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the roll cycle, and the black arrows indicate the direction of rotation of the Lissajous. The set of
Lissajous plots for the tip-launcher case is slightly different from the clean-wing case seen in
Figure 6-31. First, the tip-launcher plots include two extra span stations, one on the tip launcher
and one at the LE antennae. The Lissajous figures for the pitch oscillation cases are very
different from the roll oscillation cases. However, the overall trends are similar for the tip-
launcher Grid8 and clean-wing Grid9 pitch cases. In the lower left-hand potion of the plot, a 0°
to 45° phase shift is observed with counter-clockwise rotation. The phase suddenly shifts to
180°, essentially mapping out the pitch axis. There is also a corresponding phase shift on the tip
launcher (LAU) for Grid8 at the 13% chord location indicative of the pitch axis. The phase then
shifts to 180° with clockwise rotation, with a delayed shift in the 42-59% span, 28-68% chord
region, and begins to open up aft along the wing with 90° phase shift along the inboard, TE
portion of the wing. The phase maintains a 180° phase shift near and along the tip for Grid8.
A transition from clockwise to counter-clockwise rotation is apparent in the 78% chord
region at the root and extending back to the 68% chord region near the tip. This shift in rotational
direction can be attributed to the shock transition. It is interesting to note that the rotational
directions for the pitch cases are opposite of those of the roll cases. This has to do with the roll
beginning left-wing-up and the pitch beginning left-wing-down. Additionally, the region of
change is much further forward moving toward the tip launcher. The tip-launcher plots show a
more narrow nature in the shock transition region than the rounder clean-wing case, and a more
open nature near the tip. There are also a few regions on the wing, mostly near the tip launcher
and shock transition, where the Lissajous plots form a figure-eight shape, indicating a continuous
phase variation within 1 cycle. Overall, the Lissajous figures for both pitch oscillation cases
differ significantly near the tip (88-100% span) and shock transition region.
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