Flapping Wing Flight Can Save Aerodynamic Power Compared to Steady Flight

Abstract

Flapping flight is more maneuverable than steady flight. It is debated whether this advantage is necessarily accompanied by a trade-off in the flight efficiency. Here we ask if any flapping motion exists that is aerodynamically more efficient than the optimal steady motion. We solve the Navier-Stokes equation governing the fluid dynamics around a 2D flapping wing, and determine the minimal aerodynamic power needed to support a specified weight. While most flapping wing motions are more costly than the optimal steady wing motion, we find that optimized flapping wing motions can save up to 27% of the aerodynamic power required by the optimal steady flight. We explain the cause of this energetic advantage.

Surging and plunging oscillations of an airfoil at low Reynolds number

“…However, with clear understanding of the flow, unsteady effects associated with separations can be utilized to improve manoeuvrability and performance of MAVs (Pesavento & Wang 2009). The unsteady motion associated with flapping flight of insects and birds produces much higher lift than the corresponding steady case (Ellington et al 1996), and a number of studies have focused on this topic to understand the corresponding flow structures (Dickinson & Gotz 1993;Ellington et al 1996;Wang 2005;Pesavento & Wang 2009), which could be potentially useful for MAVs.…”

“…However, with clear understanding of the flow, unsteady effects associated with separations can be utilized to improve manoeuvrability and performance of MAVs (Pesavento & Wang 2009). The unsteady motion associated with flapping flight of insects and birds produces much higher lift than the corresponding steady case (Ellington et al 1996), and a number of studies have focused on this topic to understand the corresponding flow structures (Dickinson & Gotz 1993;Ellington et al 1996;Wang 2005;Pesavento & Wang 2009), which could be potentially useful for MAVs. The presence of a leading-edge vortex (LEV) was found to be essential for providing sufficient lift in insect flight (Dickinson & Gotz 1993;Ellington et al 1996) and the aerodynamic power required in flapping motions was reduced by capturing its own wake that was generated in the previous stroke cycle (Pesavento & Wang 2009).…”

A hovering flapping-wing microrobot with altitude control and passive upright stability

“…In our group we have made progress in solving these problems by taking inspiration from insects. We use muscle-like piezoelectric actuators to generate forces, flexures for pivot joints, and harness unsteady aerodynamic forces by flapping wings [7] because flapping-wing flight has been shown to be potentially more efficient than fixedwing flight at insect-scale [8]. Our group has demonstrated constrained liftoff [7] and vertical position control [9] of the Harvard RoboBee, an insect-scale flapping-wing robot, using these techniques.…”

Comparison of Power Requirements: Flapping vs. Fixed Wing Vehicles

“…There is a number of papers and investigations concerned with the flight performance of flapping wing vehicles, e.g., [5][6][7][8][9][10]. Thus, significant progress in that field was achieved and important findings were obtained.…”