covered by the first vehicle is (37a), and since it travels at the relative velocity the time of closest approach is the ratio (37b).