What is the difference between slant range and horizontal distance near the NAVAID and at high altitude?

The distinction between slant range and horizontal distance is pivotal in understanding navigation and positioning relative to a NAVAID (Navigational Aid) at varying altitudes. At high altitudes, the angle of the line of sight to the NAVAID becomes more acute, resulting in a greater disparity between slant range, which is the straight-line distance measured through the air to the NAVAID, and horizontal distance, which is the flat distance measured on the ground.

As altitude increases, the curvature of the Earth becomes more pronounced relative to the aircraft's position. Therefore, at high altitudes, the slant range significantly increases compared to the horizontal distance because the aircraft is much farther away in a three-dimensional space. In essence, the steepness of the angle tends to exaggerate the slant range compared to the direct horizontal distance on the ground.

Understanding this relationship is crucial for pilots and air traffic controllers as it impacts aircraft navigation, approach procedures, and traffic separation strategies. Knowing that the slant range is comparatively greater at high altitudes helps in planning approaches and ensuring safe separation from terrain and other aircraft.