Page 289 - Aerodynamics for Engineering Students

Finite wing theory 271

2 A glider has wings of elliptical planform of aspect ratio 6. The total drag is given by
CD = 0.02 + 0.06G. Find the change in minimum angle of glide if the aspect ratio is
increased to 10.
3 Discuss the statement that minimum induced drag of a wing is associated with
elliptic loading, and plot a curve of induced drag coefficient against lift coefficient for
a wing of aspect ratio 7.63.
4 Obtain an expression for the downward induced velocity behind a wing of span 2s
at a point at distance y from the centre of span, the circulation around the wing at
any point y being denoted by I?. If the circulation is parabolic, i.e.

calculate the value of the induced velocity w at mid-span, and compare this value
with that obtained when the same lift is distributed elliptically.
5 For a wing with modified elliptic loading such that at distance y from the centre of
the span, the circulation is given by

where s is the semi-span, show that the downward induced velocity at y is
ro
11
-(-+-) y2
4s 12 2s2
Also prove that for such a wing of aspect ratio (AR) the induced drag coefficient at
lift coefficient CL is
c 628
Do - 625 TAR
6 A rectangular, untwisted, wing of aspect ratio 3 has an aerofoil section for which
the lift-curve slope is 6 in two-dimensional flow. Take the distribution of circulation
across the span of a wing to be given by

and use the general theory for wings of high aspect ratio to determine the approximate
circulation distribution in terms of angle of incidence by retaining only two terms in the
above expression for circulation and satisfying the equation at 6' = ~/4 and ~12.
(Answer: A1 = 0.372~~ = 0.0231~)
A2
7 A wing of symmetrical cross-section has an elliptical planform and is twisted so
that when the incidence at the centre of the span is 2" the circulation r at a distance y
from the wing root is given by

Find a general expression for the downwash velocity along the span and determine
the corresponding incidence at the wing-tips. The aspect ratio is 7 and the lift-curve
slope for the aerofoil section in two-dimensional flow is 5.8.
(Answer: a,* = 0.566")