6 - Incompressible Flow about Wings of Finite Span

Summary

In 1908, Lanchester visited Göttingen (University), Germany and fully discussed his wing theory with Ludwig Prandtl and his student, Theodore von Kàrmàn. Prandtl spoke no English, Lanchester spoke no German, and in light of Lanchester's unclear ways of explaining his ideas, there appeared to be little chance of understanding between the two parties. However, in 1914, Prandtl set forth a simple, clear, and correct theory for calculating the effect of tip vortices on the aerodynamic characteristics of finite wings. It is virtually impossible to assess how much Prandtl was influenced by Lanchester, but to Prandtl must go the credit …

John D. Anderson, Jr., Introduction to Flight, 1978

Introduction

This chapter considers steady, inviscid, incompressible flow about a lifting wing of arbitrary section and planform. Because the flow around a wing is not identical at all stations between the two ends of the wing, the lifting finite wing constitutes a three-dimensional flow problem. The two wing tips are located at distance ±b/2, where b is the wing span.

Certain terms must be defined before a study of finite wings can be begun (Fig. 6.1). The coordinate axis system used is shown in Fig. 6.1a. A wing section is defined as any cross section of a wing as viewed in any vertical plane parallel to the x-z plane. It also is called an airfoil section. The wing may be of constant section or variable section. If a wing is of constant section, wing sections at any spanwise station have the same shape (e.g., NACA 2312). If a wing is of variable section, the wing-section shape varies at different spanwise locations. For example, a wing of variable section might have a NACA 0012 at the root section (i.e., the section in the plane of symmetry at y = 0), then smoothly change in the spanwise direction until the wing had, a NACA 2312 section at the tip.