Calculate the line-of-sight distance for radar waves, accounting for atmospheric refraction.
📡 Atmospheric-standard approximation only. Uses 4/3 Earth radius model assuming standard atmosphere. Real radar horizon depends on temperature profile, humidity, pressure gradients, and local weather. Actual detection range also depends on target RCS, clutter, system noise figure, and propagation losses. This estimates line-of-sight only, not detection probability.
Height of the object you are trying to detect.
The radar horizon is the maximum distance at which a radar system can reliably detect an object on or near the Earth's surface. This limit exists because the Earth is spherical; objects eventually disappear behind the horizon regardless of how powerful the radar is.
Why the Radar Horizon Exceeds the Visual Horizon: The radar horizon is approximately 15% further than the visual horizon due to atmospheric refraction. Radio waves (especially microwaves used in radar) are bent (refracted) as they pass through the Earth's atmosphere, which has decreasing density with altitude. This bending allows radio waves to follow the Earth's curvature slightly longer than light waves do.
The 4/3 Earth Radius Factor: To account for refraction without complex atmospheric modeling, engineers use an empirical adjustment: the "effective Earth radius" is assumed to be 4/3 times the actual Earth radius (approximately 8,500 km instead of 6,371 km). This single number captures average atmospheric refraction effects for most radar systems operating in standard conditions.
Practical Implications: For maritime radar at 25 meters height, the horizon is about 25 km. For an airport surveillance radar at 50 meters, it's roughly 35 km. Higher antenna placement dramatically extends range (proportional to the square root of height). This is why radar antennas are mounted on tall structures, and why low-altitude aircraft can be detected from much greater distances than those at altitude.
Atmospheric density decreases exponentially with altitude, causing radio waves to bend downward as they travel upward. This refraction allows them to travel slightly over the Earth's curvature. The effect is strongest in the lower atmosphere where density changes most rapidly. This is why the 4/3 effective radius works so well—it empirically captures this bending.
Ducting is an extreme form of refraction where radio waves become trapped between atmospheric layers (temperature inversions). This can allow radar signals and radio communications to travel hundreds or thousands of miles beyond the normal horizon. Ducting is unpredictable and varies with weather patterns, altitude, and humidity.
Not significantly for most frequencies. The 4/3 Earth radius approximation works well from VHF through Ku-band microwaves (roughly 30 MHz to 15 GHz). Very low frequencies (VLF) can propagate even further via ground waves. Millimeter-wave radars may experience slightly different performance due to atmospheric absorption.
Antenna height has a sqrt(h) relationship with horizon distance. Doubling height increases range by 41%. Tripling height increases range by 73%. For example, raising a 10m antenna to 40m quadruples the horizon distance from ~12.6 km to ~25.2 km. This is why long-range radars use tall towers.
Radar horizon is the maximum theoretical distance to the horizon. Communication range depends on additional factors: transmitted power, receiver sensitivity, antenna gain, reflection/scattering from targets, and signal modulation. A radar can 'see to the horizon' but not necessarily detect a small object there.
Ocean waves don't extend the horizon, but rough seas can enhance radar returns from targets and reduce false alarms. Wave troughs create clutter at short range. Most maritime radars operate near the mathematical horizon; improving detection beyond it requires higher antenna placement or more transmit power.
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