V. Sudhakar

Closed form surface ray tracing on ogival surfaces

A novel method based on the geodesic constant has been developed for surface ray tracing on an ogive. The surface ray geometric parameters required in the high-frequency EM (electromagnetic) calculations are obtained in explicit analytical form. The ogive is treated as a coordinate surface of the bispherical coordinate system which is a geodesic coordinate system. All the ray geometric parameters are obtained in one-parameter form in terms of the first geodesic constant h. These ray parameters can be used in antenna radiation pattern, mutual coupling, and radar cross section calculations.<<ETX>>

Closed form expressions for integral ray geometric parameters for wave propagation on general quadric surfaces of revolution

The integral ray geometric parameters consisting of the relation between the geodesic coordinates v and u, the arc length, and the generalized Fock parameter are presented for the complete class of QUASORs (quadric surfaces of revolution). A geodesic constant method permits the derivation of these ray parameters in terms of the geodesic constant h alone. Since h can be expressed in terms of the source and observation point coordinates in the case of the sphere and cone, in these cases the ray parameters are in closed form. On the other hand, in the case of the ellipsoid of revolution and the general paraboloid and hyperboloid of revolution, h can be obtained using a simple univariate search. Hence in these cases, the ray parameters are in a one-parameter dependent form. Using this approach, it is possible to readily calculate the various radiation characteristics of the antenna in the vicinity of a general QUASOR.<<ETX>>

Closed form expressions for integral ray geometric parameters for wave propagation on general quadric cylinders

The integral ray geometric parameters consist of (i) the relation between the geodesic coordinates, (ii) the arc length, and (iii) the generalised Fock parameter. The authors present these parameters for quadratic cylinders (QUACYLs) in a closed form. The QUACYLs consist of right circular, elliptic, general parabolic, and hyperbolic cylinders. The rectangular hyperbolic cylinder, which is a special case of the general hyperbolic cylinder, has also been included due to its frequent use in surface modeling. The geodesic constant method (GCM) yields these analytical expressions in the one-parameter form, i.e. in terms of the first geodesic constant h. The derived ray geometric parameters can be applied to the ray-theoretic determination of mutual coupling, radiation patterns of antennas in the presence of large scatterers, and the monostatic and bistatic radar cross sections of scatterers.<<ETX>>

Analytical evaluation of element coupling coefficients on general paraboloids of revolution (conformal phased array)

Mutual coupling results between individual elements in a conformal phased array on a general paraboloid of revolution are presented. The formulation presented yields all the surface ray geometric parameters required in the ray analysis in explicit one-parameter form. The parameter involved is the first geodesic constant h, whose determination involves a simple univariate search.<<ETX>>

Closed form surface ray analysis for antennas located on a class of aircraft wings

A novel method is developed to derive the surface ray geometric parameters required in the high-frequency computations of antenna characteristics for radiators located on an aircraft wing modeled by finite sections of a general parabolic cylinder (GPCYL) and right circular cylinder. This hybrid quadric cylinder (h-QUACYL) is treated by the geodesic constant method (GCM) which expresses all the surface ray geometric parameters in terms of the first geodesic constant, which can be determined in closed form. Results are presented for wings designed for different flight regimes.<<ETX>>

Closed form evaluation of element coupling coefficients ion conformal arrays on general quadric cylinders

A closed-form geodesic constant method (GCM) is developed to model the ray-geometric aspects of conformal arrays on QUACYLs (quadric cylinders). The formulation incorporates a shaping parameter, permitting the modeling of surfaces of different sharpness. Mutual coupling results for the general parabolic cylinder are presented to illustrate the application of the formulation.<<ETX>>

Geodesic splitting on general paraboloid of revolution and its implications to the surface ray analysis

The authors have observed geodesic splitting in the case of surface ray propagation over a general paraboloid of revolution (GPOR). Since even the primary geodesics are split in both clockwise and counterclockwise directions, this leads to a double of the ray paths to be considered in antenna characteristics computations. The authors provide an insight into the ray-splitting phenomenon for the simplest (i.e. lowest order) possible convex surface. It is noted that, in general, the ray tracing over a GPOR would require a bivariate search. The ray splitting in the case of the GPOR tends to further increase the computer time required for the determination of the surface ray geometric parameters. The authors have developed a geodesic constant method (GCM) involving an accurate simple univariate search which has brought the electromagnetic field computations within the ambit of tractability.<<ETX>>

Applicability of artificial intelligence languages to solving the scattering and diffraction problems using a personal computer

The applicability of AI (artificial intelligence) mathematical software packages to EM (electromagnetic) theory is examined using high-frequency ray-theoretic problems as specific examples. It is possible to generate expressions in both readable and FORTRAN format so that the task of computer code generation is greatly simplified. Although some of the mathematical operations available have a limited range, the users can nevertheless employ such packages to cross-check their mathematical analyses. In the high-frequency ray-theoretic approach, as indeed in the entire field of electromagnetics, the expressions obtained at each step of the mathematical analysis are often quite complex and unwieldy. It is now possible to consign most of these operations to such AI packages as REDUCE to generate the symbolic codes accurately. Finally, once the analysis has been verified, the same program can be used to generate the familiar FORTRAN codes. Hence, nonnumeric logic and AI languages can be used as valuable tools for antenna analysis and design problems.<<ETX>>

Surface ray contribution to bistatic radar cross section of a general paraboloid of revolution

A theoretically comprehensive method is proposed for the determination of the RCS (radar cross section) of a general paraboloid of revolution utilizing the geodesic constant method (GCM). Analytical expressions are obtained for al the surface ray parameters required in the bistatic RCS computation in one-parameter form. The inclusion of the diffraction due to higher order geodesics in the analysis increases the accuracy of the theoretical RCS predictions.<<ETX>>

A surface modeling paradigm for electromagnetic applications in aerospace structures

A systematic approach has been developed to model the surfaces encountered in aerospace engineering for electromagnetic applications. The basis of this modeling is the quadric canonical shapes which are the coordinate surfaces of the Eisenhart coordinate systems. The building blocks are visualized as sections of quadric cylinders and surfaces of revolution. The surface modeling paradigm facilitates the treatment of hybrid nondevelopable QUASORs (quadric surfaces of revolution) such as a satellite launch vehicle modeled as a GPOR (general paraboloid of revolution)-cylinder combination. Some examples of hybrid QUASORs are presented.<<ETX>>