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Figure 6-31 corresponds to the LE of the wing, and the right-hand side corresponds to the TE of
the wing. The top of the figure corresponds to the wingtip and the bottom to the root of the wing.
The left-hand side of Figure 6-30 and Figure 6-32 corresponds to the same 2-D Lissajous plots
seen in Figure 6-29 and Figure 6-31, respectively; 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 the lower left-hand portion of Figure 6-29 that there is a 0° (diagonal line
downward to the left) phase shift region with counter-clockwise rotation. Progressing aft, the
phase abruptly shifts to 180° (diagonal line downward to the right) with clockwise rotation. This
shift is indicative of the pitch axis. Once in the 63% chord region, the Lissajous plots begin to
open up, indicating the shock structure region. The plots then flip back to a 0° shift in the 78%
chord region upon aft and inboard progression. However, in the outboard region, the phase
remains at 180° and takes on a highly “odd” shape. This “odd” shape is also seen along the LE
upon outboard movement from the 68% span section, and all along the tip of the wing. Any plot
that is not a symmetric oval about an arbitrary axis is the result of a phase variation within 1
cycle. The figure-eight plot is not a harmonic, as is normally associated with figure-eights, but
the result of the phase changing sign. The phase changes from a lead to a lag, or vice-versa.
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. The region beginning at the top
(tip) in the 23-28% chord region and extending at the bottom (root) to the 43-48% chord-region,
indicates a transition from clockwise to counter-clockwise rotation. Increased suction (increased
lift) is seen with increased displacement (increase in AOA) in front of the pitch axis, as is
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