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where ao = ao(Y) is the sectionallift-curve slope, we have
dF = _;2 p Vo2,OS2 A(l+ p tan A)
x [aoa2 sec2 Ap tan A + CDO.I(1 + B tan A) + CDa.la sec A]
x c(yh) dyh (3.291)
The yawing moment caused by the right wing is given by
NR = -ydF . (3.292)
= g p Vo?- COS2 A(l + p tan A)
x [aoa,2 sec2 Ap tan A + CDO.I(1 + p tan A) + CDar.la sec A]
X [,- (yh)yhdy,r (3.293)
Similarly, the yawing moment caused by the left wing is given by
N, = gp Vo2.OS2 A(l - p tan A)
. X [aoa2 sec2 Ap tan A - CDO.I(1 - p tan A) - CDa.La sec A]
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
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动力机械和机身手册2(20)
