# Experimental Study of the Performance of a Novel Vertical-Axis Wind Turbine
## 4 Results and Discussion  
Experimental data are used to estimate the parameters expressed in Equations (8)-(23) and tabulated in Tables 2-4. Figures 6-12 depict graphs plotted from experimental results. The average induction factor \(\overline{a}\) calculated from experimental measurements of upwind and downwind free-stream speeds using Equations (20) and (21) is \(0.642\pm 0.0876\) and the downwind speed can be expressed as \(U_{2}=U_{0}(1-\overline{m}a)\), where \(\overline{m}\) is an average value estimated from measured upwind and downwindspeeds using Equations (22) and (23) and is \(1.34\pm 0.1122\). Thus, the AVAWT rotor inlet and outlet air speeds are given by  
\[U_{1}=U_{0}(1-\overline{a}) \tag{24}\]  
\[U_{2}=U_{0}(1-(1.34\pm 0.1122)\overline{a}) \tag{25}\]  
respectively. The difference in pressure between the AVAWT inlet and outlet as a function of the free-stream speed is shown in Figure 6, where rhombic points are data points calculated from experimental measurements and the best fit for the data is a quadratic curve generated using the MATLAB curve fitting tool. A coefficient of determination of 86.1% is determined for this fit, resulting in a correlation coefficient of 92.8%. The coefficients of Equations (26)-(36) have been estimated within a 95% confidence interval. The expression for the difference in pressure as a function of the free-stream speed is  
\[P_{2}-P_{1}=0.2147U_{0}^{2}-2.33U_{0}+7.269 \tag{26}\]  
It is discernible from the curve in Figure 6 that the difference in pressure across the AVAWT rotor increases parabolically with the free-stream speed. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\mathbf{U_{0}}\) (m/s) & \(\mathbf{\lambda}\) & **Torque (Nm)** & \(\mathbf{P_{actual}}\) (W) & \(\mathbf{P_{area}}\) (W) & \(\mathbf{C_{actual}}\) & \(\mathbf{C_{p,area}}\) \\ \hline
4.22 \(\pm\) 0.1300 & 0.23 \(\pm\) 0.0540 & 0.046 \(\pm\) 0.0001 & 0.56 \(\pm\) 0.0020 & 1.45 \(\pm\) 0.1244 & 0.162 \(\pm\) 0.0150 & 0.420 \(\pm\) 0.0938 \\
7.65 \(\pm\) 0.2300 & 0.33 \(\pm\) 0.0580 & 0.052 \(\pm\) 0.0001 & 1.45 \(\pm\) 0.0055 & 5.12 \(\pm\) 0.3860 & 0.071 \(\pm\) 0.0064 & 0.249 \(\pm\) 0.0131 \\
9.39 \(\pm\) 0.2820 & 0.57 \(\pm\) 0.1070 & 0.161 \(\pm\) 0.0004 & 9.17 \(\pm\) 0.0355 & 14.02 \(\pm\) 1.6900 & 0.241 \(\pm\) 0.0210 & 0.369 \(\pm\) 0.0200 \\
9.65 \(\pm\) 0.2890 & 0.60 \(\pm\) 0.1720 & 0.172 \(\pm\) 0.0004 & 10.60 \(\pm\) 0.0395 & 15.50 \(\pm\) 1.9400 & 0.257 \(\pm\) 0.0231 & 0.375 \(\pm\) 0.0203 \\
10.35 \(\pm\) 0.3110 & 0.58 \(\pm\) 0.1790 & 0.170 \(\pm\) 0.0004 & 10.53 \(\pm\) 0.0395 & 17.19 \(\pm\) 2.0527 & 0.207 \(\pm\) 0.0187 & 0.338 \(\pm\) 0.0186 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calculated actual power, aerodynamic power and power coefficients. Figure 6: Difference in pressure as a function of the free-stream speed. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\mathbf{U_{0}}\) (m/s) & \(\mathbf{Power}\) & **Torque (Nm)** & **RFM** & \(\mathbf{\omega}\) (rad/s) & \(\mathbf{U_{1}}\) & \(\mathbf{U_{2}}\) & \(\mathbf{\lambda}\) & **Rotational** \\  & **Output (W)** & & & & & & & **Power (W)** \\ \hline
4.22 \(\pm\) 0.1300 & 0.60 \(\pm\) 0.0020 & 0.046 \(\pm\) 0.0001 & 105 \(\pm\) 0.2620 & 11.00 \(\pm\) 0.0270 & 1.80 \(\pm\) 0.0540 & 0.50 \(\pm\) 0.0100 & 0.23 \(\pm\) 0.0290 & 0.51 Figure 7 depicts the measured torque as a function of the free-stream speed, where square points are experimental data points and the best fit curve is generated using the MATLAB curve fitting tool. A coefficient of determination of 86.14% is determined for this fit, resulting in a correlation coefficient of 92.81%. It is seen from the curve that the torque of the AVAWT increases exponentially with the free-stream speed. The expression for the torque as a function of the free-stream speed is  
\[T(U_{0})=0.008922e^{0.2943U_{0}} \tag{27}\]  
Figure 8 depicts the measured torque as a function of the tip-speed ratio, where square points are experimental data points and the best fit curve is generated using the MATLAB curve fitting tool.