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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; ┃
┃i-, ,.                ┃                                  ┃
┣━━━━━━━━━━━╋━━━━━━━━━━━━━━━━━┫
┃~     -\           6  ┃                                  ┃
┃~-y                   ┃                                  ┃
┃i-y                   ┃                                  ┃
┗━━━━━━━━━━━┻━━━━━━━━━━━━━━━━━┛
Fig. 3.94    Concept of static lateral stabiLity.
295
Here, L is the rolling moment, (Remember that Lhe symbol L is also used to de-
note the lift,) Thus, an airplane with Ctp  < O is said to be laterally stable and that
with Cip > 0 is laterally unstable. An airplane with Ctp = 0 is said to be neutrally
stable. An airplane that is neutrally stable or unstable in roll can still be fiown
but needs constant intervention from the pilot to counter roll disturbances, which
can be quite annoying. Usually, such airplanes are made closed-loop stable using
feedback control systems, which we will study in Chapters 5 and 6.
3.6.2   Evaluation of Lateral Startn7itjr
　
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