Radar cross section

Encyclopedia

**Radar cross section**is a measure of how detectable an object is with a radar

Radar

Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...

. A larger RCS indicates that an object is more easily detected.

An object reflects a limited amount of radar energy. A number of different factors determine how much electromagnetic energy returns to the source such as:

- material of which the target is made;
- absolute size of the target;
- relative size of the target (in relation to the wavelengthWavelengthIn physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

of the illuminating radar); - the incident angle (angle at which the radar beam hits a particular portion of target which depends upon shape of target and its orientation to the radar source);
- reflected angle (angle at which the reflected beam leaves the part of the target hit, it depends upon incident angle);

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

Radar cross section is used to detect planes in a wide variation of ranges. For example, a stealth aircraft

Stealth aircraft

Stealth aircraft are aircraft that use stealth technology to avoid detection by employing a combination of features to interfere with radar as well as reduce visibility in the infrared, visual, audio, and radio frequency spectrum. Development of stealth technology likely began in Germany during...

(which is designed to have low detectability) will have design features that give it a

**low**RCS (such as absorbent paint, smooth surfaces, surfaces specifically angled to reflect 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, lots of bumps like the engines, antennae, etc.). RCS is integral to the development of radar stealth technology

Stealth technology

Stealth technology also termed LO technology is a sub-discipline of military tactics and passive electronic countermeasures, which cover a range of techniques used with personnel, aircraft, ships, submarines, and missiles, to make them less visible to radar, infrared, sonar and other detection...

, particularly in applications involving aircraft

Aircraft

An aircraft is a vehicle that is able to fly by gaining support from the air, or, in general, the atmosphere of a planet. An aircraft 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.Although...

and ballistic missile

Ballistic missile

A ballistic missile is a missile that follows a sub-orbital ballistic flightpath with the objective of delivering one or more warheads to a predetermined target. The missile is only guided during the relatively brief initial powered phase of flight and its course is subsequently governed by the...

s. RCS data for current military aircraft is most highly classified.

## 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.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

Isotropic radiator

An isotropic radiator is a theoretical point source of electromagnetic or sound waves which radiates the same intensity of radiation in all directions. It has no preferred direction of radiation. It radiates uniformly in all directions over a sphere centred on the source...

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 is a complex statement that can be understood by examining the monostatic (radar transmitter and receiver co-located) radar equation one term at a time:

where

- = power transmitted by the radar (watts)
- = gainGainIn electronics, gain is a measure of the ability of a circuit to increase the power or amplitude of a signal from the input to the output. It is usually defined as the mean ratio of the signal output of a system to the signal input of the same system. It may also be defined on a logarithmic scale,...

of the radar transmit antenna (dimensionless) - = distance from the radar to the target (meters)
- = radar cross section of the target (meters squared)
- = effective area of the radar receiving antenna (meters squared)
- = 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 , 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.

### 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 planes and balloons used to be commonly made) or plastic and fibreglass are less reflective or indeed transparent to Radar making them suitable for radomeRadome

A radome is a structural, weatherproof enclosure that protects a microwave or radar antenna. The radome is constructed of material that minimally attenuates the electromagnetic signal transmitted or received by the antenna. In other words, the radome is transparent to radar or radio waves...

s. 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 antennae and this will increase RCS.

#### Radar absorbent paint

The SR-71 BlackbirdSR-71 Blackbird

The Lockheed SR-71 "Blackbird" was an advanced, long-range, Mach 3+ strategic reconnaissance aircraft. It was developed as a black project from the Lockheed A-12 reconnaissance aircraft in the 1960s by the Lockheed Skunk Works. Clarence "Kelly" Johnson was responsible for many of the...

and other planes were painted with a special "iron ball paint". This consisted of small metallic-coated balls. Radar energy 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 rayReflection (physics)

Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...

) 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.

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 reflectorCorner reflector

A corner reflector is a retroreflector consisting of three mutually perpendicular, intersecting flat surfaces, which reflects waves back directly towards the source, but shifted . Unlike a simple mirror, they work for a relatively wide-angle field of view. The three intersecting surfaces often have...

s 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.

## Measurement

Measurement of a target's RCS is performed at a radar reflectivity rangeReflectivity range

Reflectivity range is the term used in X-ray reflectometry and several other radar-related or emission related sciences to describe the range at which reflected emissions become indecipherable due to the reflection angle and/or 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

Anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or electromagnetic waves.They are also insulated from exterior sources of noise...

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, RCS is calculated in three-dimensions asWhere is the RCS, is the incident power density

Power density

Power density is the amount of power per unit volume....

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

where and are the far field scattered and incident electric field

Electric field

In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

intensities, respectively.

In the design phase, it is often desirable to employ a computer

Computer

A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...

to predict what the RCS will look like before fabricating an actual object. Many iteration

Iteration

Iteration means the act of repeating a process usually with the aim of approaching a desired goal or target or result. Each repetition of the process is also called an "iteration," and the results of one iteration are used as the starting point for the next iteration.-Mathematics:Iteration in...

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

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.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

Maxwell's equations

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

through numerical algorithms

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

is called computational electromagnetics

Computational electromagnetics

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

, and many effective analysis methods have been applied to the RCS prediction problem.

RCS prediction software are often run on large supercomputer

Supercomputer

A supercomputer is a computer at the frontline of current processing capacity, particularly speed of calculation.Supercomputers are used for highly calculation-intensive tasks such as problems including quantum physics, weather forecasting, climate research, molecular modeling A supercomputer is a...

s and employ high-resolution CAD models of real radar targets.

High frequency approximation

High frequency approximation

A high frequency 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.Classical mechanics and geometric...

s such as geometric optics, Physical Optics

Physical optics

In physics, physical optics, or wave optics, is the branch of optics which studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid...

, the geometric theory of diffraction, the uniform theory of diffraction and the physical theory of diffraction

Diffraction

Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

are used when the wavelength

Wavelength

In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

is much shorter than the target feature size.

Statistical models include chi-square

Chi-square target models

Swerling models were introduced by Peter Swerling and are used to describe the statistical properties of the radar cross-section of complex objects.-General Target Model:...

, Rice

Rice distribution

In probability theory, the Rice distribution or Rician distribution is the probability distribution of the absolute value of a circular bivariate normal random variable with potentially non-zero mean. It was named after Stephen O...

, 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

Monte Carlo method

Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...

simulations.

Purely numerical methods such as the boundary element method

Boundary element method

The boundary element method is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations . It can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, and fracture...

(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 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, 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. Whilst 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) radarPassive radar

Passive radar systems 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...

s.

Purpose-shaping can be seen in the design of surface faceting on the F-117A Nighthawk

F-117 Nighthawk

The Lockheed F-117 Nighthawk was a single-seat, twin-engine stealth ground-attack aircraft formerly operated by the United States Air Force . The F-117A's first flight was in 1981, and it achieved initial operating capability status in October 1983...

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

B-2 Spirit

The Northrop Grumman B-2 Spirit is an American heavy bomber with low observable stealth technology designed to penetrate dense anti-aircraft defenses and deploy both conventional and nuclear weapons. The bomber has a crew of two and can drop up to eighty -class JDAM GPS-guided bombs, or sixteen ...

stealth bomber benefited from increased computing power, enabling its contoured shapes and further reduction in RCS. The F-22 Raptor

F-22 Raptor

The Lockheed Martin/Boeing F-22 Raptor is a single-seat, twin-engine fifth-generation supermaneuverable fighter aircraft that uses stealth technology. It was designed primarily as an air superiority fighter, but has additional capabilities that include ground attack, electronic warfare, and signals...

and F-35 Lightning II

F-35 Lightning II

The Lockheed Martin F-35 Lightning II is a family of single-seat, single-engine, fifth generation multirole fighters under development to perform ground attack, reconnaissance, and air defense missions with stealth capability...

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 materialRadar absorbent material

Radar-absorbent material, or RAM, is a class of materials used in stealth technology to disguise a vehicle or structure from radar detection. A material's absorbency at a given frequency of radar wave depends upon its composition...

(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 (a Salisbury screen

Salisbury screen

The Salisbury screen, invented by American engineer Winfield Salisbury in 1952, was one of the first concepts in radar absorbent material, later known as "stealth technology", used to prevent enemy radar detection of military vehicles. It was first applied to ship radar cross section reduction...

). 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

Ferrite (magnet)

Ferrites are chemical compounds consisting of ceramic materials with iron oxide as their principal component. Many of them are magnetic materials and they are used to make permanent magnets, ferrite cores for transformers, and in various other applications.Many ferrites are spinels with the...

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

Electrical resistance

The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

carbon

Carbon

Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

loading added to fiberglass

Fiberglass

Glass fiber is a material consisting of numerous extremely fine fibers of glass.Glassmakers throughout history have experimented with glass fibers, but mass manufacture of glass fiber was only made possible with the invention of finer machine tooling...

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

Aerogel

Aerogel is a synthetic porous material derived from a gel, in which the liquid component of the gel has been replaced with a gas. The result is a solid with extremely low density and thermal conductivity...

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 LeontovichMikhail Leontovich

Mikhail Alexandrovich Leontovich was a Soviet physicist, member of USSR Academy of Sciences, specializing in plasma and radiophysics....

impedance boundary condition (see also Electrical impedance

Electrical impedance

Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...

). 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

Boundary element method

The boundary element method is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations . It can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, and fracture...

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 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

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

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

Physical optics

In physics, physical optics, or wave optics, is the branch of optics which studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid...

to include the contributions from illuminated smooth surfaces and Fock

Fock

Fock can refer to:* Vladimir Fock , a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics** Fock space, an algebraic system used in quantum mechanics for a variable or unknown number of particles...

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. 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.

## 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.## External links

- Hip-pocket formulas for high-frequency RCS backscatter; useful reference sheet (PDF)
- Method to measure radar cross section parameters of antennas
- Puma-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