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       As before, we assume that the lateral stability of an airplane, as measured by the
parameter Cip, is equal to the sum ofindividual contributions from the fuselage,
wing, and tail surfaces. The effects ofpower on lateral stability are generally small
 and ignored.
    Fuse/age contribution.    The direct contribution ofthe fuselage to lateral sta-
bility is neYgligible. However, because of its significant interference effect on the
wing, it makes an indirect contribution as discussed in the following section under
wing contribution.
     Wing contribution.     The wing contribution to lateral stability mainly depends
on 1) wing-fuselage interference, 2) wing dihedral angle, and 3) wing leading-edge
sweep. A brief discussion of these effects is given in the following section.
    Wing-fuse/age interference.    This interference effect depends on the loca-
tion of the wing~A high wing produces a stable contribution, and a low wing
produces an unstable or destabilizing contribution.
~p = ~~
Cl = q~-b
296           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
a) High-wing configuration
b) Low-wing configuration
Fig. 3.95    Schematicillustration of wing-fuselage interfeRnce in sideslip.
Ctl = ct i:pr
 qi = ;p\/o2
(3.341)
(3.342)
The wing contribution to lateral stability at low subsonic speeds can be estimated
using the strip theory as follows.
      Let c(y) be the local chord and ao(Y) be the local sectional lift-curve slope. The
lift force developed by the elemental strip RT of width dy on the'right wing is
given by
STA11C STABILITY AND CONTROL
dL = qtc(y)dy Cu
     = 2ip Vo2c(y)ao(Y)(a + f3r)dy
The rolling moment due to the e,lemental strip RT is given by
dL = -~p Vo2c(y)ao(Y)(cy + f/r)y dy
The rolling moment due to the right wing is given by
297
(3.343)
(3.344)
(3.345)
~R  = - ~p \/o2 ['/2 c(y)ao(y)(a, + pr)y dy                    (3.346)
Similarly, the rolling moment due to the left wing is given by
L, = ~p\jo2  "1~c(y)ao(y)(ce - pI')ydy             (3.347)
The total rolling moment
-   ~ = -p I/o2f/~ [b/2c(y)ao(Y)Y dy
or, in coefficient form,
                                                   P b/2
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
　
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