Overview of MM and UTD methods at the Ohio State University ...

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approximate morecomplexones. The basic shapes are mul- 2 tiple-sided flat plates, multiple-section cone frustums, and -40t ' I -SOL I I I t I 180 I20 60 0 TAIL ANGLE NOSE Fig. 9. UTD calculated near zone backscatter pattern from a cone-cylinder geometry at 864-in. range, horizontal polarization, and 10 GHr. - D - 20: 0 5 m -20 cn U (r -40 -60 180 90 0 TAIL ANGLE NOSE Fig. 10. Measured backscatter pattern from a cone-cylinder geometry at 864-in. range, horizontal polarization, and 10 CHz. manner. It is still necessary to provide transition functions that correct the ray picture in some cases. For example, the scattering from a circular rim can be found in closed form [41] for the bistatic scattering case. In addition, the bistatic scattering in the specular region of the side of a cone frustum can be found [42]. With these techniques the bistatic scattering from a cylinder or cone frustum of any size can be calculated by just summing the scattering from up to four points. The corner diffraction coefficient can also be taken care of using modern equivalent current concepts [27], [28]. With this technique the bistatic scattering from a multiple-sided flat plate can be found by summing terms from only the corners of the plate or complex structure made up of plate facets. A computer code called the radar cross section-basic scattering code (RCS-BSC) is being developed [43], which will provide the far zone scattering from complex structures using these techniques. It uses basic shapes to finite-composite section ellipsoids at the present time. The RCS-BSC will include some plate-to-plate interactions. In preparation of understanding what needs to be included in these situations in a UTD sense, a two-dimensional code has been developed [44]. This code includes up to and including all third order interactions between two plates. In addition, some fourth order interaction terms have been included. This code is ideal for analyzing dihedral configurations. It is necessary to include only the diffraction from the edges and their reflection in the other plate. In addition, double diffraction between edges with possible intervening reflections have been included. The newly developed far zone double diffraction coefficients [29]are used. With this formulation for double, it is not necessary to use false edges, or imposed edges as some people call them. As an example, a 9-in. two-dimensional dihedral has been analyzed in the E-plane using UTD as shown in Fig. 11 and MM as shown in Fig. 12 at 10 GHz. Note that the two agree very well even in the low-level regions. The interaction between plates and curved surfaces can also be handled in a similar way as in the near zone [45], [46]. 0 5 -20 W -30- +-I /-- -401 I I I I 1 I 0 90 180 ANGLE Fig. 11. Backscatter from a two-dimensional 9-in. dihedral at 10 GHz in the E-plane calculated using UTD. 0 90 180 ANGLE Fig. 12. Backscatter from a two-dimensional 9-in. dihedral at 10 CHz in the E-plane calculated using MM. NEWMAN AND MARHEFKA: Mh4 AND UTD METHODS AT OHIO STATE UNIVERSITY 705 1
As in the case of plate-to-plate interaction, these terms can be formulated in a numerically efficient way without multiple integrations being needed. As an example of how UTD can be used to analyze the far zone scattering from a model of an aircraft, a Boeing 737 has been analyzed using the techniques discussed above. The computer model is shown in Fig. 13. It is composed of Fig. 13. Computer model of Boeing 737 aircraft. a composite cone frustum model for the fuselage and engines. The wings and stabilizers are modeled as flat plates with thick edges. Obviously, this is not an exact match with the 1/20 scale model tested against measurements, let alone the real aircraft. The important thing here, however, is to be able to model the salient features of the aircraft as they pertain to the most important scattering centers for this case. The pattern cut of interest is in the plane of the wings, that is, the azimuth cut. The UTD fields from the model are calculated using only first order terms without the engines included. The results are compared with measurements made on the OSU-ESL compact range at 10 GHz for backscatter. The 1/20 scale model of the aircraft measured would not allow the engines to be removed so absorber was placed over the front and back faces. The results are in dB relative to a square meter at the 1/20 scale model size at 10 GHz. The calculated result for the horizontal polarization is shown in Fig. 14, and the measured result in Fig. 15. In general the agreement is verygood. The fuselage return is even close though the calculated results are somewhat narrower as anticipated because of the flat-sided repre- sentation of the curved surface. The major differences in the peaks associated with the sp,ecular from the leading edge of the wings and stabilizers are due to two possible mechanisms. First, the rounded edge model used could be improved, since the radii of curvature of the edge is small in terms of a wavelength in this case. In addition, it can be shown that theedgewaveson the leading edgeof thewings can strongly affect these peaks. This is not a low cross-section aircraft, so the first order solution used here may be determined to be sufficient. If a different aircraft had been studied, it might be necessary to include more of these 706 IO 0 - 10 - 20 - 30 ')I r 1 1 ' ' 1 ' 1 ' I 1 - 50 0 90 180 TAIL ANGLE NOSE Fig. 14. First order UTD backscattered result for horizontal polarization in the azimuth plane of a 1/20 scale model of a Boeing 737 without engines at 10 CHz. 5 m V v, 0 a -50 wu 0 90 180 TAIL ANGLE NOSE Fig. 15. Measured backscattered result for horizontal polarization in the azimuth plane of a 1/20 scale model of a Boeing 737 without engines at 10 CHz. higher order terms. The computer time to calculate the models without the engines was just under 8 min on a VAX 11l780. In addition to the RCS-BSC code mentioned above, a good approximation to the backscattered signal can be obtained by an envelope description of the scattering of complex structure by combining the backscattered signal of basic shapes forming the structure [47]. Analytic expres- sions for the envelope of the backscattered fields of some basic shapes, such as finite circular cylinder, circular cone, cone frustum, hemisphere, circular disk, and a straight edge have been developed. This type of technique is very useful for initial design work and for very large structures where the side lobe details would need to be sampled at very small angular increments to be assured of obtaining the peaks. PROCEEDINGS OF THE IEEE, VOL. 77, NO. 5, MAY 1989
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