1 Introduction

For the naval vessels, the scattering body′s size is far more than the wavelength of incident electromagnetic wave, so the measure for computing the naval vessel′s RCS is usually based on high-frequency approach. With the rapid development of the GRECO technique and the improvement of computer capability, high-frequency approach is widely used for the naval vessel RCS computing and design. High-frequency approach is suitable for the large and complex target′s RCS computing depending on high speed and high precision.

2 Process of RCS theoretical prediction

First the ship model is constructed by 3D modeling software, then geometry of the target is always modeled in terms of facets and edges[1]. Now we can obtain a data file which includes coordinates of each facet′s vertex, and from coordinates we can obtain unit normal to each facet.

The RCS is obtained in the following steps:

? Shadowed and eclipsed facets identification. Judge whether each illuminated facet is shadowed by other illuminated facets;

? If an illuminated facet is not shadowed by other illuminated facets, PO is applied to calculate the single scattering from this illuminated facet;

? Using ray tracing of GO to judge whether there is double bouncing scattering between two illuminated facets, then PO is applied to calculate scattering from this facet pair;

? PTD is applied to calculate scattering from edges;

? The composite scattering between naval vessel and rough sea surface must be considered.

We must program to carry out all above steps.

3 Electromagnetic computing

3.1 Facet scattering—PO

According to high-frequency theory, the currents are assumed to be zero over the facets or edges shadowed by other parts or not illuminated by the incident wave, so the inductive current only exits over the region of the target illuminated by the incident field. The inductive current is

(1)

The RCS of one facet is obtained according to the PO surface integral[2] .

(2)

3.2 Diffraction of edges—MEC+ PTD

Equivalent electric and magnetic currents on an edge are expressed by[3]：

(3)

Another method-Incremental Length Diffraction Coefficients(ILDC)can extend PTD to arbitrary scattering directions, adapt to calculate bistatic scattering from an edge, then the scattered far field from a differential unitdtcan be expressed by

(4)

3.3 Double Bouncing scattering—GO+ PO

The strong multiple scattering mainly comes from:

1. scattering from complex structures composed by many small parts, for example, mast and varied antennas on mast. The path of multiple scattering is very complicated, and the scattering is always wide-angle. If the last reflection is specular reflection, it is the best part contribution.

2. scattering from big planes or curve surfaces combination, for example, scattering between cabins, between cabin and equipment, between one equipment and the other equipment.In RCS calculation, the double bouncing scattering is always considered to represent the main contribution of interaction between two parts of the scatter, we limit the calculation to facet-facet interactions, triple scattering or more can be neglected.

Computing double bouncing scattering from a facet pair (Fig.1) uses GO and PO.

Fig.1 Double bouncing facet pair

4 An example for naval vessel’s RCS computing

3D model of a notional naval vessel (above waterline) constructed by COTIA and MAYA is shown in Fig.2.It is 80 meters long. RCS contribution and influence of the mast to total RCS at frequency 5GHz with incident elevation of 0 degree is computed and analyzed with the azimuth angle from 0οto 180ο(fig.7), 0° is the direction that the EM wave points to the bow.

From Fig.3 we can see that there are many antennas on the mast and the structure of the mast is very complex, so EM coupling will exists among the antennas, the mast and superstructure. To reduce this coupling, a notional stealthy mast with antennas embedded and integrated in it is constructed (Fig.4).

Fig.2 3D notional naval vessel model

Fig.3 Traditional mast

Fig.4 Stealthy mast

To analyze the influence and contribution of this mast to total RCS in detail, following models are simulated and RCS of different status are computed.

— notional ship with traditional mast(Fig.2);

— traditional mast(Fig.3);

— stealthy mast(Fig.4);

— notional ship with stealthy mast(Fig.5) ;

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— notional ship without mast (Fig.6).

Fig.5 The ship model with the stealthy mast

Fig.6 The ship model without the mast

The synthetic RCS is obtained by transforming RCS of every azimuth degree with unit dBsm to square meter, then computing their arithmetic mean with the following formula：

(5)

The synthetic RCS is shown in table 1 and table 2.

Table 1 Influence of traditional mast on total RCS

Table 2 Influence of stealthy mast on total RCS

From table 1, synthetic RCS of the notional ship is 926.1 m2, but it is 357.3 m2when mast and antennas are removed, so the RCS contribution of the mast and antennas is 568.8 m2.In fact, the synthetic RCS of the mast and antennas is only 278.7 m2.It clearly shows that the RCS coupling effect among the antennas, the superstructure and the mast is prominent.

From table 2, synthetic RCS of the notional ship with stealthy mast is 412.6 m2, and it is 357.3 m2without mast, so the RCS contribution of the stealthy mast is 55.3 m2.In fact, the synthetic RCS of the stealthy mast is 30.5 m2.It clearly shows that:

? RCS of the stealthy mast is much less than the traditional mast;

? the integration and embedment largely reduce the coupling among the antennas, the superstructure and the mast.

5 Conclusion

High-frequency V method can be used for RCS computation and analysis of ship which has electrical-large size and complex structure characteristics, and it has obvious advantages on computation speed and accuracy compared to other approaches. According to concrete design requirements and prediction results, the material, structure of the mast, disposal of the superstructure can all be adjusted and changed dynamically using the analysis method presented in this paper.

Reference

1. Ying-zheng Ruan, et al. RCS and stealthy techniques. National Defence Industry Publication, 1998.

2. Shu-jun Xu, Wei-jiang Zhao, et al. An approach to RCS computation based on AUTOCAD modeling. Electronics Transaction, 1996.

3. Dong-lin Su,Bao-fa Wang, Cai-lai Zhang.The complex aim’s figure modeling and RCS computing. System Engineering and Electronics Technique,1990.

4. A-xiang Liu,Qin-feng Cao,Zhen-yu Sun.A Method of two bouncing in RCS predicting. Journal of Microwaves, Vol.15，No.2，June 1999.