Aerodynamic investigation on shifted-back vertical stroke plane of flapping wing in forward flight.

In order to properly understand aerodynamic characteristics in a flapping wing in forward flight, additional aerodynamic parameters apart from those in hover-an inclined stroke plane, a shifted-back stroke plane, and an advance ratio-must be comprehended in advance. This paper deals with the aerodynamic characteristics of a flapping wing in a shifted-back vertical stroke plane in freestream. A scaled-up robotic arm in a water towing tank was used to collect time-varying forces of a model flapping wing, and a semi-empirical quasi-steady aerodynamic model, which can decompose the forces into steady, quasi-steady, and unsteady components, was used to estimate the forces of the model flapping wing. It was found that the shifted-back stroke plane left a part of freestream as a non-perpendicular component, giving rise to a time-course change in the aerodynamic forces during the stroke. This also brought out two quasi-steady components (rotational and added-mass forces) apart from the steady one, even the wing moved with a constant stroke velocity. The aerodynamic model underestimated the actual forces of the model flapping wing even it can cover the increasingly distributed angle of attack of the vertical stroke plane with a blade element theory. The locations of the centers of pressure suggested a greater pressure gradient and an elongated leading-edge vortex along a wingspan than that of the estimation, which may explain the higher actual force in forward flight.

Aerodynamic performance of flexible flapping wings deformed by slack angle.

Wing flexibility is unavoidable for flapping wing flyers to ensure a lightweight body and for higher payload allowances on board. It also effectively minimizes the inertia force from high-frequency wingbeat motion. However, related studies that attempt to clarify the essence of wing flexibility remain insufficient. Here, a parametric study of a flexible wing was conducted as part of the effort to build an aerodynamic model and analyze its aerodynamic performance. The quasi-steady modeling was adopted with experimentally determined translational forces. These forces were determined from 84 flexible wing cases while varying the angle of attack at the wing rootαrand the flexibility parameter, slack angleθS, with 19 additional rigid wing cases. This study foundαrfor optimum lift generation to exceed 45° irrespective ofθS. The coefficient curves were well-fitted with a cubed-sine function. The model was rigorously validated with various wing kinematics, giving a good estimation of the experimental results. The estimated error was less than 5%, 6%, and 8% for the lift, drag, and moment, respectively, considering fast to moderate wing kinematics. The study was extended to analyze the pure aerodynamic performance of the flexible wing. The most suitable wing for a flapping-wing micro-aerial vehicle wing design with a simple vein structure was found to be the 5° slack-angled wing. The inference from this study further shows that a small amount of deformation is needed to increase the lift, as observed in natural flyers. Thus, wing deformation could allow living flyers to undertake less pitching motion in order to reduce the mechanical power and increase the efficiency of their wings.

A contralateral wing stabilizes a hovering hawkmoth under a lateral gust.

Previous analysis on the lateral stability of hovering insects, which reported a destabilizing roll moment due to a lateral gust, has relied on the results of a single wing without considering a presence of the contralateral wing (wing-wing interaction). Here, we investigated the presence of the contralateral wing on the aerodynamic and flight dynamic characteristics of a hovering hawkmoth under a lateral gust. By employing a dynamically scaled-up mechanical model and a servo-driven towing system installed in a water tank, we found that the presence of the contralateral wing plays a significant role in the lateral static stability. The contralateral wing mitigated an excessive aerodynamic force on the wing at the leeward side, thereby providing a negative roll moment to the body. Digital particle image velocimetry revealed an attenuated vortical system of the leading-edge vortex. An excessive effective angle of attack in the single wing case, which was caused by the root vortex of previous half stroke, was reduced by a downwash of the contralateral wing. The contralateral wing also relocated a neutral point in close proximity to the wing hinge points above the actual center of gravity, providing a practical static margin to a hovering hawkmoth.

Aerodynamic effects of deviating motion of flapping wings in hovering flight.

Nature's flyers adopt deviating motion when they fly, however, the effect of deviating motion on the aerodynamics of flapping wings is not yet clearly understood. In this study, the aerodynamic characteristics of figure-of-eight deviating motion were investigated by comparing the aerodynamic force obtained from an experiment and the quasi-steady (QS) model in wide ranges of both the pitch and deviation amplitude. A flapping-wing robotic manipulator with a one-ton water tank was used in the experiment. Digital particle image velocimetry (DPIV) was also conducted in several chordwise cross-sections and different time instants. The results showed that the increment of deviating angle dramatically reduced the aerodynamic lift in the middle of the up- or downstroke from the quasi-steady estimation. The DPIV showed a vortex loop, which inhibits lift generation, at the middle of the up- or downstroke in deviating motion. The deviating motion delayed a development of the vortices, and more stroke angle was necessary for trailing edge vortex shedding. The QS model could not properly predict the aerodynamic force of the flapping wing with significant deviation angles. The error between the experiments and the QS estimation with regard to the aerodynamic lift was as high as 35% in the middle of the up- or downstroke with a high deviation amplitude ([Formula: see text]), reducing the cycle-averaged value of the lift coefficient up to 30%.

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.

Effect of body aerodynamics on the dynamic flight stability of the hawkmoth Manduca sexta.

This study explores the effects of the body aerodynamics on the dynamic flight stability of an insect at various different forward flight speeds. The insect model, whose morphological parameters are based on measurement data from the hawkmoth Manduca sexta, is treated as an open-loop six-degree-of-freedom dynamic system. The aerodynamic forces and moments acting on the insect are computed by an aerodynamic model that combines the unsteady panel method and the extended unsteady vortex-lattice method. The aerodynamic model is then coupled to a multi-body dynamic code to solve the system of motion equations. First, the trimmed flight conditions of insect models with and without consideration of the body aerodynamics are obtained using a trim search algorithm. Subsequently, the effects of the body aerodynamics on the dynamic flight stability are analysed through modal structures, i.e., eigenvalues and eigenvectors in this case, which are based on linearized equations of motion. The solutions from the nonlinear and linearized equations of motion due to gust disturbances are obtained, and the effects of the body aerodynamics are also investigated through these solutions. The results showed the important effect of the body aerodynamics at high-speed forward flight (in this paper at 4.0 and 5.0 m s-1) and the movement trends of eigenvalues when the body aerodynamics is included.

Hovering and forward flight of the hawkmoth Manduca sexta: trim search and 6-DOF dynamic stability characterization.

We show that the forward flight speed affects the stability characteristics of the longitudinal and lateral dynamics of a flying hawkmoth; dynamic modal structures of both the planes of motion are altered due to variations in the stability derivatives. The forward flight speed u e is changed from 0.00 to 1.00 m s(-1) with an increment of 0.25 m s(-1). (The equivalent advance ratio is 0.00 to 0.38; the advance ratio is the ratio of the forward flight speed to the average wing tip speed.) As the flight speed increases, for the longitudinal dynamics, an unstable oscillatory mode becomes more unstable. Also, we show that the up/down (w(b)) dynamics become more significant at a faster flight speed due to the prominent increase in the stability derivative Z(u) (up/down force due to the forward/backward velocity). For the lateral dynamics, the decrease in the stability derivative L(v) (roll moment due to side slip velocity) at a faster flight speed affects a slightly damped stable oscillatory mode, causing it to become more stable; however, the t(half) (the time taken to reach half the amplitude) of this slightly damped stable oscillatory mode remains relatively long (∼12T at u(e) = 1 m s(-1); T is wingbeat period) compared to the other modes of motion, meaning that this mode represents the most vulnerable dynamics among the lateral dynamics at all flight speeds. To obtain the stability derivatives, trim conditions for linearization are numerically searched to find the exact trim trajectory and wing kinematics using an algorithm that uses the gradient information of a control effectiveness matrix and fully coupled six-degrees of freedom nonlinear multibody equations of motion. With this algorithm, trim conditions that consider the coupling between the dynamics and aerodynamics can be obtained. The body and wing morphology, and the wing kinematics used in this study are based on actual measurement data from the relevant literature. The aerodynamic model of the flapping wings of a hawkmoth is based on the blade element theory, and the necessary aerodynamic coefficients, including the lift, drag and wing pitching moment, are experimentally obtained from the results of previous work by the authors.

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.