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of attack.33 (Courtesy AGARDJ
static rolling moment with roll angle for the 65-deg delta wing at a = 30 deg and
p : 0 is shown in Fig. 8.42. It is evident that the existence of roll attractors is
caused by the stable zero crossing of the rolling-moment curve at @ : 0 and :t21
deg. The zero crossing at 4 = +7 deg is unstable. The rnultiple~zero crossings of
the rolling moment occur because of the complex variation of vortex breakdown
point over the 65-deg delta wing.33 However, a clear physical understanding of
this phenomenon is still not available at present.
   The sideslip has an interestino effectFon the roll attractor of the 60-deg delta
wing as shown in Fig. 8.43. With the increase of sideslip, the two attractors move
towards each other and, at p - 20, the two attractors merge into one,i.e., for p = 20,
the attractor is at -45 deg and, at )3 = -20, the attractor is at +45 deg.
   Another interesting effect of the sideslip is the development of wing rock as
indicated by the hatched line in Fig. 8.43 anvd the t,ime history of Fig. 8.44. As can
be observed, the 60-deg delta wing develops wing rock about one roll attractor,
undergoes some wing rock cycles, and then jumps to another attractor and contin-
ues wing rock. At present, no clear physicajI explanation exists for such complex
behavior.
   An interesting consequence of the existence of multiple-roll attractors is that,
in the presence of a long slender fuselage, it can lead to a wing rock with nonzero
mean roll angle:34 The wing rock is apparently induced by the forebody, and the
existence ofthe multiple, nonzero attractors causes the wing rock to develop around
one of the nonzero attractors.
STABILITY AND CONTROL PROBLEMS AT HIGH ANGLES OF ATTACK   713
t}eta, dag
Flig. 8.43    Effect of sideslip on roll attractors of 60-deg delta wing at a = 30 deg and
p = -15 deg.32 (CourtesyICAS.)
Fig. 8.44    Development ofwing rock and jump phenomenon.32 (CourtesyICAS.)
714            PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
8.10   Forebody-Induced Wing Rock
     As stated earlier, the vortices shed from the slender, pointed fuselage forebodies
at high angles of attack significantly affect the static stability characteristics of
fighter aircraft. At high angles of attack, the forebody vortices assume asymmetric,
bistable configuration similar to that observed on slender delta wings. Furthermore,
the forebody vorticesinteract with LEX/wing vortices and produce nonlinearitiesin
static aerodynamic coefficients. Therefore, it is natural to expect that the forebody
has a significant effect on the dynamic motions like wing roc~. In this section, we
will study how the forebody vorticcs affect the wing rock.
       Consider a generic fighter aircraft model shownin Fig. 8.45. This generic aircraft
model has a swept-back wing with a leading-edge sweep of 26 deg and a slender,
pointed forebody. A typical, single-degree-of-freedom, free-to-roll time history at
an angle of attack of35 deg is shown in Fig. 8.46a with corresponding phase plane
plotin Fig. 8.46b. As stated before, the isolated delta wing with 26 deg sweep is not
likely to generate the wing rock. Therefore, the wing rock of this geeneric fighter
model must be generated by the forebody vortex flow field. This type of wing rock
is called forebody-induced wing rock. The fact that the limit cycle condition is
reached within three or four cycles indicates that the forebody-induced wing rock
can be much more violent compared to that due to the slender-delta wing.
      This generic aircraft model exhibited wing rock when fitted with different wings
of varying aspect ratio and sweep. The wing rock was observed even on a model
 without the wing. This implies that the geometry of the wing has virtually no effect
 on the forebody-induced wing rock. For the configuration without the wing, the hor-
 izontal and vertical tail surfaces coming under theinfluence of the forebody vortex
Fig. 8.45    Generic fighter ain:raft modeIP (Courtesy AGARD.)
STABILITY AND CONTROL PROBLEMS AT HIGH ANGLES OF ATTACK   715
W
N, o
deg
-20
                                                                                                 
　
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