10 - Wing theory

Summary

The flows about wings of finite span are sufficiently analogous to those about propeller blades to warrant a brief examination before embarking on the construction of a mathematical model of propellers. A more detailed account of wing theory is given for example by von K ármán & Burgers (1935).

A basic feature of the flow about a straight upward-lifting wing of finite span and starboard-port symmetry in a uniform axial stream is that the velocity vectors on both the lower and upper surfaces are not parallel to the longitudinal plane of symmetry. On the lower side the vectors are inclined outboard and on the upper side they are inclined inwardly in any vertical plane or section parallel to the vertical centerplane. This is a consequence of the pressure relief at the wing tips and the largest increase in pressure being in the centerplane on the lower side and the greatest decrease in pressure being in the centerplane on the upper or suction side. Thus there are positive spanwise pressure gradients on the lower side and negative spanwise gradients on the upper side which give rise to spanwise flow components which are obviously not present in two-dimensional flows.

In many treatments of wing theory one finds figures purporting to show the flow about a wing of finite aspect ratio in which there is a continuous line of stagnation points near the leading edge, extending from one wing tip to the other.