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

Sophie Ramananarivo, Thomas Mitchel, Leif Ristroph

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number20180375
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2221
StatePublished - Jan 1 2019


  • Evolutionary algorithm
  • Flapping flight
  • Flow–structure interaction
  • Optimal locomotion
  • Undulatory swimming

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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