Biomimetic propulsion of elastic structures

Applied Mathematics Laboratory

Courant Institute of Mathematical Sciences, New York University

Birds and aquatic animals interact with the surrounding fluid to propel themselves in air or water. In inertial regimes, the mechanisms of propulsion are based on momentum transfer; by flapping wings or fins, animals accelerate fluid in their wake, creating a jet that propels them forward. The structures used to move can be flexible, and are thus likely to experiment large bending. Literature showed that those passive deformations can improve propulsive performance, when exploited in a constructive way. The mechanisms at play however are not fully understood. I will present two experimental biomimetic models, which we used to study how a flapping elastic structure generates thrust. The first setup is a simplified mechanical insect with flexible wings, and the second one is a swimmer whose elastic body mimics the undulating motion of an eel. We show that propulsive performance is significantly influenced by the way the systems passively bend, and that their elastic response can be described by simplified theoretical models of forced oscillators. Those models also bring forward the important role of the quadratic fluid damping that resists the flapping motion. This result introduces the counter-intuitive idea that it is sometimes desirable to dissipate part of the energy in the fluid, in order to improve performance.