# Experimental Study of the Performance of a Novel Vertical-Axis Wind Turbine
## 4 Results and Discussion
A coefficient of determination of 99.48% was determined for the fit, resulting in a 99.90% correlation coefficient. The curve shows that there is a quadratic relationship between the tip-speed ratio and the torque developed by the AVAWT rotor. The expression for the torque developed as a function of the tip-speed ratio is  
\[T(\lambda)=0.9861\lambda^{2}+0.4562\lambda+0.09753 \tag{28}\]  
Figure 9 depicts the measured power output as a function of the free-stream speed, where asterisks are experimental data points and the best fit curve is generated using the MATLAB curve fitting tool. The fitted actual power curve is an exponential curve whose equation is  
\[P_{actual}(U_{0})=0.118e^{0.477U_{0}}-1.209\times 10^{11}e^{-6.408U_{0}} \tag{29}\]  
Figure 8: Measured torque as a function of the tip-speed ratio. Figure 7: Measured torque as a function of the free-stream speed. It is discernible from the curve that the actual power generated by the AVAWT increases exponentially with the free-stream speed. A coefficient of determination of 88.21% is determined for this fit, resulting in a correlation coefficient of 93.92%. Also shown in Figure 9 is the calculated aerodynamic power as a function of the free-stream speed, where square points are data calculated from experimental measurements and the best fit curve is generated using the MATLAB plotting tool. There is a quadratic relationship between the aerodynamic power and the free-stream speed:  
\[P_{a\sigma n}(U_{0})=0.5205U_{0}^{2}-4.799U_{0}+12.120 \tag{30}\]  
A coefficient of determination of 97.83 is determined for this fit, resulting in a 99.91% correlation coefficient. It is discernible from Figure 9 that the aerodynamic curve follows the same trend as the measured power curve, but the aerodynamic power values are higher than the actual power values. The aerodynamic power increases from \(1.45\pm 0.1244\) W at \(4.22\pm 0.1300\) m/s to a maximum of about 18.4 W at \(10.35\pm 0.3110\) m/s, while the actual power rises from \(0.56\pm 0.1244\) W to about 12.1 W within the same free-stream speed range. It is also discernible from Figure 9 that for free-stream speeds between about 4.6 m/s and 5.4 m/s, the aerodynamic power curve and the actual power curve nearly merge. This propensity for the curves to merge is a result of the fact that the power values are nearly equal within this free-stream speed range. The actual power generated and the aerodynamic power as functions of the tip-speed ratio are shown in Figure 10. The aerodynamic power curve runs above the actual power curve because the aerodynamic power is higher than the actual power generated at all tip-speed ratios. This difference is evident due to friction loss on torque transducer bearings and power loss due to conversion from the kinetic energy of the rotor to resistance heating in windings of the torque transducer. Both curves in Figure 10 rise from minima at a tip-speed ratio of \(0.23\pm 0.0290\), at which the aerodynamic power is about 2.5 W with the actual power being \(0.56\pm 0.0020\) W, to maxima at a tip-speed ratio of about \(0.6\pm 0.1720\). At a tip-speed ratio of \(0.6\pm 0.1720\), the actual power read from the graph is about 10.9 W, while the aerodynamic power is about 16.8 W. The best fit for the actual power as a function of the tip-speed ratio determined with the MATLAB plotting tool is a quadratic polynomial expressed as  
\[P_{actual}(\lambda)=67.44\lambda^{2}-27.81\lambda+3.351 \tag{31}\]  
Figure 6:0 Power output as a function of the free-stream speed. A coefficient of determination of 99.44% is determined for this fit, resulting in a correlation coefficient of 99.71%. An exponential curve is the best fit for the aerodynamic power curve as a function of the tip-speed ratio. The relationship between the tip-speed ratio and the aerodynamic power is given by  
Figure 6:1  
A coefficient of determination of 95.94% is determined for this fit using the MATLAB plotting tool, resulting in a correlation coefficient of 97.95%.