Typical RCS diagram (B-26 Invader)

Radar cross section (RCS) describes the extent to which an object reflects an incident electromagnetic wave. It is a measure of the strength of the radar signal backscattered from a "target" object for a given incident wave power. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ...

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 (σ) can also be represented as:^[1]

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 the radar wavelength and the angle of incidence of the radio wave relative to the object. This long range radar antenna, known as ALTAIR, is used to detect and track space objects in conjunction with ABM testing at the Ronald Reagan Test Site on the Kwajalein atoll. ... The wavelength is the distance between repeating units of a wave pattern. ... Fig. ...

When the object's size spans several wavelengths, the RCS of a target object is equal to the cross-sectional area of a perfectly conducting sphere that would produce the same magnitude of reflection as that observed from the target object.^[2] Cross section may refer to the following In geometry, Cross section is the intersection of a 3-dimensional body with a plane. ...

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. Calabi-Yau manifold Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. ... A 3-D view of a beverage-can stove with a cross section in yellow. ...

The RCS is integral to the development of radar stealth technology, particularly in applications involving aircraft and ballistic missiles. RCS data for current military aircraft are almost all classified. F-117 stealth attack plane Stealth technology is a sub-discipline of electronic countermeasures which covers a range of techniques used with aircraft, ships and missiles, in order to make them less visible (ideally invisible) to radar, infrared and other detection methods. ... Look up aircraft in Wiktionary, the free dictionary. ... Diagram of V-2, the first ballistic missile. ...

Measurement

Measurement of a target's RCS is performed at a radar reflectivity range or scattering 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. A picture of an anechoic chamber An anechoic chamber is a room that is isolated from external sound or electromagnetic radiation sources, sometimes using sound proofing, and prevents the reflection of wave phenomena (reverberation). ...

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, σ is defined in three-dimensions as An isotropic radiator is a theoretical point source which exhibits the same magnitude or properties when measured in all directions. ...

Where σ 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 engineering, specific power (sometimes also power per unit mass or power density) refers to the amount of power delivered by an energy source, divided by some measure of the sources size or mass. ...

In electromagnetic analysis this is also commonly written as

where E_s and E_i are the scattered and incident electric field intensities, respectively. In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ...

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, none the less. The NASA Columbia Supercomputer. ... Prediction of future events is an ancient human wish. ... The word iteration is sometimes used in everyday English with a meaning virtually identical to repetition. ... In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ...

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. In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ... Numerical analysis is the study of approximate methods for the problems of continuous mathematics (as distinguished from discrete mathematics). ... Computational electromagnetics, computational electrodynamics or electromagnetic modeling refers to the process of modeling the interaction of electromagnetic fields with physical objects and the environment. ... A supercomputer is a computer that led the world (or was close to doing so) in terms of processing capacity, particularly speed of calculation, at the time of its introduction. ... CAD is a TLA that may stand for: Cadiz Railroad (AAR reporting mark CAD) Canadian dollar – ISO 4217-code Capital Adequacy Directive Card Acceptance Device Children of the Anachronistic Dynasty Computer-aided design Computer-aided detection (medical) Computer-aided diagnosis (medical) Computer-assisted dispatch Computer-assisted drafting Coronary artery disease...

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. A high frequency approximation (or high energy approximation) for scattering or other wave propagation problems, in physics or engineering, is an approximation whose accuracy increases with the size of features on the scatterer or medium relative to the wavelength of the scattered particles. ... See also list of optical topics. ... Physical Optics is the name of a high frequency approximation (short wavelength approximation) used in the electromagnetism of optics and radio. ... The intensity pattern formed on a screen by diffraction from a square aperture Diffraction refers to various phenomena associated with wave propagation, such as the bending, spreading and interference of waves passing by an object or aperture that disrupts the wave. ... The wavelength is the distance between repeating units of a wave pattern. ...

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. Chi-Square target models were introduced by Peter Swerling and are used to describe the statistical properties of the radar cross-section of complex objects. ... In probability theory and statistics, the Rice distribution distribution is a continuous probability distribution. ... In probability and statistics, the log-normal distribution is the probability distribution of any random variable whose logarithm is normally distributed. ... Monte Carlo methods are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems, and for other computations. ...

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. This article discusses the use of the word Number in Mathematics. ... The boundary element method is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i. ... Finite-Difference Time-Domain (FDTD) is a popular electromagnetic modeling techniques. ... Finite-Difference Time-Domain (FDTD) is a popular electromagnetic modeling technique. ... Finite element analysis (FEA) or finite element method (FEM) is a numerical technique for solution of boundary-value problems. ...

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. F-117 stealth attack plane Stealth technology is a sub-discipline of electronic countermeasures which covers a range of techniques used with aircraft, ships and missiles, in order to make them less visible (ideally invisible) to radar, infrared and other detection methods. ...

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. Passive radar systems (also referred to a passive coherent location and passive covert radar) encompass a class of radar systems that detect and track objects by processing reflections from non-cooperative sources of illumination in the environment, such as commercial broadcast and communications signals. ...

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. 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. This article is about the stealth fighter. ... Year 1988 (MCMLXXXVIII) was a leap year starting on Friday (link displays 1988 Gregorian calendar). ... The Northrop Grumman B-2 Spirit is a multi-role stealth bomber able to drop conventional and nuclear weapons. ... The F-22 Raptor is a fifth generation fighter aircraft which utilizes fourth generation Stealth technology. ... The F-35 Lightning II is a single-seat, single-engine, stealth-capable military strike fighter, a multi-role aircraft that can perform close air support, tactical bombing, and air-to-air combat. ...

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. Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ...

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 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 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 resistive carbon loading added to fiberglass 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 space craft. Radar absorbent material, or RAM, is a class of materials used in stealth technology to disguise a vehicle or structure from radar detection. ... Ferrite may refer to: Ferrite (magnet)s (e. ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... General Name, Symbol, Number carbon, C, 6 Chemical series nonmetals Group, Period, Block 14, 2, p Appearance black (graphite) colorless (diamond) Standard atomic weight 12. ... Bundle of fiberglass Fiberglass (also called fibreglass and glass fibre) is material made from extremely fine fibers of glass. ... A 2. ...

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 (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. This article or section does not cite its references or sources. ... In mathematics, boundary conditions are imposed on the solutions of ordinary differential equations and partial differential equations, to fit the solutions to the actual problem. ... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ... The boundary element method is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i. ... Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ... The ohm (symbol: Ω) is the SI unit of electric resistance. ... In physics, free space is a concept of electromagnetic theory, corresponding roughly to the vacuum, the baseline state of the electromagnetic field, or the replacement for the electromagnetic aether. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ...

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. Numerical analysis is the study of approximate methods for the problems of continuous mathematics (as distinguished from discrete mathematics). ... Vladimir Aleksandrovich Fock (or Fok, Владимир Александрович Фок) (22 December 1898 - December 27, 1974) was a Soviet physicist, who did foundational work on quantum mechanics. ...

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.

See also

• Electromagnetic modeling

Computational electromagnetics, computational electrodynamics or electromagnetic modeling refers to the process of modeling the interaction of electromagnetic fields with physical objects and the environment. ...

References

1. ^ http://www.aerospaceweb.org/question/electronics/q0168.shtml
2. ^ http://www.ccrs.nrcan.gc.ca/glossary/index_e.php?id=2827

• 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

• Epsilon^TM RCS Prediction Software by Roke Manor Research Limited
• Indoor Microwave Measurement Facility at System Planning Corporation
• lucernhammer RCS Prediction Software by Tripoint Industries, Inc.
• Hip-pocket formulas for high-frequency RCS backscatter; useful reference sheet (PDF)