Lifting Line Theory for Transonic Flow

Abstract

Lifting line theory is applied to describe the flow about a lifting wing at transonic speeds $( {M_\infty < 1} )$. The method extends that of Van Dyke [1], in which lifting line theory is viewed as a singular perturbation problem, to transonic flows. Inner and outer expansions as the aspect ratio $ \to \infty $ of the transonic small disturbance equations are found. It is shown that the solutions match asymptotically. A boundary value problem is formulated which describes the first aspect ratio correction to the two dimensional cross sectional transonic flow. The theory is especially applicable to wings of similar cross-sections.