The scope and accuracy of vortex lattice theory

Abstract

The report gives an outline of the development of the principles on which potential problems in lifting plane theory are solved by the use of a vortex lattice for the purpose of computing downwash. The conditions of convergence necessary for an accurate solution are defined, and the main purpose of the report is to show that those connected with the lattice have been, or can easily be satisfied. Published solutions by this method have been mainly concerned with spanwise load grading and local aerodynamic centre and examples are given here of earlier checks on accuracy for rectangular and triangular wings, and a yawed infinite wing, based either on an alteration of the lattice spacing or on comparison with downwash obtained by surface integrals. The study of accuracy is now advanced by a comparison based on exact values calculated from surface integrals given by W. P. Jones, and applied to a rectangular and a sweptback wing. The downwashes obtained from the lattice are shown to converge to the exact values, but by a comparison of two solutions for the sweptback wing it is shown that the beneficial coupling effect of the lattice makes it unnecessary to obtain individual downwash values to great accuracy, at least for spanwise load grading and aerodynamic centre calculations. Trial calculations reveal that there would be no difficulty in extending the convergence to detailed pressure distribution or other properties of any thin wing, but it is desirable to give prior attention to the main effects of wing thickness and viscosity.