Page 596 - Aircraft Stuctures for Engineering Student

Problems 577

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P.13.1 An initially untwisted rectangular wing of semi-span s and chord c has its
flexural axis normal to the plane of symmetry, and is of constant cross-section with
torsional rigidity GJ. The aerodynamic centre is ec ahead of the flexural axis, the
lift-coefficient slope is a and the pitching moment coefficient at zero lift is Cm.o. At
speed V in air of density p the wing-root incidence from zero lift is ao.
Using simple strip-theory, i.e. ignoring downwash effects, show that the incidence
at a section distant y from the plane of symmetry is given by
ao+e= (2+ao)
COS X(S - Y) Cm.0
ea
cos As -~
where
ea+pv2c2
A=
GJ
Hence, assuming Cm,o to be negative, find the condition giving the speed at which the
lift would be reduced to zero.
Ans. V = d- ~ G J
2pec2s2a
P.13.2 The rectangular wing shown in Fig. P. 13.2 has a constant torsional rigidity
GJ and an aileron of constant chord. The aerodynamic centre of the wing is at a
constant distance ec ahead of the flexural axis while the additional lift due to
operation of the aileron acts along a line a distance hc aft of the flexural axis; the
local, two-dimensional lift-curve slopes are al for the wing and a2 for aileron deflec-
tion. Using strip theory and considering only the lift due to the change of incidence
arising from aileron movement, show that the aileron reversal speed is given by
.I (e + h)
tan Xks 1; y sin Ay dy - tan As y sin Xy dy - y cos Xy dy = 2h cos Xks [ (ks) - s2]
where
X2 = ;pV2alec2/GJ

axis

I I
Fig. P.13.2