Radar cross section

The radar cross-section , in some publications also called the reflecting surface or effective reflection surface and in English radar cross section ( RCS ), in some sources also called English equivalent echoing area , indicates how large the reflection of a radio wave ( radar ) by an object back into Direction of the source is. It specifies the size of an isotropically reflecting surface that delivers the same radar echo as the object.

The radar cross-section is an object-specific variable that has a significant influence on the probability of an object being detected by a radar device . It depends on the shape of the object, the properties of the material and the wavelength and the angle of incidence and emergence of the radiation. In the radar equation , the reflecting surface is designated with the Greek letter σ  (sigma), it has the unit of measurement square meter. A high radar cross-section is desirable, for example, for civil ships, buoys ( navigation marks ), bridge crossings or weather balloons in order to be able to locate them better, and is often achieved with radar reflectors additionally attached to the objectreached. A small radar cross-section, on the other hand, is desirable in military applications such as a military missile, for example, since an aircraft with a small radar cross-section is more difficult to detect for opposing radar systems than an aircraft of the same size with a larger radar cross-section. Stealth techniques are used to reduce the radar cross-section , the specifics of which are usually considered military secrets.

Reference value

Of the isotropic reference (spherical reflector), only a very small proportion of the surface can be effective in retroreflection. The majority is steered in directions that cannot be used by the radar device.

A spherical reflector with an ideally conductive surface is given as a reference, whose parallel projection onto a plane perpendicular to the direction of projection (figuratively its shadow on this plane) has an area of ​​one square meter. This circular area has a diameter of about 1.13 m. Of this reference reflector, however, only a very small area is effective as a reflector: there are only a few square centimeters exactly in the middle that can reflect the incoming transmission energy back in the direction of the radar device. All other surfaces of this sphere distribute the incoming energy in space in other directions, so they are not involved in the retroreflection. However, this reference has the advantage that it is direction-independent: it reflects equally well in all directions.

The radar cross-section is the ratio of the reflected power of this spherical reflector to the power that is reflected back to the radar device by an often irregularly shaped reflector to be examined. This power is proportional to the area of ​​the isotropic reflector, but not proportional to the geometric area of ​​the irregularly shaped reflector.

Since only a very small part of the area of ​​the reference is effective, the result often appears an area that is significantly larger than the geometric dimensions of the reflector to be examined. The often very large numerical values ​​of the reflecting surface of corner reflectors , depending on the size and structure, values ​​of the radar cross-section of over 10,000 m² are common, can also be given logarithmically as decibel value dBm² and refer to the reference value of 1 m².

Measurement

Diagram of the experimentally determined, angle-dependent, relative reflective surface of the Douglas B-26 bomber at 3 GHz

The measurement of the radar cross-section of an object is typically done with radar devices . It can be carried out in the open air or in a free field space that completely absorbs electromagnetic waves of the relevant frequency.

Typical values ​​for a centimeter wave radar

Radar cross section [m²]	object
≈00.000.00001	insect
≈00.000.0002	Aircraft with stealth technology using the Lockheed Martin F-22 as an example
≈00.000.01	bird
00.00<0.1	Aircraft with stealth technology
00.00≈0.1	Anti-aircraft missiles
≈00.001	human
≈00.002-3	Small fighter plane
≈00.005-6	Big fighter plane
00.<100	Transport plane
≈00.300-4,000	Coaster (55 m length)
≈05,000-100,000	Frigate (103 m length)
≈10,000-80,000	Container ship (212 m length)
≈20,000	Corner reflector with 1.5 m edge length

calculation

The reflecting area depends on many factors. An analytical determination of the reflective surface is only possible for simple bodies. It depends on the shape of the body and the wavelength or, better said, on the ratio of the structural dimensions of the body to the wavelength. In quantitative terms, the radar cross-section indicates an effective area that captures the incoming wave and radiates it isotropically into the room. These formulas only apply to the optical (frequency-independent) range, i.e. for objects whose dimensions are at least ten times larger than the wavelength. If the objects have approximately the dimensions of the wavelength of the radar beam, resonance phenomena occur, which significantly increase the radar cross-section. In three dimensions, the radar cross-section is defined as: ${\displaystyle \sigma }$

${\displaystyle \sigma =4\pi R^{2}{\frac {P_{\rm {s}}}{P_{\rm {i}}}}}$

Here, the power density on the radar target and the scattered power density at a distance from the radar target. ${\displaystyle P_{\rm {i}}}$ ${\displaystyle P_{\rm {s}}}$ ${\displaystyle R}$

Alternatively you can write:

${\displaystyle \sigma =4\pi R^{2}{\frac {|E_{\rm {s}}|^{2}}{|E_{\rm {i}}|^{2}}}}$

with - radiated field strength - scattered field strength ${\displaystyle E_{\rm {i}}}$ ${\displaystyle E_{\rm {s}}}$

If they are large compared to the wavelength λ, simple forms have the following theoretical radar cross-sections σ:

Sphere with radius r:

${\displaystyle \sigma =\pi \cdot r^{2}}$

Plate perpendicular to the beam direction (aligned plane mirror) with area A:

${\displaystyle \sigma ={\frac {4\pi \cdot A^{2}}{\lambda ^{2}}}}$

Corner reflector ( retroreflector ) made of three square surfaces with the side lengths a:

${\displaystyle \sigma ={\frac {12\pi \cdot a^{4}}{\lambda ^{2}}}}$

Instead of measurements, it is now common practice to calculate the radar cross-section using computer simulations. In the design phase of the development of military aircraft or other radar targets, it is possible to calculate the radar cross-section at relatively low cost and to optimize it accordingly.

Reduction of the radar cross-section

→ Main article : Stealth technology

Setup on a warship with a small radar cross section. The flat surfaces and outwardly directed corners, which have a small radar cross-section, are typical

Passive procedures

The reduction of the radar cross-section can in principle by

• the design
• the use of absorbent material ( ferrite or graphite particles bound in resin )
• permeable material (plastic materials)

be achieved.

The (low) reflection on dielectric materials can be additionally reduced by using suitable layer thicknesses of different types of material , analogous to optical methods such as antireflection layers , but the effect is dependent on the wavelength.

A military aircraft such as the Lockheed F-117 not only has a microwave-absorbing surface, but also a shape that prevents radar radiation from being reflected to the transmitter: one uses straight surfaces - the probability that they are perpendicular to the source is low. You avoid inside edges / corners and any metal parts on the outer skin. Particularly right-angled inner corners made of metal lead in a wide area to an almost complete reflection of the incoming radiation to the transmitter.

Active procedures

An active reduction of the radar cross section is based on destructive interference. The radar signal is received and transmitted again with almost the same amplitude, but with a phase shift of around 180 °. The amplifiers for this work with a very low gain in order to avoid self-excitation, so they only compensate for the antenna losses and turn the phase. This procedure is mainly used with VHF radar.

Increase in the radar cross-section

Corner reflectors for flight navigation with a large radar cross section

Passive procedures

I.a. In civil shipping, at civil and military ports and airports, on navigation signs and buoys, at bridge crossings and also on weather balloons, measures are used to increase the radar echo. The aim is to safely navigate, locate and coordinate the sea routes. For this purpose, corner reflectors are used, which enlarge the radar cross-section to many thousands of times its geometric area.

Objects made of metal generally have a higher radar echo than non-metals. Even relatively small metal parts can therefore cause an increase in the radar cross-section in order to, for. B. to make a boat with a plastic hull visible on the radar. Such small boats often carry small radar targets with dimensions in the centimeter range, those in the X-band (approx. 6… 12 GHz) or in the I-band (Europe, 8… 10 GHz) often used by radar systems as resonant secondary radiators deliver increased echo and only act as a corner reflector at shorter wavelengths due to their shape.

Active procedures

Radar reflectors are also available that work on the transponder principle or as repeater jammers. The radar signal is received and transmitted again amplified at the same frequency. These devices also offer the option of an acoustic signal tone for the crew to signal the detection by a radar device.

The time delay imposed on the radar echo by the reception and processing must only be a few microseconds in order not to display the target on the radar screen at an excessively incorrect distance. The received signal is analyzed and the response is retransmitted one pulse train period later.

literature

• Merill Ivan Skolnik, Radar Handbook ISBN 0-07-057908-3
• Merill Ivan Skolnik, Introduction to Radar Systems 2nd Edition, McGraw-Hill, Inc 1980, ISBN 0-07-288138-0

Individual evidence

1. ↑ Radar Cross Section Measurements (8-12 GHz) ... (English, PDF; 90 kB)
2. ↑ Ship RCS Table (PDF; 9 kB)
3. ^ Measuring Stealth Technology's Performance. Aviation Week, June 29, 2016, accessed July 1, 2016 . 
4. ↑ www.radartutorial.eu (Effective reflecting surface (RCS); eng.)
5. ^ M. Skolnik: Introduction to radar systems. 2nd Edition, McGraw-Hill, Inc., 1980, p. 44