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Fig. 8.29   Schematicillustration ofhysteresisin rolling moment-z4
8.8.1   Wmg Rockof a Detta Wing Model
     To understand the wing rock generated by the wing,let us study the wing rock of
a single-degree-of-freedonx free-to-roll delta wing model. It is interesting to note
that only those delta wings whose leading-edge sweep is 75 deg or more exhibit
wing rock. The angle of attack for the onset of wing rock of such a wing is below
 that for the vortex breakdown to occur at the trailing edge. Therefore,it is generally
accepted that only thin, highly swept (slender) delta wings exhibit wing rock, and
 vortex breakdown is not the cause for the onset of wing rock of such wing models.
 As an example, let us consider the wing rock of a thin, sharp-edged 80-deg delta
 wing model, which has received considerable attention in the literature.
      At high angles of attack, the 80-deg delta wing model loses roll damping. On
 receiving a disturbance, the free-to-roll model starts oscillating, and the amplitude
of oscillation builds up rapidly as'shown in Fig. 8.30. Even a small disturbance
in the form of wind-tunnel turbulence or fiow unsteadiness is usually sufficient
 to initiate the rocking motion. In view of this, such wing rock is often called a
 self-induced wing rock.
     It is interesting to observe that the limit cycle amplitude is reached within few
 oscillations. The maximum amplitude and the frequency of wing rock vary with
 angle of attack as shown in Fig. 8.31. For the 80-deg delta wing model, the angle
  of attack for the onset of'wing rock is around 20 deg and, below this value of angle
  of attack, any imparted disturbance will be damped out. In Fig.  8.32, the angle of
  attack boundaries of vortex asymmetry and 'vortex breakdown for the 80-deg delta
 wing are shown. From Figs. 8.31 and 8.32, we observe that the angle of attack of
  20 deg for the onset of wing rock is below the angle of attacK for the vortex asym-
  metry. Also, it is-below that for the vortex breakdown occurring at the trailing edge.
       There are some variations in the values of angle of attack for the onset of wing
 rock, the peak amplitude, and the angle of attack at which the peak amplitude
 occurs as measured by vanous researchers. The main reason for these variations
  is believed to be the bearing friction in the free-to-roll apparatus. If the bearing
  friction is high, the wing rock starts at a higher value of angle of attack because
  a larger destabilizing aerodynamic moment is necessar)r to set the model -rolling.
  On the other hand, if such a wing were in free fiight (no bearing friction), it will
  exhibit wing rock at a much lower angle of attack than measured in the ground-
 based, free-to-roll tests. For the data presented in Fig. 8.31, the peak wing rock
STABILITY AND CONTROL PROBLEMS AT HIGH ANGLES OF ATTACK   701
+,
deg
   +
deg/sec
 TIME:s
a) Time history
+,deg
                                 b) Phase plane plot
Fig. 8.30    Typicalwing rock bulildup of 80-dcg delta wing.:"
amplitude occurs around a - 25 deg and, for a > 50 deg, the orderly periodic
large amplitude motion characteristic of wing rock degenerates into an unsteady,
low-amplitude, random oscillation.
702           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
┏━┳━━━━━┓
┃  ┃      -,  ┃
┃- ┃          ┃
┗━┻━━━━━┛
a [~9]
Fig. 831    Variation of wing rock amplitude and frequency with angle of attack for
80-deg delta wing.zr
rF,
o
Z
o     5'    10    13    20    ZS    30    U    40
Fig. 8.32    Boundaries for -,ortex asymmetry and yortex burst.zs
STABILI-fY AND CONTROL PROBLEMS AT HIGH ANGLES OF ATTACK   703
  .002
           o
r   ~.002
ULp -,ffl4
deg'l -.006
                                     - .008
　
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