Lift vs. drag based mechanisms for vertical force production in the smallest flying insects

• Both drag and lift have been suggested as mechanisms used by tiny insects.
• We used CFD to compare the force generated by lift- and drag-based hovering.
• We compared three idealized hovering kinematics.
• At the Re of tiny insects, there is little difference between the two strategies.

We used computational fluid dynamics to determine whether lift- or drag-based mechanisms generate the most vertical force in the flight of the smallest insects. These insects fly at Re on the order of 4–60 where viscous effects are significant. Detailed quantitative data on the wing kinematics of the smallest insects is not available, and as a result both drag- and lift-based strategies have been suggested as the mechanisms by which these insects stay aloft. We used the immersed boundary method to solve the fully-coupled fluid-structure interaction problem of a flexible wing immersed in a two-dimensional viscous fluid to compare three idealized hovering kinematics: a drag-based stroke in the vertical plane, a lift-based stroke in the horizontal plane, and a hybrid stroke on a tilted plane. Our results suggest that at higher Re, a lift-based strategy produces more vertical force than a drag-based strategy. At the Re pertinent to small insect hovering, however, there is little difference in performance between the two strategies. A drag-based mechanism of flight could produce more vertical force than a lift-based mechanism for insects at Re<5; however, we are unaware of active fliers at this scale.