Elastic deformation and energy loss of flapping fly wings

Abstract

SUMMARY During flight, the wings of many insects undergo considerable shape changes in spanwise and chordwise directions. We determined the origin of spanwise wing deformation by combining measurements on segmental wing stiffness of the blowfly Calliphora vicina in the ventral and dorsal directions with numerical modelling of instantaneous aerodynamic and inertial forces within the stroke cycle using a two-dimensional unsteady blade elementary approach. We completed this approach by an experimental study on the wing's rotational axis during stroke reversal. The wing's local flexural stiffness ranges from 30 to 40 nN m2 near the root, whereas the distal wing parts are highly compliant (0.6 to 2.2 nN m2). Local bending moments during wing flapping peak near the wing root at the beginning of each half stroke due to both aerodynamic and inertial forces, producing a maximum wing tip deflection of up to 46 deg. Blowfly wings store up to 2.30 μJ elastic potential energy that converts into a mean wing deformation power of 27.3 μW. This value equates to approximately 5.9 and 2.3% of the inertial and aerodynamic power requirements for flight in this animal, respectively. Wing elasticity measurements suggest that approximately 20% or 0.46 μJ of elastic potential energy cannot be recovered within each half stroke. Local strain energy increases from tip to root, matching the distribution of the wing's elastic protein resilin, whereas local strain energy density varies little in the spanwise direction. This study demonstrates a source of mechanical energy loss in fly flight owing to spanwise wing bending at the stroke reversals, even in cases in which aerodynamic power exceeds inertial power. Despite lower stiffness estimates, our findings are widely consistent with previous stiffness measurements on insect wings but highlight the relationship between local flexural stiffness, wing deformation power and energy expenditure in flapping insect wings.

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

“…The Reynolds number for species such as hummingbirds is Re ¼ O(10 4 ), while for smaller insects, such as fruit flies or honeybees, Re ¼ O(10 2 2 10 3 ). These small insect flyers have flexible wings that experience large deformations just like birds and bats [11,12]. It has been, for example, shown that wing deformations [13,14] can enhance the force generation and efficiency of a locust operating at Re % 4 Â 10 3 [13], or a hawkmoth at Re % 6.3 Â 10 3 [15].…”

“…Moreover, tethered flying Drosophila actively control left/right wing rotation timing to initiate yaw turns [20]. However, hovering fruit flies [21] and honeybees [22], beetles [11] and hymenopterans in general exhibit symmetric rotation [11], which means that they rotate their wings around the same time as they reverse the stroke.…”

It's Not a Bug, It's a Feature: Functional Materials in Insects

“…[97] While all patterns tend to promote an exponential decay in bending stiffness from wing base to tip, spatial mapping of veins plays an important role in flexibility variation between the leading and trailing edges of wings ( Figure 6). [98,99] As a method to promote further deformations within this relatively rigid venous structure, the cuticle of certain insect wings contains flexible linear segments, which act as fold lines. [100] Such bands are distributed independently of support veins-those running radially (base to tip) mediate bending and twisting, while others oriented transversely (leading edge to trailing edge) act as one-way hinges to help the wings bend and reset after the completion of a downstroke.…”

Wing Geometry and Kinematic Parameters Optimization of Flapping Wing Hovering Flight

“…Firstly, the energetic cost consumed by hovering insect only considers the time-averaged positive mechanical power output used to overcome aerodynamic damping and inertial power [54][55][56]. Secondly, the elastic storage can be recovered completely and thus be treated as a part of the negative power of the system [55][56][57]. Thirdly, the wing motions are powered by actuators located at the wing shoulder.…”

“…Here, the optimal values for non-dimensional location of the pitch axis, which consistently approach the leading edge for the optimization involving WGP (Table 3), is only the numerical solution but not reflect the real situation since the pitch axis might be not a straight line. In engineering design, the location of pitch axis needs to be determined by experimentally measuring the optimal angle of attack [57]. In order to survive in a complex environment such as predation or evading maneuverability with limited energy, fruit fly might evolve to have pony-size WGP adaptive to its body size in millimeter scale but high flapping frequency and large flapping amplitude under the strategy of minimum power consumption.…”