Page 271 - Aerodynamics for Engineering Students

254 Aerodynamics for Engineering Students

As a comparison, the equivalent elliptic distribution with the same coefficient of lift gives a
series of values
rm2s-l 0 14.9 27.6 36.0 38.8
The aerodynamic characteristics follow from the equations given in Section 5.5.4. Thus:

CL = r(AR)A1 = 0.3406
+
C, =- ‘ = 0.007068
[l
61
4AR)
since

i.e. the induced drag is 2% greater than the minimum.
For completeness the total lift and drag may be given

1
Lift = C,-pVZS= 0.3406 x 139910 =47.72kN
2

1
Drag (induced) = CD,-PV’S = 0.007068 x 139910 = 988.82N
2
Example 5.4 A wing is untwisted and of elliptic planform with a symmetrical aerofoil section,
and is rigged symmetrically in a wind-tunnel at incidence a1 to a wind stream having an axial
velocity V. In addition, the wind has a small uniform angular velocity w, about the tunnel axis.
Show that the distribution of circulation along the wing is given by

r = 4sV[A1 sin 8 + A2 sin281
and determine A1 and A2 in terms of the wing parameters. Neglect wind-tunnel constraints.
(CUI
From Eqn (5.60)

In this case QO = 0 and the effective incidence at any section z from the centre-line
W W
V
~=Q~+z-==Q~--~~~~~
V
Also since the planform is elliptic and untwisted p = po sin 8 (Section 5.5.3) and the equation
becomes for this problem
“
v I
hsin8 a1 --scosB = EA,sinn8
[
Expanding both sides: