Understanding Aerodynamics: Arguing from the Real Physics

8.6.1 Simple Sweep Theory

The original idealized argument for the effectiveness of sweep is amazingly simple, thus the name. It can also be called infinite-span yawed-wing theory. The theory is exact for inviscid flows that satisfy the steady Euler equations and the geometric assumptions described below, and for real flows over real wing geometries, it can still be close enough to the truth to provide useful insight. The theory not only shows why sweep is effective in increasing critical Mach number; it provides a simple way of understanding the kinematics of sweptwing flows, and it predicts the “2D” effects of sweep on sectional lift and pitching moment. It does not predict the effects of sweep on profile drag or maximum lift, because these are viscous effects.

We assume the wing is a cylinder of airfoil cross-section and infinite span, with its generators parallel to the y′-axis, which is yawed at an angle Λ relative to the y-axis as shown in Figure 8.6.1. Thus in the x′,z′ system, the wing is a 2D airfoil, and in the x,y,z system, it is just a yawed version of the airfoil. The freestream velocity U_∞ is taken to be in the x direction and is assumed uniform far from the airfoil. Note that the sweep angle Λ is thus measured in the x-y plane, which contains U_∞. Tying our definition of Λ to U_∞ in this way makes the formulas we'll arrive at below simpler than they would be if we used a sweep angle measured in the more conventional way, in the chord plane of the wing, which moves with ...