Page 276 - Aerodynamics for Engineering Students

Finite wing theory 259

(5.66)

where an is the angle of incidence defined with respect to the x' direction and aon is
the corresponding angle of incidence for zero lift. Thus
a!, = a!/ COS A (5.67)
-- - rz)2~s
so the lift-curve slope for the infinite yawed wing is given by

dCL
da! - A N 27~~0s A (5.68)
and
LmcosA (5.69)

5.7.2 Swept wings of finite span
The yawed wing of infinite span gives an indication of the flow over part of a swept
wing, provided it has a reasonably high aspect ratio. But, as with unswept wings,
three-dimensional effects dominate near the wing-tips. In addition, unlike straight
wings, for swept wings three-dimensional effects predominate in the mid-span region.
This has highly significant consequences for the aerodynamic characteristics of swept
wings and can be demonstrated in the following way. Suppose that the simple lifting-
line model shown in Fig. 5.26, were adapted for a swept wing by merely making
a kink in the bound vortex at the mid-span position. This approach is illustrated by
the broken lines in Fig. 5.37. There is, however, a crucial difference between straight
and kinked bound-vortex lines. For the former there is no self-induced velocity or
downwash, whereas for the latter there is, as is readily apparent from Eqn (5.7).
Moreover, this self-induced downwash approaches infinity near the kink at mid-
span. Large induced velocities imply a significant loss in lift.

Fig. 5.37 Vortex sheet model for a swept wing