- Radar cross section
**Radar cross section**(RCS) is a measure of how detectable an object is with aradar . For example astealth aircraft (which is designed to be undetectable) will have design features that give it a**low**RCS, as opposed to a passenger airliner that will have a**high**RCS.**Definitions**An object's RCS depends on its size,

**reflectivity**of its surface, and the**directivity**of the radar reflection caused by the object's geometric shape.Radar cross section (RCS) = Geometric cross section × Reflectivity × Directivity

RCS ($sigma$) can also be represented as: [

*[*]*http://www.aerospaceweb.org/question/electronics/q0168.shtml Aerospaceweb.org | Ask Us - Radar Cross Section*]$sigma\; =\; 4\; pi\; dfrac\{P\_\{backscatter\{P\_\{intercepted$

where the power that is reflected toward the radar is "P

_{backscatter}", and the power intercepted by the object is "P_{intercepted}", both of which depend on theradar wavelength and theangle of incidence of theradio wave relative to the object.When the object's size spans several wavelengths, the RCS of a target object is equal to the

cross-section al area of aperfectly conducting sphere that would produce the same magnitude of reflection as that observed from the target object. [*[*]*http://www.ccrs.nrcan.gc.ca/glossary/index_e.php?id=2827 Glossary of remote sensing terms*]The usual definition or RCS differs by a factor of (4π) from the standard geometric definition of cross section at 180 degrees. Bistatic radar cross section is defined similarly for other angles.

The RCS is integral to the development of radar

stealth technology , particularly in applications involvingaircraft andballistic missile s. RCS data for current military aircraft are almost all classified.**Measurement**Measurement of a target's RCS is performed at a radar

reflectivity range orscattering range . 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.**Calculation**Quantitatively, the RCS is an effective surface area that intercepts the incident wave and that scatters the energy isotropically in space. For the RCS, $sigma$ is defined in three-dimensions as

:$sigma\; =\; 4\; pi\; R^\{2\}\; frac\{P\_\{s\{P\_\{i$

Where $sigma$ is the RCS, $P\_\{i\}$ is the incident

power density measured at the target, and $P\_\{s\}$ is the scattered power density seen at a distance $R$ away from the target.In electromagnetic analysis this is also commonly written as

:$sigma\; =\; 4\; pi\; R^\{2\}\; frac\{|E\_\{s\}|^\{2\{|E\_\{i\}|^\{2$

where $E\_\{s\}$ and $E\_\{i\}$ are the far field scattered and incident

electric field intensities, respectively.In the design phase, it is often desirable to employ a

computer topredict what the RCS will look like before fabricating an actual object. Manyiteration 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 ofMaxwell'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 calledcomputational electromagnetics , and many effective analysis methods have been applied to the RCS prediction problem.RCS prediction software are often run on largesupercomputer s and employ high-resolutionCAD models of real radar targets.High frequency approximation s such asgeometric optics ,Physical Optics , thegeometric theory of diffraction , the uniform theory of diffraction and the physical theory ofdiffraction are used when thewavelength 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 theboundary element method (method of moments),finite difference time domain method (FDTD ) andfinite 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 methods .**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 or other vehicles. 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. cite book | last = Sweetman | first = Bill | title = YF-22 and YF-23 Advanced Tactical Fighters: Stealth, Speed and Agility for Air Superiority | origyear = 1991 | publisher = Motorbooks International | location = Osceola, Wisconsin, United States | id = ISBN 0-87938-505-7] Therefore, in order to cut the detection distance to one tenth, the RCS should be reduced by a factor of 10,000.**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 that limited available computing power for the design phase kept the number of surfaces to a minimum. TheB-2 Spirit stealth bomber benefited from increased computing power, enabling its contoured shapes and further reduction in RCS. TheF-22 Raptor andF-35 Lightning II continue the trend in purpose shaping and promise to have even smaller monostatic RCS.**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**With

radar absorbent material (RAM), it 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. 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 usesferrite 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 at the cost of 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 resistivecarbon loading added tofiberglass hexagonal cell aircraft structures or other non-conducting components. Fins of resistive materials can also be added. Thin resistive sheets spaced by foam oraerogel may be suitable for space craft.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 impedanceboundary condition (see alsoElectrical 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 usingboundary element method calculations. The surface impedance can be calculated and tested separately.For anisotropic surface the ideal surface impedance is equal to the 377 ohm impedance offree 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 η_{0}× η_{1}= 377^{2}Ω^{2}, where η_{0}and η_{1}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 andFock calculations to calculatecreeping 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. One should avoid large numerical calculations that run too slowly for numerical optimization or distract workers from the physics, even when massive computing power is available.

**ee also***

Electromagnetic modeling **References*** Shaeffer, Tuley and Knott. "Radar Cross Section". SciTech Publishing, 2004. ISBN 1-891121-25-1.

* Harrington, Roger F. "Time-Harmonic Electromagnetic Fields". McGraw-Hill, Inc., 1961. ISBN 047120806X

* 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*** [

*http://www.mariettascientific.com/hippocket/ref_2-97.pdf Hip-pocket formulas*] for high-frequency RCS backscatter; useful reference sheet (PDF)**Free Software*** [

*http://sourceforge.net/projects/puma-em/ Puma-EM*] A high performance, parallelized, open source Method of Moments / Multilevel Fast Multipole Method electromagnetics code

*Wikimedia Foundation.
2010.*