LIFT OF WINGS IN INCOMPRESSIBLE FLOW

3- 3-1 Methods of Wing Theory

The theoretical basis for this section was laid in Sec. 3-2. For practical applications, the computational methods discussed below (simple and extended lifting-line theories, lifting-surface theory) proved to be particularly convenient and may be characterized as follows: The simple lifting-line theory applies only to wings with straight cl4 lines in symmetric flow, that is, to unswept wings. It gives good results for larger aspect ratios (Л>3) and allows the determination of lift distributions over the span from which total lift, rolling moment, and induced drag, but not pitching moment, may be computed. The extended lifting-line theory (three-quarter – point method) applies to wings of any planform and aspect ratio. Thus, it applies to swept-back and yawed wings. It gives the lift distribution over the span from which total lift, rolling moment, induced drag, and, approximately, pitching moment are obtained. The lifting-surface theory, like the extended lifting-line theory, applies to any wing and aspect ratio, but gives lift distributions over the span and over the chord from which total lift, rolling moment, induced drag, and also pitching moment, and thus the neutral-point position of the wing, are found. Accurate knowledge of the neutral-point position is particularly important for swept-back wings.

Summaries and detailed presentations on the methods of wing theory in incompressible flow are given by Betz [6], von Karman and Burgers [88], Robinson and Laurmann [70], Thwaites [82], Weissinger [96], von Karman [89], Flax [15], Hess and Smith [28], and Landahl and Stark [52]. The development of the lifting-line theory as a “singular perturbation problem” is due to van Dyke [87]; see also the references on page 111. Extensions of wing theory to include nonlinear angle-of-attack effects and the behavior of wings near the ground (ground effects) are found, for example, in [8, 19, 21, 40] and [2, 81, 100], respectively. Although it is not possible in this book to treat the questions of nonsteady flow that are important for airplane aerodynamics, the references [2, 50, 52, 53] shall be mentioned in this connection. Problems of flexible wings are discussed in [22].

Studies on design aerodynamics have been prompted by Kiichemann and accomplished for swept-back wings in particular [3].