The radar horizon is a critical area of performance for aircraft detection systems, defined by the distance at which the radar beam rises enough above the Earth's surface to make detection of a target at the lowest level possible. It is associated with the low elevation region of performance, and its geometry depends on terrain, radar height, and signal processing. This concept is associated with the notions of radar shadow, the clutter zone, and the clear zone. Airborne objects can exploit the radar shadow zone and clutter zone to avoid radar detection by using a technique called nap-of-the-earth navigation.
Definition Without taking into account the refraction through the atmosphere, the radar horizon would be the geometrical distance D h {\displaystyle D_{h}} from the radar to the horizon only taking into account the height H {\displaystyle H} of the radar above sea-level, and the radius of the earth R e {\displaystyle R_{e}} (approximately 6.4·103 km):
D h = 2 × H × R e + H 2 {\displaystyle D_{h}={\sqrt {2\times H\times R_{e}+H^{2}}}}
When H is small compared to R e {\displaystyle R_{e}} , this can be approximated by:
D h = 2 × H × R e {\displaystyle D_{h}={\sqrt {2\times H\times R_{e}}}}
[The percentage error, which increases roughly in proportion to the height, is less than 1% when H is less than 250 km.] With this calculation, the horizon for a radar at a 1-mile (1.6 km) altitude is 89-mile (143 km). The radar horizon with an antenna height of 75 feet (23 m) over the ocean is 10-mile (16 km). However, since the pressure and water vapor content of the atmosphere varies with height, the path used by the radar beam is refracted by the change in density. With a standard atmosphere, electromagnetic waves are generally bent or refracted downward. This reduces the shadow zone, but causes errors in distance and height measuring. In practice, to find D h {\displaystyle D_{h}} , one must be using a value of 8.5·103 km for the effective Earth's radius R e {\displaystyle R_{e}} (4/3 of it), instead of the real one. So the equation becomes:
D h = 2 × H × ( 4 R e 3 ) {\displaystyle D_{h}={\sqrt {2\times H\times \left({\frac {4R_{e}}{3}}\right)}}}
And for the same examples : the radar horizon for the radar at a 1-mile (1.6 km) altitude will be 102-mile (164 km) and the one at 75 feet (23 m) will be 12-mile (19 km). Furthermore, layers with an inverse trend of temperature or humidity cause atmospheric ducting, which bends the beam downward or even traps radio waves so that they do not spread out vertically. This phenomenon occurs in two circumstances:
A thin stable layer of elevated humidity Stable temperature inversion Ducting influence becomes stronger as frequency drops. Below 3 MHz, the whole volume of the air acts as a waveguide to fill in the radar shadow and also reduces radar sensitivity above the duct zone. Ducting fills in the shadow zone, extends the distance of the clutter zone, and can create reflections for low PRF radar that are beyond the instrumented range.
Limiting factors
Shadow Zone Objects beyond Dh will be visible only if the height satisfies the following requirement:
H T > ( R T − 2 × H × R e ) 2 2 × R e {\displaystyle H_{T}>{\frac {\left(R_{T}-{\sqrt {2\times H\times R_{e}}}\right)^{2}}{2\times R_{e}}}}
where H T {\displaystyle H_{T}} is the target height and R T {\displaystyle R_{T}} is the target range. Objects below this height are in the radar shadow.
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