Page 277 - Aerodynamics for Engineering Students

260 Aerodynamics for Engineering Students

Nature does not tolerate infinite velocities and a more realistic vortex-sheet model
is also shown in Fig. 5.37 (full lines). It is evident from this figure that the assump-
tions leading to Eqn (5.32) cannot be made in the mid-span region even for high
aspect ratios. Thus for swept wings simplified vortex-sheet models are inadmissible
and the complete expression Eqn (5.31) must be used to evaluate the induced
velocity. The bound-vortex lines must change direction and curve round smoothly
in the mid-span region. Some may even turn back into trailing vortices before
reaching mid-span. All this is likely to occur within about one chord from the mid-
span. Further away conditions approximate those for an infinite-span yawed wing.
In effect, the flow in the mid-span region is more like that for a wing of low aspect
ratio. Accordingly, the generation of lift will be considerably impaired in that region.
This effect is evident in the comparison of pressure coefficient distributions over
straight and swept wings shown in Fig. 5.38. The reduction in peak pressure over the
mid-span region is shown to be very pronounced.

(b)
Fig. 5.38 A comparison between the pressure distributions over straight and swept-back wings