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elevator defiection to trim the aircraft at a higher lift coefficient (lower speed) and
a downward (positive) elevator deflection to trim at a lower lift coefficient (higher
speed) compared to an existing trim condition.
3.3.10   Most Forward Location of the Center of Gravity

8, = 8e.o + dd2  C,
     (.C.), C,
 =8e.o- C.
214             PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
8e
+
Z
6e, min
┏━━━━━━━━━━━┓
┃   Icg.t   :c92 lc9.  ┃
┣━┳━━━━━━━━━┫
┃  ┃)A/ .        icg  ┃
┣━┻━━━━━━━━━┫
┃                      ┃
┗━━━━━━━━━━━┛
mg.339   Elevator required fortrim at CL,   .
   The most forward location of the center of gravity Xc8J can be obtained as
follows:
                         .  J-  . d8e
8e = 8^o + dCL
=8e.o-( C.N)C,
Xcg. f  = No - (8e.max - 8.o) C,.
(3.108)
(3.109)
(3.110)
where 8e,max denotes the maximum permissible upward elevator deflection. Note
that, according to our sign convention, downward defiection is positive and upward
deflection is negative. Hence, 8e.m" happens to be a negative quantity. Beyond this
value, the elevator effectiveness falls off rapidly because of stall/fiow separation.
3.3.11  Permissible Centerof Gravity Travel
     For an airplane to be statically stablein pitch, the center ofgravity mustlie ahead
of the stick-fixed neutral point. From a stability point of view,itis desirable that the
center of gravity be located as much forward of the neutral point No as possible.
On the other hand, from the longitudinal control point of view, it is preferable
that the center of gravity be located as much aft of XcgJ  as possible. Therefore, to
satisfy both these requirements, the center of gra\rity must always lie within these
two limits as schematically shown in Fig. 3.40. The parameter Ax denotes the
stick- fixed permissible center of gravity travel, expressed in terms of the mean
aerodynamic chord
where
Ax; = No - Xcg. f
  Ax
Ax - -.
       c
(3.111)
(3.112)
Liad
STATIC STABILITY AND CONTROL
xcg,t                                        N o
                                                         
                                                         
┏━━━━━━━━━━━┳━━━━━━━━┳━━━━━━┓
┃                      ┃                ┃ f          ┃
┃                      ┃                ┃ t          ┃
┃                      ┃                ┃ .          ┃
┃                      ┃                ┃ t          ┃
┃                      ┃-- A:--         ┃.           ┃
　
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