## 2 Methodology
### Methodology for Calculating Fatigue Damage  
Figure 1 shows a general scheme of the proposed methodology used in this work. The primary output is the predicted fatigue damage \(D(v_{i},\text{TI},\text{reg})\) of the blade for a given average wind speed \(v_{i}\), a given level of Turbulence Intensity (TI) (high or low), and the turbine configuration, where \"reg\" stands for the turbine regulation scheme used,  
\[T[\text{years}]=\frac{\tau[\text{min}]}{24\times 60\times 365\times D\left(v_{i}, \text{TI},\text{reg}\right)} \tag{6}\]  
where \(\tau\) is the simulation time in minutes. In this work, \(\tau=10\) min in all cases. An average fatigue life can then be calculated by convoluting the fatigue damage for a given wind speed class \(v_{i}\) with a Weibull distribution function \(f_{\text{ Weibull}}(v;v_{s},k)\), where \(v_{s}\) is the Weibull scale factor in m/s and the dimensionless quantity \(k\) is the Weibull shape factor. Note that the average wind speed \(\tilde{v}\) is related to the shape factor by \(\tilde{v}=v_{s}\Gamma(1+1/k)\), where \(\Gamma\) is the gamma function.  
The proposed methodology combines two software packages, the public-domain suite QBlade and a set of codes implemented in MATLAB, shown on the left- and right-hand side of Figure 1, respectively. QBlade can be used for (1) simulating and designing airfoils, (2) simulating rotor aerodynamics using Blade Element Momentum (BEM) theory, (3) simulating steady-state operation based on prescribed curves for rotor speed vs. wind speed and blade pitch angle vs. wind speed, (4) simulating stochastic wind fields, and (5) conducting aeroelastic simulations using the rotor setup and operational characteristics defined in Steps (1)-(3). Step (5) is carried out with the tool FAST [34], developed by NREL and embedded in QBlade, whereas Step (1) is based on another public-domain tool, XFoil. In addition to Tools (1)-(5) QBlade allows for finite-element simulation of the mechanical state of the blade for given stationary load conditions, which can be used to conduct a preliminary structural design of the blade.  
In all three turbine configurations studied in this work, the QBlade tools (1)-(3) were used iteratively to reach the given design objectives. In the case of the stall design, as mentioned before, additional evaluations were carried out outside of the QBlade framework for an optimization of the start-up behavior, which is not part of the present work. For all three turbine configurations, an electric nominal output power of 10 kW was specified, to be reached at a rotor speed of about 130 rpm. In the case of a pitch-regulated wind turbine, the requirement of a constant nominal rotor speed can be met always, at least theoretically, by adjusting the pitch angle correspondingly, although an optimal design is far from trivial. In a stall-regulated turbine, however, this additional degree of freedom is not available, so all regulation has to be conducted through the prescription of the rotor speed, which is achieved in practical terms by the control of the generator torque (for a modern application of small wind turbine control through generator torque control, see, e.g., [35]).