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university of florida thesis or dissertation formatting template

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otation is delayed f<strong>or</strong> the area in 32-46% span and 28-58% ch<strong>or</strong>d. Fewer regions on the wing<br />

where the Lissajous plots f<strong>or</strong>m a figure-eight shape are observed, indicating a continuous phase<br />

variation within 1 cycle. The transition from clockwise to counter-clockwise rotation is again<br />

seen. However, this transition occurs much farther aft f<strong>or</strong> the 8Hz ±0.5°, in the 53-73% ch<strong>or</strong>d<br />

region. Aft <strong>of</strong> this change the phase changes to 90° (circle).<br />

Figure 6-32 A) and D) are individual Lissajous figures taken at 98% span vs. 54% ch<strong>or</strong>d<br />

location, which c<strong>or</strong>responds to the shock transition region as seen in Figure 6-26 C). In this<br />

region, a figure-eight shape f<strong>or</strong>ms due to the continuous phase variation caused by the oscillat<strong>or</strong>y<br />

behavi<strong>or</strong> in the shock transition region. The figure-eight plot is not a harmonic, as is n<strong>or</strong>mally<br />

associated with figure-eights, but the result <strong>of</strong> the phase changing sign; from a lead to a lag, <strong>or</strong><br />

vice-versa. The shape <strong>of</strong> the figure-eight provides insight into phase/time lag. A fat top <strong>or</strong><br />

bottom shows where Cp is lagging behind the motion; alternatively a narrow top <strong>or</strong> bottom<br />

indicates where the Cp is leading the motion, trying to catch up. The transition across the shock is<br />

indicated by the change in lift (i.e., the change in value <strong>of</strong> Cp shown by position <strong>of</strong> starting red<br />

circle). An increase in -Cp is ahead <strong>of</strong> shock, whereas decrease in -Cp is behind shock. The 3-D<br />

plot in C) provides m<strong>or</strong>e insight as to how the Cp varies with time, with an s-shape.<br />

Figure 6-32 B) and E) are individual Lissajous figures taken at 93% span vs. 58% ch<strong>or</strong>d<br />

location, which c<strong>or</strong>responds to shock recovery region as seen in Figure 6-27 C). In this region, a<br />

figure-eight shape also f<strong>or</strong>ms due to the continuous phase variation caused by the oscillat<strong>or</strong>y<br />

behavi<strong>or</strong> in the shock transition region. The 3-D plot in E) shows an s-shaped feature. Figure 6-<br />

32 C) and F) are individual Lissajous figures taken at 88% span vs. 58% ch<strong>or</strong>d location, which<br />

c<strong>or</strong>responds to the region ahead <strong>of</strong> the shock recovery region as seen in Figure 6-28 C). The<br />

90

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