# Simulative Investigation of the Radar Cross Section of Wind Turbines
## 2 Method
### Simulation Setup  
Taking into account the factors and limitations given above, the simulation setup was planned. The simulation frequency was chosen to be 1.345 GHz, the center of an air traffic surveillance radar frequency band. This choice presents a balance between computational effort, computational method, and desired radar target size. Higher frequencies cause super-linear increase in computation time and memory consumption, which is beyond the limit of available computational resources. For the parts made of metal, the material was chosen as \"Perfect Electric Conductor\" (PEC), a virtual material with zero electrical resistance, a common simplification for high-frequency problems when the resistance's influence is negligible in practice.  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Shape** & **Height** & **Bottom Radius** & **Top Radius** \\ \hline
**Tower v1** & truncated cone & 113 m & 3.4 m & 1.5 m \\
**Tower v2** & exponentially tapered truncated cone & 137 m & 2.5 m & 1.5 m \\ \hline \end{tabular}
\end{table}
Table 2: Parameters of the wind-turbine tower models.  
Figure 1: CAD models of the investigated wind-turbine components, with increasing complexity: (**a**) WT v1: tower, nacelle, and hub; (**b**) WT v2: tower, nacelle, and hub; (**c**) blades: bottom; and (**d**) blades: top.  
For the turbine blades, several materials and combinations were investigated. PEC material was chosen as an approximation for CRP. This might not be ideal, as the carbon fiber used in lightweight construction is usually chosen for its fitness of the construction purpose (not by its electrical material properties), but it can serve as a baseline because the fiber strings will be placed so close to one another that electromagnetic penetration into the turbine blade will be unlikely, which is also the case for PEC. For FRP, the dielectric permittivity was chosen \(\varepsilon_{\mathrm{r}}=4.35\) (see Section 2.2.1 above). In lightweight construction, a \"sandwich\" layering is usually employed: a layer of very stiff foam is placed between two layers of FRP or CRP. Therefore, different layering setups were also investigated. For the foam, a relative permittivity \(\varepsilon_{\mathrm{r}}=1.1\) was assumed. Other surface coating was neglected, as the layers are very thin (\(\ll 0.5\,\mathrm{mm}\)) compared to the wavelength \(\lambda\approx 22.3\,\mathrm{cm}\) at \(1.345\,\mathrm{GHz}\). The blades were assumed to be hollow in order to limit the investigated parameters to the aerodynamic shape of the blades, and the material thickness was assumed to be constant along the blade.  
Where only PEC was used, a Fast Multipole Method [39] (FMM) with the combined-field integral equation (CFIE) was used where computationally feasible. The FMM is a variation of the Method of Moments (see Reference [40] for a derivation from [PERSON]'s equations). It delivers exact results (within numerical precision) at the price of a huge demand in computational resources, especially memory.  
The numerical method of \"Geometrical Optics/Ray Launching\" (GORL) was chosen for all simulation setups containing materials other than PEC. It is derived and described in depth in Reference [41] as the \"shooting and bouncing rays\" (SBR) method. This method considers multiple propagation paths but, due to its discrete \"rays\", might underreport signal return. This method has a significantly lower memory demand than the FMM. The method of Physical Optics (PO) [42] was not considered, as it neglects multiple reflections and penetration into the investigated object. This will make the simulated RCS value lower than expected in reality [32].  
In all cases, the radar source was assumed to be an incident plane wave with an elevation angle of \(0^{\circ}\) (i.e., the direction of propagation is parallel to the x-y plane). Both methods are available in the Altair FEKO [43] software suite, which was used for this study.