## 2 Structural Analysis and Design of the Blade  
### Wind Turbine Blade Design  
Designing the shape of the wind turbine blade is one of the most complex and important steps in order to manufacture a wind turbine blade. Firstly, the pitch-regulated turbines were selected based on the design of a single airfoil (NACA 4412). This airfoil is well-established, tested, and used for small wind turbine blades [20]. There are many theories to predict aerodynamic performance to calculate the ideal chord length and the optimal twist angle distribution [21]. The simplest model of the ideal concept for wind turbine blade design was developed by [PERSON] [22]. In order to obtain the optimum aerodynamic design of the blade, it was applied the blade element momentum theory (BEM) [8]. Where QBlade software is built based on the BEM theory [23]. This software is used to optimize the shape of the wind blade and determine the aerodynamic loads. A new code was developed using MATLAB software based on the [PERSON] concept to calculate the parameter of the blade geometry (relative angle (\(\varphi\)), chord length (\(c\)), twist angle (\(\theta\))). Then, all the parameters are transferred to QBlade software to estimate the load and performance of the blade based on the BEM method. Figure 2 shows the aerodynamic loads for each blade element. BEM theory splits the blade into a finite number of independent sections that are uniformly distributed along the blade's length. A two-dimensional airfoil was used to determine the aerodynamic forces that were generated in each blade section based on a certain radial position. In this work, the blade is divided into 10 sections. The first step in QBlade is to calculate the airfoil's coefficients (lift and drag), where the lift and drag are affected by the Reynolds number (\(Re\)) and the angle of attack. Reynolds number is defined as the ratio between the inertial force to the viscous force, which is given by the following equation [21]:  
\[Re=\frac{\rho UL_{rel}c}{\mu} \tag{1}\]  
and  
\[U_{rel}=\sqrt{\left(\Omega R\right)^{2}+\left(U_{design}\right)^{2}} \tag{2}\]  
Figure 1: The main steps to optimize small wind turbines. where \(\mu\) is the air viscosity, \(U_{rel}\) is the relative velocity [m/s], \(c\) is the chord length [m], \(\Omega\) is the rotational speed of the blade [rad/s], \(R\) is the blade length [m], and \(U_{design}\) is the design wind speed [m/s]. The design parameters of the actual blade are listed in Table 1.  
According to Equation (1), the Reynolds number changes in terms of the chord (\(c\)) and the radius (\(r\)). Therefore, it is difficult to determine the initial value to start the calculation process, so it assumed the average value of the Reynolds number to facilitate the calculation process of a 5 kW HAWT with a rotor diameter of 5 m. It was found that the value of Reynolds number is about 450,000 at the tip chord of 0.106 m of the blade. In order to calculate the lift and drag coefficients, the XFoil software was used. Where the XFoil is embedded in QBlade, and the results are shown in Figure 3. The maximum ratio \(Cl/Cd\) is 119 at the angle of attack (AOA) which is equal to 6\({}^{\circ}\). This angle is called the design or optimal angle of attack. The lift coefficient at the optimal angle is \(Cl_{design}=1.12\). can be used to find the relative angle [21]:  
\[\varphi=\left(\frac{2}{3}\right)\tan^{-1}\left(\frac{1}{\lambda_{r}}\right) \tag{3}\] \begin{table}
\begin{tabular}{l c c} \hline \hline
**Design Parameter** & **Value** & **Unit** \\ \hline Rated power & 5 & [kW] \\ Design Wind speed & 10.5 & m/s] \\ Number of blades & 3 & [-] \\ Design tip speed ratio & 6 & [-] \\ Design angle of attack & 6 & [\({}^{\circ}\)] \\ Rotor radius & 2.5 & [m] \\ Design rotational speed & 240 & [rpm] \\ Density of air & 1.22 & [kg/m\({}^{3}\)] \\ Airfoil type & NACA4412 & [-] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial design parameters of 5 kW small wind turbine. Figure 2: Airfoil section with aerodynamic loads.