## 4 Results
### Aerodynamic Load
The mean displacement of the tower top in theoretical model overestimates the mean offset, while FAST seems to have fit better with the experiments. The standard deviation of the displacement in the simulations compared to the experiment seems to underestimate the oscillations. The large discrepancies between the experimental and simulated mean offset and standard deviation of the TLP suggest that the aerodynamic performance of the physical wind turbines blades is not consistent with the theoretical calculated performance. Therefore, an identification of the aerodynamic performance of the physical blades should be conducted. Furthermore, a redesign of the blades should be done, in order to achieve the correct scaled aerodynamic performance. This is out of the scope for this paper. To compare the experiment and simulations, the distribution of power are the displacement time series is compared. Therefore, the PSD of the displacement time series from both the experimental and simulation data is calculated. By inspection of the tower PSD, a large peak at the 1P frequency was found, this was not found in the initial simulations. This large peak was taken into account by introducing an equal offset in opposite direction on the blade pitch angle on two of the blades. The pitch angle offset of the two blades was set to \(\pm 5^{\circ}\), this value was found by comparing the power at 1P on the power spectrum of the motion, as seen on Figure 10, between the simulation and experiment. Furthermore, it was found reasonable that an offset in the pitch angle with a value of \(\pm 5^{\circ}\) could occur in the experiments, as the pitch angle offset was manually initialized. Furthermore, a substantial amount of energy was located at the 3P frequency in the experiments, which was not captured in the simulations. This was thought to originate from the high chord to length ratio of the blade, which brought the blade trailing edge close the tower. To accommodate this, the overhang length in the simulations was reduced to half of its physical value. Furthermore, the top of the rotor plane exceeded the physical wind field by 5 cm, which also contributed to peak at the 3P frequency. To accomodate this in the theoretical model, a wind speed reduction in the top of the wind field was incorporated. In FAST, this was not possible to incorporate, therefore a smaller peak at 3P was to be expected. The PSD of the TLP and nacelles displacement in surge, at three different wind speeds, can be seen in Figure 10. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**6 m/s**} & \multicolumn{2}{c}{**7 m/s**} & \multicolumn{2}{c}{**8.6 m/s**} \\ \cline{3-8}  & & \(\mu\) **(mm)** & \(\sigma\) **(mm)** & \(\mu\) **(mm)** & \(\sigma\) **(mm)** & \(\mu\) **(mm)** & \(\sigma\) **(mm)** \\ \hline \multirow{3}{*}{TLP} & Experiment & 15.4 & 1.3 & 21.6 & 1.7 & 21.2 & 1.7 \\  & FAST & 23.0 & 3.9 & 31.6 & 5.4 & 32.7 & 6.2 \\  & Theoretical & 26.6 & 2.6 & 34.9 & 3.5 & 32.2 & 3.0 \\ \hline \multirow{3}{*}{Tower Top} & Experiment & 5.3 & 1.5 & 8.8 & 1.7 & 7.2 & 1.9 \\  & FAST & 5.3 & 1.1 & 7.6 & 0.9 & 7.3 & 1.8 \\ \cline{1-1}  & Theoretical & 8.8 & 1.1 & 11.2 & 1.3 & 9.5 & 1.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The mean (\(\mu\)) and standard deviation (\(\sigma\)) of the displacement of the TLP and tower top from the experimental data and simulation in FAST and by the theoretical model at three applied mean wind speeds: 6 m/s, 7 m/s and 8.6 m/s. frequency appears to be wider than the simulations. This indicates that the rotational speed in the experimental setup has been more fluctuating then in the simulations.