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Figure 6-45 A) and D) are individual Lissajous figures taken at 98% span vs. 45% chord
location, which corresponds to the primary shock formation region as seen in Figure 6-41 C). In
this region, an odd circular shape forms due to the continuous phase variation caused by the
formation of the shock in the tip launcher’s presence. The 3-D plot in C) provides more insight
as to how the Cp varies with time, revealing a loop feature in the first quarter of the cycle.
Figure 6-45 B) and E) are individual Lissajous figures taken at 93% span vs. 62% chord
location, which corresponds to the shock recovery region as seen in Figure 6-42 C). In this
region, a figure-eight shape forms due to the continuous phase variation caused by the oscillatory
behavior in the shock transition region. The figure-eight plot is not a harmonic, as is normally
associated with figure-eights, but the result of the phase changing sign; from a lead to a lag, or
vice-versa. The shape of the figure-eight provides insight into phase/time lag. A fat top or
bottom shows where Cp is lagging behind the motion; alternatively a narrow top or bottom
indicates where the Cp is leading the motion, trying to catch up. The transition across the shock is
indicated by the change in lift (i.e., the change in value of Cp shown by position of starting red
circle). An increase in -Cp is ahead of shock, whereas decrease in -Cp is behind shock. The 3-D
plot in C) provides more insight as to how the Cp varies with time, with an s-shape.
Figure 6-45 C) and F) are individual Lissajous figures taken at 88% span vs. 62% chord
location, which corresponds to the region ahead of the shock recovery region as seen in Figure 6-
43 C). The shape of this Lissajous is nonlinear with a phase closer to 135°. This is due to shock
formation. The 3-D plot in F) exhibits a loop feature in the first quarter of the cycle.
Wavelet Analysis
Wavelet analysis is applied to points of interest on the wing in Figure 6-46, Figure 6-47,
and Figure 6-48 for the tip-launcher Grid8 8Hz pitch case, in order to gain further insight into the
temporal nature of the results. In each set of figures, A) gives the time history of the Cp variation,
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