Reducing the Induced Drag: Experimental Comparison of the Bell-Shaped and Elliptical Lift Distributions

The concept of a Bell-Shaped Lift Distribution (BSLD) was initially introduced by Ludwig Prandtl in 1933 as an alternative to the conventional Elliptical Lift Distribution (ELD). The ELD minimizes the induced drag for a given wingspan; a BSLD can further minimize induced drag for the same root bending moment if the wingspan is unconstrained. To study the minimization of induced drag, we designed wings with bell-shaped and elliptical lift distributions using multidisciplinary design optimization and computer-aided design. Both wings were then analyzed using XFOIL, XFLR5, and NX Nastran. Once a final design was chosen, the wings were manufactured using a wet carbon fiber layup process, and then tested in the University of Michigan’s 5’ by 7’ wind tunnel. The wings were tested in the wind tunnel at Reynolds number of 125,000 and 250,000 to represent radio-controlled (RC) aircraft designed by the University of Michigan student project team, M-Fly. Furthermore, tufts made of red yarn were placed on the wings to visualize flow. Based on this analysis and testing, it is concluded that the BSLD is a viable lift distribution to decrease induced drag through wind tunnel tests, showing that the BSLD has about 14% lower induced drag compared to the ELD at the design