Some remarks on the solution of the lifting line equation

Abstract

The present work offers a simplification in the solution of Prandtl's lifting line equation. The equation for the local circulation is usually solved using a sine series in a collocation method. Using the fact that local circulation and local geometric angle of attack are related by a linear operator, an expression can be obtained for the drag coefficient containing only the square of the unknown constants, which implies that the loadings are orthogonal in Graham's sense (1952). Expressions are derived for the unknown constants, making use of the orthogonality of the loadings. The solution gives an approximate solution along the entire span, so that discontinuities, flap deflections, etc., can be accounted for.