Radar Cross-section
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Radar cross-section (RCS), also called radar signature, is a measure of how detectable an object is by
radar Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
. A larger RCS indicates that an object is more easily detected. An object reflects a limited amount of radar energy back to the source. The factors that influence this include: *the material with which the target is made; *the size of the target relative to the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
of the illuminating radar signal; *the absolute size of the target; *the incident angle (angle at which the radar beam hits a particular portion of the target, which depends upon the shape of the target and its orientation to the radar source); *the reflected angle (angle at which the reflected beam leaves the part of the target hit; it depends upon incident angle); *the polarization of the transmitted and the received radiation with respect to the orientation of the target. 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 An aircraft is a vehicle that is able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines ...
and
ballistic missile A ballistic missile is a type of missile that uses projectile motion to deliver warheads on a target. These weapons are guided only during relatively brief periods—most of the flight is unpowered. Short-range ballistic missiles stay within the ...
s. RCS data for current military aircraft is mostly 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: :\sigma^0 = \left\langle \right\rangle where: * RCSi is the radar cross-section of a particular object, and * Ai is the area on the ground associated with that object.


Definition

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.C. A. Balanis, "Advanced Engineering Electromagnetics", 2nd ed. New York, NY, USA: Wiley, 2012. 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. This statement can be understood by examining the monostatic (radar transmitter and receiver co-located)
radar equation Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, ...
one term at a time: :P_r = \sigma A_\mathrm where *P_t = transmitter's input power (watts) *G_t =
gain Gain or GAIN may refer to: Science and technology * Gain (electronics), an electronics and signal processing term * Antenna gain * Gain (laser), the amplification involved in laser emission * Gain (projection screens) * Information gain in de ...
of the radar transmit antenna (dimensionless) *r = distance from the radar to the target (meters) *\sigma = radar cross-section of the target (meters squared) *A_\mathrm =
effective area In electromagnetics and antenna theory, the aperture of an antenna is defined as "A surface, near or on an antenna, on which it is convenient to make assumptions regarding the field values for the purpose of computing fields at external points. T ...
of the radar receiving antenna (meters squared) *P_r = power received back from the target by the radar (watts) 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 \sigma, which has units of area (meters squared). Thus, the product \sigma 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 \sigma 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 A_\mathrm, 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 P_r/P_t. 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.


Factors


Size

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.


Material

Materials such as metal are strongly radar reflective and tend to produce strong signals. Wood and cloth (such as portions of airplanes and balloons used to be commonly made) or plastic and fibreglass are less reflective or indeed transparent to radar making them suitable for
radome A radome (a portmanteau of radar and dome) is a structural, weatherproof enclosure that protects a radar antenna. The radome is constructed of material transparent to radio waves. Radomes protect the antenna from weather and conceal antenna e ...
s. Even a very thin layer of metal can make an object strongly radar reflective.
Chaff Chaff (; ) is the dry, scaly protective casing of the seeds of cereal grains or similar fine, dry, scaly plant material (such as scaly parts of flowers or finely chopped straw). Chaff is indigestible by humans, but livestock can eat it. In agri ...
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 aircraft were painted with a special "
iron ball paint In materials science, radiation-absorbent material, usually known as RAM, is a material which has been specially designed and shaped to absorption (electromagnetic radiation), absorb incident RF radiation (also known as non-ionising radiation), ...
" 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 rounded surfaces which are normal at some point to the radar source. As any ray incident along the normal will reflect back along the normal, rounded surfaces make for a strong reflected signal. From the side, a fighter aircraft will present a much larger area than the same aircraft viewed from the front. All other factors being equal, the aircraft will have a stronger signal from the side than from the front; hence the orientation of the target relative to the radar station 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 material In materials science, radiation-absorbent material, usually known as RAM, is a material which has been specially designed and shaped to absorb incident RF radiation (also known as non-ionising radiation), as effectively as possible, from as m ...
s.


Measurement

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 ''A''2 / ''λ''2 (where ''A''=area, ''λ''=wavelength), or 13,962 m2 at 10 GHz if the radar is perpendicular to the flat surface. 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, 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. Measurement of a target's RCS is performed at a radar
reflectivity range The reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electronic ...
or
scattering range Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
. 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 An anechoic chamber (''an-echoic'' meaning "non-reflective") is a room designed to stop reflections of either sound or electromagnetic waves. They are also often isolated from energy entering from their surroundings. This combination means t ...
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: * Insect: 0.00001 m2 * Bird: 0.01 m2 * Stealth aircraft: <0.1 m2 (e.g. F-117A: 0.001 m2) * Surface-to-air-missile: ≈0.1 m2 * Human: 1 m2 * small combat aircraft: 2–3 m2 * large combat aircraft: 5–6 m2 * Cargo aircraft: up to 100 m2 * Coastal trading vessel (55 m length): 300–4000 m2 * Corner reflector with 1.5 m edge length: ≈20,000 m2 *
Frigate A frigate () is a type of warship. In different eras, the roles and capabilities of ships classified as frigates have varied somewhat. The name frigate in the 17th to early 18th centuries was given to any full-rigged ship built for speed and ...
(103 m length): 5000–100,000 m2 *
Container ship A container ship (also called boxship or spelled containership) is a cargo ship that carries all of its load in truck-size intermodal containers, in a technique called containerization. Container ships are a common means of commercial intermodal ...
(212 m length): 10,000–80,000 m2


Calculation

Quantitatively, RCS is calculated in three-dimensions as :\sigma = \lim_ 4 \pi r^ \frac Where \sigma is the RCS, S_ is the incident
power density Power density is the amount of power (time rate of energy transfer) per unit volume. In energy transformers including batteries, fuel cells, motors, power supply units etc., power density refers to a volume, where it is often called volum ...
measured at the target, and S_ is the scattered power density seen at a distance r away from the target. In electromagnetic analysis this is also commonly written as :\sigma = \lim_ 4 \pi r^ \frac where E_ and E_ are the far field scattered and incident
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
intensities, respectively. In the design phase, it is often desirable to employ a
computer A computer is a machine that can be programmed to Execution (computing), carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as C ...
to predict what the RCS will look like before fabricating an actual object. Many
iteration Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. ...
s 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 Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
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 Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
through
numerical algorithms Numerical may refer to: * Number * Numerical digit * Numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distin ...
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
supercomputer A supercomputer is a computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second ( FLOPS) instead of million instructions ...
s and employ high-resolution
CAD Computer-aided design (CAD) is the use of computers (or ) to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve co ...
models of real radar targets. High frequency approximations such as
geometric optics Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
,
Physical Optics In physics, physical optics, or wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effec ...
, the geometric theory of diffraction, the uniform theory of diffraction and the physical theory of
diffraction Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
are used when the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
is much shorter than the target feature size. Statistical models include chi-square,
Rice Rice is the seed of the grass species ''Oryza sativa'' (Asian rice) or less commonly ''Oryza glaberrima ''Oryza glaberrima'', commonly known as African rice, is one of the two domesticated rice species. It was first domesticated and grown i ...
, and the
log-normal In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable is log-normally distributed, then has a 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 Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is ...
simulations. Purely numerical methods such as the
boundary element method The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in ''boundary integral'' form), including fluid mechanics, acoustics, el ...
( method of moments),
finite difference time domain method Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis technique used for modeling computational electrodynamics (finding approximate solutions to ...
(
FDTD Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis technique used for modeling computational electrodynamics (finding approximate solutions to ...
) and
finite element The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat t ...
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.


Reduction

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. 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. 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 The Lockheed F-117 Nighthawk is a retired American single-seat, twin-engine stealth attack aircraft developed by Lockheed's secretive Skunk Works division and operated by the United States Air Force (USAF). It was the first operational ai ...
stealth attack aircraft. 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 that limited available computing power for the design phase kept the number of surfaces to a minimum. The
B-2 Spirit The Northrop (later Northrop Grumman) B-2 Spirit, also known as the Stealth Bomber, is an American heavy strategic bomber, featuring low-observable stealth technology designed to penetrate dense anti-aircraft defenses. A subsonic flying ...
stealth bomber benefited from increased computing power, enabling its contoured shapes and further reduction in RCS. The
F-22 Raptor The Lockheed Martin F-22 Raptor is an American single-seat, twin-engine, all-weather stealth tactical fighter aircraft developed for the United States Air Force (USAF). As the result of the USAF's Advanced Tactical Fighter (ATF) program, th ...
and
F-35 Lightning II The Lockheed Martin F-35 Lightning II is an American family of single-seat, single-engine, all-weather stealth multirole combat aircraft that is intended to perform both air superiority and strike missions. It is also able to provide elect ...
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.A. Y. Modi; M. A. Alyahya; C. A. Balanis; C. R. Birtcher, "Metasurface-Based Method for Broadband RCS Reduction of Dihedral Corner Reflectors with Multiple Bounces," in IEEE Transactions on Antennas and Propagation, vol.67, no.12, pp. -, Dec. 2019. A. Y. Modi; C. A. Balanis; C. R. Birtcher; H. Shaman, "New Class of RCS-Reduction Metasurfaces Based on Scattering Cancellation Using Array Theory," in IEEE Transactions on Antennas and Propagation, vol. 67, no. 1, pp. 298-308, Jan. 2019. A. Y. Modi; C. A. Balanis; C. R. Birtcher; H. Shaman, "Novel Design of Ultra-Broadband Radar Cross Section Reduction Surfaces using Artificial Magnetic Conductors," in IEEE Transactions on Antennas and Propagation, vol. 65, no. 10, pp. 5406-5417, Oct. 2017. 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. 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. 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 In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
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) 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. *Resonant but somewhat 'lossy' materials are applied to the reflecting surfaces of the target. The thickness of the material corresponds to one-quarter wavelength of the expected illuminating radar-wave (a Salisbury screen). The incident radar energy is reflected from the outside and inside surfaces of the RAM to create a destructive wave interference pattern. This results in the cancellation of the reflected energy. Deviation from the expected frequency will cause losses in radar absorption, so this type of RAM is only useful against radar with a single, common, and unchanging frequency. *Non-resonant magnetic RAM uses ferrite particles suspended in epoxy or paint to reduce the reflectivity of the surface to incident radar waves. Because the non-resonant RAM dissipates incident radar energy over a larger surface area, it usually results in a trivial increase in surface temperature, thus reducing RCS without an increase in infrared signature. A major advantage of non-resonant RAM is that it can be effective over a wide range of frequencies, whereas resonant RAM is limited to a narrow range of design frequencies. *Large volume RAM is usually
resistive The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels ...
carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent In chemistry, the valence (US spelling) or valency (British spelling) of an element is the measure of its combining capacity with o ...
loading added to
fiberglass Fiberglass (American English) or fibreglass (Commonwealth English) is a common type of fiber-reinforced plastic using glass fiber. The fibers may be randomly arranged, flattened into a sheet called a chopped strand mat, or woven into glass cloth ...
hexagonal cell aircraft structures or other non-conducting components. Fins of resistive materials can also be added. Thin resistive sheets spaced by foam or aerogel may be suitable for spacecraft. 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.


Optimization methods

Thin non-resonant or broad resonance coatings can be modeled with a Leontovich impedance
boundary condition In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to th ...
(see also
Electrical impedance In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. Quantitatively, the impedance of a two-terminal circuit element is the ratio of the comp ...
). 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 The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in ''boundary integral'' form), including fluid mechanics, acoustics, el ...
calculations. The surface impedance can be calculated and tested separately. For an
isotropic Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...
surface the ideal surface impedance is equal to the 377
ohm Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm. Ohm or OHM may also refer to: People * Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm'' * Germán Ohm (born 1936), Mexican boxer * Jörg Ohm (b ...
impedance of free space The impedance of free space, , is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. That is, , where is the electric field strength and is the magnetic fie ...
. For non-isotropic (
anisotropic Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
) 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 In physics, physical optics, or wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effec ...
to include the contributions from illuminated smooth surfaces and Fock calculations to calculate
creeping waves According to the principle of diffraction, when a wave front passes an obstruction, it spreads out into the shadowed space. A creeping wave in electromagnetism or acoustics is the wave that is diffracted around the shadowed surface of a smooth b ...
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.


See also

*
System Planning Corporation System Planning Corporation (SPC) is a Virginia-based corporation founded in 1970 that produces military electronics, such as flight control systems, radar, and Systems Engineering and Technical Assistance in airwarfare, cybersecurity, program ...
*
Electromagnetic modeling Computational electromagnetics (CEM), computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects and the environment. It typically involves using computer ...
*
Infrared signature Infrared signature, as used by defense scientists and the military, is the appearance of objects to infrared sensors. An infrared signature depends on many factors, including the shape and size of the object, temperature, and emissivity, reflectio ...
*
Survivability Survivability is the ability to remain alive or continue to exist. The term has more specific meaning in certain contexts. Ecological Following disruptive forces such as flood, fire, disease, war, or climate change some species of flora, fauna, ...


References

* Shaeffer, Tuley and Knott. ''Radar Cross Section''. SciTech Publishing, 2004. . * Harrington, Roger F. ''Time-Harmonic Electromagnetic Fields''. McGraw-Hill, Inc., 1961. * Balanis, Constantine A. ''Advanced Engineering Electromagnetics''. Wiley, 1989. {{ISBN, 0-471-62194-3. * “A Hybrid Method Based on Reciprocity for the Computation of Diffraction by Trailing Edges”David R. Ingham, ''IEEE Trans. Antennas Propagat.'', 43 No. 11, November 1995, pp. 1173–82. * “Revised Integration Methods in a Galerkin BoR Procedure” David R. Ingham, ''Applied Computational Electromagnetics Society (ACES ) Journal'' 10 No. 2, July, 1995, pp. 5–16. * “A Hybrid Approach to Trailing Edges and Trailing Ends” David R. Ingham, ''proceedings of the ACES Symposium'', 1993, Monterey. * “Time-Domain Extrapolation to the Far Field Based on FDTD Calculations” Kane Yee, David Ingham and Kurt Shlager, ''IEEE Trans. Antennas Propagat.'', 39 No. 3, March 1991, pp. 410–413. * “Numerical Calculation of Edge Diffraction, using Reciprocity” David Ingham, ''Proc. Int. Conf. Antennas Propagat.'', IV, May 1990, Dallas, pp. 1574–1577. * “Time-Domain Extrapolation to the Far Field Based on FDTD Calculations”Kane Yee, David Ingham and Kurt Shlager, invited paper, ''Proc. URSI Conf.'', 1989, San José .


External links


Radar Cross Section, Optical Theorem, Physical Optics Approx, Radiation by Line Sources
for detailed lecture on introduction to the Radar Cross-Section (RCS)
Hip-pocket formulas
for high-frequency RCS backscatter; useful reference sheet (PDF)
Method to measure radar cross section parameters of antennasPuma-EM
A high performance, parallelized, open source Method of Moments / Multilevel Fast Multipole Method electromagnetics code
Radar Cross Section Reduction Course
A GA Tech course geared toward techniques used to reduce radar signature

provides great visuals of RCS Radar theory