Understanding Radar Horizon and The Earth's Curvature

Because the Earth is a sphere, a radar beam traveling in a straight line will eventually shoot out into space, leaving the surface curving away beneath it. This creates a "radar shadow" where low-flying aircraft or ships cannot be detected until they cross the horizon line.

However, radar waves do not travel in perfectly straight lines. Due to atmospheric refraction, radio frequency (RF) waves bend slightly downward, tracing the curve of the Earth. This means the radar horizon is actually about 15% further than the visual horizon.

The Aviation Radar Math

To calculate the maximum theoretical detection range between an airborne radar and a target, aviation engineering utilizes the "4/3 Earth Radius" atmospheric model. When altitudes are measured in feet, the distance ($D$) in Nautical Miles (NM) is found using the square root of both altitudes:

$$ D = 1.23 \cdot (\sqrt{h_r} + \sqrt{h_t}) $$

$D$: Maximum detection distance in Nautical Miles (NM).
$h_r$: Height of the radar antenna (or observing aircraft) in feet.
$h_t$: Height of the target aircraft or vessel in feet.

Note: This tool calculates the mathematical geometric line-of-sight. Real-world detection also depends on the radar's power output and the target's Radar Cross Section (RCS).