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c,=_2SPbr "/ c(y)ao(y)ydy
)
b/2
Cip =-2t~ b/: c(y)ao(y)ydy
(3.348)
(3.349)
(3.350)
For a rectangular wing with a constant chord c and a constant sectional lift-curve
slope ao (constant airfoil section), Eq. (3.350) simplifies to
The flow over a fuselage in sideslip,in principle, is similar to that over a circular
cylinder in crossfiow as shown in Fig. 3.95. In positive sideslip for a high wing
airplane, the inboard sections of the right wing experience a local upwash and an
increasein angle ofattack, whereas the inboard sections ofthe port wing experience
a downwash and a decrease in angle of attack. As a result, the lift on the right wing
is higher compared to that on the left wing. This imbalance in lift gives rise to a
stable or restoring rolling moment for a high-wing configuration (see Fig. 3.95a).
In a similar way, we observe that for a Iow-wing configuration (Fig. 3.95b), the
induced rolling moment is destabilizing. If the wing is located in midplane, the
interference effects are small, and the induced rolling moment is virtually zero.
Effect of wing diheadral. In general, the wing dihedralhas a stabilizing effect
on lateral stability. To understand how the dihedral influences the lateral stabilitjr,
let us refer back to Fig. 3.70 and consider an unswept, rectangular wing with
a constant dihedral angle :r operating at an angle of attack a, sideslip f/, and a
forward velocity Vo. The local angle of attack and local dynamic pressures, as
given by Eqs. (3.248) and (3.250) are
298 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Effect of wing sweep. In general, the sweep-back has a stabilizing effect,
and the sweep-forward has the opposite or destabilizing effect. To understand
how the wing leading-edge sweep infiuences the wing contribution to static lateral
stability, let us refer back to F.gY '3.72 and consider a swept-back wing with no
dihedral and operating at an angle of attack a and sideslip P and moving with a
forward velocity Vo.
As before, let us assume tbat both ct and t3 arc small so that higher order
terms involving these two parameters can be ignored. Then, from Eqs. (3.280) and
(3.285), the effective angle of attack and effective dynanuc pressure are given by
a -.
(1 :1 p tan A)cos A
qt = ,}:P Vo)- COS2 A2(1 +- p tan A)2
(3.352)
(3.353)
where the first (upper) sign applies to the right wing and second (lower) sign
applies to the left wing when the sideslip is positive.
At low speeds, the contribution of a sufficiently high-aspect ratio swept-back
wing to lateral stability can be approximately evaluated using the strip theory as
follows.
Consider a strip RT of width dyh on the right wing. Let yh denote the spanwise
coordinate along the quarter chordline and c(yh) denote the local chord normal
to the wing leading edge. Then the lift on the right wing elemental sU:ip RT is
given by
d Lift - qtc(yh) dyhaoaf
= gp Vo2 ,OS2 A(l + p Mri A)2tro
(1 + p tan A)cos A
= /Z p Vo2 COS A(l + p tan A)aoac(yh)dyh
The rolling moment due to strip RT is given by
(3.354)
] (yh)dy,
(3.355)
(3.356)
dL = - ~p Vo2 COS A(l + p tan A)aoac(yh)yhcos A-dyh (3.357)
The rolling moment due to the right wing is given by
~ sec A
LR=-;pVo7-cos2A(l+ptanA aoc(yh)yhdyh (3.358)
Similarly, the rolling moment due to the left wing is given by
g sec A
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