## 5 Response of FOWT-SFFC Driven by Environmental Loads
### Extreme Load Cases  
In extreme load cases LC2 and LC3, the wind conditions are modeled by a turbulence model, and wind profiles are assumed to have a power law profile. Kaimal wind spectrum model [51] is used to represent the turbulence model. Both extreme wind conditions in LC2 and LC3 have a turbulence intensity of 11% and a power law exponent of 0.11 [51]. The theoretical and FAST simulated Kaimal spectra at hub height of FOWT-SFFC in LC2 and LC3 are given in Figure 9. Besides, the wind and wave directions are assumed in line with the positive direction of axis \(X\). In load case LC3, the mean wind speed at hub height is 28.556 m/s for FOWT-SFFC and 28.397 m/s for OC3 Hywind  
Figure 8: Pierson-Moskowitz wave spectra for LC2 and LC3. \begin{table}
\begin{tabular}{c c c c c} \hline
**Concepts of FOWT** & **Surge (m)** & **Heave (m)** & **Pitch (deg)** & **Tower Base Stress (MPa)** \\ \hline OC3 Hywind & 24.69 & \(-\)0.530 & 4.94 & 75.48 \\ OC4 DeepCwind & 8.73 & \(-\)0.046 & 3.48 & 69.68 \\ FOWT-SFFC & 6.12 & \(-\)0.093 & 2.96 & 66.95 \\ \hline \end{tabular}
\end{table} 
Table 8: Foundation motions and tower base stress under steady wind speed of 11.4 m/s. and OC4 DeepCwind, beyond the cut-out wind speed of NREL-5 MW wind turbine. As a result, the turbine has entered the parked state. Rather than initializing the blade-pitch angles to equal feathered pitch (90 degrees), the initial blade-pitch angles are set to be zeros in this parked state for the most unfavorable condition. The stochastic response in LC2 and LC3 are simulated in FAST with a time length of 11,200 s and time step of 0.0125 s. The first 400 s time history of turbine run-up is truncated. The statistical and spectral analyses are based on 3-h time duration between 400 s and 11,200 s. The response in this duration can be regarded as stationary. Statistical quantities of foundation surge, heave and pitch motions as well as the stresses at tower base of three concepts  
Noticeably, in both LC2 and LC3, the surge, heave and pitch motions of FOWT-SFFC are significantly lower than those of OC3 Hywind and OC4 DeepCwind. In particular, the maximum surge of FOWT-SFFC is only about 26% of the OC3 Hywind wind turbine in LC3. Even using the ratio of surge to water depth, the relative surge of FOWT-SFFC is still the smallest. For maximum heave of FOWT-SFFC, the motions are only 0.196 m in LC2 and 0.559 m in LC3, respectively 17% and 21% of the maximum heave of OC4 DeepCwind. With regards to maximum pitch, the respective ratios of FOWT-SFFC to OC3 Hywind in LC2 and LC3 are 54% and 55%. Pitch of FOWT-SFFC would not exceed 5 degrees in harsh environments. The maximum tower base stresses of FOWT-SFFC in LC2 and LC3 are almost identical to stresses in OC4 DeepCwind, but over 25% lower than stresses in OC3 Hywind. The statistics in Tables 9 and 10 demonstrate that the FOWT-SFFC has least dynamic effects caused by combined random wind and waves and its seakeeping and station keeping performances are the best among three floating concepts. It can be seen in Tables 9 and 10 that the three floating wind turbines contain both left-skewed and right-skewed responses in LC2 and LC3, though the skew is not remarkable. The level of non-Gaussianity in FOWT-SFFC's responses is very weak because almost all skewness values of surge, heave, pitch and tower base stress are smaller than 0.1, and kurtosis values are around 3. In Figure 10, the response power spectra of surge, heave, pitch and tower base stress of FOWT-SFFC for extreme load cases LC2 and LC3 are illustrated. From Figure 10a, it can be seen that the spectrum of surge motion in LC2 has three peaks at 0.0102 Hz, 0.0333 Hz and 0.0759 Hz, which actually are around the surge natural frequency \(f_{\text{surge}}\) (Table 5), pitch natural frequency \(f_{\text{pitch}}\) (Table 6) and peak wave frequency \(f_{\text{p}}=1/\text{T}_{\text{p}}\) (Table 7). Obviously, pitch motion also contributes to the overall surge. The peak at \(f_{\text{surge}}\) is the lowest, because at 0.0102 Hz the energy in wave spectrum is very small.