Wing Inertia Research Articles

Moth resonant mechanics are tuned to wingbeat frequency and energetic demands.

An insect's wingbeat frequency is a critical determinant of its flight performance and varies by multiple orders of magnitude across Insecta. Despite potential energetic benefits for an insect that matches its wingbeat frequency to its resonant frequency, recent work has shown that moths may operate off their resonant peak. We hypothesized that across species, wingbeat frequency scales with resonance frequency to maintain favourable energetics, but with an offset in species that use frequency modulation as a means of flight control. The moth superfamily Bombycoidea is ideal for testing this hypothesis because their wingbeat frequencies vary across species by an order of magnitude, despite similar morphology and actuation. We used materials testing, high-speed videography and a model of resonant aerodynamics to determine how components of an insect's flight apparatus (stiffness, wing inertia, muscle strain and aerodynamics) vary with wingbeat frequency. We find that the resonant frequency of a moth correlates with wingbeat frequency, but resonance curve shape (described by the Weis-Fogh number) and peak location vary within the clade in a way that corresponds to frequency-dependent biomechanical demands. Our results demonstrate that a suite of adaptations in muscle, exoskeleton and wing drive variation in resonant mechanics, reflecting potential constraints on matching wingbeat and resonant frequencies.

Small deviations in kinematics and body form dictate muscle performances in the finely tuned avian downstroke.

Avian takeoff requires peak pectoralis muscle power to generate sufficient aerodynamic force during the downstroke. Subsequently, the much smaller supracoracoideus recovers the wing during the upstroke. How the pectoralis work loop is tuned to power flight is unclear. We integrate wingbeat-resolved muscle, kinematic, and aerodynamic recordings in vivo with a new mathematical model to disentangle how the pectoralis muscle overcomes wing inertia and generates aerodynamic force during takeoff in doves. Doves reduce the angle of attack of their wing mid-downstroke to efficiently generate aerodynamic force, resulting in an aerodynamic power dip, that allows transferring excess pectoralis power into tensioning the supracoracoideus tendon to assist the upstroke-improving the pectoralis work loop efficiency simultaneously. Integrating extant bird data, our model shows how the pectoralis of birds with faster wingtip speed need to generate proportionally more power. Finally, birds with disproportionally larger wing inertia need to activate the pectoralis earlier to tune their downstroke.

Small deviations in kinematics and body form dictate muscle performances in the finely tuned avian downstroke

Avian takeoff requires peak pectoralis muscle power to generate sufficient aerodynamic force during the downstroke. Subsequently, the much smaller supracoracoideus recovers the wing during the upstroke. How the pectoralis work loop is tuned to power flight is unclear. We integrate wingbeat-resolved muscle, kinematic, and aerodynamic recordings in vivo with a new mathematical model to disentangle how the pectoralis muscle overcomes wing inertia and generates aerodynamic force during takeoff in doves. Doves reduce the angle of attack of their wing mid-downstroke to efficiently generate aerodynamic force, resulting in an aerodynamic power dip, that allows transferring excess pectoralis power into tensioning the supracoracoideus tendon to assist the upstroke—improving the pectoralis work loop efficiency simultaneously. Integrating extant bird data, our model shows how the pectoralis of birds with faster wingtip speed need to generate proportionally more power. Finally, birds with disproportionally larger wing inertia need to activate the pectoralis earlier to tune their downstroke.

Kinematic modeling and analysis of transmission mechanism with joint clearance for flapping wing micro aerial vehicle

A theoretical model is built to reveal the effect of the joint clearance on the kinematic performance of the transmission mechanism of a flapping wing micro aerial vehicle (FWMAV). Massless link approach is used to model the joint clearance and the reciprocal screw is introduced to solve the kinematic model. Finite element method simulations are also performed to validate the model. The kinematic model reveals that the inertia force of the transmission mechanism contributes little to the flapping motion whereas the sign of the resultant moment of aerodynamic drag and wing inertia force plays decisive role. Besides, the joint clearance can either increase or decrease the flapping angle of the wing during a flapping period and it will significantly affect the flapping amplitude while involves little in the mean flapping angle. The effects of the positions of the joint with clearance and its magnitude on the flapping motion are also revealed.

Role of wing inertia in maneuvering bat flights

The role of aerodynamics and wing inertia on the motion dynamics for the maneuvering flight of two bats from two species of roundleaf bats, H. armiger and H. pratti are investigated. Comparative studies among a straight flight, two ascending sweeping right turns, and a U-turn reveal that inertial forces play an essential and sometimes crucial role in the maneuvers. The translational trajectory of the bat is mostly driven by aerodynamic forces generated by the wings along the flight path, whereas inertial forces for the most part drive the intra-cycle fluctuations. However, inertial forces are found to contribute non-trivially to the ascending motion of the H. armiger during the sweeping turn and the U-turn. The roll maneuver is found to be primarily driven by aerodynamic asymmetries during flight, whereas the yaw maneuver is primarily driven by imbalances in wing inertial moments. Inertial moments resulting from Coriolis and centrifugal forces are found to play an important role in accurate yaw prediction. The moment due to Coriolis force plays a very prominent role in predicting the correct yaw angle during the extreme 180° U-turn.

Transition Flight Trajectory Optimization for a Flapping-Wing Micro Air Vehicle with Unsteady Vortex-Lattice Method

Flapping-wing micro air vehicles (FWMAVs) have the capability of performing various flight modes like birds and insects. Therefore, it is necessary to understand the various flight modes of FWMAVs in order to fully utilize the capability of the vehicle. The unique flight modes of FWMAVs can be studied through the trajectory optimization. This paper proposes a trajectory optimization framework of an FWMAV. A high-fidelity simulation model is included in the framework to sufficiently consider the complicated dynamics of the FWMAV. The unsteady aerodynamics are modeled with the unsteady panel method (UPM) and the unsteady vortex-lattice method (UVLM). The effect of wing inertia is also considered in the simulation model. In this study, transition flight trajectories are searched with the proposed framework. An optimal control problem is formulated for the transition flight from hovering to forward flight and transcribed to the parameter optimization problem with the direct shooting method. The cost function is defined as energy consumption. The same converged solution can be obtained with different initial guesses. The optimization results show that the FWMAV utilizes the pitch-up maneuver to increase altitude, although the forward speed is reduced. This pitch-up maneuver is performed more actively when the target velocity of transition is low, or the wind condition is favorable to acceleration.

Revisiting the flight dynamics of take-off of a butterfly: experiments and CFD simulations for a cabbage white butterfly.

ABSTRACTWe conducted measurements of the taking-off motion of a butterfly (Pieris rapae) and numerical simulations using a computational model reflecting its motion. The computational butterfly model is composed of a thorax, an abdomen, and four wings (left and right wings with fore and hind parts), i.e. a six-link, rigid-body system. The present model is more sophisticated than any models that have ever been constructed in existing studies. In the butterfly model, the body trajectory and thoracic pitching angle can be calculated from the equations of motion, whereas the abdominal angle and wings’ joint angles are prescribed by the measured data. We calculated the flow field, aerodynamic force and torque generated by the butterfly model using the immersed boundary–lattice Boltzmann method. As a result, the butterfly generates the horizontal vortex ring and aerodynamic lift force during the downstroke, while it generates the vertical vortex ring and aerodynamic thrust force during the upstroke. The leg impulsion is essential in the upward motion of the taking-off butterfly rather than the aerodynamic lift force by the flapping wings. The inertial forces of the abdomen and wings are comparable in magnitude with the aerodynamic forces, but the net influence of the inertial forces on the position of the butterfly is not significant due to the offsetting of the body and wing inertia. The net aerodynamic and gravitational torques raise the thorax of the butterfly, and the net inertial torques suppress the rise of the thorax.

Fluid–structure interaction analysis of flexible flapping wing in the Martian environment

Flapping-wing micro air vehicle (FWMAV) is an attractive idea for Mars exploration because of its high capability in a thin atmosphere. The biggest challenge for its development is an appropriate understanding of a flapping flight with flexible wings, which is significantly complicated because flexible flapping wings can undergo large-scale deformations due to the effects of wing inertia and the aerodynamic forces exerted by the surrounding atmosphere. Fluid–structure interaction (FSI) analysis is a powerful tool for accurate investigations, but it usually has a very high computational cost, making it challenging to perform necessary parametric studies for practical designing. An efficient FSI analysis method is required. On Mars, whose atmospheric density is around 1% that of Earth, aerodynamic forces have a relatively small influence on wing deformation and may even be negligible in some cases. We thus investigate the relative contributions of the inertial force of a flapping wing and the aerodynamic forces exerted by the surrounding Martian atmosphere using a two-way coupled FSI simulation, and identify the conditions under which the aerodynamic forces are negligible. Then, we develop a computationally efficient one-way coupled FSI analysis system based on the interface-capturing method to design a flexible flapping wing for Mars exploration. Under the obtained conditions, we perform parametric studies on hovering flight with flexible flapping wings in the Martian environment with multiple aerodynamic parameters, various kinematic parameters, and material properties of the wing. We conclude that an FWMAV with a payload of around 5 g can fly for more than 1 min for the maximum density of the Martian atmosphere.

Low-Order Modeling of Flapping Flight with Highly Articulated, Cambered, Heavy Wings

A three-dimensional low-order modeling technique is described for modeling both wing inertial and aerodynamic forces of animals and robots flapping heavy and morphing wings. The model is applied to prescribed kinematics from a previously measured flight of a lesser-nosed, dog-faced fruit bat (Cynopterus brachyotis) in straight and climbing flight. Quasi-steady blade element momentum theory is used to model the aerodynamic forces of the highly articulated wing, and a Lagrangian equation of motion is adopted to describe the overall wing–body dynamics that includes the wing inertia. These two distinct and independent models yield a good prediction of the thrust/drag balance, and are in excellent agreement of lift production. Unique to this approach, the quantitative effect of wing camber was examined within the framework, which contributes as much as 27% of the cycle-averaged lift, with a smaller price (10%) paid to drag.

A multi-body control approach for flapping wing micro aerial vehicles

Flapping wing micro aerial vehicle (FWMAV) has a multi-body and periodic dynamics, which is influenced by unsteady aerodynamics. These features make it more difficult to control. Ignoring the wing inertia, dynamics averaging, and using a simple aerodynamic model are the simplifying assumptions for conventional model-based control, although they may result in inaccurate control. To overcome these difficulties, a multi-body control is proposed based on a model-free adaptive variable structure control (MFAVSC) approach. MFAVSC takes advantage of input/output data, while not including any explicit model information. At first, the nonlinear FWMAV dynamics is transformed into an equivalent dynamic linearization description with a concept called pseudo-partial derivative (PPD). After estimating the PPD matrix, model-free adaptive control law is designed based on the optimal criteria. Then, it is augmented by a variable structure control term to guarantee the stability, as well as speeding up its convergence. Finally, simulation results demonstrate the effectiveness of the proposed scheme to trajectory control of the FWMAV.

On the Preliminary Structural Design Strategy of the Wing of the Next-Generation Civil Tiltrotor Technology Demonstrator

The T-WING project is a Clean Sky 2 research project aimed at designing, manufacturing, qualifying and flight-testing the new wing of the Next-Generation Civil Tiltrotor Technology Demonstrator (NGCTR-TD), as part of the Fast Rotorcraft Innovative Aircraft Demonstrator Platforms (FRC IADP) activities. Requirements, design strategy, methodology and main steps followed to achieve the composite wing preliminary design are presented. The main driving requirements have been expressed in terms of dynamic requirements (e.g., limitations on natural frequencies), aeroelastic requirements, i.e., compliance with European Aviation Safety Agency (EASA) CS-25 and CS-29 Airworthiness Requirements), structural requirements (e.g., target wing structural mass), functional requirements (e.g., fuel tanks, accessibility, assembly and integration, etc.) and wing preliminary loads. Based on the above-mentioned requirements, the first design loop is performed by targeting an optimal wing structure able to withstand preliminary design loads, and simultaneously with stiffness and inertia distributions leading to a configuration free from flutter within the flight envelope. The outcome from the first design loop is then used to refine the model and compute more reliable flight loads and repeat aeroelastic analysis, returning further requirements to be fulfilled in terms of wing stiffness and inertia distributions. The process is iterated till the fulfillment of all the project requirements.

Nonlinear flow-induced instability of an elastically mounted pitching wing

Abstract

Metode Balancing Jig Procedure pada Tab Elevator Pesawat Boeing 737-800 untuk Mengurangi Dampak Flutter

Primary flight control pada pesawat udara terdiri dari aileron, rudder dan elevator, Secondary flight control terdiri dari flaps, slats, spoiler dan trim tab. Pesawat sebelum terbang harus dipastikan semua flight control dalam keadaan balance. Jika tidak, maka flutter akan terjadi ketika pesawat tersebut mengudara. Flutter adalah salah satu fenomena aeroelastisitas, yaitu fenomena getaran yang mengakibatkan sayap pesawat terbang “mengepak” seperti sayap burung. Hal ini diakibatkan karena kombinasi efek kekakuan struktur sayap, aerodinamika serta inersia (berat) dari struktur. Untuk menghindari terjadinya flutter harus dilakukan balancing flight control, salah satunya pada Tab Elevator. Tab elevator sering disebut dengan trim tab pada elevator. Trim Tab tersebut melekat pada elevator yang terletak pada horizontal stabilizer. Meskipun trim tab merupakan secondary flight control, harus tetap dipastikan balance. Cara balancing tab elevator adalah dengan metode jig procedure, dimana tab harus dilepas terlebih dahulu. Balance atau tidaknya tab elevator ditentukan dari nilai Tab Assembly Moment (TAM). Hasil yang didapat dari penelitian ini adalah 15.22 lbfinch dan tab dikatakan balance, karena menurut Structural Repair Manual (SRM) Boeing 737-800 range maksimal nilai TAM adalah 15.48 lbfinch. Jika pada penelitian didapatkan hasil lebih dari 15.48 lbfinch, maka tab harus dikembalikan ke paint shop untuk dilakukan pengelupasan beberapa lapisan catnya agar mengurangi beban tab tersebut. Apabila pengurangan beban pada tab tidak bisa dilakukan lagi, maka Tab tersebut dianggap reject (tidak layak) dan harus diganti dengan yang baru.

How the hummingbird wingbeat is tuned for efficient hovering.

Both hummingbirds and insects flap their wings to hover. Some insects, like fruit flies, improve efficiency by lifting their body weight equally over the upstroke and downstroke, while utilizing elastic recoil during stroke reversal. It is unclear whether hummingbirds converged on a similar elastic storage solution, because of asymmetries in their lift generation and specialized flight muscle apparatus. The muscles are activated a quarter of a stroke earlier than in larger birds, and contract superfast, which cannot be explained by previous stroke-averaged analyses. We measured the aerodynamic force and kinematics of Anna's hummingbirds to resolve wing torque and power within the wingbeat. Comparing these wingbeat-resolved aerodynamic weight support measurements with those of fruit flies, hawk moths and a generalist bird, the parrotlet, we found that hummingbirds have about the same low induced power losses as the two insects, lower than that of the generalist bird in slow hovering flight. Previous analyses emphasized how bird flight muscles have to overcome wing drag midstroke. We found that high wing inertia revises this for hummingbirds - the pectoralis has to coordinate upstroke to downstroke reversal while the supracoracoideus coordinates downstroke to upstroke reversal. Our mechanistic analysis aligns with all previous muscle recordings and shows how early activation helps furnish elastic recoil through stroke reversal to stay within the physiological limits of muscles. Our findings thus support Weis-Fogh's hypothesis that flies and hummingbirds have converged on a mechanically efficient wingbeat to meet the high energetic demands of hovering flight. These insights can help improve the efficiency of flapping robots.

Optimal wing hinge position for fast ascent in a model fly

It was thought that the wing hinge position can be tuned to stabilize an uncontrolled fly. However here, our Floquet stability analysis shows that the hinge position has a weak dependence on the flight stability. As long as the hinge position is within the fly’s body length, both hovering and ascending flight are unstable. Instead, there is an optimal hinge position, $h^{\ast }$, at which the ascending speed is maximized. $h^{\ast }$ is approximately half way between the centre of mass and the top of the body. We show that the optimal $h^{\ast }$ is associated with the anti-resonance of the body–wing coupling, and is independent of the stroke amplitude. At $h^{\ast }$, the torque due to wing inertia nearly cancels the torque due to aerodynamic lift, minimizing the body oscillation thus maximizing the upward force. Our analysis using a simplified model of two coupled masses further predicts, $h^{\ast }=(m_{t}/2m_{w})(g/\unicode[STIX]{x1D714}^{2})$. These results suggest that the ascending speed, in addition to energetics and stability, is a trait that insects are likely to optimize.

Nonlinear dynamics of a flapping rotary wing: Modeling and optimal wing kinematic analysis

The analysis of the passive rotation feature of a micro Flapping Rotary Wing (FRW) applicable for Micro Air Vehicle (MAV) design is presented in this paper. The dynamics of the wing and its influence on aerodynamic performance of FRW is studied at low Reynolds number (∼103). The FRW is modeled as a simplified system of three rigid bodies: a rotary base with two flapping wings. The multibody dynamic theory is employed to derive the motion equations for FRW. A quasi-steady aerodynamic model is utilized for the calculation of the aerodynamic forces and moments. The dynamic motion process and the effects of the kinematics of wings on the dynamic rotational equilibrium of FWR and the aerodynamic performances are studied. The results show that the passive rotation motion of the wings is a continuous dynamic process which converges into an equilibrium rotary velocity due to the interaction between aerodynamic thrust, drag force and wing inertia. This causes a unique dynamic time-lag phenomena of lift generation for FRW, unlike the normal flapping wing flight vehicle driven by its own motor to actively rotate its wings. The analysis also shows that in order to acquire a high positive lift generation with high power efficiency and small dynamic time-lag, a relative high mid-up stroke angle within 7–15° and low mid-down stroke angle within −40° to −35° are necessary. The results provide a quantified guidance for design option of FRW together with the optimal kinematics of motion according to flight performance requirement.

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

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, Allomyrinadichotoma 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.

Effects of spanwise flexibility on the performance of flapping flyers in forward flight.

Flying animals possess flexible wings that deform during flight. The chordwise flexibility alters the wing shape, affecting the effective angle of attack and hence the surrounding aerodynamics. However, the effects of spanwise flexibility on the locomotion are inadequately understood. Here, we present a two-way coupled aeroelastic model of a plunging spanwise flexible wing. The aerodynamics is modelled with a two-dimensional, unsteady, incompressible potential flow model, evaluated at each spanwise location of the wing. The two-way coupling is realized by considering the transverse displacement as the effective plunge under the dynamic balance of wing inertia, elastic restoring force and aerodynamic force. The thrust is a result of the competition between the enhancement due to wing deformation and induced drag. The results for a purely plunging spanwise flexible wing agree well with experimental and high-fidelity numerical results from the literature. Our analysis suggests that the wing aspect ratio of the abstracted passerine and goose models corresponds to the optimal aeroelastic response, generating the highest thrust while minimizing the power required to flap the wings. At these optimal aspect ratios, the flapping frequency is near the first spanwise natural frequency of the wing, suggesting that these birds may benefit from the resonance to generate thrust.

Effect of mass ratio on thrust production of an elastic panel pitching or heaving near resonance

Flapping wings of aerial insects and undulating fins of fish typically experience significant elastic chordwise deformations, and such deformations have been shown in previous studies to be beneficial on force production and/or power efficiency for both types of animal locomotion. However, it is still not conclusive whether the resonant vibration plays a common role in these problems. For fish fins, passive deformations are predominantly due to the hydrodynamic force of the surrounding fluid, while for insect wings, the wing inertia becomes also important in driving the surface deformation in addition to the aerodynamic force. In the current study, we use a two-dimensional elastic panel pitching or heaving in a free stream as a model to represent the animal wings or fins. Bending rigidity of the panel and the flapping frequency are varied so that the panel flaps near or away from resonance of the coupled fluid–structure system. The results show that at low mass ratios where the fluid force is dominant over the panel inertia, or at intermediate mass ratios where the fluid force is comparable with the panel inertia, the system resonance significantly improves or maximizes the thrust force and also efficiency; in addition, thrust performance is improved around resonance for a wide range of flapping frequencies or Strouhal numbers. On the other hand, at high mass ratios where the panel inertia is dominant, the system resonance makes thrust production increasingly difficult and propulsion much less efficient. In conclusion, the role of resonant vibration in thrust production of flapping wings and fins depends on participation of the fluid inertia in the process.

Flight Control of Biomimetic Air Vehicles Using Vibrational Control and Averaging

A combination of vibrational inputs and state feedback is applied to control the flight of a biomimetic air vehicle. First, a control strategy is developed for longitudinal flight, using a quasi-steady aerodynamic model and neglecting wing inertial effects. Vertical and forward motion is controlled by modulating the wings’ stroke and feather angles, respectively. Stabilizing control parameter values are determined using the time-averaged dynamic model. Simulations of a system resembling a hawkmoth show that the proposed controller can overcome modeling error associated with the wing inertia and small parameter uncertainties when following a prescribed trajectory. After introducing the approach through an application to longitudinal flight, the control strategy is extended to address flight in three-dimensional space.