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┃------- Acg= No ┃
┃ - CL ┃
┣━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃ ┃
┣━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃LittiCodfk ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
a)
┏━━━━━┓
┃ / ┃
┃ - ┃
┃ - ┃
┃N\..- g ┃
┃/ ┃
┣━━━━━┫
┃ ┃
┗━━━━━┛
ble
Fig. 3.30 Variation of static stability lerrel with center of gravity position.
STATIC STABILITY AND CONTROL
203
Then, the static longitudinal stability at any other center of gravity location can be
expressed as
d Cm -
d~L = Xcg - No
(3.71)
The concept of neutral point has a close similarity with that of the aerodynamic
center As we know, with respect to the aerodynamic center, wing-pitching ::oment
remains constant with angle of attack. In other words, all the incremental wing
Iift due to a change in the angle of attack acts at the wing aerodynamic center.
Remember that the contribution of drag force to pitching moment is ignored. At
the neutral point, we have dCmldCL = 0, which also implies that the incremental
lift (of the complete airplane) due to a change in the angle of attack acts through
the neutral point. Thus, the neutral point is, in essence, the aerodynamic center of
the complete aircraft.
The static margin is another term often used to describe the level of stick-fixed
longitudinal static stability of the airplane. The static margin is defined as
= No - Xcg
-~~:, ),x
For a stable ailrplane, the static margin is positive.
3.3.8 Tad Lif;t for Trim
(3.72)
(3.73)
For the conventional airplane, the tail lift for pitch trim or equilibrium is given
CL.t = CL.wXa + Cmac.w + Cmf
V117t
(3.74)
Generally, Cm f iS positive. Whether Cmac.w iS positive or negative depends on the
wing cambcr. For positive camber (convex upward), Cmac.w < O and vice versa.
Usually, the magnitude of Cmac*w iS small compared to that of Cm f .
The dominant term on the right-hand side of Eq. (3.74) is the wing-lift term,
which is positive. Furthermore, xa > O for a conventional airplane with aerody-
namic center ahead of the center of gravity. Therefore, the tail lift is positive. In
other words, the tail carries a portion of the aircraft weight, and the wing lift is
correspondingly reduced. We have
Lrn = W - Lr
(3.75)
For modern high-speed aircraft with long slender fuselages and highly swept-
back wings, Lhe wing aerodynamic center is usually aft of the center of gravity or
xo < 0. For such aircraft, the tail load for pitch trim in steady level flight may be
downward as shown in Fig. 3.31. To understand how this happens, let us consider
the equilibrium in pitch as follows:
Cm - -CL,rvXa + Cmac.w + Cm f - CLJ V 7 T7r (3.76)
~:f\
dCL
STA-flC STABILtTY AND CONTROL
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