Insect Flight Dynamics Research Articles

A semi-empirical model of the aerodynamics of manoeuvring insect flight.

Blade element modelling provides a quick analytical method for estimating the aerodynamic forces produced during insect flight, but such models have yet to be tested rigorously using kinematic data recorded from free-flying insects. This is largely because of the paucity of detailed free-flight kinematic data, but also because analytical limitations in existing blade element models mean that they cannot incorporate the complex three-dimensional movements of the wings and body that occur during insect flight. Here, we present a blade element model with empirically fitted aerodynamic force coefficients that incorporates the full three-dimensional wing kinematics of manoeuvring Eristalis hoverflies, including torsional deformation of their wings. The two free parameters were fitted to a large free-flight dataset comprising N = 26 541 wingbeats, and the fitted model captured approximately 80% of the variation in the stroke-averaged forces in the sagittal plane. We tested the robustness of the model by subsampling the data, and found little variation in the parameter estimates across subsamples comprising 10% of the flight sequences. The simplicity and generality of the model that we present is such that it can be readily applied to kinematic datasets from other insects, and also used for the study of insect flight dynamics.

Charles Porter Ellington. 31 December 1952—30 July 2019

Charles Ellington graduated at Duke University, North Carolina, and came to Cambridge in 1973 to work for a PhD on insect flight dynamics. He developed novel methodology and software for the kinematic analysis of freely hovering insects and applied them to his own high-speed films of a range of species. He identified five new non-steady-state mechanisms for lift generation, was the first to develop a vortex theory for flapping flight and developed and extended the use of morphometric parameters in calculating the forces and power requirements of flight. He remained in Cambridge, married a colleague, joined the staff of the Department of Zoology, became a fellow of Downing College and continued to work on insect aerodynamics and energetics, publishing on flight muscle efficiency, the factors limiting flight performance and the aerodynamic implications of the origin of insect flight. Building a closed-circuit wind tunnel connected with a sensitive oxygen analyser, he studied with colleagues how the aerodynamics and metabolic power input of bumblebees vary with flight speed, challenging the orthodox theory that this should follow a U-shaped curve. Outstanding among later research was the discovery that hawkmoths, and by implication many other insects, gain high levels of lift by generating a vortex above the leading edge, stabilized by spiralling out along the span—a major focus of animal flight research ever since. His many administrative roles included editorship of theJournal of Experimental Biology. He became a British citizen in 1995, was elected FRS in 1998 and to a chair of animal mechanics in 1999. Awards include the Scientific Medal of the Zoological Society and the University of Cambridge Pilkington Prize for teaching excellence. He was diabetic throughout his adult life, and suffered progressive ill health following a heart attack in 1996. He took early retirement in 2010, lived quietly with his wife and two sons at home near Newmarket, and died in July 2019.

Chordwise wing flexibility may passively stabilize hovering insects.

Insect wings are flexible, and the dynamically deforming wing shape influences the resulting aerodynamics and power consumption. However, the influence of wing flexibility on the flight dynamics of insects is unknown. Most stability studies in the literature consider rigid wings and conclude that the hover equilibrium condition is unstable. The rigid wings possess an unstable oscillatory mode mainly due to their pitch sensitivity to horizontal velocity perturbations. Here, we show that a flapping wing flyer with flexible wings exhibits stable hover equilibria. The free-flight insect flight dynamics are simulated at the fruit fly scale in the longitudinal plane. The chordwise wing flexibility is modelled as a linear beam. The two-dimensional Navier-Stokes equations are solved in a tight fluid-structure integration scheme. For a range of wing flexibilities similar to live insects, all eigenvalues of the system matrix about the hover equilibrium have negative real parts. Flexible wings appear to stabilize the unstable mode by passively deforming their wing shape in the presence of perturbations, generating significantly more horizontal velocity damping and pitch rate damping. These results suggest that insects may passively stabilize their hover flight via wing flexibility, which can inform designs of synthetic flapping wing robots.

Insect flight dynamics: Stability and control

Insects can hover, fly forward, climb, and descend with ease while demonstrating amazing stability, and they can also maneuver in impressive ways as no other organisms can. Is their flight inherently stable? If so, how can they maneuver so well? In recent years, significant progress has been made in revealing the dynamic flight stability and flight control mechanisms of insects and has partially answered these questions. Here the most recent advances in this active area are reviewed. The aim is to provide the background necessary to do research in the area and raise questions that need to be addressed in the future. This review begins with an overview of the flapping kinematics and aerodynamics of insect flight. It is followed by a summary of the governing equations of insect motion and the simplified theoretical models used for analysis of dynamic stability and control. Next, the stability properties of hovering flight and forward flight are scrutinized. Then the flight control properties are explored, dealing in turn with flight stabilization control, steady-state control for changing from hovering to forward flight and from one forward-flight speed to another, and control for maneuvers near hovering. Finally, remarks are given on the state of the art of this research field and speculation is made on its outlook in the near future.

A novel model of dipteran flight mechanism

In this paper, a novel model for the mechanism of dipteran flight motor is proposed and a flight dynamics is explored by nonlinear dynamics techniques. This model comprises a lumped mass, a pair of inclined rigid bars and a pair of horizontal springs. Even the springs are linear, this system is irrationally nonlinear which causes difficulty for classical nonlinear analysis. We investigate the original irrational equation by direct numerical simulation avoiding Taylor’s expansion to retain the intrinsic character of dipteran flight. This enables us to reveal the bounded characteristics of depteran flight including “click”, bursting and the “complex” flight patterns. Equilibrium analysis demonstrates the “click” mechanism and the “non-click” condition for the unperturbed system. While for the perturbed system, Poincare section and basin analysis are carried out to demonstrate the bursting behaviour, transitions between different flight modes and their coexistence. The results obtained herein reveal that the complex bifurcations of equilibria, periodic behaviours and the chaotic motions of the presented system associate respectively with “resting”, “calm” and “complex” flight. All the results related to the perturbed system are obtained by the fourth order Runge–Kutta method which ensures the accuracy of the computation. This study provides an additional insight into the understanding of various flight dynamics of insects and bridges a gap between the nonlinear dynamics and the biology.

A Neural Adaptive Controller in Flapping Flight

In this paper, we propose a neural adaptive controller for attitude control in a flapping-wing insect model. The model is nonlinear and subjected to periodic force/torque generated by nominal wing kinematics. Two sets of model parameters are obtained from the fruit flyDrosophila melanogasterand the honey beeApis mellifera. Attitude control is achieved by modifying the wing kinematics on a stroke-by-stroke basis. The controller is based on filtered-error with neural network models approximating system nonlinearities. Lyapunov-based stability analysis shows the asymptotic convergence of system outputs. We present simulation results for angular position stabilization and trajectory tracking. Trajectory tracking is illustrated by two cases: saccadic turning and sinusoidal variation in the yaw angle. The proposed controller successfully regulates flight orientation – roll, pitch and yaw angles – by generating desired torque resulting from tuning parameterized wing motion. Results furthermore show similarities between simulated and observed turning from real insects, suggesting some inherent properties in insect flight dynamics and control. The proposed controller has potential applications in future flapping-wing Micro Air Vehicles (MAVs).

Dipteran insect flight dynamics. Part 2: Lateral–directional motion about hover

The purpose of this study is to determine computationally tractable models describing the lateral–directional motion of a Drosophila-like dipteran insect, which may then be used to estimate the requirements for flight control and stabilization. This study continues the work begun in Faruque and Humbert (2010) to extend the quasi-steady aerodynamics model via inclusion of perturbations from the hover state. The aerodynamics model is considered as forcing upon rigid body dynamics, and frequency-based system identification tools used to derive the models. The analysis indicates two stable real poles, and two very lightly damped and nearly unstable complex poles describing a decoupling of roll/sideslip oscillatory motion from a first order subsidence yaw behavior. The results are presented with uncertainty variation for both a smaller male and larger female phenotype.

Recent developments in miniature flying robots

PurposeThe purpose of this paper is to provide a review of recent developments in miniaturised flying robots.Design/methodology/approachFollowing a brief consideration of micro‐ and nano‐aerial vehicles, the paper discusses recent US and European research into the development of miniaturised flying robots.FindingsThis paper shows that research into miniaturised flying robots is gaining pace and much is being funded by the US military. Two major strands of research are devices which mimic the flight dynamics of insects and living insect‐microtechnology hybrids (cyborgs). The technologies remain at an early stage of development but covert surveillance and intelligence gathering are key future applications.Originality/valueThe paper provides a technical review of the latest developments in miniaturised flying robots.

The aerodynamics of free-flight maneuvers in Drosophila.

Using three-dimensional infrared high-speed video, we captured the wing and body kinematics of free-flying fruit flies as they performed rapid flight maneuvers. We then "replayed" the wing kinematics on a dynamically scaled robotic model to measure the aerodynamic forces produced by the wings. The results show that a fly generates rapid turns with surprisingly subtle modifications in wing motion, which nonetheless generate sufficient torque for the fly to rotate its body through each turn. The magnitude and time course of the torque and body motion during rapid turns indicate that inertia, not friction, dominates the flight dynamics of insects.

On aerodynamic modelling of an insect–like flapping wing in hover for micro air vehicles

This theoretical paper discusses recent advances in the fluid dynamics of insect and micro air vehicle (MAV) flight and considers theoretical analyses necessary for their future development. The main purpose is to propose a new conceptual framework and, within this framework, two analytic approaches to aerodynamic modelling of an insect-like flapping wing in hover in the context of MAVs. The motion involved is periodic and is composed of two half-cycles (downstroke and upstroke) which, in hover, are mirror images of each other. The downstroke begins with the wing in the uppermost and rearmost position and then sweeps forward while pitching up and plunging down. At the end of the half-cycle, the wing flips, so that the leading edge points backwards and the wing's lower surface becomes its upper side. The upstroke then follows by mirroring the downstroke kinematics and executing them in the opposite direction. Phenomenologically, the interpretation of the flow dynamics involved, and adopted here, is based on recent experimental evidence obtained by biologists from insect flight and related mechanical models. It is assumed that the flow is incompressible, has low Reynolds number and is laminar, and that two factors dominate: (i) forces generated by the bound leading-edge vortex, which models flow separation; and (ii) forces due to the attached part of the flow generated by the periodic pitching, plunging and sweeping. The first of these resembles the analogous phenomenon observed on sharp-edged delta wings and is treated as such. The second contribution is similar to the unsteady aerodynamics of attached flow on helicopter rotor blades and is interpreted accordingly. Theoretically, the fluid dynamic description is based on: (i) the superposition of the unsteady contributions of wing pitching, plunging and sweeping; and (ii) adding corrections due to the bound leading-edge vortex and wake distortion. Viscosity is accounted for indirectly by imposing the Kutta condition on the trailing edge and including the influence of the vortical structure on the leading edge. Mathematically, two analytic approaches are proposed. The first derives all the quantities of interest from the notion of circulation and leads to tractable integral equations. This is an application of the von Kármán-Sears unsteady wing theory and its nonlinear extensions due to McCune and Tavares; the latter can account for the bound leading-edge vortex and wake distortion. The second approach uses the velocity potential as the central concept and leads to relatively simple ordinary differential equations. It is a combination of two techniques: (i) unsteady aerodynamic modelling of attached flow on helicopter rotor blades; and (ii) Polhamus's leading-edge suction analogy. The first of these involves both frequency-domain (Theodorsen style) and time-domain (indicial) methods, including the effects of wing sweeping and returning wake. The second is a nonlinear correction accounting for the bound leading-edge vortex. Connections of the proposed framework with control engineering and aeroelasticity are pointed out.

Shil'nikov homoclinic dynamics and the escape from roll autorotation in an F–4 model

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Lowenberg M. H. and Champneys A. R. 1998Shil'nikov homoclinic dynamics and the escape from roll autorotation in an F–4 modelPhil. Trans. R. Soc. A.3562241–2256http://doi.org/10.1098/rsta.1998.0272SectionRestricted accessShil'nikov homoclinic dynamics and the escape from roll autorotation in an F–4 model M. H. Lowenberg M. H. Lowenberg Department of Aerospace Engineering, University of Bristol, Queen's Building, University Walk, Bristol BS8 1TR, UK Google Scholar Find this author on PubMed Search for more papers by this author and A. R. Champneys A. R. Champneys Department of Engineering Mathematics, University of Bristol, Queen's Building, University Walk, Bristol BS8 1TR, UK Google Scholar Find this author on PubMed Search for more papers by this author M. H. Lowenberg M. H. Lowenberg Department of Aerospace Engineering, University of Bristol, Queen's Building, University Walk, Bristol BS8 1TR, UK Google Scholar Find this author on PubMed Search for more papers by this author and A. R. Champneys A. R. Champneys Department of Engineering Mathematics, University of Bristol, Queen's Building, University Walk, Bristol BS8 1TR, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:15 October 1998https://doi.org/10.1098/rsta.1998.0272AbstractAn investigation is undertaken into the nonlinear dynamics of an 8th–order model for the F–4J Phantom fighter aircraft in a neighbourhood of its autorotation flight regime. This regime is characterized by high roll rates with no roll control inputs. It is found that the basic state goes unstable via a supercritical Hopf bifurcation as the value of the stabilator (the pitch axis control surface) is increased (i.e. the control column is pushed forward). The ensuing stable limit cycle behaviour is itself destroyed at a higher stabilator value in a certain homoclinic bifurcation first analysed by Shil'nikov. A careful numerical continuation analysis is performed using spline interpolation of the tabulated data in the model. The limit cycle is found to reach infinite period along a complex wiggly bifurcation curve, as predicted by the theory of Shil'nikov homoclinic orbits. Several period–doubling and secondary–Hopf (torus) bifurcations are discovered. Direct simulation of the aircraft dynamics, using linear interpolation of the data, is shown to give good agreement with the continuation results. It is found that the homoclinic bifurcation marks an escape from autorotation. That is, varying stabilator slowly through the critical value results in a jump from oscillatory autorotation to symmetric flight. Possible implications of these results for other flight phenomena are discussed. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Paranjape A and Ananthkrishnan N (2012) The Bifurcation and Continuation Method from an Aerospace Systems Design Point of View AIAA Atmospheric Flight Mechanics Conference, 10.2514/6.2012-4408, 978-1-62410-184-7, Online publication date: 13-Aug-2012. Pauck S and Engelbrecht J (2012) Bifurcation Analysis of the Generic Transport Model with a view to Upset Recovery AIAA Atmospheric Flight Mechanics Conference, 10.2514/6.2012-4646, 978-1-62410-184-7, Online publication date: 13-Aug-2012. Żbikowski R, Ansari S and Knowles K (2006) On mathematical modelling of insect flight dynamics in the context of micro air vehicles, Bioinspiration & Biomimetics, 10.1088/1748-3182/1/2/R02, 1:2, (R26-R37), Online publication date: 1-Jun-2006. Richardson T, Charles G, Stoten D, di Bernardo M and Lowenberg M Continuation based control of aircraft dynamics 42nd IEEE International Conference on Decision and Control, 10.1109/CDC.2003.1272402, 0-7803-7924-1, (4932-4938) Lowenberg M (1998) Development of control schedules to modify spin behaviour 23rd Atmospheric Flight Mechanics Conference, 10.2514/6.1998-4267, , Online publication date: 10-Aug-1998. This Issue15 October 1998Volume 356Issue 1745Theme Issue ‘Nonlinear flight dynamics of high-performance aircraft’ compiled by J. M. T. Thompson and F. B. J. Macmillen Article InformationDOI:https://doi.org/10.1098/rsta.1998.0272Published by:Royal SocietyPrint ISSN:1364-503XOnline ISSN:1471-2962History: Published online15/10/1998Published in print15/10/1998 License: Citations and impact Keywordsnumerical continuationflight dynamicsglobal bifurcationnonlinear dynamicsautorotation