## 5 Results and Discussion
It can also be discerned from Figure 8 that the load on the WT rotor is linear as exhibited by the ADT and RAST curves, whereas the VRT curve shows that the load on the WT rotor blades is nonlinear. plots are shown in Figure 9. It is discernible from Figure 9 that both the curves of the vortex ring and actuator disk theories follow the same trend as both the existing numerical and experimental curves, even though for tip-speed ratios between 1.6 and about 6.5, the experimental values are higher than those of the VRT, while for tip-speed ratios between 1.6 and about 7.8, the numerical values are higher than those of the VRT. For tip-speed ratios between 1.6 and about 3, both the numerical and experimental curves nearly coincide after which the experimental curve leaves the numerical curve and runs above it up to a tip-speed ratio of about 4.3 and then runs below the numerical curve thereafter. For tip-speed ratios between about 7.8 and 8.5, the VRT curve runs above the numerical curve, while it runs above the experimental curve for tip-speed ratios between 6.5 and 10.2. Beyond these limits of tip speed ratios, both the experimental and numerical curves run above the VRT curve. The VRT curve intersects with the experimental curve at tip-speed ratios of about 6.5 and 10.2, while it intersects with the numerical curve at tip-speed ratios of about 7.8 and 8.5. It is discernible from the plot that the RAST curve, even though a fourth-degree polynomial like the rest of the curves, is not valid for tip-speed ratios greater than 2.973 because beyond this limit, the power coefficients estimated from the RAST are greater than 0.593 in most cases; beyond this limit, they are greater than unity. On the contrary, both the curves of the vortex ring and actuator disk theories have upward concavity like the numerical and experimental curves. The values of the power coefficient estimated from the ADT are higher than those of the VRT at tip-speed ratios between 1.6 and 4, with both curves intersecting at tip-speed ratios of 4 and about 9.7, respectively. At tip-speed ratios between 4 and about 9.7, the values of the VRT are higher than those of  
\begin{table}
\begin{tabular}{c c c} \hline
**Tip-Speed Ratio** & **Numerical \(\mathbf{C_{p}}\)** & **Experimental \(\mathbf{C_{p}}\)** \\ \hline
1.600 & 0.030 & 0.029 \\
2.100 & 0.060 & 0.050 \\
2.800 & 0.100 & 0.120 \\
4.000 & 0.350 & 0.400 \\
5.000 & 0.520 & 0.450 \\
5.600 & 0.540 & 0.470 \\
6.000 & 0.550 & 0.480 \\
6.300 & 0.560 & 0.470 \\
7.000 & 0.570 & 0.450 \\
8.100 the ADT, while the numerical values are higher than those of the ADT at all the tip-speed ratios considered. At tip-speed ratios greater than 9.7, the values of the power coefficient estimated from the ADT are higher than those of the VRT. It is worth noting that at tip-speed ratios below 2.2, the RAST curve shows negative values of the power coefficient, while at tip-speed ratios beyond 10.4, the VRT curve shows negative values of the power coefficient, and the experimental curve shows negative values of the power coefficient at a tip-speed ratio of 11.2 and beyond. Clearly, among the three theories, the VRT is the most reliable since the values predicted from the VRT lie between the numerical and experimental values and between the values predicted from the ADT and the experimental values within the range of tip-speed ratios at which the VRT is valid. Suffice it to say that the predictions of the VRT agree with the numerical and experimental results at the points of intersection of the curves.