Wing inertia as a cause of aerodynamically uneconomical flight with high angles-of-attack in hovering insects

Abstract

Flying insects can maintain maneuverability in the air by flapping their wings, and, to save energy, the wings should operate following optimal kinematics. However, unlike conventional rotary wings, insects operate their wings at aerodynamically uneconomical and high angles of attack (AoA). Although insects have continuously received attention from biologists and aerodynamicists, the high AoA operation in insect flight has not been clearly explained. Here, we used a theoretical blade-element model to examine the impact of wing inertia on the power requirement and flapping AoA, based on 3D free-hovering flight wing kinematics of a horned beetle, The relative simplicity of the model allowed us to search for the best AoA distributed along the wingspan, which generate the highest vertical force per unit power. We show that, although elastic elements may be involved in flight muscles to store and save energy, the insect still has to use substantial power to accelerate its wings, because inertial energy stores should be used to overcome aerodynamic drag before being stored elastically. At the same flapping speed, a wing operating at a higher AoA requires lower inertial torque, and therefore lower inertial power output, at stroke reversals than a wing operating at an aerodynamically optimal low AoA. An interactive aerodynamic-inertial effect thereby enables the wing to flap at sufficiently high AoA, which causes an aerodynamically uneconomical flight in an effort to minimize the net flight energy.

KUBeetle-S: An insect-like, tailless, hover-capable robot that can fly with a low-torque control mechanism

“…The tailless robot is developed aiming to mimic the flight of horned beetle (Allomyrina dichotoma) known to be capable of hovering flight. 26 Since the mechanical design of the flapping-wing mechanism was presented in detail in ref., 17 this paper shows only a brief summary.…”

Wing Morphology and Inertial Properties of Bumblebees

“…Note that, in [3,4,5], the area density distribution was determined as the dissected wing segment mass divided by the respective area. Our approach of calculating separately the vein mass and the membrane mass is less straightforward, but it allows us to use only a small number of segments and still account for the important area density variation near the leading edges and the roots, because it is mainly due to the veins.…”

“…Calculation of the moments of inertia yields the following isometric scaling relationships: = 0.0014 5 , = 0.0426 5 , = −0.0010 5 , where R is in meters and the result is in kg ⋅ m 2 . For a wing of length = 15.2 mm , we obtain = 1.14 ⋅ 10 −12 kg ⋅ m 2 , = 34.6 ⋅ 10 −12 kg ⋅ m 2 , = −0.81 ⋅ 10 −12 kg ⋅ m 2 .…”

“…We thus obtained sequences of values for each component of the inertia tensor. They have the mean values equal up to the last digit to the nominal values shown above, and the standard deviations equal to Δ = 0.00006 5 , Δ = 0.00140 5 , Δ = 0.00023 5 , respectively. The full wing center of mass is located remarkably near to the rotation axis at xc = 0.379R, yc = -0.019R.…”

“…This paper aims to provide a detailed account of the procedure that we have followed to determine the geometrical and inertial properties of the bumblebee wings. Although there have been previous studies describing the wing mass distribution in flies [3], dragonflies [4] and beetles [5], to the best of our knowledge, there have been no such measurement reported for bumblebees. The novelty of our work resides not only in the choice of the target species, but also in the measurement method that differentiates between the vein mass and the membrane mass.…”