Radar cross section

thumb|300px|A normalized [[log–log plot of the radar cross section of a metallic sphere as a function of the radiation frequency. For cases in which the circumference of the sphere is less than three-fourths of the wavelength, the radar cross section is approximately proportional to ƒ4 (ƒ=the frequency of radiation). For cases in which the circumference of the sphere is greater than 20 wavelengths, the radar cross section is approximately the same as the physical cross section of the sphere. This plot is known as Mie scattering.]]

thumb|300px|A typical RCS diagram (using the [[A-26 Invader as the scattering object). The diagram is a polar plot of the RCS as a function of angle, with the image of the plane in the center helping to relate the angles in the diagram to physical features of the scattering object]]

Radar cross section (RCS), denoted σ, also called radar signature, is a measure of how detectable an object is by radar. 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 NRCS has units of area per area, or in MKS units.

Formulation

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 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 one term at a time:

:<math>P_r = \sigma A_\mathrm{eff}</math>

where

<math>P_t</math> = transmitter's input power (watts)
<math>G_t</math> = gain of the radar transmit antenna (dimensionless)
<math>r</math> = distance from the radar to the target (meters)
<math>\sigma</math> = radar cross section of the target (meters squared)
<math>A_\mathrm{eff}</math> = effective area of the radar receiving antenna (meters squared)
<math>P_r</math> = 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 <math display=inline>\sigma</math>, which has units of area (meters squared). Thus, the product

<math display=inline> \sigma</math>

has the dimensions of power (watts), and represents a hypothetical total power intercepted by the radar target. The second <math display=inline></math> term represents isotropic spreading of this intercepted power from the target back to the radar receiver. Thus, the product

<math display=inline> \sigma </math>

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 <math display=inline>A_\mathrm{eff}</math>, 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 as a correction factor that makes the radar equation "work out right" for the experimentally observed ratio of <math display=inline>P_r/P_t</math>. However, RCS 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 function of the orientation of the radar and target. A target's RCS depends on its size, reflectivity of its surface, and the directivity of the radar return 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 radomes. Even a very thin layer of metal can make an object strongly radar reflective. Chaff is often made from metallised plastic or glass (in a similar manner to metallised foils on food stuffs) with microscopically thin layers of metal.

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

Radar absorbent paint

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

Shape, directivity and orientation

The surfaces of the F-117A are designed to be flat and very angled. This has the effect that radar will be incident at a large angle (to the normal ray) that will then bounce off at a similarly high reflected angle; it is forward-scattered. The edges are sharp to prevent 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. 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 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.

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 (103 m length): 5000–100,000 m2
Container ship (212 m length): 10,000–80,000 m2

Calculation

Quantitatively, RCS is calculated in three-dimensions as Therefore, in order to cut the detection distance to one tenth, the RCS should be reduced by a factor of 10,000. While this degree of improvement is challenging, it is often possible when influencing platforms during the concept/design stage and using experts and advanced computer code simulations to implement the control options described below.

Purpose shaping

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

Purpose-shaping can be seen in the design of surface faceting on the F-117A Nighthawk stealth 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 stealth bomber benefited from increased computing power, enabling its contoured shapes and further reduction in RCS. The F-22 Raptor and F-35 Lightning II continue the trend in purpose shaping and promise to have even smaller monostatic RCS.

Redirecting scattered energy without shaping

This technique is relatively new compared to other techniques chiefly after the invention of metasurfaces. 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.

Bistatic RCS

For the bistatic radar configuration—transmitter and receiver separated (not co-located) -- the bistatic radar cross section (BRCS) is a function of both the transmitter-target orientation and the receiver-target orientation.

A normalized bistatic radar cross section (NBRCS) or bistatic normalized radar cross section (BNRCS) may also be defined, similar to the monostatic NRCS.

References

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 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
Radar Tutorial provides great visuals of RCS