## 2 Methodology
### Methodology for Calculating Fatigue Damage
#### 2.2.1. Blade Characteristics and Geometry  
For the stall-regulated turbine simulated in this work, airfoils from the series DU-210_xx were considered. The selection of this series was in part motivated by its favorable starting performance. On the other hand, both pitch-regulated turbines were based on a design using one single airfoil, namely the NACA 4412. Figure 2 shows representative airfoils used for stall and pitch design, respectively. Figure 3 shows a 3D rendering of both blades. The chord and twist angle functions are shown in Figure 4. The blade designed for pitch control had a roughly optimal chord function, with a transition to a circular root section to allow for convenient flanging to the rotor hub (as usual in wind turbine engineering, an \"optimal\" blade is one with an optimal power extraction at a constant tip-speed ratio, considering negligible airfoil drag). The twist function was obtained from a performance optimization using QBlade, taking the twist function proposed in [36] as a starting point, and a smoothing process to allow for a manufacturable blade. The stall design, on the other hand, was based on the requirement that at a given wind speed, all blade sections simultaneously enter the stall regime, thereby leading to a sharp drop in the power coefficient of the rotor. This was achieved using the optimization feature provided by the QBlade suite. As discussed above, the DU210 xx airfoil series was selected in part because of the relative sharp drop in the lift coefficient for angles of attack larger than a critical angle (the stall angle), which greatly facilitates a good rotor stall behavior. The other reason for choosing the DU201 xx airfoil series lies with its favorable starting performance, as mentioned before. The geometry of the stall blade considered previous designs from the authors. Table 11 shows the densities, Young's module, the maximum tension strength \((X_{t})\), and the maximum compression strength \((X_{c})\). Table 12 shows information about the geometry of the stall blade, as well as the aerodynamic profiles for each section and the Reynolds numbers. The blades have a length of 3.58 m, divided into 30 sections or blade stations. The blades were manufactured with two distinct kinds of Fiber Glass-Reinforced Polymeric (FGRP) and epoxy resin. The root and shell of the blade were built from tri-axial material, while the crossbar used a bidirectional material. The design of the pitching blade was inspired by a blade design published by [PERSON] et al. [36]. To adapt this model to the present work, the original blade, with a total length of 40 m and divided into 14 sections, was scaled to match the length of the stall-regulated blade. The geometry was interpolated to 30 blade stations. To reach the final blade design, the scaled and interpolated chord function was used directly, whereas the twist distribution was used as a starting point for a final twist optimization using QBlade [26]. The same characteristics of the materials used in the stall blade were considered at a given blade section. The data of the geometry of the pitching blade are shown in Table 13. Finally,  
Figure 1: Overall methodology used in this work. forces and moments acting on the blade sections located at a given radial position, determined from empirical or simulated airfoil data, plus a number of empirical corrections, such as for rotor thrust under heavy loading conditions and tip and rotor losses. The local differences in Reynolds number along the blade radius can be taken into account by simulating each required airfoil with a different Reynolds number, depending on the blade station where this airfoil is going to be placed. While in utility-scale wind turbines, the effect of making this distinction is marginal, given the large Reynolds numbers prevailing at most parts of the blades, in small-scale wind turbines, this differentiation is critical, particularly near the root where the Reynolds number may be as low as several tens of thousands.