A comprehensive and practical guide to the Hess and Smith constant source and dipole panel

Abstract

ABSTRACT In a series of landmark reports and papers, J.L. Hess and A.M.O. Smith of Douglas Aircraft Company, Inc. introduced the quadrilateral constant source panel to solve three-dimensional nonlifting potential flow problems. Later a panel with constant dipole (doublet) distribution was added for lifting flow computations. Hess and Smith's publications provide equations for the computation of the velocities induced by the singularity distributions along with required geometric properties of the panel. Equations are presented considering an implementation in Fortran (Versions II and IV), the commonly used programming language for numerical methods at the time. The present paper builds on Hess and Smith's groundbreaking work, restating equations with modern programming languages in mind capable of fast vector operations like Fortran 95, Python or Julia. Formulas are provided for the computation of geometric properties, coordinate transformations, as well as first and second-order potential derivatives. Example input and output data allow readers to test and validate their own implementation.