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            f21t
               = V-            (3.179)
                                               (n - l)l,g
                                = ~2                    (3.180)
e_ _ _/...__
250            PERFORMANCE, STABILtTY, DYNAMfCS, AND CONTROL
\
\
   -
 V
n
    /
-<Flight Path
Fig. 3.63    Induced angle of attack at horizontal tail during a pull-out maneuver.
With An :n - 1,
Actt.r  lr9
 A~ = \/2
Because both Aau and An are assumed to be small, we can write
(3.181)
dry/.r            lr 9
 d z7 - V2                                 (3.182)
       At D, L'  = n W  and at A, L  -  W.. The airplane at Dis disturbedin angle of attack
and load factor compared to the steady lcveJ flight at A. These two disturbances
together lead to a net increase in lift AL so that
or
n-l= AC~
    CL
An   1
dn   1
dCL = CL
(3.183)
(3.184)
(3.185)
(3.186)
(3.187)
Then we have
STATIC STABtLITY AND CONTROL
dcy,.,  dor/.r dn
dCL = dzdCL
  lt9
- 2CL
      lr pgS
N-
 2W
       1
251
(3.188)
(3.189)
(3.190)
= 2p,i                         (3.191)
where /ri - W]pgSI,. The parameter p.i is often called the longitudinal relative
density parameter.
     The total angle of attack of the horizontal tail is given by
at - (aw - iw + /r - €) + Acr/.r                             (3.192)
d~Yt   ]
d~ ='  (1-:1 )+2;_
Stick-fixed maneuverpoint.   We have
Cm - CLXa + Cmac*rn + Cmf - a,a;Vi 77t
(3.193)
(3.194)
              = CLXa + Cmac.rn + Cm f  - at[aw - iw + it - € + Aat.t] Vi r7,        (3.195)
Differentiating with respect to CL, we get
                                                                                    ar fVi r/,
~C~),=a+(tlC~_)f--..V,,7,(1-:1: : 7/ (3.196)
                 2)ul
The stick-fixed maneuver point Nm is that position of the center of gravity where
(dCm]dCL)m - O and is given by
Nm =  a.- (:C/  ),+V 7  [(1- ~) + 2p~,]            (3.197)
                                            Hm = Nm - Xc8
For a stable airplane, Hm is positive.
(3.198)
 L' -. L + AL
n=1+ \CC,
252           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
      Elevator required per g.     Because ofincreased stability level during the ma-
neu'ver, the magnitude of the elevator deflection required for trim also increases.
　
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