PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL2(99)

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  v : -p, then O  = ct, and finally a rotation 4 of any given value (Fig. 4,6) so that
using Eq. (4.22) we get
         cosacosp          -cosasinp      -sin,
T3= sinctsin4cosp+sinpcos4 -sin)3sinasin4+cospcos4 s,.4':/oo~]
                     sin cr cos 4 cos f/ - sin p sin4     -sin p sin a cos 4 - cos p sin a     cos4 cc
              (4.37)
Thevelocit5rvectormea ssystemisgivenby
             (4.38)
X b( X:,,X
                         
┏━┳━━━━━━━━━┓
┃  ┃~ ~y:             ┃
┃  ┃                . ┃
┗━┻━━━━━━━━━┛
Fiig.4.6   Wind and body axes systems.
yv:) (a)
yw
 ( yb)
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 329
                                 : flight velocity. In the body axes system,

X [U:o]
                 -cos cr sin p
-sin p sina sin~+cos pcos4
-sin  p sin a cos4 - cos p sin a
                              cosa cos p
      - Uo    sina sin4 cos p +sin p cos 4
                     sin cy cos 4 cos p - sin p sin ~
so that
                                                    U - Uo cosa cos p
                                          V  -. Uo (sin a sin 4 cos p + sin p cos ~)
                   ,    W = Uo(sinacos~cosp - sinpsin~)
The angle of attack and sideslip are customaril:         ined as
          a=_-,( )define
(4.39)
(4.40)
(4.41)
(4.42)
(4.43)
(4.44)
                                        p = si.-, (j/)                               (4.45)
With U, V, W given by the Eqs. (4.41-4.43), we find that the above definitions
of a and p hold only when the bank angle # -. 0.If ~ + 0, part of the angle of
attack gets converted to sideslip. As a result, the effective angle of attack aet:r will
be smaller than the given angle of attack a, and the effective sideslip peff will riot
be zero. This can be visualized as follows.
     Consider an aircraft model mounted in a wind-tunnel test section. Let ct be the
angle between the modellongitudinal axis (zero-lift line) and the tunnel axis and
4 denote the bank angle about the modellongitudinal axis. Assume that the model
is not given sideslip or p - 0. .
    With p = O, using Eqs. (4.41-4.45), we have
Cteff = taDc-l
(:)
= tari-l(tari ce cos 4)                                     (4.46)

jl:}il~a~]
                             cos a cos p
　
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