Effects of wing-to-body mass ratio on insect flapping flights

Abstract

Bio-flyers of insects, birds, and bats are observed to have a broad range of wing-to-body mass ratio (WBMR) from 0.1% to 15%. The WBMR and wing mass distribution can lead to large inertial forces and torques in fast-flapping wings, particularly in insect flights, comparable with or even greater than aerodynamic ones, which may greatly affect the aerodynamic performance, flight stability, and control, but still remain poorly understood. Here, we address a simulation-based study of the WBMR effects on insect flapping flights with a specific focus on unraveling whether some optimal WBMR exists in balancing the flapping aerodynamics and body control in terms of body pitch oscillation and power consumption. A versatile, integrated computational model of hovering flight that couples flapping-wing-and-body aerodynamics and three degree of freedom body dynamics was employed to analyze free-flight body dynamics, flapping aerodynamics, and power cost for three typical insects of a fruit fly, a bumblebee, and a hawkmoth over a wide range of Reynolds numbers (Re) and WBMRs. We found that the realistic WBMRs in the three insect models can suppress the body pitch oscillation to a minimized level at a very low cost of mechanical power. We further derived a scaling law to correlate the WBMR with flapping-wing kinematics of stroke amplitude (Φ), flapping frequency (f), and wing length (R) in terms of ΦRf2−1, which matches well with measurements and, thus, implies that the WBMR-based body pitch minimization may be a universal mechanism in hovering insects. The realistic WBMR likely offers a novel solution to resolve the trade-off between body-dynamics-based aerodynamic performance and power consumption. Our results indicate that the WBMR plays a crucial role in optimization of flapping-wing dynamics, which may be useful as novel morphological intelligence for the biomimetic design of insect- and bird-sized flapping micro-aerial vehicles.

Solving the thoracic inverse problem in the fruit fly

“…uniform thicknessan assumption which will be conservative [80], given that wing veins and vein junctions are disproportionately located nearer to the wing root. Our estimate of wing inertia (table 2) is consistent with existing literature estimates [81,82]; but a coarse analysis given in the supporting information indicates that thickness variation consistent with observed flexural stiffness variation in D. melanogaster wings [83] could lead to 30% reduction in inertia with respect to the estimate given in table 2. This latter estimate should be regarded as an overestimate.…”

Inherently stable descending flight of a tailless flapping wing micro air vehicle by upward wing elevation

“…These approximations are fair, since the wings together make up only 2.5% of total system mass. 27,21,28…”

“…These approximations are fair, since the wings together make up only 2.5% of total system mass. 27,21,28 The relation between the vehicle rotational velocity and the vehicle attitude is given by Etkin B and Reid, 24 Karásek M and Preumont 33 :…”

“…The term fast body dynamics refers to the motion of the system within one flapping cycle. 23,21,27 This work does not use direct averaging. Because force production and body acceleration are computed at each time step in the flapping cycle, fast body dynamics are taken into account.…”

“…Many studies rely on simulation data instead. 17,7,27,16,21 This work performs a computational study on the effects of wing elevation on the stability characteristics of an FWMAV.…”