# A Study on Aerodynamic and Structural Design of Fairing Using Glass Fabric Composite Structure
## 4 Structural Design
### Design of Uniform Thickness for Sandwich Composite Structure  
The design concept was improved by applying the sandwich structure for a lightweight fairing. GFRP, same as the simple flat plate design, was applied to the face skin, and polyurethane foam was used for the core. Polyurethane foam was selected considering the manufacturing aspect when actually manufacturing the fairing. The mechanical property of GFRP and polyurethane for the design of sandwich structures is as shown in Table 6[13]. The safety evaluation of sandwich structures uses the material property of GFRP and polyurethane when designing, and the safety factor of 3 is considered for two yield stress values. In this study, the allowable stress of GFRP and polyurethane was more than the safety factor value of 3 when designing based on the allowable stress, so it was verified to be safe enough. Figure 9 is the shape of sandwich structures.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Face Skin** & **Core** \\  & **[Glass/Epoxy Fabric]** & **[Polyurethane]** \\ \hline E\({}_{1}\) (Elastic modulus of x axis) & 10,500 MPa & 60.86 MPa \\ E\({}_{2}\) (Elastic modulus of y axis) & 10,500 MPa & 59.86 MPa \\ G\({}_{12}\) (Shear modulus) & 1450 MPa & 19.18 MPa \\ v (Poisson’s ratio) & 0.27 & 0.2 \\ X\({}_{1}\) (Tensile strength of x axis) & 283.9 MPa & 2.63 MPa \\ X\({}_{\rm c}\) (Compressive strength of x axis) & 184.6 MPa & 1.41 MPa \\ Y\({}_{\rm t}\) (Tensile strength of y axis) & 283.9 MPa & 2.49 MPa \\ Y\({}_{\rm c}\) (Compressive strength of y axis) & 184.6 MPa & 1.41 MPa \\ S\({}_{1}\) (Shear strength of x axis) & 15.0 & 0.71 \\ S\({}_{2}\) (Shear strength of y axis) & 1.705 & 0.1197 \\ Thickness & 0.25 mm & 19.78 mm \\ Density & 1800 kg/m\({}^{3}\) & 50 kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Mechanical properties of materials used in the present fairing design [17].  
Figure 9: The shape of sandwich structures.  
The theoretical equation for the thickness of the fairing using sandwich structures is determined by the following equation after the finding moment [16]:  
\[I_{1}=\frac{b}{12}\left(h^{3}-h_{c}^{3}\right) \tag{17}\]  
In Equation (17), \(I_{1}\), \(b\), \(h\), and \(h_{c}\) are the moment of inertia about glass fiber, length of the fairing's top, height of sandwich structures, and height of the foam, respectively.  
\[I_{2}=\frac{b}{12}h_{c}^{3} \tag{18}\]  
In Equation (18), \(I_{2}\) is the moment of inertia about polyurethane.  
\[\left(\sigma_{1}\right)_{max}=\pm\frac{M(h/2)E_{1}}{E_{1}I_{1}+E_{2}I_{2}} \tag{19}\]  
In Equation (19), \(\sigma_{1}\) is the compressive strength of glass fiber considering the safety factor of 3. The reason for selecting compressive strength is that glass fiber is more vulnerable to compression than tension. \(E_{1}\) and \(E_{2}\) are elastic coefficients of glass fiber and polyurethane foam, respectively.  
\[\left(\sigma_{2}\right)_{max}=\pm\frac{M(h_{c}/2)E_{2}}{E_{1}I_{1}+E_{2}I_{2}} \tag{20}\]  
In Equation (20), \(\sigma_{2}\) is the compressive strength of polyurethane considering the safety factor of 3. The thickness and mass of GFRP and foam are derived by Equations (17)-(20), the thickness of the foam was derived according to the number of plies of the skin satisfying the safety factor of 3 or more, and at that time, 1-24 was applied to the number of the skin's plies. It could be shown that as the number of glass fiber plies increases, the thickness of the fairing decreases and the mass grows. This is because the density of GFRP is 36 times larger than polyurethane. Because the mass of the fairing is targeted as 10% reduction of the mass of the preceding product, five plies of GFRP were applied in this study. This is because the thickness reduction rate gradually gets lower when being five plies, and the fairing mass value desired in this study could be checked. The total mass of the fairing could be checked to be 30.563 kg when designing the fairing structure with five plies of GFRP.