Improving the propulsion speed of a heaving wing through artificial evolution of shape

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Abstract

Aeronautical studies have shown that subtle changes in aerofoil shape substantially alter aerodynamic forces during fixed-wing flight. The link between shape and performance for flapping locomotion involves distinct mechanisms associated with the complex flows and unsteady motions of an air- or hydro-foil. Here, we use an evolutionary scheme to modify the cross-sectional shape and iteratively improve the speed of three-dimensional printed heaving foils in forward flight. In this algorithmic-experimental method, ‘genes’ are mathematical parameters that define the shape, ‘breeding’ is the combination of genes from parent wings to form a daughter, and a wing’s measured speed is its ‘fitness’ that dictates its likelihood of breeding. Repeated over many generations, this process automatically discovers a fastest foil whose cross-section resembles a slender teardrop. We conduct an analysis that uses the larger population to identify what features of this shape are most critical, implicating slenderness, location of maximum thickness and fore-aft asymmetries in edge sharpness or bluntness. This analysis also reveals a tendency towards extremely thin and cusp-like trailing edges. These findings demonstrate artificial evolution in laboratory experiments as a successful strategy for tailoring shape to improve propulsive performance. Such a method could be used in related optimization problems, such as tuning kinematics or flexibility for flapping propulsion, and for flow–structure interactions more generally.

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Ramananarivo, S., Mitchel, T., & Ristroph, L. (2019). Improving the propulsion speed of a heaving wing through artificial evolution of shape. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2221). https://doi.org/10.1098/rspa.2018.0375

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