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university of florida thesis or dissertation formatting template

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Figure 6-8 A) and C) are individual Lissajous figures taken at 93% span vs. 64% ch<strong>or</strong>d<br />

location, which c<strong>or</strong>responds to the shock recovery region as seen in Figure 6-5 A). In this region,<br />

a great deal <strong>of</strong> unsteadiness is observed along with the previously mentioned odd figure-eight-<br />

like shape due to the continuous phase variation. The 3-D plot in C) reveals that the Cp varies<br />

little time, although the signal is noisy. The sinusoidal shape is due to the fact that the local<br />

vertical displacement is sinusoidal. Figure 6-8 B) and D) are individual Lissajous figures taken at<br />

88% span vs. 81% ch<strong>or</strong>d location, which c<strong>or</strong>responds to the region aft <strong>of</strong> the shock recovery as<br />

seen in Figure 6-6 A). Similarly, a great deal <strong>of</strong> unsteadiness and another odd figure-eight-like<br />

shape due to the continuous phase variation is seen. The 3-D plot in D) is similar to that in C).<br />

Figure 6-9 shows the set <strong>of</strong> Lissajous plots f<strong>or</strong> the 8Hz ±0.5° case. Most <strong>of</strong> the plots are<br />

open in nature. Much <strong>of</strong> the f<strong>or</strong>ward p<strong>or</strong>tion <strong>of</strong> the wing exhibits the 90° phase shift seen in the<br />

1Hz ±2° case. However, upon movement inboard toward the wing root, a m<strong>or</strong>e elliptical<br />

behavi<strong>or</strong> emerges. Near the transition from counter-clockwise to clockwise rotation, regions <strong>of</strong><br />

180° phase shift are seen. Observation <strong>of</strong> the figure-eights and other “odd” shapes are seen in<br />

this region, indicating a continuous phase variation within 1 cycle. However, there is no “noise”<br />

observed along the TE as is seen in the 1Hz ±2° case. Overall, the Lissajous figures f<strong>or</strong> both roll<br />

oscillation cases differ significantly at and aft <strong>of</strong> the shock region.<br />

Figure 6-10 A) and C) are individual Lissajous figures taken at 93% span vs. 65% ch<strong>or</strong>d<br />

location, which c<strong>or</strong>responds to the shock recovery region as seen in Figure 6-5 C). In this region,<br />

an odd figure-eight-like shape due to the continuous phase variation is observed which is much<br />

different from the one seen with the 1Hz case. The 3-D plot in C) provides m<strong>or</strong>e insight as to<br />

how the Cp varies with time. Notably, a loop feature is seen occurring in the first half <strong>of</strong> the<br />

cycle. This is due to both the sinusoidal response <strong>of</strong> the Cp and the local displacement being out<br />

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