Radar cross-section

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Typical RCS diagram (A-26 Invader) Sigma invader RCS.png
Typical RCS diagram (A-26 Invader)

Radar cross-section (RCS) is a measure of how detectable an object is by radar. Therefore, it is called electromagnetic signature of the object. A larger RCS indicates that an object is more easily detected. [1]


An object reflects a limited amount of radar energy back to the source. The factors that influence this include: [1]

While important in detecting targets, strength of emitter and distance are not factors that affect the calculation of an RCS because RCS is a property of the target's reflectivity.

Radar cross-section is used to detect airplanes in a wide variation of ranges. For example, a stealth aircraft (which is designed to have low detectability) will have design features that give it a low RCS (such as absorbent paint, flat surfaces, surfaces specifically angled to reflect the signal somewhere other than towards the source), as opposed to a passenger airliner that will have a high RCS (bare metal, rounded surfaces effectively guaranteed to reflect some signal back to the source, many protrusions like the engines, antennas, etc.). RCS is integral to the development of radar stealth technology, particularly in applications involving aircraft and ballistic missiles. [2] RCS data for current military aircraft is most highly classified.

In some cases, it is of interest to look at an area on the ground that includes many objects. In those situations, it is useful to use a related quantity called the differential scattering coefficient (also called the normalized radar cross-section or backscatter coefficient) σ0 ("sigma nought"), which is the average radar cross-section of a set of objects per unit area:



Informally, the RCS of an object is the cross-sectional area of a perfectly reflecting sphere that would produce the same strength reflection as would the object in question. (Bigger sizes of this imaginary sphere would produce stronger reflections.) Thus, RCS is an abstraction: The radar cross-sectional area of an object does not necessarily bear a direct relationship with the physical cross-sectional area of that object but depends upon other factors. [4]

Somewhat less informally, the RCS of a radar target is an effective area that intercepts the transmitted radar power and then scatters that power isotropically back to the radar receiver.

More precisely, the RCS of a radar target is the hypothetical area required to intercept the transmitted power density at the target such that if the total intercepted power were re-radiated isotropically, the power density actually observed at the receiver is produced. [5] This statement that can be understood by examining the monostatic (radar transmitter and receiver co-located) radar equation one term at a time:


The term in the radar equation represents the power density (watts per meter squared) that the radar transmitter produces at the target. This power density is intercepted by the target with radar cross-section , which has units of area (meters squared). Thus, the product has the dimensions of power (watts), and represents a hypothetical total power intercepted by the radar target. The second term represents isotropic spreading of this intercepted power from the target back to the radar receiver. Thus, the product represents the reflected power density at the radar receiver (again watts per meter squared). The receiver antenna then collects this power density with effective area , yielding the power received by the radar (watts) as given by the radar equation above.

The scattering of incident radar power by a radar target is never isotropic (even for a spherical target), and the RCS is a hypothetical area. In this light, RCS can be viewed simply as a correction factor that makes the radar equation "work out right" for the experimentally observed ratio of . However, RCS is an extremely valuable concept because it is a property of the target alone and may be measured or calculated. Thus, RCS allows the performance of a radar system with a given target to be analysed independent of the radar and engagement parameters. In general, RCS is a strong function of the orientation of the radar and target, or, for the bistatic (radar transmitter and receiver not co-located), a function of the transmitter-target and receiver-target orientations. A target's RCS depends on its size, reflectivity of its surface, and the directivity of the radar reflection caused by the target's geometric shape.



As a rule, the larger an object, the stronger its radar reflection and thus the greater its RCS. Also, radar of one band may not even detect certain size objects. For example, 10 cm (S-band radar) can detect rain drops but not clouds whose droplets are too small.


Materials such as metal are strongly radar reflective and tend to produce strong signals. Wood and cloth (such as portions of planes and balloons used to be commonly made) or plastic and fibreglass are less reflective or indeed transparent to radar making them suitable for radomes. Even a very thin layer of metal can make an object strongly radar reflective. Chaff is often made from metallised plastic or glass (in a similar manner to metallised foils on food stuffs) with microscopically thin layers of metal.

Also, some devices are designed to be Radar active, such as radar antennas and this will increase RCS.

Radar absorbent paint

The SR-71 Blackbird and other planes were painted with a special "iron ball paint" that consisted of small metallic-coated balls. Radar energy received is converted to heat rather than being reflected.

Shape, directivity and orientation

The surfaces of the F-117A are designed to be flat and very angled. This has the effect that radar will be incident at a large angle (to the normal ray) that will then bounce off at a similarly high reflected angle; it is forward-scattered. The edges are sharp to prevent there being rounded surfaces. Rounded surfaces will often have some portion of the surface normal to the radar source. As any ray incident along the normal will reflect back along the normal, this will make for a strong reflected signal. [2]

From the side, a fighter plane will present a much larger area than the same plane when viewed from the front. All other factors being equal, the plane will have a stronger signal from the side than from the front so the orientation between the Radar station and the target is important.

Smooth surfaces

The relief of a surface could contain indentations that act as corner reflectors which would increase RCS from many orientations. This could arise from open bomb-bays, engine intakes, ordnance pylons, joints between constructed sections, etc. Also, it can be impractical to coat these surfaces with radar-absorbent materials.


The size of a target's image on radar is measured by the radar cross section or RCS, often represented by the symbol σ and expressed in square meters. This does not equal geometric area. A perfectly conducting sphere of projected cross sectional area 1 m2 (i.e. a diameter of 1.13 m) will have an RCS of 1 m2. Note that for radar wavelengths much less than the diameter of the sphere, RCS is independent of frequency. Conversely, a square flat plate of area 1 m2 will have an RCS of σ = 4π A2 / λ2 (where A=area, λ=wavelength), or 13,962 m2 at 10 GHz if the radar is perpendicular to the flat surface. [2] At off-normal incident angles, energy is reflected away from the receiver, reducing the RCS. Modern stealth aircraft are said to have an RCS comparable with small birds or large insects, [6] though this varies widely depending on aircraft and radar.

If the RCS was directly related to the target's cross-sectional area, the only way to reduce it would be to make the physical profile smaller. Rather, by reflecting much of the radiation away or by absorbing it, the target achieves a smaller radar cross section. [7]

Measurement of a target's RCS is performed at a radar reflectivity range or scattering range.[ citation needed ] The first type of range is an outdoor range where the target is positioned on a specially shaped low RCS pylon some distance down-range from the transmitters. Such a range eliminates the need for placing radar absorbers behind the target, however multi-path interactions with the ground must be mitigated.

An anechoic chamber is also commonly used. In such a room, the target is placed on a rotating pillar in the center, and the walls, floors and ceiling are covered by stacks of radar absorbing material. These absorbers prevent corruption of the measurement due to reflections. A compact range is an anechoic chamber with a reflector to simulate far field conditions.

Typical values for a centimeter wave radar are: [8] [9]


Quantitatively, RCS is calculated in three-dimensions as [4]

Where is the RCS, is the incident power density measured at the target, and is the scattered power density seen at a distance away from the target.

In electromagnetic analysis this is also commonly written as [2]

where and are the far field scattered and incident electric field intensities, respectively.

In the design phase, it is often desirable to employ a computer to predict what the RCS will look like before fabricating an actual object. Many iterations of this prediction process can be performed in a short time at low cost, whereas use of a measurement range is often time-consuming, expensive and error-prone. The linearity of Maxwell's equations makes RCS relatively straightforward to calculate with a variety of analytic and numerical methods, but changing levels of military interest and the need for secrecy have made the field challenging, nonetheless.

The field of solving Maxwell's equations through numerical algorithms is called computational electromagnetics, and many effective analysis methods have been applied to the RCS prediction problem. RCS prediction software are often run on large supercomputers and employ high-resolution CAD models of real radar targets.

High frequency approximations such as geometric optics, Physical Optics, the geometric theory of diffraction, the uniform theory of diffraction and the physical theory of diffraction are used when the wavelength is much shorter than the target feature size.

Statistical models include chi-square, Rice, and the log-normal target models. These models are used to predict likely values of the RCS given an average value, and are useful when running radar Monte Carlo simulations.

Purely numerical methods such as the boundary element method (method of moments), finite difference time domain method (FDTD) and finite element methods are limited by computer performance to longer wavelengths or smaller features.

Though, for simple cases, the wavelength ranges of these two types of method overlap considerably, for difficult shapes and materials or very high accuracy they are combined in various sorts of hybrid method.


The B-2 Spirit was one of the first aircraft to successfully become 'invisible' to radar. B-2 Spirit 3.jpg
The B-2 Spirit was one of the first aircraft to successfully become 'invisible' to radar.
A Chengdu J20 incorporating stealth technology J-20 fighter (cropped).jpg
A Chengdu J20 incorporating stealth technology
Detail of the Forbin, a modern frigate of the French navy. The faceted appearance reduces radar cross-section for stealth. Cheminee tribord du forbin.JPG
Detail of the Forbin , a modern frigate of the French navy. The faceted appearance reduces radar cross-section for stealth.

RCS reduction is chiefly important in stealth technology for aircraft, missiles, ships, and other military vehicles. With smaller RCS, vehicles can better evade radar detection, whether it be from land-based installations, guided weapons or other vehicles. Reduced signature design also improves platforms' overall survivability through the improved effectiveness of its radar counter-measures. [2]

Several methods exist. The distance at which a target can be detected for a given radar configuration varies with the fourth root of its RCS. [12] Therefore, in order to cut the detection distance to one tenth, the RCS should be reduced by a factor of 10,000. While this degree of improvement is challenging, it is often possible when influencing platforms during the concept/design stage and using experts and advanced computer code simulations to implement the control options described below.

Purpose shaping

With purpose shaping, the shape of the target's reflecting surfaces is designed such that they reflect energy away from the source. The aim is usually to create a “cone-of-silence” about the target's direction of motion. Due to the energy reflection, this method is defeated by using passive (multistatic) radars.

Purpose-shaping can be seen in the design of surface faceting on the F-117A Nighthawk stealth fighter. This aircraft, designed in the late 1970s though only revealed to the public in 1988, uses a multitude of flat surfaces to reflect incident radar energy away from the source. Yue suggests [13] that limited available computing power for the design phase kept the number of surfaces to a minimum. The B-2 Spirit stealth bomber benefited from increased computing power, enabling its contoured shapes and further reduction in RCS. The F-22 Raptor and F-35 Lightning II continue the trend in purpose shaping and promise to have even smaller monostatic RCS.

Redirecting scattered energy without shaping

This technique is relatively new compared to other techniques chiefly after the invention of metasurfaces. [14] [15] [16] As mentioned earlier, the primary objective in geometry alteration is to redirect scattered waves away from the backscattered direction (or the source). However, it may compromise performance in terms of aerodynamics. [14] [15] [17] One feasible solution, which has extensively been explored in recent time, is to utilize metasurfaces which can redirect scattered waves without altering the geometry of the target. [15] [16] Such metasurfaces can primarily be classified in two categories: (i) Checkerboard metasurfaces, (ii) Gradient index metasurfaces.

Active cancellation

With active cancellation, the target generates a radar signal equal in intensity but opposite in phase to the predicted reflection of an incident radar signal (similarly to noise canceling ear phones). This creates destructive interference between the reflected and generated signals, resulting in reduced RCS. To incorporate active cancellation techniques, the precise characteristics of the waveform and angle of arrival of the illuminating radar signal must be known, since they define the nature of generated energy required for cancellation. Except against simple or low frequency radar systems, the implementation of active cancellation techniques is extremely difficult due to the complex processing requirements and the difficulty of predicting the exact nature of the reflected radar signal over a broad aspect of an aircraft, missile or other target.

Radar absorbent material

Radar absorbent material (RAM) [2] can be used in the original construction, or as an addition to highly reflective surfaces. There are at least three types of RAM: resonant, non-resonant magnetic and non-resonant large volume.

Thin coatings made of only dielectrics and conductors have very limited absorbing bandwidth, so magnetic materials are used when weight and cost permit, either in resonant RAM or as non-resonant RAM.

Plasma-based RCS reduction

Plasma stealth is a proposed process to use ionized gas (plasma) to reduce the RCS of an aircraft. Interactions between electromagnetic radiation and ionized gas have been extensively studied for many purposes, including concealing aircraft from radar as stealth technology. Various methods might plausibly be able to form a layer or cloud of plasma around a vehicle to deflect or absorb radar, from simpler electrostatic or radio frequency (RF) discharges to more complex laser discharges. It is theoretically possible to reduce RCS in this way, but it may be very difficult to do so in practice.[ citation needed ] Although the RCS effect was shown in experiments, pre injection for a rocket as well as a fighter jets improved manoeuvrability and speed.[ clarification needed ]

Optimization methods

Thin non-resonant or broad resonance coatings can be modeled with a Leontovich impedance boundary condition (see also Electrical impedance). This is the ratio of the tangential electric field to the tangential magnetic field on the surface, and ignores fields propagating along the surface within the coating. This is particularly convenient when using boundary element method calculations. The surface impedance can be calculated and tested separately. For an isotropic surface the ideal surface impedance is equal to the 377 ohm impedance of free space. For non-isotropic (anisotropic) coatings, the optimal coating depends on the shape of the target and the radar direction, but duality, the symmetry of Maxwell's equations between the electric and magnetic fields, tells one that optimal coatings have η0 × η1 = 3772 Ω2, where η0 and η1 are perpendicular components of the anisotropic surface impedance, aligned with edges and/or the radar direction.

A perfect electric conductor has more back scatter from a leading edge for the linear polarization with the electric field parallel to the edge and more from a trailing edge with the electric field perpendicular to the edge, so the high surface impedance should be parallel to leading edges and perpendicular to trailing edges, for the greatest radar threat direction, with some sort of smooth transition between.

To calculate the radar cross-section of such a stealth body, one would typically do one-dimensional reflection calculations to calculate the surface impedance, then two dimensional numerical calculations to calculate the diffraction coefficients of edges and small three dimensional calculations to calculate the diffraction coefficients of corners and points. The cross section can then be calculated, using the diffraction coefficients, with the physical theory of diffraction or other high frequency method, combined with physical optics to include the contributions from illuminated smooth surfaces and Fock calculations to calculate creeping waves circling around any smooth shadowed parts.

Optimization is in the reverse order. First one does high frequency calculations to optimize the shape and find the most important features, then small calculations to find the best surface impedances in the problem areas, then reflection calculations to design coatings. Large numerical calculations can run too slowly for numerical optimization or can distract workers from the physics, even when massive computing power is available.

RCS of an antenna

For the case of an antenna the total RCS can be divided into two separate components as Structural Mode RCS and Antenna Mode RCS. The two components of the RCS relates to the two scattering phenomena that takes place at the antenna. When an electromagnetic signal falls on an antenna surface, some part of the electromagnetic energy is scattered back to the space. This is called structural mode scattering. The remaining part of the energy is absorbed due to the antenna effect. Some part of the absorbed energy is again scattered back into the space due to the impedance mismatches, called antenna mode scattering. [18] [19] [20]

See also

Related Research Articles

In physics, the cross section is a measure of the probability that a specific process will take place when some kind of radiant excitation intersects a localized phenomenon. For example, the Rutherford cross-section is a measure of probability that an alpha-particle will be deflected by a given angle during a collision with an atomic nucleus. Cross section is typically denoted σ (sigma) and is expressed in units of area, more specific in barns. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process.

Radar Object detection system using radio waves

Radar is a detection system that uses radio waves to determine the distance (range), angle, or velocity of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. A radar system consists of a transmitter producing electromagnetic waves in the radio or microwaves domain, a transmitting antenna, a receiving antenna and a receiver and processor to determine properties of the object(s). Radio waves from the transmitter reflect off the object and return to the receiver, giving information about the object's location and speed.

Antenna (radio) Electrical device

In radio engineering, an antenna or aerial is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies an electric current to the antenna's terminals, and the antenna radiates the energy from the current as electromagnetic waves. In reception, an antenna intercepts some of the power of a radio wave in order to produce an electric current at its terminals, that is applied to a receiver to be amplified. Antennas are essential components of all radio equipment.

Stealth technology Military technology to make personnel and material less visible

Stealth technology, also termed low observable technology, is a sub-discipline of military tactics and passive and active electronic countermeasures, which covers a range of methods used to make personnel, aircraft, ships, submarines, missiles, satellites, and ground vehicles less visible to radar, infrared, sonar and other detection methods. It corresponds to military camouflage for these parts of the electromagnetic spectrum.

Near and far field

The near field and far field are regions of the electromagnetic field (EM) around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative near-field behaviors dominate close to the antenna or scattering object, while electromagnetic radiation far-field behaviors dominate at greater distances.

Dipole antenna Antenna consisting of two rod shaped conductors

In radio and telecommunications a dipole antenna or doublet is the simplest and most widely used class of antenna. The dipole is any one of a class of antennas producing a radiation pattern approximating that of an elementary electric dipole with a radiating structure supporting a line current so energized that the current has only one node at each end. A dipole antenna commonly consists of two identical conductive elements such as metal wires or rods. The driving current from the transmitter is applied, or for receiving antennas the output signal to the receiver is taken, between the two halves of the antenna. Each side of the feedline to the transmitter or receiver is connected to one of the conductors. This contrasts with a monopole antenna, which consists of a single rod or conductor with one side of the feedline connected to it, and the other side connected to some type of ground. A common example of a dipole is the "rabbit ears" television antenna found on broadcast television sets.

Synthetic-aperture radar Form of radar used to create images of landscapes

Synthetic-aperture radar (SAR) is a form of radar that is used to create two-dimensional images or three-dimensional reconstructions of objects, such as landscapes. SAR uses the motion of the radar antenna over a target region to provide finer spatial resolution than conventional stationary beam-scanning radars. SAR is typically mounted on a moving platform, such as an aircraft or spacecraft, and has its origins in an advanced form of side looking airborne radar (SLAR). The distance the SAR device travels over a target during the period when the target scene is illuminated creates the large synthetic antenna aperture. Typically, the larger the aperture, the higher the image resolution will be, regardless of whether the aperture is physical or synthetic – this allows SAR to create high-resolution images with comparatively small physical antennas. For a fixed antenna size and orientation, objects which are further away remain illuminated longer - therefore SAR has the property of creating larger synthetic apertures for more distant objects, which results in a consistent spatial resolution over a range of viewing distances.

Metamaterial Materials engineered to have properties that have not yet been found in nature

A metamaterial is any material engineered to have a property that is not found in naturally occurring materials. They are made from assemblies of multiple elements fashioned from composite materials such as metals and plastics. The materials are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Metamaterials derive their properties not from the properties of the base materials, but from their newly designed structures. Their precise shape, geometry, size, orientation and arrangement gives them their smart properties capable of manipulating electromagnetic waves: by blocking, absorbing, enhancing, or bending waves, to achieve benefits that go beyond what is possible with conventional materials.

Kolchuga passive sensor

The Kolchuga passive sensor is an electronic-warfare support measures system developed in the Soviet Union and manufactured in Ukraine. Its detection range is limited by line-of-sight but may be up to 800 km (500 mi) for very high altitude, very powerful emitters. Frequently referred to as Kolchuga Radar, the system is not really a radar, but an ESM system comprising three or four receivers, deployed tens of kilometres apart, which detect and track aircraft by triangulation and multilateration of their RF emissions.

Pulse-Doppler radar

A pulse-Doppler radar is a radar system that determines the range to a target using pulse-timing techniques, and uses the Doppler effect of the returned signal to determine the target object's velocity. It combines the features of pulse radars and continuous-wave radars, which were formerly separate due to the complexity of the electronics.

Plasma stealth is a proposed process to use ionized gas (plasma) to reduce the radar cross-section (RCS) of an aircraft. Interactions between electromagnetic radiation and ionized gas have been extensively studied for many purposes, including concealing aircraft from radar as stealth technology. Various methods might plausibly be able to form a layer or cloud of plasma around a vehicle to deflect or absorb radar, from simpler electrostatic or radio frequency discharges to more complex laser discharges. It is theoretically possible to reduce RCS in this way, but it may be very difficult to do so in practice. Some Russian systems e.g. the 3M22 Zircon (SS-N-33) missile have been reported to make use of plasma stealth.

Antenna measurement techniques refers to the testing of antennas to ensure that the antenna meets specifications or simply to characterize it. Typical parameters of antennas are gain, bandwidth, radiation pattern, beamwidth, polarization, and impedance.

Computational electromagnetics Branch of physics

Computational electromagnetics (CEM), computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment.

Radiation-absorbent material

Radiation-absorbent material, usually known as RAM, is a material which has been specially designed and shaped to absorb incident RF radiation, as effectively as possible, from as many incident directions as possible. The more effective the RAM, the lower the resulting level of reflected RF radiation. Many measurements in electromagnetic compatibility (EMC) and antenna radiation patterns require that spurious signals arising from the test setup, including reflections, are negligible to avoid the risk of causing measurement errors and ambiguities.

Constantine A. Balanis American scientist

Constantine A. Balanis is a Greek-born American scientist, educator, author, and Regents Professor at Arizona State University. Born in Trikala, Greece on October 29, 1938. He is best known for his books in the fields of engineering electromagnetics and antenna theory. He emigrated to the United States in 1955, where he studied electrical engineering. He received United States citizenship in 1960.

Fluctuation loss is an effect seen in radar systems as the target object moves or changes its orientation relative to the radar system. It was extensively studied during the 1950s by Peter Swerling, who introduced the Swerling models to allow the effect to be simulated. For this reason, it is sometimes known as Swerling loss or similar names.

Bistatic radar Radio wave detection and transmission system defined by its separation

Bistatic radar is a radar system comprising a transmitter and receiver that are separated by a distance comparable to the expected target distance. Conversely, a radar in which the transmitter and receiver are co-located is called a monostatic radar. A system containing multiple spatially diverse monostatic radar or bistatic radar components with a shared area of coverage is called multistatic radar. Many long-range air-to-air and surface-to-air missile systems use semi-active radar homing, which is a form of bistatic radar.

Clutter (radar)

Clutter is a term used for unwanted echoes in electronic systems, particularly in reference to radars. Such echoes are typically returned from ground, sea, rain, animals/insects, chaff and atmospheric turbulences, and can cause serious performance issues with radar systems.

An electromagnetic metasurface refers to a kind of artificial sheet material with sub-wavelength thickness. Metasurfaces can be either structured or unstructured with subwavelength-scaled patterns in the horizontal dimensions.

The shooting and bouncing rays (SBR) method in computational electromagnetics was first developed for computation of radar cross section (RCS). Since then, the method has been generalized to be used also for installed antenna performance. The SBR method is an approximate method applied to high frequencies. The method can be implemented for GPU computing, which makes the computation very efficient.


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