Wind and Sea

Wing Shape Optimization
Optimal Flapping
(click on images below to see a larger image)

Michele Milano, Matthew Ringuette

We use Machine Learning techniques to assess from a fluid dynamics perspective the trajectory and the shape of a flapping appendage. We formulated a novel vortex formation parameter to help interpreting the results of trajectory optimization for a pitching and heaving flat plate. Our findings show that to maximize the average lift produced, flapping appendages must generate vortices of maximal circulation during a flap.

Shown above: three still images from an animation. DPIV measurements taken at 50% span of the vorticity generated by a pitching and heaving flat plate maximizing the average lift produced: the plate turns right before the leading edge vortex pinches off. (Click on each still to see larger graphic.)

To show that similar constraints hold for the appendage shapes also, we consider Drosophila Melanogaster as a case study, extending further the vortex formation parameter to account for general shapes and flapping trajectories.

Shown left: left graph: elliptic wing following the trajectory of a fruit fly wing; right graph: corresponding generalized formation parameter. Click here or on image to view animation.

The evolutionary algorithm evolves families of wing shapes that optimize vortex formation, for a given flapping trajectory. When the flapping trajectory is fixed to that of Drosophila melanogaster (fruit fly), our evolutionary algorithm evolves a family of wing shapes that correlate very closely to natural fruit fly wings. (Picture, above right, of an actual Drosophila wing.)

Figure shown at left: blue: digitized shape of a real fruit fly wing; red and black: two ellipting wings belonging to the family evolved by our evolutionary algorithm to produce the same maximal formation parameter as the real fruit fly wing. See larger image of graphic.