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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)
where K N is an empirical wing-body interference factor that is a function of the
fuselage geometry and the center of gravity position, K RL is an empirical factor
that is a function of the fuselage Reynolds number, SB.S iS the projected side area
of the fuselage, S is the reference wing area, and lf is the length of the fuselage.
According to Datcom,i Eq. (3.300) is valid for both subsonic and supersonic
speeds. The parameters KN and KRt can be determined using the data given in
Figs. 3.73 and 3.74.
Ta17 contribution. The contribution of the horizontal tail, similar to that of the
wing, depends on dihedral and sweep. Furthermore, the horizontal tail is usually
much smaller in size than the wing. Hence, the contribution of the horizontal tail
to static directional stability can be safely ignored.
The vertical tail is perhaps the single largest contributor to static directional
stability. Its contribution depends on its moment arm from "the center of gravity,
surface area, aspect ratio,sweep, and aft fuselage geometry. The aft fuselage and the
horizontal tail provide the beneficial endplate effect, which increases its effective
aspect ratio, hence the Iift-curve slope. The contribution of the vertical uul is also
affected by the fuselage sidewash.
For subsonic speeds, the side force developed by the vertical tail when the rudder
is held in neutral position (rudder-fixed) is given by Datcom:l
or
Yv = -kqvav(f/ + a)Su (3.301)
C),.v = -kay~ + )-7, (SS ) (3.302)
STATIC STABILITY AND CONTROL
t -Jcm ri
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