Radar_horizon - Wikiparency

# Radar horizon **Radar horizon** is the maximum range at which a target can, at least in principle, be seen by a ground-based or airborne [[Radar|radar]], set not by the transmitter's power but by the curvature of the Earth and by how the atmosphere bends the beam along the way. A beam does not simply stop at some fixed distance; it rises, relative to the ground, until it clears whatever lies between the antenna and the target, so a low-flying aircraft can vanish from a display long before its echo would otherwise grow too weak to detect. Because both the radar and its target sit some height above the surface, the horizon distance is really the sum of two separate horizons, one for each end of the path, and each lengthens with the square root of its own height rather than with height itself. A three.js microsim elsewhere on this page renders that curved-Earth geometry directly, showing a beam clear the horizon as antenna height changes. The same limit that hides a low target also creates the shadow and clutter zones described below, and it is the reason a handful of over-the-horizon techniques exist to see past it at all. ## Definition The geometric radar horizon follows from simple curvature: a straight line from an antenna of height h is tangent to a spherical [[Earth|Earth]] of radius R_E at a distance `d = sqrt(2·R_E·h)`, beyond which the surface itself drops out of the line of sight. The [[Atmosphere_of_Earth|atmosphere]] extends that reach a little further, because its refractive index normally decreases with altitude and bends a radio ray gently downward, following the Earth's curve more closely than a straight optical line would. The standard engineering shortcut folds this bending into the geometry itself by replacing the true Earth radius with an effective radius four-thirds as large,[^43earth] so the same formula, `d = sqrt(2·k·R_E·h)` with k ≈ 4/3, gives a usably accurate horizon distance for an ordinary, well-mixed atmosphere. The term itself distinguishes this radar-specific limit from the more general [[Line-of-sight_propagation|radio horizon]] used for communication links, though both follow the same geometry.[^termorigin] Because a radar's antenna and its target each sit at their own height, the full radar horizon adds the two contributions, `d_total = sqrt(2·k·R_E·h_radar) + sqrt(2·k·R_E·h_target)`, and each term grows only with the square root of its height: a target must climb four times higher to double how far away it can first be seen. An airliner cruising at about 10.7 kilometres, for instance, has a radio horizon of roughly 430 kilometres to a receiver at ground level, essentially the whole of the aircraft's own line of sight rather than any property of the radar illuminating it. ## Limiting factors Three named regions divide the space in front of a radar sited above the surface, built from the same horizon geometry above but adding what the beam actually illuminates rather than simply whether a line can be drawn between two points. Moving outward from directly beneath the antenna, a target passes through a shadow zone it cannot be seen from at all, a clutter zone where the ground competes with it, and finally a clear region where the beam's job matches the textbook assumption of empty space. ### Shadow Zone The shadow zone is the region a beam genuinely cannot reach, geometrically blocked by the curvature of the Earth itself or, at shorter range, by hills, ridgelines and buildings that sit directly in the path. Nothing a receiver does afterward can recover a target hidden here, since no energy from the transmitter ever illuminates it and no echo of any strength returns; the loss is total rather than a matter of signal quality. Terrain masking is the same shadow effect at much shorter range than the curved-Earth case, and it is why a radar sited in a valley or behind high ground needs a relay, or a second, better-placed set, to cover what its own antenna cannot see directly. Aircrews have long exploited both forms of shadow deliberately, flying low enough and close enough behind terrain to stay below a defending radar's beam for as long as the route allows, trading fuel and structural margin for a lower chance of ever being illuminated. ### Clutter Zone The clutter zone sits at short range and low elevation angle, where the main beam still grazes the ground or sea even as it also reaches a genuine low-flying target at the same range. Unlike the shadow zone, this is a detection problem rather than a geometric one: the beam does illuminate the target and an echo does return, but it arrives mixed with a much stronger reflection from the terrain or waves the beam is also striking, the same ground and sea [[Clutter_(radar)|clutter]] that competes with genuine returns throughout radar processing. Because most clutter sits still or drifts slowly compared with an aircraft, [[Moving_target_indication|moving-target indication]] and other Doppler-based processing, most fully developed in a [[Pulse-Doppler_radar|pulse-Doppler radar]], can often pull a fast target back out of a clutter zone that a simple amplitude threshold could never see through. The blind speeds that processing introduces are themselves set by the radar's own [[Pulse-repetition_frequency|pulse-repetition frequency]], so a target moving at just the wrong speed, or crossing the beam rather than approaching along it, can still disappear inside this zone regardless of how carefully it is filtered. ### Clear Region Beyond the clutter zone, once the beam has climbed clear of the ground or sea it was grazing, a target competes only with the receiver's own noise rather than with a reflecting surface, and detection follows the ordinary radar range equation without a separate clutter term. This clear region is what most range calculations implicitly assume: a target's [[Signal-to-noise_ratio|signal-to-noise ratio]], not its contrast against the ground, sets whether it is seen, and the usual tools for pulling a weak signal out of noise work exactly as they would in free space. A target climbing from the clutter zone into the clear region can therefore become easier to detect even as its range from the radar keeps increasing, the opposite of what the simple range equation alone would suggest. ## Over-the-horizon Because the horizon distance grows only with the square root of height, the most direct way past it is simply to get higher: an airborne early-warning radar carried at several kilometres of altitude sees a horizon many times that of the same set on the ground, and a satellite-borne radar has effectively none whose curvature matters at all. Fixed ground radars instead compensate by siting: the United Kingdom's wartime [[Chain_Home|Chain Home]] stations were built on coastal high ground specifically to push their beams' horizon as far out to sea as the terrain allowed, at a time when lifting the radar itself into the air was not yet practical.[^chainhome] Two further techniques ignore height altogether and instead choose a wavelength the horizon does not apply to in the usual way. A surface-wave, or ground-wave, radar operates at a frequency low enough that the wave itself follows the curvature of a conductive sea surface by diffraction, reaching well beyond where a straight or even a refracted line-of-sight beam would. A skywave radar goes further still, aiming its beam upward into the [[Ionosphere|ionosphere]] deliberately and letting the ionosphere's own reflection bring the energy back down thousands of kilometres away, trading the fine angular and range resolution of an ordinary set for coverage no line-of-sight radar could match. Both approaches are usually grouped together as [[Over-the-horizon_radar|over-the-horizon radar]], and both were pursued seriously during the Cold War for exactly the long-range early-warning problem the horizon otherwise makes impossible to solve.[^duga] ## Microsims A three.js microsim elsewhere on this page renders the curved-Earth geometry behind this article directly: a radar mast and a target each rise above a spherical Earth, and the line between them lifts clear of the surface once the two heights add up to enough horizon distance to connect. Neither this article nor that companion carries a two-dimensional p5.js sketch of its own, so the reader is pointed instead to the sketches on neighbouring articles that model the beam and the echo the horizon eventually lets through or blocks. *Try:* in the [[Radar]] sketch, freeze the sweep with the space bar and picture the whole rotating scope simply going dark below some fixed range on one bearing — that is the shadow zone's effect on a real display, a blocked bearing rather than a faded echo. *Try:* in the [[Sonar]] sketch, drag the assumed sound speed away from the true value and watch every measured range slide off its tick — the same kind of ray-bending, in water rather than air, that lets a radar beam curve slightly further than a straight line would over the horizon. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Radar_horizon) : [Wikitube](https://en.wikitube.io/wiki/Radar_horizon) Skeleton mirrored at revision 1363132386. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Radar]] - [[Line-of-sight_propagation]] - [[Over-the-horizon_radar]] - [[Radar_altimeter]] - [[Chain_Home]] - [[Moving_target_indication]] - [[Ionosphere]] ## References The tangent-line horizon geometry, the four-thirds effective-Earth-radius approximation for standard atmospheric refraction, and the radar range equation's ordinary, clutter-free form are standard radio-propagation and radar-engineering material and are not separately footnoted, per the Wikitube style guide's §6.1. None of this run's sub-manuals treat radar horizon geometry directly, so the historical claims below are marked accordingly rather than pinned to a page. Page numbers, where given, are PDF pages of the open editions linked from this portal's book list. [^43earth]: Citation needed: the engineering history and first formal derivation of the four-thirds effective-Earth-radius approximation for standard atmospheric refraction would fix its date and originator. [^termorigin]: Citation needed: the first published formal use of "radar horizon" as distinct from the general radio horizon would identify which service or text introduced the narrower term. [^chainhome]: Citation needed: a primary Air Ministry or Bawdsey Research Station record describing the siting criteria for Chain Home stations would confirm how explicitly horizon distance drove the choice of coastal high ground. [^duga]: Citation needed: a primary declassified record of a specific Cold War over-the-horizon radar programme, such as a Soviet or United States system, would let this article name one, with dates, rather than describing the class generically.