Page 275 - Aerodynamics for Engineering Students

258 Aerodynamics for Engineering Students

,Streamline

Fig. 5.36 Streamline over a sheared wing of infinite span

approaches the wing it will depart from the freestream conditions. The total velocity
field can be thought of as the superposition of the free stream and a perturbation field
(u', 6,O) corresponding to the departure from freestream conditions. Note that the
velocity perturbation, w' = 0 because the shape of the wing remains constant in the
z' direction.
An immediate consequence of using the above method to construct the velocity
field is that it can be readily shown that, unlike for infinite-span straight wings, the
streamlines do not follow the freestream direction in the x-z plane. This is an
important characteristic of swept wings. The streamline direction is determined by

Urn cosA + ut
(g) U, sin A (5.65)
sL=
When ut = 0, downstream of the trailing edge and far upstream of the leading edge,
the streamlines follow the freestream direction. As the flow approaches the leading-
edge the streamlines are increasingly deflected in the outboard direction reaching
a maximum deflection at the fore stagnation point (strictly a stagnation line) where
u' = U,. Thereafter the flow accelerates rapidly over the leading edge so that
u' quickly becomes positive, and the streamlines are then deflected in the opposite
direction - the maximum being reached on the line of minimum pressure.
Another advantage of the (2, y, 2) coordinate system is that it allows the theory
and data for two-dimensional aerofoils to be applied to the infinite-span yawed wing.
So, for example, the lift developed by the yawed wing is given by adapting Eqn (4.43)
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