## 5 Design of Shutters Based on Side Wing Efficiency
### Optimization of Shutters' Geometry  
#### 5.1.1 Fin Shape  
The commonly used fins in aerodynamics are airfoil fins. Considering the chaotic flow field of side wing, an airfoil may not fully perform its role, so a simplified airfoil (flat plate type and bending plate type) is considered. Four representative fin shapes are preliminarily selected: bending plate, flat airfoil (BABIC), flat plate, and thick airfoil (ch10). BABIC is chosen as a representative of flat airfoil since it is one of the usual airfoils used in low-speed glider, and has the trait of curved middle line, which allows for a smoother diversion of air flow. Ch10 is selected as a representative for thick airfoil since it is one of the 3 most used airfoils in negative lift wing for FSAE cars [14]. Fin shapes are shown in Figure 12, and other parameters are preliminarily kept the same. The parameters are shown in Table 2, and the simulation results are shown in Table 3. \begin{table}
\begin{tabular}{p{113.8 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Fin Shape** & **Chord Length** & **Max Thickness** & **Angle of Attack of Fin \(\alpha\)/\(\alpha\)** & **Number of Fin \(\alpha\)/\(\alpha\)** & **Average Inertia \(\alpha\)/\(\alpha\)** & **Gross Height/mm** & **Blocking Ratio \(p\)/\(\alpha\)** \\ \hline blending plate & 90.00 & 3.00 & 6.00 & 6 & 35.00 & 220.00 & 8.20 \\ blending plate & 90.00 & 3.00 & 6.00 & 5 & 35.00 & 185.00 & 8.10 \\ flap plate & 90.00 & 3.00 & 6.00 & 6 & 35.00 & 220.00 & 8.20 \\ flap airfoil & 90.00 & 6.50 & 6.00 & 6 & 35.00 & 220.00 & 17.70 \\ thick airfoil & 90.00 & 11.00 & 6.00 & 6 & 35.00 & 220.00 & 30.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Corresponding parameters in the simulation of fin shape optimization. Figure 12: CAD model of different shutters with distinct fin shape. (**a**) Shutters with blending plate fin (\(n=6\), with leading edge fin, explained in the next paragraph). (**b**) Shutters with blending plate fin (\(n=5\), without leading edge fin). (**c**) Shutters with flap airfoil (BABIC) fin. (**d**) Shutters with flap plate fin. (**e**) Shutters with thick airfoil (ch10) fin. \begin{table}
\begin{tabular}{p{113.8 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Fin Shape** & \(I_{perfm}\) & **Side Wing Lift/N** & **Overall Lift/N** & **Side Wing Drag/N** & **Overall Drag/N** \\ \hline blending plate (\(n=6\)) & 6.75 & \(-101.183\) & \(-96.0432\) & 31.2908 & 31.8456 \\ blending plate (\(n=5\)) & 5.77 & \(-99.8378\) & \(-94.8368\) & 31.0486 & 31.596 \\ flap plate & 5.81 & \(-99.9818\) & \(-95.5382\) & 31.211 & 31.9524 \\ flap airfoil & 9.03 & \(-103.89\) & \(-96.6426\) & 31.0142 & 31.5454 \\ thick airfoil & 7.27 & \(-102.574\) & \(-94.9196\) & 31.1868 & 31.488 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation results of fin shape optimization (\(15\,\mathrm{m/s}\)). The leading edge fin has a trailing edge that is directly in front of the leading edge of side wing. The function of fins is verified at this special position. Other groups all have six fins, except for group B in Figure 12, which has five fins and lacks the leading edge fin. Other quantities are controlled in the same manner, except for the change in relevant parameters of the airfoil. In Table 3, overall indicates the combination of a side wing and shutters in front of it. The results show that the flat airfoil leads to the largest increase in the lift of side wing, the smallest increase in the drag of side wing, and the largest overall lift (overall refers to the combination of \"side wing + shutters\"), and the overall drag is moderate. Therefore, the flat airfoil is the best shape among the several fin shapes considered at present. Given that the computational resources of a student formula team are limited, exploring a profusion of flat airfoil subtypes is difficult. The presence or absence of leading edge fins has a significant impact on results.