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

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... el 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, Allomyrina dichotoma. 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. obtained, and the wing kinematics was measured using three synchronized high-speed cameras. Using the theoretical bladeelement model as an effective tool, we were able to estimate the force generation, power requirement and contribution of each power component to the total power budget. In addition, we investigated the effect of the torsion axis by artificially adjusting its location with respect to the CG wc because the actual location of the torsion axis is difficult to determine. Based on the parameters of the beetle's hindwing, we then searched for the best AoA distributed along the wingspan for hovering flight, which provide the highest local power loading (PL, vertical force/power ratio) at each wing section, for each position of the torsion axis. Unlike other optimization studies, which were based solely on the aerodynamics using simplified 2D wing kinematics (Usherwood, 2009; Usherwood and Ellington, 2002; Taha et al., 2013; Pesavento and Wang, 2009) , our approach was based on both aerodynamic and inertial terms associated with the measured wing kinematics of a real beetle. Finally, the effect of wing inertia was addressed and is discussed.