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

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 (Phi), flapping frequency (f), and wing length (R) in terms of open Phi R f 2 - 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.