## 5 Assessment of Different Sailing Strategies
### Evaluation of the Different Sailing Strategies Presented  
To assess the different sailing strategies presented beforehand, Equations (13) and (16) are utilised to determine the effective power in both Downwind&Upwind and Circle for an exemplary scenario. Due to the conceptual character of this study, no distinct values for either the wetted surface and total resistance coefficient of the hull or the projected surface and resistance coefficient of the brake are known. Thus, it is assumed that \(A_{\text{Wetted}}\) is 10% and \(A_{\text{Brake}}\) is 1% of the swept area of the wind turbine rotor. All specific parameter values used in the exemplary scenario for calculating the effective power values are listed in Table 11. With Equation (6), this results in a drift velocity that is around 20% of the wind speed. Figure 10 shows, for the two sailing strategies Downwind&Upwind and Circle, as well as for a fixed-location wind turbine, the produced power over the undisturbed wind speed (Note: Here, it is not referred to the power curve of the wind turbine but to the power output of a system that implements a sailing strategy, and, hence, the power based on the energy generated over time for one cycle is meant by the term produced power.). The Vestas V150-4.2 MW\({}^{\text{TM}}\), with a 150 m rotor diameter, 4 MW rated power (\(P_{\text{rated}}\)), and 22.5 m/s cut-out wind speed [39], is used in this exemplary scenario to sketch the power curve for the fixed-location wind turbine, which is indicated by a dashed line after having reached rated power. From this, the curves for the produced power following the two different strategies are derived and included in Figure 10 by means of dashed lines as well. For Circle and the fixed-location wind turbine, the wind speed range in which 4 MW are generated is assumed to be the same length. For Downwind&Upwind, the cut-out wind speed is the same as for Circle, since Downwind&Upwind in the downwind phase is the same as Circle. Furthermore, the upper limit for the power produced by a system implementing the Downwind&Upwind sailing strategy is 2 MW because the rated power of 4 MW can only be reached for half of the time. One can see in Figure 10 that the main effect of the sailing strategies Circle and Downwind&Upwind is a shift of the effective power curve towards higher wind speeds. This is also clear from the term (\(v_{\text{wind}}-v_{\text{drift}}\)) in Equation (10). A second and related effect  
Figure 10: Effective power of different sailing strategies; dashed lines indicating the produced power curves after reaching rated power. is a reduced growth rate of the power curve. The gradient at 4 MW for Downwind&Upwind is smaller than the gradient of the fixed-location wind turbine at the same power. While for Circle and Downwind&Upwind, the rated power range (i.e., the range in which rated power is delivered) is shifted to higher wind speeds compared to a fixed-location wind turbine, it is expected that the rated power range of Beam Reach starts at lower wind speeds and ends at higher ones. The decreased start of the rated power range is expected because sailboats can get faster than the true wind speed when sailing in a beam reach style [38]. The increased end of the operational range is expected because the sailing style becomes more and more similar to downwind sailing when increasing the angle \(\beta\) (cf. Figure 9). The capacity factors for offshore fixed-location wind turbines were in the range of about 20-58% in the years 2010-2018 [40]. This range comes from the variety of environmental offshore sites and the installed wind turbine systems. For example, the Hywind Scotland wind farm, with moored-floating wind turbines off the North Sea coast of Scotland, achieved a capacity factor of around 57% [41]. The wind farm Nordsee Ost 1, with bottom-fixed wind turbines in the German North Sea, achieved just a yearly capacity factor of about 36% in 2019 [42].