Keeve Milton Siegel

Far field scattering from bodies of revolution

SummaryBy 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 elliptic ogive, 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 wedge-like 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 of the same perimeter.

The theoretical and numerical determination of the radar cross section of a prolate spheroid

The exact curve is found for the nose-on radar cross section of a perfectly conducting prolate spheroid whose ratio of major to minor axis is 10:1, for values of \pi times the major axis divided by the wavelength less than three. The exact acoustical cross section is also found. The mathematical solution is obtained by setting up a series expansion for the scattered wave in terms of two sets of solutions of the vector Helmholtz equation and evaluating the undetermined coefficients in this series by applying the boundary conditions on the surface of the spheroid.

Electromagnetic and Acoustical Scattering from a Semi‐Infinite Cone

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.

Comments on far field scattering from bodies of revolution

SummaryA previous paper1) on the subject, although 35 pages in length, omitted a good many physical explanations and mathematical details. As a result this paper discusses Rayleigh and resonance scattering for a cone. Two minus sign errors are corrected in the cones cross section obtained by the local wedge field approximation

Radiation from slot arrays on cones

A method is obtained for determining far field patterns, sidelobes as well as the main beam, for an array of slots on the surface of a cone. It is found that accurate results can be obtained for a single slot by using geometric optics for the main beam and an extension of Fock theory for fields in the shadow region. The tip contribution is computed by physical optics and, for reasonably thin cones, is found to be negligible. The array pattern is obtained by appropriately summing the single slot fields. To test the validity of the method and to test the ease with which computations could be performed, a radiation pattern from a linear array of 65 slots on the surface of a cone was computed and compared with experiment. The agreement is excellent. The major theoretical part of this paper is the generalization and simplification of Fock theory as applied to the surface of a cone.