Analysis of the electric field distribution on perfectly conducting wing sections by application of a conformal mapping

Abstract

Abshact - The metallic structure of an aircraft interacts with the atmospheric electric field and modifies its distribution. The knowledge of the possible pattern of inception points can be interesting in the study of Ughtningaircraft interactions. In this work we consider the electric field induced over a wing section by an uniform undisturbed field by using Joukowsky transformation. I. INTRODUCTION The metallic structure of an aircraft interacts with the atmospheric electric field and modifies its distribution; in particular it is known both from experimental and numerical studies that such a structure is interested by a distribution of electric field which presents high intensity regions; such regions, in certain situations, may be the inception points of a lightning discharge. The knowledge of a possible distribution of points on the surface of the aircraft which can be interested by discharge is a starting step in the study of lightning-aircraft interaction. In this work we consider the electric field induced over a wing section by an uniform undisturbed field as a model problem; from the field distribution it is possible to find regions possibly interested by discharge. In particular, we propose an analytical solution to the problem, making extensive use of the conformal mapping technique. This solution provides an analytical tool which will be useful to test the results obtained by specific numerical implementations (i.e. panel method), and to perform parametric studies on the effects of geomehy on the field distribution.