Hawkmoth Wing Research Articles

Study of vertically ascending flight of a hawkmoth model

This paper provides insight into the wing kinematics, the power requirement and the dynamic stability characteristics of a hawkmoth model in vertically ascending flight. The wing kinematics of the hawkmoth model is obtained based on the minimum required power assumption. The optimization process is conducted using genetic and simplex algorithms that are coupled with an artificial neural network to rapidly predict the aerodynamic force and required power. The training data for the neural network are generated from an unsteady vortex-lattice method. Compared to hover, the results in this study show the larger flapping frequency and the smaller rotation amplitude of the hawkmoth wing kinematics in ascending flight. Additionally, more power is required when the ascending speed increases. While conducting a dynamic modal analysis based on a cycle-average approach, the certain effect of the ascending speed on the modal structures of the hawkmoth model was observed.

Aerodynamics of the Wells turbine with a Hawkmoth-inspired blade design

This work introduces a new biomimetic design for the well-known Wells turbine to enhance its efficiency for harvesting energy. In this paper, a biomimetic Wells turbine inspired by the geometry of hawkmoth wings is presented. Aerodynamics of both the bio-inspired design and the conventional design are investigated through computational fluid dynamics. Non-dimensional performance indicators of the bio-inspired design are compared to those of the conventional turbine, including the torque coefficient, the pressure drop coefficient, the turbine efficiency. The velocity and pressure distribution as well as the vortices shed from the blades are illustrated to understand the differences in flow phenomena. The results indicate that the biomimetic design changes the flow field and can attain a higher peak efficiency, especially at high angle of attack. Finally, the performance of blades with various aspect ratios is investigated to better understand the biomimetic design.

One-way FSI analysis of bio-inspired flapping wings

Aerodynamics and structural dynamics of the insect wings are widely considered in flapping wing micro air vehicle (FWMAV) applications. In this paper, the aerodynamic characteristics of the three-dimensional flapping wing models mimicked from the bumblebee and hawkmoth wings are numerically investigated under steady flow conditions. This study aims to simulate the one-way fluid-structure interaction (FSI) of these bio-inspired wings by transferring the aerodynamic load obtained from the computational fluid dynamics (CFD) into the finite element method (FEM) solver as a pressure load. The static aeroelastic responses of the wings under the pressure load are compared for different materials, namely, cuticle, aluminium alloy, and titanium alloy at various angles of attack (α = 0°-90°). CFD analysis shows that the hawkmoth wing model at α = 5° has the highest lift-to-drag ratio (L/D). FSI analysis demonstrates that the cuticle hawkmoth wing model at α = 90° undergoes the highest tip deflection.

Effects of hawkmoth-like flexibility on the aerodynamic performance of flapping wings with different shapes and aspect ratios

The effect of hawkmoth-like flexibility on the aerodynamic hovering performance of wings at a Reynolds number of 400 has been assessed by conducting fluid structure interaction simulations incorporating a finite difference based immersed boundary method coupled with a finite-element based structure solver. The stiffness distribution of a hawkmoth forewing was mapped onto three wing shapes (r¯1 = 0.43, 0.53, and 0.63) defined by the radius of the first moment of wing area each with aspect ratios, AR = 1.5, 2.96, 4.5, and 6.0 using elliptic mesh generation, the Jacobi method for iterations, and the concept of the barycentric coordinate system. The results show that there is a dominant chordwise deformation at AR = 1.5, and the wings also deform in the spanwise direction and their tips deviate from the horizontal stroke plane as AR increases. At AR = 1.5, 2.96, and 4.5, flexibility increases the mean lift (up to 39%, 18%, and 17.6%, respectively) for all wing shapes. At AR = 6.0, the r1¯ = 0.53 and 0.63 flexible wings give lesser lift than the rigid equivalents because of negative lift or small positive lift during the early stroke as the vortical structures remain on the bottom surface. This is attributed to the rapid pitch-down rotation, lesser stroke angular velocity than the rigid wing, and upward motion of the wingtip, away from the horizontal stroke plane. From the design perspective, the anisotropic flexible wings (except r1¯ = 0.53 and 0.63 with AR = 6.0) can be used in micro aerial vehicles for high lift requirements, such as for a high payload. Results here show that in nature, the hawkmoth wings with r1¯ and AR of 0.43-0.44 and 2.73-2.92, respectively, appear to have a combination of the shape, AR, and flexibility that optimizes power economy.

Environment identification in flight using sparse approximation of wing strain

This paper addresses the problem of identifying different flow environments from sparse data collected by wing strain sensors. Insects regularly perform this feat using a sparse ensemble of noisy strain sensors on their wing. First, we obtain strain data from numerical simulation of a Manduca sexta hawkmoth wing undergoing different flow environments. Our data-driven method learns low-dimensional strain features originating from different aerodynamic environments using proper orthogonal decomposition (POD) modes in the frequency domain, and leverages sparse approximation to classify a set of strain frequency signatures using a dictionary of POD modes. This bio-inspired machine learning architecture for dictionary learning and sparse classification permits fewer costly physical strain sensors while being simultaneously robust to sensor noise. A measurement selection algorithm identifies frequencies that best discriminate the different aerodynamic environments in low-rank POD feature space. In this manner, sparse and noisy wing strain data can be exploited to robustly identify different aerodynamic environments encountered in flight, providing insight into the stereotyped placement of neurons that act as strain sensors on a Manduca sexta hawkmoth wing.

Extended Unsteady Vortex-Lattice Method for Insect Flapping Wings

An extended unsteady vortex-lattice method is developed to study the aerodynamics of insect flapping wings while hovering and during forward flight. Leading-edge suction analogy and vortex-core growth models are used as an extension, which is incorporated into a conventional unsteady vortex-lattice method in an effort to overcome the challenges that arise when simulating insect aerodynamics such as wing–wake interaction and leading-edge effects. A convergence analysis was carried out to derive an optimal aerodynamic mesh and a time-step size for flapping-wing models. A parallel computing technique was used to reduce computational time. The aerodynamics of hawkmoth (Manduca sexta) wing models was simulated, and the results were validated against previous numerical and experimental data.

Gyroscopic sensing in the wings of the hawkmoth Manduca sexta: the role of sensor location and directional sensitivity

The wings of the hawkmoth Manduca sexta are lined with mechanoreceptors called campaniform sensilla that encode wing deformations. During flight, the wings deform in response to a variety of stimuli, including inertial-elastic loads due to the wing flapping motion, aerodynamic loads, and exogenous inertial loads transmitted by disturbances. Because the wings are actuated, flexible structures, the strain-sensitive campaniform sensilla are capable of detecting inertial rotations and accelerations, allowing the wings to serve not only as a primary actuator, but also as a gyroscopic sensor for flight control. We study the gyroscopic sensing of the hawkmoth wings from a control theoretic perspective. Through the development of a low-order model of flexible wing flapping dynamics, and the use of nonlinear observability analysis, we show that the rotational acceleration inherent in wing flapping enables the wings to serve as gyroscopic sensors. We compute a measure of sensor fitness as a function of sensor location and directional sensitivity by using the simulation-based empirical observability Gramian. Our results indicate that gyroscopic information is encoded primarily through shear strain due to wing twisting, where inertial rotations cause detectable changes in pronation and supination timing and magnitude. We solve an observability-based optimal sensor placement problem to find the optimal configuration of strain sensor locations and directional sensitivities for detecting inertial rotations. The optimal sensor configuration shows parallels to the campaniform sensilla found on hawkmoth wings, with clusters of sensors near the wing root and wing tip. The optimal spatial distribution of strain directional sensitivity provides a hypothesis for how heterogeneity of campaniform sensilla may be distributed.

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.

Effects of wing deformation on aerodynamic performance of a revolving insect wing

Flexible wings of insects and bio-inspired micro air vehicles generally deform remarkably during flapping flight owing to aerodynamic and inertial forces, which is of highly nonlinear fluid-structure interaction (FSI) problems. To elucidate the novel mechanisms associated with flexible wing aerodynamics in the low Reynolds number regime, we have built up a FSI model of a hawkmoth wing undergoing revolving and made an investigation on the effects of flexible wing deformation on aerodynamic performance of the revolving wing model. To take into account the characteristics of flapping wing kinematics we designed a kinematic model for the revolving wing in two-fold: acceleration and steady rotation, which are based on hovering wing kinematics of hawkmoth, Manduca sexta. Our results show that both aerodynamic and inertial forces demonstrate a pronounced increase during acceleration phase, which results in a significant wing deformation. While the aerodynamic force turns to reduce after the wing acceleration terminates due to the burst and detachment of leading-edge vortices (LEVs), the dynamic wing deformation seem to delay the burst of LEVs and hence to augment the aerodynamic force during and even after the acceleration. During the phase of steady rotation, the flexible wing model generates more vertical force at higher angles of attack (40°–60°) but less horizontal force than those of a rigid wing model. This is because the wing twist in spanwise owing to aerodynamic forces results in a reduction in the effective angle of attack at wing tip, which leads to enhancing the aerodynamics performance by increasing the vertical force while reducing the horizontal force. Moreover, our results point out the importance of the fluid-structure interaction in evaluating flexible wing aerodynamics: the wing deformation does play a significant role in enhancing the aerodynamic performances but works differently during acceleration and steady rotation, which is mainly induced by inertial force in acceleration but by aerodynamic forces in steady rotation.

EXPERIMENTAL STUDY OF GROUND EFFECT ON THREE-DIMENSIONAL INSECT-LIKE FLAPPING MOTION

This paper focuses on an experimental investigation aimed at evaluating the aerodynamics force characteristics of three-dimensional (3D) insect-like flapping motion in the vicinity of ground. The purpose is to establish whether flapping wing insects can derive aerodynamic benefit from ground effect similar to that experienced by a fixed wing aircraft. To evaluate this, force measurements were conducted in a large water tank using a 3D flapping mechanism capable of executing various insect flapping motions. Here, we focus on three types of flapping motions, namely simple harmonic flapping motion, hawkmoth-like hovering motion and fruitfly-like hovering motion, and two types of wing planforms (i.e. hawkmoth-like wing and fruitfly-like wing). Results show that hawkmoth-like wing executing simple harmonic flapping motion produces average lift to drag ratio [Formula: see text] similar to that of fruitfly wing executing the same motion. In both cases, they are relatively independent of the wing distance from the ground. On the other hand, a hawkmoth wing executing hawkmoth flapping motion produces [Formula: see text] characteristic different from that of fruitfly wing executing fruitfly motion. While the [Formula: see text] value of the former is a function of the wing distance from the ground, the latter is minimally affected by ground effect. Unlike fixed wing aerodynamics, all the flapping wing cases considered here do not show a monotonic increase in [Formula: see text] with decreasing wing distance from the ground.

A multi-fidelity modelling approach for evaluation and optimization of wing stroke aerodynamics in flapping flight

AbstractThe aerodynamics of hovering flight in a hawkmoth (Manduca sexta) are examined using a computational modelling approach which combines a low-fidelity blade-element model with a high-fidelity Navier–Stokes-based flow solver. The focus of the study is on understanding the optimality of the hawkmoth-inpired wingstrokes with respect to lift generation and power consumption. The approach employs a tight coupling between the computational models and experiments; the Navier–Stokes model is validated against experiments, and the blade-element model is calibrated with the data from the Navier–Stokes modelling. In the first part of the study, blade-element and Navier–Stokes modelling are used concurrently to assess the predictive capabilities of the blade-element model. Comparisons between the two modelling approaches also shed insights into specific flow features and mechanisms that are lacking in the lower-fidelity model. Subsequently, we use blade-element modelling to explore a large kinematic parameter space of the flapping wing, and Navier–Stokes modelling is used to assess the performance of the wing-stroke identified as optimal by the blade-element parameter survey. This multi-fidelity optimization study indicates that even within a parameter space constrained by the animal’s natural flapping amplitude and frequency, it is relatively easy to synthesize a wing stroke that exceeds the aerodynamic performance of the hawkmoth wing stroke. Within the prescribed constraints, the optimal wing stroke closely approximates the condition of normal hover, and the implications of these findings on hawkmoth flight capabilities as well as on the issue of biomimetic versus bioinspired design of flapping wing micro-aerial vehicles, are discussed.

Experimental Structural Dynamic Characterization of the Hawkmoth (Manduca Sexta) Forewing

While many bio-inspired flapping wing micro air vehicle wing designs continue to be conceived and studied in earnest, a general consensus of which physical attributes of the biological entity are important for flight is still at-large. It is proposed herein that the eigenstructure of the wing should figure prominently among rigorous engineering metrics for guiding flapping wing micro air vehicle wing designs at the scales of large insects. With virtually no compelling work done in this area to date, the method and results of system identification tests for the forewings of a representative sample of hawkmoth ( Manduca Sexta) are presented, revealing the underlying structural nature of this incredibly agile flyer's wings. Despite their inherent biological variability, these wings show very little variability in eigenstructure which may suggest it as a critical attribute for robust flight. Further supporting this hypothesis, the wings of four other insect species are briefly examined and show remarkable similarity with the hawkmoth wing's eigenstructure.

A fluid–structure interaction model of insect flight with flexible wings

We present a fluid–structure interactions (FSI) model of insect flapping flight with flexible wings. This FSI-based model is established by loosely coupling a finite element method (FEM)-based computational structural dynamic (CSD) model and a computational fluid dynamic (CFD)-based insect dynamic flight simulator. The CSD model is developed specifically for insect flapping flight, which is capable to model thin shell structures of insect flexible wings by taking into account the distribution and anisotropy in both wing morphology involving veins, membranes, fibers and density, and in wing material properties of Young’s modulus and Poisson’s ratios. The insect dynamic flight simulator that is based on a multi-block, overset grid, fortified Navier–Stokes solver is capable to integrate modeling of realistic wing-body morphology, realistic flapping-wing and body kinematics, and unsteady aerodynamics in flapping-wing flights. Validation of the FSI-based aerodynamics and structural dynamics in flexible wings is achieved through a set of benchmark tests and comparisons with measurements, which contain a heaving spanwise flexible wing, a heaving chordwise-flexible wing with a rigid teardrop element, and a realistic hawkmoth wing rotating in air. A FSI analysis of hawkmoth hovering with flapping flexible wings is then carried out and discussed with a specific focus on the in-flight deformation of the hawkmoth wings and hovering aerodynamic performances with the flexible and rigid wings. Our results demonstrate the feasibility of the present FSI model in accurately modeling and quantitatively evaluating flexible-wing aerodynamics of insect flapping flight in terms of the aerodynamic forces, the power consumption and the efficiency.

Micro air vehicle-motivated computational biomechanics in bio-flights: aerodynamics, flight dynamics and maneuvering stability

Aiming at developing an effective tool to unveil key mechanisms in bio-flight as well as to provide guidelines for bio-inspired micro air vehicles (MAVs) design, we propose a comprehensive computational framework, which integrates aerodynamics, flight dynamics, vehicle stability and maneuverability. This framework consists of (1) a Navier–Stokes unsteady aerodynamic model; (2) a linear finite element model for structural dynamics; (3) a fluid-structure interaction (FSI) model for coupled flexible wing aerodynamics aeroelasticity; (4) a free-flying rigid body dynamic (RBD) model utilizing the Newtonian-Euler equations of 6DoF motion; and (5) flight simulator accounting for realistic wing-body morphology, flapping-wing and body kinematics, and a coupling model accounting for the nonlinear 6DoF flight dynamics and stability of insect flapping flight. Results are presented based on hovering aerodynamics with rigid and flexible wings of hawkmoth and fruitfly. The present approach can support systematic analyses of bio- and bio-inspired flight.

Power distribution in the hovering flight of the hawk moth Manduca sexta

We investigated inertial and aerodynamic power consumption during hovering flight of the hawk moth Manduca sexta. The aerodynamic power was estimated based on the aerodynamic forces and torques measured on model hawk-moth wings and hovering kinematics. The inertial power was estimated based on the measured wing mass distribution and hovering kinematics. The results suggest that wing inertial power (without consideration of muscle efficiency and elastic energy storage) consumes about half of the total power expenditure. Wing areal mass density was measured to decrease sharply from the leading edge toward the trailing edge and from the wing base to the wing tip. Such a structural property helps to minimize the wing moment of inertia given a fixed amount of mass. We measured the aerodynamic forces on the rigid and flexible wings, which were made to approximate the flexural stiffness (EI) distribution and deformation of moth wings. It has been found that wings with the characteristic spanwise and chordwise decreasing EI (and mass density) are beneficial for power efficiency while generating aerodynamic forces comparative to rigid wings. Furthermore, negative work to aid pitching in stroke reversals from aerodynamic forces was found, and it showed that the aerodynamic force contributes partially to passive pitching of the wing

Aerodynamic force generation of an insect-inspired flapper actuated by a compressed unimorph actuator

We examined experimentally the flapping performance in terms of aerodynamic force generation of an insect-inspired flapper actuated by both of original LIPCA and compressed LIPCA. Flapping tests for two artificial wing shapes of horse botfly and hawk moth were conducted at the wing rotation angle of 60° and a flapping frequency range from 6 Hz to 12 Hz to find the optimum flapping frequency and to investigate the effect of compressed LIPCA and wing shape on the force generation. Flapping tests in the vacuum were also undertaken to measure the induced inertia force. The aerodynamic force was calculated by subtracting the inertia force from the total force measured in the air. It was found that the average inertia force was relatively small when compared with the average total force. The use of the compressed LIPCA could significantly improve the flapping angle of the flapper from 110° to 130° (18.2% increase) resulting in 24.5% increase in the average aerodynamic force. It was also found that flapper with hawk moth wings could produce larger force than the flapper with horse botfly wings.

Design of Bio-inspired Flexible Wings for Flapping-Wing Micro-sized Air Vehicle Applications

The unmatched performance of insect flight is a motivation for bio-inspired designs of synthetic wings that can undergo large deformations in flapping flight. In this paper, we experimentally study the aerodynamic performance of a bio-inspired flexible flapping wing, which has the static load–deformation characteristics of a hawkmoth (Manduca sexta) wing, and compare it with a similar geometry rigid wing. The bio-inspired wing is designed using finite element analysis, coupled with an optimization solver, to match the static load–deflection characteristics of the synthetic wing with that of real hawkmoth wings. A flexible synthetic wing is constructed using a combination of materials (carbon, nylon and rubber) for the veins and a latex membrane. The aerodynamic performance of the synthetic deformable wing is tested on a robotic flapper, using commonly observed kinematic templates of insect flapping (and rotation). Our results show increased thrust by the flexible wing for all kinematic patterns in comparison to the rigid wing. A host of important advantages provided by wing flexibility are mentioned in the context of flapping flight.

The effects of corrugation and wing planform on the aerodynamic force production of sweeping model insect wings

The effects of corrugation and wing planform (shape and aspect ratio) on the aerodynamic force production of model insect wings in sweeping (rotating after an initial start) motion at Reynolds number 200 and 3500 at angle of attack 40° are investigated, using the method of computational fluid dynamics. A representative wing corrugation is considered. Wing-shape and aspect ratio (AR) of ten representative insect wings are considered; they are the wings of fruit fly, cranefly, dronefly, hoverfly, ladybird, bumblebee, honeybee, lacewing (forewing), hawkmoth and dragonfly (forewing), respectively (AR of these wings varies greatly, from 2.84 to 5.45). The following facts are shown. (1) The corrugated and flat-plate wings produce approximately the same aerodynamic forces. This is because for a sweeping wing at large angle of attack, the length scale of the corrugation is much smaller than the size of the separated flow region or the size of the leading edge vortex (LEV). (2) The variation in wing shape can have considerable effects on the aerodynamic force; but it has only minor effects on the force coefficients when the velocity at r 2 (the radius of the second moment of wing area) is used as the reference velocity; i.e. the force coefficients are almost unaffected by the variation in wing shape. (3) The effects of AR are remarkably small: when AR increases from 2.8 to 5.5, the force coefficients vary only slightly; flowfield results show that when AR is relatively large, the part of the LEV on the outer part of the wings sheds during the sweeping motion. As AR is increased, on one hand, the force coefficients will be increased due to the reduction of 3-dimensional flow effects; on the other hand, they will be decreased due to the shedding of part of the LEV; these two effects approximately cancel each other, resulting in only minor change of the force coefficients.

Flexural Stiffness in Insect Wings: Effects of Wing Venation and Stiffness Distribution on Passive Bending

American Entomologist • Spring 2005 During flight, insect wings bend and twist dramatically, and the instantaneous, threedimensional shape of wings may influence many aspects of flight performance. Insects have little control over this bending and twisting—wing deformations are largely passive and are controlled primarily by the architecture and material properties of the wing. However, our understanding of how insect wing design affects flexibility and passive wing deformation remains limited. Here, we discuss how insect wing venation affects overall bending stiffness, how stiffness varies throughout wings, and how these features of wing design affect passive bending. The pattern of supporting veins in insect wings varies widely among insect orders and families. Given the large phylogenetic changes in wing venation pattern (Fig. 1), one might expect insect wings to display large mechanical differences that would affect their deformability during flight. We examined the relationship between insect wing flexibility and venation by measuring flexural stiffness (EI) and quantifying venation pattern in 16 insect species from six orders. Flexural stiffness is a composite measure of the overall bending stiffness of a wing, combining the material properties of the wing (E, Young’s modulus) and the geometric distribution of this material (I, second moment of area). We measured overall EI of wings in the spanwise direction (from base to tip) and the chordwise direction (from leading to trailing edge) by performing static bending tests. We attached each wing at the base (or leading edge), applied a known force at the tip (or trailing edge), and measured the displacement of the wing. We then calculated EI with a simple beam equation (see Combes and Daniel 2003a). We also digitized the wing venation of each species and derived five measures of venation pattern (Combes and Daniel 2003a). To remove the effects of phylogeny, we calculated standardized independent contrasts of venation and stiffness measurements and examined the correlations between these contrasts. Our measurements show that EI is strongly correlated with wing size (Fig. 2), but the details of venation pattern do not appear to affect overall flexural stiffness (no significant correlations were found between contrasts of wing venation pattern and EI). The measurements also reveal a large anisotropy, or difference, between spanwise and chordwise flexural stiffness; spanwise EI is ≈1 to 2 orders of magnitude greater than chordwise EI in all species tested (Fig. 2). To determine how wing structure may contribute to this pattern of stiffness anisotropy, we created a simplified finite-element model of a Manduca (hawkmoth) wing. To create this model, a digitized Flexural Stiffness in Insect Wings: Effects of Wing Venation and Stiffness Distribution on Passive Bending

The aerodynamics of revolving wings II. Propeller force coefficients from mayfly to quail.

High force coefficients, similar to those observed for revolving model hawkmoth wings in the accompanying paper (for which steady leading-edge vortices are directly observed), are apparent for revolving model (mayfly, bumblebee and quail) and real (quail) animal wings ranging in Reynolds number (Re) from 1100 to 26000. Results for bumblebee and hawkmoth wings agree with those published previously for Drosophila (Re approximately 200). The effect of aspect ratio is also tested with planforms based on hawkmoth wings adjusted to aspect ratios ranging from 4.53 to 15.84 and is shown to be relatively minor, especially at angles of incidence below 50 degrees. The normal force relationship introduced in the accompanying paper is supported for wings over a large range of aspect ratios in both 'early' and 'steady' conditions; local induced velocities appear not to affect the relationship.