Aerodynamic Analysis of the Constrained NACA 8412 Airfoil for Formula SAE Application using Thin-Airfoil and Lifting-Line Theories

This project applies Thin-Airfoil Theory (TAT) and Lifting-Line Theory (LLT) to evaluate the aerodynamic characteristics of the inverted NACA 8412 airfoil as a single-element rear wing for Formula SAE. The 2D analysis was validated against XFOIL (Re = 480,000), confirming a zero- lift angle of αL=0 = -8.326° and establishing a viscous limit of cl,max ≈ 1.90 at αstall ≈ 13.0°. The 3D LLT model quantified the induced drag (CD,i), demonstrating that the wing's low aspect ratio and rectangular planform reduce efficiency compared to elliptic loading, with the induced drag being the dominant total drag component at high angles of attack. Parametric analysis demonstrated that increasing the Aspect Ratio (up to AR = 4.0) minimized the induced drag for a given lift coefficient, while dimensional downforce scaled quadratically with velocity, giving high structural loads at the 18 m/s operational limit. These results provide important data for balancing efficiency and downforce targets in the final FSAE wing design.