By use of approximations based on physical reasoning radar cross-section results for bodies of revolution are found. In the Rayleigh region (wavelength large with respect to object dimensions) approximate solutions are found. Examples given include a finite cone, a lens, an ellipticogive,.a spindle and a finite cylinder. In the physical optics region (wavelength very small with respect to all radii of curvature) Kirchhoff theory and also geometric optics can be used. When the body dimensions are only moderately large with respect to the wavelength, Fock or Franz theory can be applied, and examples of the circular and elliptic cylinder are presented. In the region where some dimensions of the body are large with respect to the wavelength and other dimensions are small with respect to the wavelength, special techniques are used. One example, the finite cone, is solved by appropriate use of the wedgelike fields locally at the base. Another example is the use of traveling wave theory for obtaining approximate solutions for the prolate spheroid and the ogive. Other results are obtained for cones the base perimeter of which is of the order of a wavelength by using known results for rings ot the same perimeter.
The results obtained by applying the current-distribution method to the problem of approximating the scattering cross section, when the transmitter and receiver are separated, are presented for several simple geometric configurations. The method is applied for the case in which the transmitter is located on the axis of revolution and the ratio l/λ is large, where l is a ``characteristic dimension'' of the body and λ is the wavelength. These results indicate that in most of the cases considered the cross section increases as the angle between the receiver and the transmitter increases.
The value of the nose-on back scattering cross section of a semi-infinite cone is determined by the exact methods of electromagnetic and acoustical theory, and by physical optics. It is shown that, to the degree of approximation used, the electromagnetic value and the physical-optics value are equal. The acoustical value is found to be less than the electromagnetic value by a factor which depends only on the cone angle; both are proportional to the square of the wavelength. It is shown that the electromagnetic and physical-optics answers agree with experimental data to within a factor of two. The electromagnetic theory results obtained hold for the cases in which the half-cone angle is close either to 0 or to π/2.
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