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X [,- (yh)yhdyh (3.294)
STATIC STABILITY AND CONTROL
The total yawing moment is given by
N - NR +NL
After some simplification, we obtain
N = p Vo2p sin A cos A
269
(3.295)
x[,-. (aoa,2se,2A+2CDO.L+CDa.lcysecA)c(yh)yhdyh (3.296)
In coefficient form,
(Cn)A.W=(p )f.-(aoa2se.A+2CDO.lcosA+CDcrjc:L)
x c(yh)yh dyh (3.297)
or, with CL.I - aoa sec A when p = O,
(Cnp)A.w = (2 S~A f,-(C,.,.
.ICt + 2CDO.I cos A + CDtrW)c(yh)yh dyh
(3.298)
From Eq. (3.298) we observe that wing sweep-back has a stabilizing effect because
all the parameters inside the integral are positive, leading to a positive value of Cnp.
Furthermore, the stabilizing effect increases with angle of attack, andits magnitude
depends on the wing leading-edgc sweep angle. In a similar way, it can be shown
that the forward wing sweep produces a destabilizing effect on static directional
stability.
Equation (3.298) is a very crude estimation of (Cnp)w because the induced drag
is ignored in the strip theory approach. As the aspect ratio becomes lower, the
induced drag becomes important and the strip theory estimation will be in error.
In spite of these shortcomings, the strip theory has helped us to understand two
important facts: 1) the sweep-back has a stabilizing effect on static directional
stability and 2) the stabilizing effect increases with angle of attack. It may be
noted that the analysis /s restricted to the linear angle of attack range.
For more accurate estimation of the wing contribution to static directional sta-
bility caused by wing sweep, the following empirical relationl can be used for
subsonic speeds.
(C,,p))x.w 1
~- = 4TA -
tari Ac/4
~A~A +4 cos Ac/4)
A A2 {-6'. ~1) (3.299)
x cosAc/4- 2 -8cosA~4+' /
1 hthjed1A~4n12 9er wing quarter chord'sweep, A is the wing aspect ratio, and xa
between the center of gravity and the wing aerodynamic center in
270 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
terms of mean aerodynamic chord of the wing. According to our sign convention,
xa > 0 if the center of gravity is aft of the wing aerodynamic center. The value of
(Cnp)A.W given by Eq. (3.299) is per radian.
The wing quarter chord sweep is given by
tanAc/4-tanAU-( b )
For supersonic speeds, no general method is available for estimaLing the wing
contribution to directional stability due to sweep effecL Datcom r gives some empir-
ical data for certain wing geometries. The interested reader may refer to Datcomi
for more information.
Fus'e/age contribution. vfhe fuselage contribution to static directional sta-
bility is generally destabilizing and is influenced by wing geometry and wing
placement with respect to the fuselage.'
The fuselage contribution can be estimated using the following empirical
relation,l
(Cnp)B(V*O = -KNKRI (SS ) (lb ) 7deg (3.300)
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