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hingeline is called hinge moment. The sign convenLion for the elevator hinge
moment is as follows. The hinge moment is considered positive if it rotates the
elevator so that the trailing edge goes down and is negative if the trailing edge
goes up. .
      Assuming that the hinge moment depends linearly on horizontal tail or stabilizer
angle of attack cts and elevator deftection 8e, we have
                                  C/r = Cho + Chacrs + Cha,c8e                        (3.116)
where
Ch = qN;_                          (3.117)
. Ch , =  aac
Ch8.e = aa~-
a) at > 0
--
                           b) ar < O
Fig.3.43    Concept of elevator floating angle.
(3.118)
(3.119)
218             PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
/
/
/II
Fig. 3.44   SchemaOc iHustration of the relation between stick-free.stability and ele-
'vator floating characteristics.
Here, Mrr is the hinge moment. Usually, both Cha and Ch;S.e are negative, and their
magnitudes depend on the location of the hingeline with respect to the leading
edge.
    When the elevator is freely floating, the hinge moment is zero. This condition
gives the floating angle of the elevator 8ef as
  Cho + Chcr(Ys
 Chb.e
(3.120)
We know that the elevator deflection required to trim the aircraft at a given lift
coefficient is directly proportional to thoe llevel of stick-fixed longitudinal stability
of the aircraft. To maintain a pitch trim during flight, the pilot has to continuously
hold the elevator at that position by'constantly applying a steady force on the stick
 (control column). This can be quite strenuous if he has to do th7s over an extended
period of time.
     Suppose that the pilot takes his hands off the stick and leaves it free. Then the
elevator will float freely and assume the floating angle given by Eq. (3.120). In
principle, this floating angle can be any one of the four possibilities shown in
Fig. 3.44.
      Let 8e.R denote the required elevator deflection to trim the aircraft at a particular
 speed or lift coefficienL Suppose it so happens that the floating elevatorPassumes
 exactly this position, i.e., 8e. f = 8e.R. Then the pilot does not have to move the ele-
  vator or the stick to trim the aircraft at that lift a~fficient or speed. The aircraft does
 it by itself. In other words, both the required elevator detlec~:on (stick movement)
 and stick force arc zero. If this is che case, then the airplanc is said to be neutrally
 stable stick-free. On the other hand, if the elevator floats in the right directio;
 (upward) but stops a little short of 8e.R assuming position I, then the pilot has to
 move the elevator only by the amount 8e.R - 8e.i. Thus, in stick-free condition, the
 airplane is still stable, but the level of stability has reduced. Suppose the elevator
 overshoots and assumes the position II; then the pilot has to move the elevator in
 the opposite (downward) direction by the amount 8c.n - 8e.R, which implies that
 the airplane has become statically unstable in stick-free condition. On the other
  hand, if the.elevator floats down to position III, the pilot has to move the elevator in
 the right direction (upward) but by an increased amount 8e.m + 8e.R. This implies
  that the airplane has become more stable in stick-free condition. Thus, the floating
 characteristics of the elevator have a direct bearing on the stick-free stability.
STATIC STABILITY AND CONTROL

　
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