The radiation resistance of surfaces of revolution, such as cylinders, spheres and cones

摘要

The paper forms the sequel to an earlier one in which the radiation resistance of the cone and the cylinder were briefly considered. In the present investigation formulae are developed for calculating the power radiated by cylinders, cones and spheres having any assigned distribution of charge. No attempt is made upon the more complex problem of determining the charge distribution appropriate to these geometrical figures. As a preliminary, methods are given for calculating the component of field which is in phase with the current, for the systems of charge and current distribution considered later in the paper. The process of calculating successive terms in the series requires considerable patience and experience. It is hoped that the labour which has been expended here will be of service as a basis for more practical developments in the future. The formulae are presented in a way suitable for numerical computation. Little computation has in fact been performed, for lack of reliable information about the charge distribution appropriate to cones and thick cylinders. When such information is forthcoming then this paper should be very helpful for calculating the radiation characteristics. The various steps involved in the derivation of the formulae have been given in full because it was realized that they could, if required, be extended so as to apply to any surface of revolution. In short, the present work will be found to be directly applicable to many practical problems, when these problems have been defined more specifically: it is not worth while to use them now on fanciful specifications. The analysis contains only one assumption, namely that there is no phase difference between the elements of charge situated on different points of a radiating surface. In an Appendix the author gives an interpretation of the parameters L and C in the equation for the long line, and calculates the self-inductance of a hollow sphere.