Radar cross section prediction and reduction for naval ships

J. Marine Sci. Appl. (2012) 11: 191-199

DOI: 10.1007/s11804-012-1122-5

Radar Cross Section Prediction and Reduction for Naval Ships

Jawad Khan*, Wenyang Duan and Salma Sherbaz

College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China

Abstract: Radar cross section (RCS) is the measurement of the reflective strength of a target. Reducing the RCS of a naval ship enables its late detection, which is useful for capitalizing on elements of surprise and initiative. Thus, the RCS of a naval ship has become a very important design factor for achieving surprise, initiative, and survivability. Consequently, accurate RCS determination and RCS reduction are of extreme importance for a naval ship. The purpose of this paper is to provide an understanding of the theoretical background and engineering approach to deal with RCS prediction and reduction for naval ships. The importance of RCS, radar fundamentals, RCS basics, RCS prediction methods, and RCS reduction methods for naval ships is also discussed. Keywords: stealth ship; naval ship; radar cross section; RCS Article ID: 1671-9433(2012)02-0191-09

1 Introduction1 Naval warfare has always assigned great importance to knowing where enemy ships are stationed while hiding one’s own position. In the early days, ships could only be detected through visual means. Detection depended on operating conditions such as available light, fog, and rain. Ship characteristics such as size, shape, and color scheme also played an important role. The curvature of earth limited the visual horizon, making the height of a ship, decided by its mast, the primary design factor for detecting enemy ships. In the era of sailing ships, the first to detect the enemy would take the windward side to aid maneuverability and close in until the enemy was within range of his guns. The exhaust plume was the primary detection factor in the early era of engine propulsion. In this area, early detection was utilized to occupy a better tactical position for firing first. With the advent of radar, detection methodology and scope in naval warfare changed completely. Detection parameters, maximum detection range, and role were a few of the factors to change. Radar detects a target by clocking time taken by a known pulse of electromagnetic energy to travel to the target and back. This energy travels in the form of electromagnetic waves. Electromagnetic wave laws were established by the year 1900 as a result of the efforts of researchers such as Hertz, Faraday, Ampere, Coulomb, and Maxwell. However, major developments were also seen in late 1930s after the invention of the cavity magnetron for transmitting high power electromagnetic waves at high frequencies (Knott et al., 2004;

Received date: 2011-02-13. Foundation item: Supported by Program for New Century Excellent Talents in University under Grant No.NCET-07-0230 and the “111” Project under Grant No.B07019 at Harbin Engineering University. *Corresponding author Email: [email protected]

© Harbin Engineering University and Springer-Verlag Berlin Heidelberg 2012

Kouemou, 2009). Since its invention, radar has influenced naval warfare enormously. Radar is extensively used on naval platforms during detection, tracking, classification, and engagement cycles (Skolnik, 2008; Kingsley and Quegan, 1999). Radar cross section (RCS) is the measurement of the reflective strength of a target, meaning that it decides how early a target can be detected. Reducing the RCS of a naval ship implies its late detection, which is key to surprise and initiative. The RCS of a naval ship is also important since most modern weapons have installed radar for use during the final engagement phase. This is because a naval ship with a lower RCS would not only be detected later but also would survive better in a hostile environment (Kolawole, 2002; Jenn, 2005). Thus, the RCS of a naval ship has transformed into a very important design factor for stealth to achieve surprise, initiative, and survivability. Consequently, accurate RCS determination and RCS reduction are matters of extreme importance for naval ships. RCS is determined by solving Maxwell’s equations. Exact methods are used for simple bodies (Crispin and Maffett, 1965). Exact methods are integral equation formulations, also called methods of moments (MOM), and differential equation formulations. High frequency methods are used for large complex bodies such as naval ships (Crispin and Maffett, 1965; Youssef, 1989). Several high frequency methods have been developed; commonly used models include geometric optics, physical optics, geometrical theories of diffraction, and physical theories of diffraction (Knott, 1985). Computer software is the method of choice for radar cross section prediction and evaluating design variations to reduce the RCS (Andersh et al., 2000; Jernejcic et al., 1994; Bhalla and Ling, 1995). Modern RCS software uses a combination of high

Jawad Khan, et al. Radar Cross Section Prediction and Reduction for Naval Ship

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frequency methods to determine the RCS of a naval ship. RCS reduction methods include passive cancellation (impedance loading), active cancellation (active loading), radar absorbing materials (RAMs), and shaping (Hirasawa, 1987; Suttie, 1992). Two practically used RCS reduction methods on naval ships at present are shaping and radar absorbing materials. This paper will provide an understanding of current RCS prediction and reduction methods for naval ships. The importance of RCS, radar fundamentals, RCS basics, RCS prediction methods, and RCS reduction methods will then be discussed. The focus will be on the theoretical background and engineering approach in order to deal with RCS prediction and RCS reduction for naval ships. 2 Radar fundamentals Radar is an acronym which stands for “radio detection and ranging.” Radar was developed to replace visual target detection for several reasons. Radar can detect a target from a much farther distance than visual instruments. Radar also works well at night with little or no ambient light to illuminate the target. Modern radar is capable of detecting, tracking, classifying, and engaging targets.

Fig.1 Sketch map of radar

Radar clocks the time taken by a known pulse of energy to travel to a target and back. It uses the following equation to determine the distance between the radar and target.

2

ctR = (1)

where R is the distance (range) between the radar and target, c the speed of light, and t the time to and from the target. The basic radar equation is defined as follows:

2 24π 4πt t

r e

PGP A

R R

σ= × × (2)

where Pr is the returned power, Pt the transmitted power, Gt the transmitter antenna gain, R the range between radar and target, σ the RCS of the target, and Ae = aperture of receiver antenna

The radar range equation (RRE) represents important factors that affect the detection range. RRE is defined as follows:

2 2

4max 3

min(4 )t tPG

RP

=π

λ σ (3)

where R is the range between radar and target, Pt the transmitted power, Gt the transmitter antenna gain, λ the wave length , σ the RCS of the target, and Pmin the minimum received signal. The RRE implies that the detection range is a function of the RCS( σ ) of the target.

4maxR α σ

3 RCS basics The RCS is the measure of the reflective strength of a target. The RCS of a target is defined as the projected area of a metal sphere that would scatter the same power in the same direction as the target. The RCS is formally defined as 4 π times the ratio of the power per unit solid angle scattered in a specified direction to the power per unit area in a plane wave incident on the scatterer from a specified direction.

2scatt

22inc

lim4R

ER

Eσ

→∞= π (4)

where σ is the RCS of the target, R the range between radar and target, Escat the scattered electric field, and Einc the incident electric field. The RCS of a naval ship is a very important design factor for achieving surprise, initiative, and survivability.

4 Important scattering mechanisms on naval ships

It is important to understand scattering mechanisms on a naval ship for accurate RCS determination and effective RCS reduction. These mechanisms provide basic understanding of the underlying physical process of scattering. Some scattering mechanisms are dominant compared to others. Scattering also depends on the target aspect angle. Multiple bounce mechanisms are very important on naval ships due to large portions of the structure above the waterline with multiple components. Free space between parts of a single component also causes multiple bounce mechanisms. Multiple bounce mechanisms depend on geometry and general arrangements above the waterline.

Journal of Marine Science and Application (2012) 11: 191-199

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Exact Methods

A = Single reflection B = Double reflection C = Triple reflection D = Edge diffraction

Fig.2 Important scattering mechanisms on naval ships

Multiple bounce mechanisms also occur from interactions with the water surface. The presence of the water surface creates complexities. This problem is tackled by including the water surface in RCS analysis and assigning dielectric properties to the water surface. The RCS of a platform is enhanced in turbulence motion in waves in the case of a naval ship (Fremouw and Ishimaru, 1992). Research on this aspect is underway for stealth aircraft RCS applications; however, this aspect has not been adequately explored for naval ships.

5 Radar cross section prediction techniques In practical situations, three methods are used to determine the RCS of a complex object such as a naval ship.

a) Full scale measurements; b) Scale measurements; c) Computational prediction techniques. For complex objects such as naval ships, full scale measurements are considered to be the most accurate since data is taken in an environment which most closely resembles an operational theatre (Dybdal, 1987; Schetne and Mount 1965; Wong et al., 2006). The limitations of this method are the use of costly resources, necessitating the ship to be at sea, and the inability to differentiate between the RCS characteristics of individual parts of the ship. Furthermore, a limited amount of latitude is available to make changes to reduce the RCS since very little can be changed at this stage.

Scale measurements consist of fabricating accurate representations of the object under investigation and determining the RCS using high frequency emitters (Nicolaescu and Oroian, 2001; Jansen et al., 2009). This method allows for very accurate determination of scattering centers. In the case of a naval ship, fabrication of a reliable model of brass or a material suitable for RCS analysis is expensive. The model is also not very flexible for evaluating the impact of changes in the structure above the waterline for reducing the RCS.

Finally, the RCS of an object can be determined using computational prediction techniques.

6 Computational prediction techniques Scattering objects are sorted into three regions based on their body size with respect to wavelength. These regions are

• Rayleigh region: typical body size < λ • Resonance region: λ <typical body size<3 λ • Optics region: 3 λ <typical body size →High Frequency

Methods The effectiveness of computational methods depends on the position of the target with a particular size. The exact methods are restricted to relatively simple and small objects in Rayleigh and Resonance regions. High frequency methods are used for complex objects in the optics region, which is also called the high frequency region. 6.1 Exact methods The RCS is determined by solving Maxwell’s equations. Maxwell’s four differential equations constitute a succinct statement of the relationship between the electric and magnetic fields produced by current and charges and by each other.

d dD S v qρ⋅ = = (5)

d dE l B St t

φ∂ ∂⋅ = − ⋅ = −∂ ∂ (6)

d ( )dD

H l J St

∂⋅ = +∂ (7)

d 0B S⋅ = (8)

By definition, the solution to Maxwell's equations includes all modes of scattering: specular, end region, diffraction, surface traveling, creeping and edge waves, shadowing, and multiple bounce (Knott et al., 2004; Skolnik, 2008). The exact methods are based on either integral or differential forms of Maxwell’s equations. The integral equation formulation technique, also called method of moments (MOM), reduces Maxwell’s equations to a pair of integral equations (also known as Stratton-Chu equations). Integral equations are then converted to a collection of homogenous linear equations that can be solved by matrix techniques (Yuceer et al., 2005; Wang and Ling, 1999; Wu, 1989). Method of moments has been the favored approach for scattering bodies in the resonance region where high frequency methods fail to predict surface travelling wave effects (Skolnik, 2008). The differential equation approach solves Maxwell's equations in a differential form over a spatial grid enveloping the body (Taflove and Umashankar, 1983;


194

Taflove and Umashankar, 1989). The differential equation approach is best suited for cavity problems and those with volume distributions of variable material properties such as permeability and permittivity (Knott et al., 2004; Skolnik, 2008). Although the size and complexity of most scattering objects prohibit the application of exact methods for RCS prediction, exact solutions for simple objects provide valuable checks for approximate methods. It is useful to understand exact methods for effective application of high frequency methods. 6.1.1 Limitations of exact methods Exact methods are not applied in high frequency regions for following reasons:

a. Exact methods require immense computational power. As a result, exact methods are restricted to small objects to validate the high frequency software and new techniques.

b. High frequency approximations are usually sufficient and much simpler to implement. The numerical computations in exact methods often lead to a large amount of useless computation of body-body interactions, most of which are not significant to the scattering process (Knott et al., 2004; Skolnik, 2008).

c. Exact solutions include all the scattering mechanisms. However, they do not by nature aid in understanding the physical phenomenon of scattering. The notions of specular, end region, edge diffraction, surface waves, shadowing, and multiple bounce do not emerge from the numerical solutions. In order to better understand the physical phenomenon of scattering, solutions are used to describe surface currents, near electric fields and most importantly form images. It is only then that one can understand the underlying physical processes by which an incident wave scatters from various geometries (Skolnik, 2008).

During the past decade, computational capabilities have been enormously enhanced with parallel processing. Before blindly using this capability, it should be noted that simple high frequency approximations are usually adequate. There is a need to find a middle ground formulation, one that includes the essential interaction physics of scattering yet does not require the detailed interactions needed for the numerical solutions of Maxwell's equations (Skolnik, 2008). 6.2 High frequency methods Several high frequency methods, also called approximate methods, have been devised for the optics region, each with its particular advantages and limitations. The foundation of high frequency theories is that the target elements scatter the incident wave independently of one another. This makes it possible to assemble a collection of relatively simple shapes, such as flat plates, cylinders, and spheroids to model a complicated target. The analytical high frequency formulas

are relatively easy to derive for specific geometries, and individual contributions are methodically added to obtain the total RCS of a large complex target (Duan et al., 1991; De Leeneer et al., 1994). The high frequency region is of great practical importance for typical threat radars and targets. For radar frequencies of 1 GHz and above, most targets of practical interest meet body size requirement for high frequency methods. The body size requirement actually applies to individual scattering features and not the overall target length. Even so, target features on naval ships are within the high frequency scattering region, and these methods can be used (Northam, 1985). 6.2.1 Geometric optics Geometric optics (GO) is derived from principles of classical optics. The behavior of the wave incident on a surface is described by Snell’s law which covers both the phenomenon of reflection and of refraction (Pinel et al., 2010). When the incident waves are planar and the direction of interest is back towards the radar, the formula for geometric optics RCS is

1 2a a= πσ (9)

where a1 and a2 are the radii of curvature.

Fig.3 GO RCS, Radii of curvature (Skolnik, 2008)

Geometric optics is limited to surfaces whose radii of curvature are large compared to wavelength. Geometric optics fails when one or both radii of curvature are infinite, as is the case for flat and singly curved surfaces. In addition, it requires that the specular point not be close to the edges of the surface since no provision is made to account for diffraction. 6.2.2 Physical optics Physical optics is derived from Maxwell’s equations (Tan and Qi, 1999; Rius and Vall-Llossera, 1991; Fang et al., 2008). The starting point is Stratton-Chu integral equations, which are obtained by transforming Maxwell’s equations into a pair of integral equations.

0{i ( ) ( ) ( ) }dsE kZ SΨ Ψ + Ψ= × + × × ∇ ⋅ ∇ n H n E n E (10)

0{ i ( ) ( ) ( ) } dsH kY SΨ + Ψ Ψ= − × × ×∇ + ⋅ ∇ + n E n H n H (11)


195

where ES and HS are the scattered electric and magnetic fields, E and H the total electric and magnetic field, k the radian frequency, ZO and YO the permeability, n the unit surface normal erected to the surface patch dS Green’s Function Ψ is

ie

4

kr

r=

πΨ

where r is the distance from the surface patch dS to the radar. The theory is based on two approximations. The first is far-field approximation, which requires that the range be large compared to any dimension of the object. The Green’s function becomes

0ik s∇ =Ψ Ψ

i-i 0

0

e e

4

kRkr s

R

× ×=π

Ψ

where s is the position vector, r the unit vector, and RO the distance from origin to radar. The second approximation is tangent plane approximation. If the surface is a good conductor, the total tangential electric field is virtually zero and the total tangential magnetic field is twice the amplitude of the incident tangential magnetic field. The tangent plane approximation results are

n × E = 0 n × H = 2n × Hi for illuminated surfaces n × H = 0 for shaded surfaces

By evaluating these integrals and integrating the approximations, the physical optics RCS formula for a rectangular plate is

2cos sin( sin )

4( sin )

A kl

kl= π ⋅θ θσ

λ θ (12)

where A is the Area of the plate, θ the Angle between the surface normal and radar direction, and l the Length of the plate in the plane containing the surface normal and radar line of sight. The physical optics RCS formula for a circular disk is

2

1cos sin( sin )16

( sin )

A J kd

kd= π ⋅θ θσ

λ θ (13)

where A is the Area of the disk, d the Diameter, and J1(x) the Bessel function of the first kind of order 1 Physical optics RCS results are available for a variety of simple shapes (Blume and Kahl, 1987; Borzi, 2004). The individual contributions from simple shapes are

methodically added to obtain the total RCS of a large complex target. Physical optics is limited in that it also does not account for edge diffraction, so accuracy of results decreases as the specular point moves closer to the edge. 6.2.3 Geometrical theory of diffraction Keller proposed the geometrical theory of diffraction (GTD) which accounts for diffraction effects from edge and surface discontinuities, not included in both geometric optics and physical optics. GTD assigns a phase and magnitude to the fields diffracted from edge and surface discontinuities using a Keller cone. Keller suggests that when a ray is incident to an edge, the result is a multitude of diffracted rays as shown in Fig.4.

Fig.4 Keller cone of diffracted rays (Skolnik, 2008) The limitation of the geometrical theory of diffraction is that it fails in the transition regions of the shadow and reflection boundaries. This limitation is addressed by the uniform theory of diffraction (UTD), also known as the uniform asymptotic theory. UTD multiplies the singularities in diffraction coefficients by a Fresnel integral that drops to zero as the diffraction coefficients rise to infinity. The product remains finite and exhibits proper change in sign from one side of a shadow or reflection boundary to the other (Skolnik, 2008). GTD also suffers the shortcoming of giving infinite results at caustics, an example of which is the important case of scattering along the axis of a ring discontinuity (Knott et al., 2004; Skolnik, 2008). The method of equivalent currents (MEC) addresses the caustic limitations of GTD. The basis for this method is the fact that any finite current distribution yields a finite result for the far field when that distribution is summed in a radiation integral. The challenge comes from determining suitable expressions for current distribution. Ryan, Peters, Knott, and Senior derived expressions for current distributions. Michaeli's current distributions are more complete and more rigorously derived (Knott et al., 2004; Skolnik, 2008). MEC offers two improvements: the edge diffracted fields remain finite in caustic directions and the scattering direction is no longer limited to the Keller cone.


196

6.2.4 Physical theory of diffraction Ufimtsev developed a physical theory of diffraction (PTD) to improve previous methods by addressing the singularity in diffraction coefficients faced in the geometrical theory of diffraction. This method seeks to determine the diffraction coefficients at the edge, but considers the coefficients as originating from two separate sources. By subtracting the coefficients of the surface from the total field, the diffraction coefficients are thus those of the edge itself. This added characteristic increases computational requirements.

Fig.5 Geometry of wedge diffraction (Skolnik, 2008)

The downside of PTD is that it is limited to directions lying on the Keller cone. This limitation is addressed by Mitzner's incremental length diffraction coefficient (ILDC) method. Mitzner devised a set of diffraction coefficients for arbitrary directions of incidence and scattering. He expressed his results as diffracted electric field components in terms of incident electric field components. The diffraction coefficients are expressed as three separate pairs representing parallel-parallel, perpendicular-perpendicular, and parallel-perpendicular contributions. One member of each pair is due to the total surface current on the diffraction edge (including the assumed filamentary edge currents), and the other is due to the uniform physical optics currents. Mitzner subtracted one member of each pair from the other, thus retaining the contributions from the filamentary currents alone (Knott et al., 2004; Skolnik, 2008). 6.3 Surface travelling wave Surface traveling waves are induced on long surfaces when the incident electric field has components perpendicular and parallel to the surface in the plane containing the surface normal and the direction of incidence. None of the four high frequency methods adequately include the surface traveling wave contributions. However, repeated application of the diffraction theories to account for multiple interactions between edges offers some promise of modeling the surface traveling wave effects (Knott et al., 2004; Skolnik, 2008). 6.4 Empirical formula for RCS of a naval ship The empirical formula for the RCS of a warship is

3/21/252 f D=σ (14)

where f is the radar frequency in megahertz and D is the full-load displacement of in kilotons. The relationship is based on measurements of several ships at low grazing angles and represents the average of the median RCS in port and starboard, bow and quarter aspects, excluding the broadside peaks. The statistics include data collected at the nominal wavelengths of 3.25, 10.7, and 23 cm for ship displacements ranging from 2 to 17 kilotons (Skolnik, 2008). 6.5 Warship RCS through computer software Computer software is widely used to make calculations in all fields of engineering due to immense computational power and ease of graphical interfacing. Computer software based on low frequency methods or high frequency methods is available. Low frequency software is used for small objects to validate high frequency software and new techniques. High frequency software is used for RCS analysis of complex objects such as naval ships. The process consists of RCS prediction and evaluating design variations to reduce the RCS on naval ships in the same way as other military platforms (Castelloe and Munson, 1997; Broek et al., 2005; Leong and Wilson, 2006). Modern high frequency RCS software uses a combination of high frequency methods to determine the RCS of a naval ship (Moore et al., 2005; Sundararajan and Niamat, 2001; Kadrovach et al., 1996; Lee et al., 2005). The most common method is to use physical optics along with one or more methods to account for different scattering mechanisms. The effectiveness of the software depends on the choice of methods used to account for different scattering mechanisms (Hastriter and Weng, 2004; Mametsa et al., 2009; Hughes and Leyland, 2000; Coburn et al., 2004; Borden, 2001), and computational time. However, computational time is a lesser concern with availability of high power computers and parallel processing.

7 Radar cross section reduction techniques The following four methods are available for reducing the RCS.

a) Passive cancellation; b) Active cancellation; c) Radar absorbing materials (RAMs); d) Shaping.

Practically used RCS reduction methods on present-day naval ships are shaping and radar absorbing materials. In current stealth designs, shaping techniques are first applied to create a design shape with low RCS in primary threat sectors. Radar absorbing materials are then applied to treat the remaining problem areas whose shape could not be optimized to reduce the RCS (Peixoto et al., 2005). 7.1 Passive cancellation Passive cancellation, also known as impedance loading, proposes introducing an echo source whose amplitude and


197

phase can be adjusted to cancel another echo source (Schindler et al., 1965; Lin and Chen, 1968). This can be achieved for simple objects, provided that a loading point can be identified on the body (Chen, 1968; Yu and Liang, 1971). Subsequently, a port is designed in the body with the size and shape of the interior cavity to present optimum impedance at the aperture. However, it is difficult to generate the required frequency dependence for this built-in impedance, and the reduction obtained for one frequency disappears as the frequency changes. This technique is generally used to control the RCS of antennas (Champagne et al., 1992; Popovic, 1971). The large and complex geometry of a naval ship results in hundreds of reflecting sources, it is not practical to devise a passive cancellation treatment for each of these sources. In addition, the cancellation can revert to reinforcement with a change in frequency or viewing angle. As a result, passive cancellation is generally discarded as a practical RCS reduction technique for naval ships. 7.2 Active cancellation Active cancellation, also known as active loading, suggests that the target must emit radiation in time coincidence with the incoming pulse whose amplitude and phase cancel the reflected energy. This implies that the target must be smart enough to sense the angle of arrival, intensity, frequency, and waveform of the incident wave. It must also be fast enough to know its own echo characteristics for that particular wave to rapidly generate the proper wave. Such a system must also be versatile enough to adjust and radiate the proper wave with a change in frequency. The relative difficulty of active cancellation increases with an increase in frequency (Knott et al., 2004; Skolnik, 2008). Active cancellation can only be considered for reducing the RCS at low frequencies where radar absorbing materials and shaping are not very effective, so research on this technique is likely to continue (Xiang et al., 2010). However, this technique is not practical for implementation on naval ships with the existing technologies. 7.3 Radar absorbing materials Radar absorbing materials (RAMs) reduce the energy reflected back to the radar by means of absorption, converting electromagnetic energy into heat. It is customary to gather the effects of all loss mechanisms into permittivity and permeability of the material because the designer is usually interested in the cumulative effect (Wang et al., 2004; Strifors and Gaunaurd, 1998; Swarner and Peters, 1963; Rezende et al., 2001). Specifically, the RAM characteristics depend on its dielectric properties (material permittivity) and its magnetic properties (material permeability). Therefore, RAM can be classified into two broad categories, either dielectric or magnetic absorbers. The foundation of RAMs is the fact that substances either exist or can be fabricated whose indices of refraction are complex numbers. In the index of refraction, an imaginary

part accounts for both electrical and magnetic losses. Dielectric radar absorbers are used for experimental and diagnostic work such as indoor microwave anechoic chambers. However, these absorbers are not flexible for applications on operational platforms due to their bulky and fragile nature. Instead, magnetic absorbers are used on operational systems. The basic ingredients of magnetic absorbers are compounds of iron, such as carbonyl iron and ferrites. Magnetic absorbers offer the advantage of compactness since they are typically a fraction of the thickness of dielectric absorbers. However, magnetic absorbers are inherently more narrowband than their dielectric counterparts. The basic absorbing material is usually embedded in a matrix or binder such that the composite structure has the appropriate electromagnetic characteristics for a given range of frequencies. 7.4 Shaping Shaping is the most suitable and extensively used technique for reducing the RCS. The concept of shaping is to orient the target surfaces and edges to deflect the scattered energy in directions away from the radar. It is accomplished by maximizing scattering into directions of space where threat receivers are not present (Knott et al., 2004; Skolnik, 2008; Jenn, 2005). In past, shaping techniques have been successfully applied on military platforms such as stealth aircraft, tanks, and trucks. The aspect of shaping is very complex in case of a naval ship due to complicated geometry and dominant multiple bounce mechanisms. Shaping is implemented by simultaneously manipulating the geometry above the waterline and general arrangements to reduce the RCS. It is evident that both aspects of geometry and general arrangements have limitations while being manipulated for reducing the RCS. However, shaping clearly has more potential on ships compared with aircrafts due to presence of dominant multiple bounce scattering effects.

8 Conclusions Radar is the basic instrument used to detect targets today. The RCS of a platform defines its ability to reflect radar electromagnetic energy. Thus the RCS is important design factor to achieve surprise, initiative and survivability. The RCS can be determined by full scale measurements, scale measurements, and computational prediction techniques. Computational prediction techniques are better suited due to reasons of flexibility and economics. Computer software is the method of choice for RCS prediction and exploring design variations to reduce the RCS. This software uses a combination of high frequency computational methods to calculate the RCS. The most common approach is to use physical optics along with one or more methods to account for different scattering mechanisms. Practical RCS reduction methods for naval ships are shaping and radar


198

absorbing materials. Shaping is very important in warships since significant advantages can be obtained by manipulating the geometry above the waterline and the general arrangements. The appropriate approach is to design the structures above the waterline with minimum echo through shaping, and then apply radar absorbing materials to remaining problem areas.

References

Andersh D, Moore J, Kosanovich S, Kapp D, Bhalla R, Kipp R, Courtney T, Nolan A, German F, Cook J, Hughes J (2000). Xpatch 4: The next generation in high frequency electromagnetic modeling and simulation software. IEEE International Radar Conference, Virginia, USA, 844-849.

Bhalla R. Ling H (1995). 3D Scattering Center Extraction from XPATCH. Antennas and Propagation Society International Symposium, AP-S Digest, Albuquerque, USA, 4, 1906-1909.

Blume S, Kahl G (1987). The physical optics radar cross section of an elliptic cone. IEEE Transactions on Antennas and Propagation, 35(4), 457- 460.

Borden B (2001). Mathematical Problems in Radar Inverse Scattering. Institute of Physics Publishing, IOP Science, R1-R28.

Borzi G (2004). Trigonometric approximations for the computation of Radar cross sections. IEEE Transactions on Antennas and Propagation, 52(6), 1596-1602.

Broek BVD, Bieker T, Ewijk LV (2005). Comparison of Modelled to Measured High-Resolution ISAR Data. Netherlands Organization for Applied Scientific Research, Netherlands, TNO Report No. RTO-MP-SET-096.

Castelloe MW, Munson DC Jr. (1997). 3-D SAR imaging via high-resolution spectral estimation methods: experiments with XPATCH. International Conference on Image Processing, Washington DC, USA, 1, 853-856.

Champagne NJ II, Williams JT, Sharpe RM, Hwu SU, Wilton DR (1992). Numerical modeling of impedance loaded multi-arm Archimedean spiral antennas. IEEE Transactions on Antennas and Propagation, 40(1), 102-108.

Chen CL (1968). Modification of the back-scattering cross-section of a long metal wire by impedance loading. Antennas and Propagation Society International Symposium, AP-S Digest, 6, Boston, USA, 184- 191.

Coburn W, Le C, Spurgeon W (2004). Potential discrepancies in radar signature predictions for ground vehicles. Users Group Conference, Virginia, USA, 45- 51.

Crispin JW Jr., Maffett AL (1965). Radar cross section estimation for simple shapes. Proceedings of the IEEE, 53(8), 833- 848.

De Leeneer I, Schweicher E, Barel A (1994). Analysis of the diffracting centers of a complex 3-dimensional structure. Antennas and Propagation Society International Symposium, AP-S Digest, Seattle, USA, 3, 2322-2324.

Duan DW, Rahmat-Samii Y, Mahon JP (1991). Scattering from a circular disk: a comparative study of PTD and GTD techniques. Proceedings of the IEEE, 79(10), 1472-1480.

Dybdal RB (1987). Radar Cross Section Measurements. Proceedings of the IEEE, 75(45), 498-516.

Fang CH, Zhao XN, Liu Q (2008). An Improved Physical Optics Method for the Computation of Radar Cross Section of Electrically Large Objects. Asia-Pacific Symposium on Electromagnetic Compatibility & 19th International Zurich

Symposium on Electromagnetic Compatibility, Singapore, 722-725.

Fremouw EJ, Ishimaru A (1992). Enhanced radar cross sections due to multiple scattering in turbulence. Antennas and Propagation Society International Symposium, AP-S Digest,. Chicago, USA, 3, 18-25.

Hastriter ML, Weng CC (2004). Comparing Xpatch, FISC, and ScaleME using a cone-cylinder. Antennas and Propagation Society International Symposium, Monterey, USA, 2, 2007- 2010.

Hirasawa K (1987). Reduction of radar cross section by multiple passive impedance loadings. IEEE Journal of Oceanic Engineering, 12(2), 453-457.

Hughes EJ, Leyland M (2000). Using multiple genetic algorithms to generate radar point-scatterer models. IEEE Transactions on Evolutionary Computation, 4(2), 147-163.

Jansen C Krumbholz N, Geise R, Enders A, Koch M (2009). Scaled radar cross section measurements with terahertz-spectroscopy up to 800 GHz. European Conference on Antennas and Propagation, Berlin, Germany, 3645-3648.

Jenn DC (2005). Radar and Laser Cross Section Engineering. American Institute Aeronautics and Astronautics, Reston, VA, USA, 1-96 and 257-388.

Jernejcic RO, Terzuoli AJ Jr., Schindel RF (1994). Electromagnetic backscatter predictions using XPATCH. Antennas and Propagation Society International Symposium, AP-S Digest, Seattle, USA, 1, 602-605.

Kadrovach BA, Wailes TS, Terzuoli AJ, Gelosh DS (1996). Codesign model for Xpatchf optimization. Antennas and Propagation Society International Symposium, AP-S Digest, Baltimore, USA, 3, 1882-1885.

Kingsley S, Quegan S (1999). Understanding Radar Systems. SciTech Publishing, Mendham, NJ, USA, 1-24.

Knott EF (1985). A progression of high-frequency RCS prediction techniques. Proceedings of the IEEE, 73(2), 252- 264.

Knott EF, Shaeffer JF, Tuley MT (2004). Radar Cross Section, Second Edition. SciTech Publishing, Raleigh, NC, USA, 1-21 and 115-223.

Kolawole MO (2002). Radar Systems, Peak Detection and Tracking. Newnes Publishing, Burlington, MA, USA, 37-54.

Kouemou G (2009). Radar Technology. In-Tech Publishing, Vukovar, Croatia, 1-61.

Lee SW, Ling H, Lu C, Moore J (2005). CrossFlux: a method for hybridizing Xpatch and other codes. Antennas and Propagation Society International Symposium, Washington DC, USA, 1A, 2-5.

Leong H, Wilson H (2006). An estimation and verification of vessel radar cross sections for high-frequency surface-wave radar. IEEE Antennas and Propagation Magazine, 48(2), 11- 16.

Lin JL, Chen KM (1968). Minimization of backscattering of a loop by impedance loading - Theory and experiment. IEEE Transactions on Antennas and Propagation, 16(3), 299- 304.

Mametsa HJ, Berges A, Douchin N (2009). Improving RCS and ISAR image prediction of terrestrial targets using random surface texture. International Radar Conference - Surveillance for a Safer World, Ordeaux, France, 1-5.

Moore JT, Yaghjian AD, Shore RA (2005). Shadow boundary and truncated wedge ILDCs in Xpatch. Antennas and Propagation Society International Symposium, Washington DC, USA, 1A, 10- 13.


199

Nicolaescu L, Oroian T (2001). Radar cross section. International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Service, Yugoslavia, 1, 65-68.

Northam DY (1985). Modeling of Electromagnetic Scattering from Ships. Advanced Techniques Branch Tactical Electronic Warfare Division Report, NRL Report 8887, Washington, D.C. USA.

Peixoto GG, De Paula AL, Andrade LA, Lopes CMA, Rezende M C (2005). Radar absorbing material (RAM) and shaping on radar cross section reduction of dihedral corners. International Conference on Microwave and Optoelectronics, Brasilia, Brazil, 460- 463.

Pinel N, Johnson JT, Bourlier C (2010). Extension of the geometric optics approximation to the scattering from rough layers. URSI International Symposium on Electromagnetic Theory, Berlin, Germany, 482-485.

Popovic BD (1971). Erratum: Theory of cylindrical antennas with arbitrary impedance loading. Proceedings of the IEEE, 119(2), 1327-1332.

Rezende MC, Martin IM, Miacci MAS, Nohara EL (2001). Radar cross section measurements (8-12 GHz) of flat plates painted with microwave absorbing materials. International Microwave and Optoelectronics Conference, Belem, Brazil, 263-267.

Rius JM, Vall-Llossera M (1991). High frequency radar cross section of complex objects in real time. Antennas and Propagation Society International Symposium, AP-S Digest, W. Ontario, Canada, 1062-1065.

Schetne KH, Mount WV (1965). Full-scale bistatic radar cross-section measurement method. Proceedings of the IEEE, 53(8), 1083- 1084.

Schindler JK, Mack RB and Blacksmith P Jr. (1965). The control of electromagnetic scattering by impedance loading. Proceedings of the IEEE, 53(8), 993-1004.

Skolnik MI (2008). Radar Handbook, Third Edition. McGraw-Hill Companies, New York, USA, 1.1-1.24 and 14.1-14.46.

Strifors HC, Gaunaurd GC (1998). Scattering of electromagnetic pulses by simple-shaped targets with radar cross section modified by a dielectric coating. IEEE Transactions on Antennas and Propagation, 46(9), 1252-1262.

Sundararajan P, Niamat MY (2001). FPGA implementation of the ray tracing algorithm used in the XPATCH software. IEEE Midwest Symposium on Circuits and Systems, Ohio , USA, Vol.1, 446-449.Suttie WK (1992).

The application of radar absorbing materials to armoured fighting vehicles. IEE Colloquium on Low Profile Absorbers and Scatterers, 6/1-6/4.

Swarner W, Peters L Jr. (1963). Radar cross sections of dielectric or plasma coated conducting spheres and circular cylinders. IEEE Transactions on Antennas and Propagation, 11(5), 558- 569.

Taflove A, Umashankar K (1983). Radar cross section of general three-dimensional scatterers. IEEE Transactions on Electromagnetic Compatibility, 25(4), 433-440.

Taflove A, Umashankar KR (1989). Review of FD-TD numerical modeling of electromagnetic wave scattering and radar cross section. Proceedings of the IEEE, 77(5), 682-699.

Tan Y, Qi LF (1999). Computation of the high-frequency RCS using a parametric geometry. International Conference on Computational Electromagnetics and Its Applications, Beijing, China, 486- 489.

Wang P, Zhou L, Tan YH, Xia MY (2004). Analysis of impacts of various RAM on RCS of 3-D complex targets using the FEM-FMA [radar absorbing materials]. International

Conference on Computational Electromagnetics and its Applications, Beijing, China, 130- 133.

Wang YX, Ling H (1999). Radar signature prediction using moment method codes via a frequency extrapolation technique. IEEE Transactions on Antennas and Propagation, 47(6), 1008-1015.

Wong SK, Riseborough E, Duff G, Chan KK (2006). Radar cross-section measurements of a full-scale aircraft duct/engine structure. IEEE Transactions on Antennas and Propagation, 54(8) 2436-2441.

Wu TK (1989). Radar cross section of arbitrarily shaped bodies of revolution. Proceedings of the IEEE, 77(5), 735-740.

Xiang YC, Qu CW, Su F, Yang MJ (2010). Active cancellation stealth analysis of warship for LFM radar. IEEE 10th International Conference on Signal Processing, Beijing, China, 2109-2112.

Youssef NN (1989). Radar cross section of Complex targets. Proceedings of the IEEE, 77(5), 722 - 734.

Yuceer M., Mautz JR, Arvas E (2005). Method of moments solution for the radar cross section of a chiral body of revolution. IEEE Transactions on Antennas and Propagation, 53(3), 1163-1167.

Yu IP, Liang S (1971). Modification of scattered field of long wire by multiple impedance loading. IEEE Transactions on Antennas and Propagation, 19(4), 554- 557.

Jawad Khan was born in 1984. He is a student at the College of Shipbuilding Engineering, Harbin Engineering University. His current research interests include stealth ships, high speed naval vessels, CFD, green ship, renewable energy, and advanced materials.

Wenyang Duan was born in 1967. He is a professor and a PhD supervisor at Harbin Engineering University. His current research interests include wave-body interactions, especially in Marine Hydrodynamics.

Salma Sherbaz was born in 1986. She is a student at the College of Shipbuilding Engineering, Harbin Engineering University. Her current research interests include CFD, green ship, ship performance optimization and high-end mathematical applications to ship design.

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Radar cross section prediction and reduction for naval ships