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(3.174)
                                             V     (n - l)g .
                                R = -W                           (3.175)
Let SZ :  V]R be the angular velocity about the center of the semicircular path O.
Then, we have
Q - (n - l)g
   V           (3.176)
As a result of this angular velocity, the horizontal Lail experiences an increase in
angle of attack Aat.r as shown in Fig. 3.63. From the geometry, we have
                                It
                             Aar.r = R                             (3.177)
                        It V
                                               = v R                                   (3.178)
            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
　
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