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STATIC STABILITY AND CONTROL
Thus, the stick force variation can be represented as
                                                 Fs  = K "V 2(K2 + Ch/S.,8t) + K"
where
                                K'= 2LpKI
              K,,=-K,CC. Vg&~ ),
233
(3.162)
(3.163)
(3.164)
Note that, for a given center of gravity location, K" is a constant. Furthermore,
if the aircraft is operating at a constant altitude as it does in a steady level flight,
 K' is also a constant. Note that K f < O and K' < 0. For a stick-free stable aircraft,
 K t' < O and, for a stick-free unstable aircraft, K'f > O.
      The stick force gradient is grven by
~:t = 2K nV (K2 + Ch8,8r)                                 (3.165)
    The tab detlection for stick force trim (Fs = 0) is given by
                                                 1
                                           8,.lrim = - C~ ( K K~ + K2)                            (3.166)
When the stick force is trimmed by tab deflection as given by Eq. (3,166), the stick
force and stick force gradient at any other speed can be expressed as
   Fs=K2y4CC.,G~)free[(...)2_-] (3.167)
dd7t = 2K2 Vl1C.  ~~ )- V.V,                   (3.168)
                                                                                            I
         .  ~~), =2K2VgCC~.,GCj_ -V:.        (3.169)
                         nm
For proper operation by the pilot, the airplane designer has to ensure that the stick
force gradient is positive, i.e.,
dd~ > 0                             (3.170)
The schematic variation of the stick force is shown in Fig. 3.56.1t is observed that
the stick-free stability provides a constant pull force on the stick and ensures a
proper sign of the stick force gradient (dFs/d V  >  O) at the trim speed.
     Airworduness requirements5.6 state that the stick force gradient must be positive
and greater than a certain minimum value. A typical nunimum value suggested is
1 lb/kn or 8.72 Ns/m.5J For short-duration applications, the recommended maxi-
mum allowable stick force to operate the pitch control (elevator) is 60 lb or 267.3
N.Itis further recommended that for sustaine~ application, the stick force for pitch
control should not exceed 10 lb or 44.60 N.5.7
234           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
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