On the Kinematics of Vehicles Relevant to Conflict Detection and Resolution

Figure 6

The distance between two paths and would be the distance of closest approach between the two trajectories and only if the two vehicles were at the closest points and at the same time . In that case the relative position is along the common normal and the relative velocity is tangential so they are orthogonal . This orthogonality condition applies at the time of closest approach (16b) in all cases, even if the vehicles pass at the closest points at different times.