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STATIC STABILITY AND CONTROL
A8e      CL(Xc8 - Nm)
Az -  Cm8
       0.4(0.25 - 0.4193)
== ---
-0.02~6
- -3.1352
=:= 1.0194
A8e - -3.1352 *1.0194
      - -3.1960 deg
Now let us calculate the stick force per g as follows:
N:n = a..  - (:g-),+~
[(l - ;f  ) _ 2y,] (1 _,CC,,.,)
                                        0.08 * 0.6 *
= 0.24 - 0.15+                   0 9) (1 _ 0.35 _ _. ,)
           0.1
    x [l - 0.l-,.]  '
- 0.3369
                   &C/ ),,=  cg - NL
                                      - 0.25 - 0.3369    '
                          - -0.0869
dc:. = G, ( V~) ,l,Se  e CC.,  (:C/  ),.
-  l.0 *1500 * 0.9 * 2.0 , 0.6 .  (-000~66)  (-0.0869)
-. 39.105 N/g
257
V..  [(l-g )+2V, (l+')]
     (3.235)
An : //-2
  Rg
  l002
        =  1000 * 9.81
258
PERFORMANCE] STABILITY, DYNAMICS, AND CONTROL
3.5   Static Directional Stability
    In Section 3.3, we considered the airplane stability with respect to a disturbance
in angle of attack. This disturbance was assumed to be contained in a vertical
plane. We assumed that the airplane response in pitch was sufficiently slow so that
the pitch rate q could be ignored. In Se'9tion 3.4, we extended this approach to the
study of airplane stability during simple maneuvers. In this section, we will study
the airplane stability with respect to a disturbance in sideslip, which is contained in
the horizontal plane. Once again, we will assume that the response of the airplane
is sufficiently slow so that yaw rate r and roll rate p can be ignored.
  The nomenclature used to describe the motion involving the six degrees of
freedom is presented in Fig. 3.66. The longitudinal motion of the aircraft involves
forward velocity u, vertical velocity w, pitch angle 0, and pitch rate q. Sometimes
the longitudinal variables u, w, O, and q  are called symmetric degrees of freedom.
The directional motion involves sideslip velocity vl'yaw angle /t, and yaw rate r,
and thelateral motioninvolves bank angle ~ and rollrate  p.However, thelateral and
the directional degrees of freedom are always coupled because a sideslip induces
both rolling and yawing motions. Similarly, a yawing motion induces both rolling
motion and sideslip. In this section, we will study the directional stability of the
aircraft with respect to a disturbance in sideslip, and we will study lateral stability
in the next section.
   Static directional stability is a measure of the aircraft's ability to realign it-
self along the direction of the resultant wind so that the disturbance in sideslip
is effectively eliminated. A disturbance in sideslip could be caused by horizontal
gust, wind turbulence, or momentary (small) rudder deflection. Therefore, on en-
countering a disturbance in the horizontal plane, the aircraft orientation in space
 changes butits heading remains the same as before with respect to the Earth. These
 concepts are illustrated in Fig. 3.67. The aircraft is in a steady (undisturbed) level
 flight in Fig. 3.67a, encounters a horizontal gust Vw blowing from starboard side
 resulting in a sideslip as shown in Fig. 3.67b, and realigns itself with the resultant
ra
Q
Fig. 3.66    Axis system and nomenclature used in static stability analysis.
STATIC STABILITY AND CONTROL
         IJ   LV = ~tg     
                           
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┃          ┃            ┃
　
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