A higher efficiency hydrofoil geometry with spanwise non-linear twist is considered in the design of a lifting body with a bell-shaped lift distribution. This design objective aims to account for the coupling of hydrodynamic and structural considerations by switching the governing hydrofoil span design constraint (leading to an elliptical lift distribution) to an integrated bending moment design constraint, resulting in a bell-shaped lift distribution. A lifting line method was used to apply non-linear geometric twist to the lifting geometry, thus creating a baseline hydrofoil with an elliptical lift distribution and variants with different bell-shaped lift distributions and corresponding aspect ratios. The hydrodynamic performance of the resulting geometries was examined numerically using a vortex lattice method to account for the highly three-dimensional flow along the span and at the wingtip. The sensitivity of the performance, quantified by lift, induced drag, and spanwise bending moment, was examined by parametrically varying the lift distribution and aspect ratio around the bell shape prescribed by lifting line theory. The results demonstrate the performance expected from lifting line theory. In addition, the difference in wingtip vortex kinematics between the lifting bodies producing elliptical versus bell-shaped lift distributions suggests higher efficiency for the latter hydrofoil designs.

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