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716 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
/.: -.
q dq
┏━━━━━━━━━━━━━━━━━━━━━━┓
┃ ┃
┣━━━━━━━━━━━━━━━━━━━━━━┫
┃-NSymbol ForeM b.cr~rC ┃
┃ o o ┃
┃-oo ┃
┃ Q o ┃
┃ A A ┃
┃ . . ┃
┗━━━━━━━━━━━━━━━━━━━━━━┛
E
b)
tL dq
o~
r7
Fig. 8.47 Effect of cross-sectional shape on static directional stability of generic
fighter.29 (Courtesy AGARDJ
STABIL17Y AND CONTROL PROBLEMS AT HIGH ANGLES OF AT1-ACK 717
(Arp )WR
deg 10
E
Angl.e ot attack, a~deg
Forebody
o
o
o
A
Fig. 8.48 Effect of forebody cross-sectional shape on wing rock of generic aircraft
model.:w (Courtesy AGARD.)
lowest levels of static directional and lateral stabilities yet displays a wing rock of
modest ampliltude.
8.70.2 Physical Flow Mechanism for Forebody-Induced Wing Rock
As we k:now, the loss of damping in roll at high angles of attack makes a config-
uration susceptible to wing rock but does not necessarily generate the wing rock.
To generate and sustain the wing rock in single-degree-of-freedom, free-to-roll
tes:s, the additional requirement is that the configuration must be statically stable,
and the roll damping must vary so that it is positive (undamping) at low roll angles
and negative (damping) at higher roll angles. However, for the forebody-induced
wing rock, the physical flow mechanism that can cause this type of variation ofroll
damping is not very clezu: Ericson has forwarded a conceptual hypothesis based on
1) the well-known Magnus effect observed on circular cylinders in crossfiow and
2) Swanson's experimental results35 on rotating circular cylinders in crossfiow.
Ericson refers to this as the moving wall effect hypothesjs.36
Swanson's experimental results on a rotating crrcular cylinder are presented in
Fig. 8.49. Ericson constructs his moving wall effect hypothesis as a conceptual
explanation to Swanson's measurements and then uses these ideas to develop a
physical explanation for the forebody-induced wing rock.
Ericson's moving wal/ effect hypothesis. Consider the fluicl flow about
a circular-cylinder. The flow pattern over a stationary cylinder depends on the
Reynolds number. Hence, it is natural to expect that, for a rotating cylinder, the
moving wall effect also depends on the Reynolds number.ln addition, the moving
wall effect depends on another parameter, the nondimensional rotation rate, p -
UW/Uoo, where Uw = cod/2 is the tangential velocity of the cylinder surface, w is
the angular velocity, and Uoo is the freestreanr'velocity. Analogous to the critical
Reynolds number, we have a critical value of the nondimensional rotation rate Pcr
associated with the given rotating cylinder.When p - Pcr, the slope of the Magnus
lift changes sign, and the Magnus lift starts building up in the opposite direction
as observed in Fig. 8.49. The value of Pcr depends on the Reynolds number. For
718 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
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