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            (3.221)
                                           - Glqrlt Sece ACL CC.,  ~~ ), ..
where Gi is the gearing ratio between the stick and the elevator. Using ACL =
AnCL, we obtain the stick-force per g as follows:
d/. = G, ( g) ,I,Se:  CC.,  G~i  ),.                   c3.222)
Usually, Ch8, < 0 and Cm8 < O. For a stable airplane, (dCmldCL)m, < 0. Then,
dFs/dn  < 0, i.e., to pull a load factor above unity, for a stable airplane, the pilot
has to apply additional negative stick force (pull) as given by Eq. (3.222)-
3-4-2  Trjrrning Flightin HorizontaIPlane
      Consider a level coordinated tuming mancuver in a horizontal plane as shown
in Fig. 3.64. Let O be the center of the turn and 02 be the angular velocity about
a vertical axis passing through O. The angular velocity vector S2 can be resolved
along the body y and z axes as
                                                               cZy = c2 siri~                                             (3.223)
                                                             g2z = -s-2 cos 4                                           (3.224)
where S2 :  V/R and R is the radius oftum. The component C2y is equivalent to a
pitch rate q about the body y axis. This apparent pitching motion gives rise to an
induced velocity qlr at the horizontal tail (see Fig. 3.65) resulting in an increase
in the horizontal tail angle of attack.
                                                                                            q Lt
                            Act/.r - -V                          (3.225)
I
      S2 sin ~lr
= -V                         (3.226)
il
Fig. 3.64    Airplane in a coordinated turn.
D
STATIC STABILITY AND CONTROL
Aa
255
Fig. 3.65     Induced angle of attack at horizontal tail due to pitch rate in a coordinated
turn.
From Chapter 2, we have
Then,
                     t, ,
Aar'.r = tV-g (. - 1)
(3.227)
(3.228)
(3.229)
(3.230)
Proceeding in a similar fashion as we did before for the case of a pull-up in a
vertical plane, we obtain
darr.r
dC  = 2/, (1+')
(3.231)
&g ), = a+&~:)f -  .V.  [(l-~)+2p, (1+')]  (3.232)
                                                ar Vi o,
　
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