Page 202 - Aerodynamics for Engineering Students

Two-dimensional wing theory 185

n-1 1
13 = LTsinnOsinOdO = -
sin(n - 2)4
14 = 1
n-2
In the usual notation CH = bla + b277, where

From Eqn (4.54):

bl = - LT( + COS 0) (cos 4 - COS 0)d0
1
giving

(4.55)
Similarly from Eqn (4.54)
1
x
b2 =- = - coefficient of r] in Eqn (4.54)
% F2
This somewhat unwieldy expression reduces to*
1
b2 = -- { (1 - cos 24) - 2(7r - $)’( 1 - 2 cos 4) + 4(7r - 4) sin $} (4.56)
47rF2
The parameter ul = dCL/da is 27r and u2 = dC~/tlq from Eqn (4.52) becomes

u2 =2(~-4+sin+) (4.57)
Thus thin aerofoil theory provides an estimate of all the parameters of a flapped
aerofoil.
Note that aspect-ratio corrections have not been included in this analysis which is
essentially two-dimensional. Following the conclusions of the finite wing theory in
Chapter 5, the parameters ul, u2, bl and b2 may be suitably corrected for end effects.
In practice, however, they are always determined from computational studies and
wind-tunnel tests and confirmed by flight tests.

4.6 The jet flap

Considering the jet flap (see also Section 8.4.2) as a high-velocity sheet of air issuing
from the trailing edge of an aerofoil at some downward angle T to the chord line of
the aerofoil, an analysis can be made by replacing the jet stream as well as the aerofoil
by a vortex distribution.+

*See R and M, No. 1095, for the complete analysis.
+D.A. Spence, The lift coefficient of a thin, jet flapped wing, Proc. Roy. SOC. A,, No. 1212, Dec. 1956.
D.A. Spence., The lift of a thin aerofoil with jet augmented flap, Aeronautical Quarterly, Aug. 1958.