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~~ = ~pjo2,OS2 A(l - p tan A)a aoc(yh)yh dyh (3.359)
)
The total rolljng moment is given by
.: sec A
L = -p'Vo2ap cOS2 A tan A aoc(yh)yh dyh (3.360)
)
Then,
STATIC STABILITY AND CONTROL
299
2ctp cos A sin
ci-- _)l,"ec\aoc(y.r)ytidyh (3.361)
Sb
=-(
2cY cos A sin A
['se'Aaoc(yh)yhdyh (3.362)
For a swept wing in level fiight with zero sideslip, the lift is given by
Also,
Lift=pVo2cos2A -'sec'Xaoa
,a sec Ac(yh) dyh (3.363)
Lift - ~p Vo2SCL
Equating Eqs. (3.363) and (3.364),
CL -
2 cos2 A
(3.364)
g sec A
aoa' sec Ac(yh) dyh (3.365)
If the sectional lift-curve slope ao is constant along the span, then Eq. (3.365)
reduces to
CL - aoa cos A
Substituting this value of CL in Eq. (3.362),
(3.366)
(2 SbAC ['se'Ac(yh)yhdyh (3.367)
From Eq. (3.367) we observe that wing sweep-back has a stabilizing effect,on static
lateral stability.lts magnitude depends on the wing leading-edge sweep angle and
the lift coefficient or angle of attack. In a similar way, it can be shown that the
forward sweep produces a destabilizing effect on lateral stability.
Estimation of combined wing contribution. For high-aspect ratio swept-
wings with dihedral, the combined9wing contribution to static lateral st.ability can
be assumed equal to the sum of the individual contributions because of sweep and
dihedral, and the scrip theory approach may be used. However, it should be noted
that the strip theory ignores the mutual interference effects between the adjacent
wing sections, i.e., the spanwise variations of downwash and induced drag are not
considered in the strip theory analysis,
For more accurate estimation ofthe wing contribution considering the combined
effects ofwing-fuselage interference, dihedral, and sweep, the following empirical
relaOoni can be used. This relation is valid for untwisted, straight tapered wings
of arbitrary aspect ratio and taper ratio. If the wing has a twist, then an additional
correction inay have to be applied, which is not given here. The interested reader
may refer to Datcoml to evaluate this correction.
300 P. ERFORMANCE, STABILITY, DYNAMiCS, AND CONTROL
For subsonic speeds,l
(Clp)W,B, = ,, [(-,,) Nn KM'x K f + (-,,),]
+F [CrKM,+ A~p] +(AC,p)zu (3.368)
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