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at 100 mts in level fiight at sea level with one engine completely out.
Solution.    Yawing moment due to asymmetric thrustis given by
Nr - Thrust *distance
        ~  10,000 * 5.0
      - 50,000 Nm
The yawing moment due to rudder defiection:
For equilibrium,
Nr = ;:p V2SbCn2Sr8r
Nr + Nr -0
so that
STATIC STABILITY AND CONTROL
Fig. 3.92    De\relopme/t ofsideslip due to bank.
8r - pV~;VC
                             -2 * 50,000
-   .225~0~2~50~~0~0 00 )
= 16.32 deg
3.6 LateraIStability
       Lateral stability is the inherent capability ofthe airplane to counter a disturbance
in bank. In level flight, both wings are in a horizontal plane and the bank angle is
zero. However, because of some disturbance,if the airplane banks but very slowly
so that the roll rate is negligibly small, then there is no aerodynamic mechanism
to generate a restoring rolling moment unless sideslip develops. Therefore, the
airplane is neutrally stable with respect to a disturbance in banikv without sideslip.
Fortunately, once banked, the airplane develops a sideslip in the direction of the
bank because ofa spanwise component ofthe weight W sin ~ as shown in Fig. 3.92.
As a result of this sideslip, if a restoring rolling moment is induced, then the
airplane is said to be Iaterally stable. Once the wings are back in level condition, the
disturbances in bank angle and sideslip are eliminated, and the airplane returns to
its original, steady level flight condition. On the other hand, if the induced rolling
moment causes the bank angle to increase further, generating more and more
sideslip, the aircraft is said to be laterally unstable. If the induced rolling moment
is zero and the airplane remains constantly banked and keeps on sideslipping, then
it is said to be neutrally stable.
      The generation of a rolling momenr due to sideslip is also called dihedral effect,
and an airplane that develops a restoring rolling moment because of sideslip is said
to have a positive or stable dihedral effect. Therefore, a laterally stable airplane
has a positive dihedral effect and vice versa. Note that the dihedral effect is dif-
ferent from the dihedral angle. The dihedral angle is the angle between the plane
of the wing and a horizontal plane, positive if the wingtip is above the wing root.
If the wingtip is below the wing root, the dihedral angle is negative (unhedral)
294           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Dihedral
Unhedral
Fig 3.93   Defirution ofwing dmedraland unhedral.
(see Fig. 3.93). The dihedral effect, on the other hand,is the rolling moment devel-
opcd by the airplane because of sideslip and depends on many factors, including
the wing dihedral angle.
       From the above discussion, we observe that, for alaterally stable aircraft, a posi-
tive sideslip induces a restoring rolling moment, which according to the usual sign
convention, is negative. Similarly, if a stable aircraft sideslips to port, i.e., sideslip
is negative, theinduced (restoring) rolling moment is positiye (see Fig. 3.94). Thus
the criterion for lateral stability can be expressed mathematically as
or, in coefficient form,
where
Lp <0
C.p < O
acl
ap
(3.336)
(3.337)
(3.338)
(3.339)
(3.340)
D
STATIC STABILITY AND CONTROL
     y     +                   4                             
                                                             
┏━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━┓
┃             CL       ┃~--\ -(,                  Ntut r; ┃
　
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