To tread or not to tread: comparison between water treading and conventional flapping wing kinematics

Abstract

Hovering insects are limited by their physiology and need to rotate their wings at the end of each back and forth motion to keep the wing's leading edge ahead of its trailing edge. The wing rotation at the end of each half-stroke pushes the leading edge vortex away from the wing which leads to a loss in the lift. Unlike biological fliers, human-engineered flapping wing micro air vehicles have different design limitations. They can be designed to avoid the end of stroke wing rotation and use so-called water-treading flapping kinematics. Flapping wings using conventional flapping kinematics have a designated leading and trailing edge. In the water-treading mode, the role of the leading and trailing edges are continuously alternated throughout the stroke. Here, we compare velocity field and force measurements for a rectangular flapping wing conducting normal hovering and water-treading kinematics to study the difference in fluid dynamic performance between the two types of flapping kinematics. We show that for similar power consumption, the water-treading mode produces more lift than the conventional hovering mode and is 50\% more efficient for symmetric pitching kinematics. In the water-treading mode, the leading edge vortex from the previous stroke is not pushed away but is captured and keeps the newly formed leading edge vortex closer to the wing, leading to a more rapid increase of the lift coefficient which is sustained for longer. This makes the water-treading mode a promising alternative for human-engineered flapping wing vehicles.