## 3 Results and Discussions
### Local Force Coefficients from Pressure Measurements  
As previously mentioned, pressures on towers were measured by simultaneous multi-channel pressure sensing systems. Pressure taps were installed along the tower heights at 13 levels at constant intervals, and all pressures were measured simultaneously. Details on pressure measurements were found in Kim and Tamura [18]. Figure 11 shows the variation of local force coefficients of tetradecagonal wind turbine at \(\theta_{pit}\) = 90\({}^{\circ}\) and \(\theta_{azi}\) = 90\({}^{\circ}\) for various wind directions. Local force coefficients were defined by the reference wind speed at hub height (\(U_{ref}\) = 5 m/s) and reference width of circular tower at 0.5 \(H_{ref}\) (\(D_{ref}\) = 0.05 m). As the effect of pitch angle on forces on the tower was very small [18], the results for a pitch angle of 90\({}^{\circ}\) were used, and \"T only\" in the legend indicates the tower-only case without topside structure. At azimuth angle \(\theta_{azi}\) = 90\({}^{\circ}\), as one of the blades was located in front of the tower for the oblique wind directions, it was found that local force coefficients near the top varied greatly. Local drag force coefficients of the wind turbine were smaller than that for the tower-only case (T only), while the local lift force coefficients showed larger absolute values than that for the tower-only case. In particular, large absolute values were found for the oblique wind directions: wind direction 40\({}^{\circ}\) for mean lift force coefficient and wind direction 60\({}^{\circ}\) for fluctuating lift force coefficient. When the azimuth angles were \(\theta_{azi}\) = 0\({}^{\circ}\) and \(\theta_{azi}\) = 30\({}^{\circ}\), the variations of the force coefficients were generally small, showing similar values to the tower-only case, and when the azimuth angle was \(\theta_{azi}\) = 60\({}^{\circ}\), the variations of the force coefficients were similar to those in Figure 11 [18]. Figure 12 shows the variations of mean lift force coefficients depending on number of sides of towers at \(\theta_{pit}\) = 90\({}^{\circ}\) and \(\theta_{azi}\) = 0\({}^{\circ}\). Although large mean lift forces were found for wind direction 20\({}^{\circ}\) for the square wind turbine, the variation of mean lift force coefficient was generally small, and this trend became more significant when the number of sides increased. Similar trends were found for azimuth angle \(\theta_{azi}\) = 30\({}^{\circ}\) and for other force components. Figure 10: Power spectral densities of wind turbine installed on various polygonal towers at \(\theta_{wd}\) = 0\({}^{\circ}\) and \(\theta_{azi}\) = 0\({}^{\circ}\). Figure 11: Variation of local force coefficients of tetradecagonal wind turbine at \(\theta_{pit}=90^{\circ}\) and \(\theta_{azi}=90^{\circ}\). Figure 12: Variation of mean lift force coefficients with number of tower sides at \(\theta_{pit}=90^{\circ}\) and \(\theta_{azi}=0^{\circ}\). In the tower's design, maximum force coefficients for all wind directions and all azimuth angles were generally used. The maximum force coefficients for all considered cases at each height were chosen, and the ratios to the circular wind turbine are shown in Figure 13. As for the mean and fluctuating local drag force coefficients, they decreased with increasing number of sides, showing the largest values for the square wind turbine and the smallest values for the tetradecagon wind turbine. For the fluctuating lift force coefficients, in essence, they also decreased with increasing number of sides, but the fluctuating lift force coefficients of the square helical wind turbine showed even smaller values than the circular wind turbine. For tall buildings and structures, the helical/twisting shape is well known to be efficient in mitigating fluctuating lift forces, and this was confirmed again, even for the wind turbine.