## 3 Results
### Sectional Forces
At radial position of 50% and 75% of the blades all the spectra are very similar in the low frequency range but it is still obvious that BEM has a higher energy content up to the 1P frequency, especially for the axial forces. Furthermore all three methods are able to capture the 1P frequency which is based on the passing of the blades through long time correlated structures. Figure 5: Radial distributions of (**a**) axial and (**b**) tangential forces per unit span. The shaded areas illustrate one standard deviation of the fluctuations. Figure 6: Radial distribution of standard deviation of (**a**) axial and (**b**) tangential forces per unit span. The shaded areas correspond to errors. At the outboard section at 95% the energy content of the BEM results in low frequencies is in the same range as for the BR case, but the AL method shows significant smaller values and the 1P frequency is not captured anymore, especially for the axial forces, which is due to a smeared out tip vortex. To illustrate the different flow structure sizes in the different simulation methods, the two point correlation of the sectional forces along the blade are measured. The argument for this approach is that the correlation of sectional forces is similar to the correlation of the wind velocity close to the blade surface, which is strongly connected to the integral scales of wind. In Figure 9 the correlation at each radial position with the forces at a reference position, here 22.5% radial location, is shown. This specific position is in principle arbitrary, but if the focus lies on the measurement of big structures, this point should not be too close to the tip or root where smaller flow structures dominate. However,  
Figure 8: PSD of tangential forces at (a) 22.5%; (b) 50%; (c) 75% and (d) 95% radial position. Figure 7: Power Spectral Density (PSD) of axial forces at (a) 22.5%; (b) 50%; (c) 75% and (d) 95% radial position. even if the tendency for the correlation functions of the three different models is the same, the larger correlation values for the BR case along the whole blade indicate that the structure sizes are also bigger than for the AL and BEM cases. To give a more detailed description of the effect of forces on the rotor blades, fatigue loads at each section have been investigated. As observed in Figure 10, the EFL distribution over the whole blade is similar to the distribution of standard deviation in Figure 6. The BEM method gives higher EFL for every section for axial forces and almost everywhere higher values for tangential forces. All other points mentioned for sectional standard deviations also hold for sectional EFL. The errors are calculated with the same method as for Figure 6.  
The sectional EFL are linearly dependent on the sectional standard deviation for all simulation methods as seen in Figure 11. This raises the point that the dynamics quantified by two different properties of the load time series, namely standard deviation and EFL, are similar for all three methods. With the Wohler Exponent \(m=8\) and the wind fields used here, this linear relation follows approximately \(EFL=4\sigma\) for axial and tangential forces. Figure 4:0 Equivalent Fatigue Loads (EFL) dependence on standard deviation for (**a**) axial and (**b**) tangential forces for all three methods. The diagonal line is governed by \(EFL=4\sigma\). Figure 4:1 Correlation of (**a**) axial and (**b**) tangential forces at different radial positions with 22.5% position.