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since it is proportional to lift, and the upper surface of the airfoil is being examined. Local
vertical displacement is chosen as the independent variable as opposed to angle of attack (AOA),
or some other more typical aerodynamic parameter, due to the fact that as this work continues to
more complex motions, i.e. vibration and flutter modes, comparison will be made in a
straightforward manner with the same technique. A low-pass filter is applied to the data at 100Hz
to filter out the noise due to turbulence effects. The left-hand side of Figure 6-7 and Figure 6-9
corresponds to the LE of the wing, and the right-hand side corresponds to the TE of the wing.
The top of the figures corresponds to the wingtip and the bottom to the root of the wing. The left-
hand side of Figure 6-8 and Figure 6-10 corresponds to the same 2-D Lissajous plots seen in
Figure 6-7 and Figure 6-9, and the right-hand side corresponds to the 3-D Lissajous plots with
time being the third dimension. The red circle in all figures indicates the starting point of the
cycle, and the black arrows indicate the direction of rotation.
It can be seen in Figure 6-7 that there is a 90° (circle) phase shift over most of the wing.
The direction of rotation on the forward portion of the wing is counter-clockwise and transitions
to clockwise on the aft portion of the wing. Near this directional rotation change (and along the
TE), regions on the wing resembling figure-eights and other “odd” shapes are observed. These
do not indicate a harmonic that is normally associated with figure-eights but a continuous phase
variation within 1 cycle. Since the solution is “cyclically steady”, solutions at 0° are identical to
360° solutions, any time lag that shows up during a cycle has to be “made up” and that fall-
behind and catch-up nature leads to the phase variation within a cycle that is shown here. This
continuous phase variation within a single cycle also accounts for the other “odd” shapes that are
not simple ovals. There is also a significant amount of “noise” along the TE.
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