An aerodynamic model for insect flapping wings in forward flight.

This paper proposes a semi-empirical quasi-steady aerodynamic model of a flapping wing in forward flight. A total of 147 individual cases, which consisted of advance ratios J of 0 (hovering), 0.125, 0.25, 0.5, 0.75, 1 and ∞, and angles of attack α of -5 to 95° at intervals of 5°, were examined to extract the aerodynamic coefficients. The Polhamus leading-edge suction analogy and power functions were then employed to establish the aerodynamic model. In order to preserve the existing level of simplicity, K P and K V, the correction factors of the potential and vortex force models, were rebuilt as functions of J and α. The estimations were nearly identical to direct force/moment measurements which were obtained from both artificial and practical wingbeat motions of a hawkmoth. The model effectively compensated for the influences of J, particularly showing outstanding moment estimation capabilities. With this model, we found that using a lower value of α during the downstroke would be an effective strategy for generating adequate lift in forward flight. The rotational force and moment components had noticeable portions generating both thrust and counteract pitching moment during pronation. In the upstroke phase, the added mass component played a major role in generating thrust in forward flight. The proposed model would be useful for a better understanding of flight stability, control, and the dynamic characteristics of flapping wing flyers, and for designing flapping-wing micro air vehicles.

An improved quasi-steady aerodynamic model for insect wings that considers movement of the center of pressure.

A quasi-steady aerodynamic model in consideration of the center of pressure (C.P.) was developed for insect flight. A dynamically scaled-up robotic hawkmoth wing was used to obtain the translational lift, drag, moment and rotational force coefficients. The translational force coefficients were curve-fitted with respect to the angles of attack such that two coefficients in the Polhamus leading-edge suction analogy model were obtained. The rotational force coefficient was also compared to that derived by the standard Kutta-Joukowski theory. In order to build the accurate pitching moment model, the locations of the C.Ps. and its movements depending on the pitching velocity were investigated in detail. We found that the aerodynamic moment model became suitable when the rotational force component was assumed to act on the half-chord. This implies that the approximation borrowed from the conventional airfoil concept, i.e., the 'C.P. at the quarter-chord' may lead to an incorrect moment prediction. In the validation process, the model showed excellent time-course force and moment estimations in comparison with the robotic wing measurement results. A fully nonlinear multibody flight dynamic simulation was conducted to check the effect of the traveling C.P. on the overall flight dynamics. This clearly showed the importance of an accurate aerodynamic moment model.

Reynolds number dependency of an insect-based flapping wing.

Aerodynamic characteristics depending on Reynolds number (Re) ranges were studied to investigate the suitable design parameters of an insect-based micro air vehicle (MAV). The tests centered on the wing rotation timing and Re ranges, and were conducted to understand the lift augmentations and unsteady effects. A dynamically scaled-up flapping wing controlled by a pair of servos was installed underwater with a micro force/torque sensor. A high-speed camera and a laser sheet were also put in front of the water tank for the time-resolved digital particle image velocimetry (DPIV). The lift augmentations clearly appeared at low Re and were well reflected on the insect's flight range. In the case of the high Re, however, the peak standing for the wing­wake interaction was delayed, and the pitching-up rotation was not able to lead to another lift enhancement, i.e., rotational lift. In such Re, the mean CL and the L/D of the advanced rotation were substantially decreased from those of the other rotations. The DPIV results at high Re well described turbulent characteristics such as the irregular, unstable, and high-intensity vortex structures with a short temporal delay. In the advanced rotation, the LEV in the rotational phase could not maintain the attachment. Thus, the rotational lift was not able to work. On the contrary, the temporal response delay benefitted the wing in the delayed rotation. Therefore, the wing in the delayed rotation had both a similar level of the mean CL and a higher marked L/D than those of the advanced rotation. Such results indicate that the high Re could interrupt lift augmentation mechanisms, and these augmentations would not be suitable for a heavier MAV. In conclusion, using adequate wing kinematics to acquire estimations of the weight and range of the Re is highly recommended at the aerodynamic design step.