Track 17. Biomechanics in Nature

demonstrate that the leading-edge vortex is a common high-lift enhancement mechanism but presents significant size-dependence in terms of the three- dimensional structure, the axial flow, the vortex break-down, and the flow instability. Furthermore, the trailing-edge vortex and the tip vortex also show sensitivity to a flyer's size; they appear to play an important role in the high-lift production as well as in flight maneuverability for tiny insects like fruitfly and thrips. The size effect in insect flight therefore implies that insects may select and/or combine the aerodynamic mechanisms of the leading-edge vortex, the trailing-edge vortex and the tip vortex dependent upon their sizes and morphologies, which points to the importance of an integrative evaluation and explanation on the large-force production mechanisms.

5066 Tu, 17:15-17:30 (P25) Efficiency of f lapping fl ight Z.J. Wang. Theoretical and Applied Mechanics, Comeli University, New York, USA

Flapping and fixed wing provide two means to fly. Birds and insects have evolved to employ the first method and we have succeeded in using the second. We do not know, however, which one is more efficient. In this talk, I will define and discuss the aerodynamic efficiency of flapping flight in simple models and in the example of dragonfly flight.

6253 We, 08:15-08:30 (P29) Dynamic flight stability and control of a hovering hoverf ly M. Sun, J.K. Wang. Institute of Fluid Mechanics, Beijing University of Aeronautics & Astronautics, Beijing, P.R. China

The longitudinal dynamic flight stability and stabilization control of a hovering hoverfly were studied using the method of computational fluid dynamics to compute the stability and control derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. Three natural modes of motion are identified: one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. Coupling of nose-up (or down) pitching with forward (or back) horizontal motion in the oscillatory mode causes the instability. Due to the existence of the unstable mode, the hovering flight is inherently unstable. However, stable hovering flight in hoverflies is often observed. Therefore, stabilization control must be applied by the insect. The following is shown. At hovering flight, ,~d~ and ~0~ 1 mainly produce changes in vertical force, ,~¢ mainly produces changes in pitching moment and ~0~ 2 mainly produces changes in pitching moment and horizontal force (hd~, h~, hal and ~ 2 denote control inputs: ,~d~ and ,~¢ represent changes in stroke amplitude and mean stroke angle, respectively, and hal represents a equal change whilst ~ 2 a differential change in the geometrical angles of attack of downstroke translation and upstroke translation). For stable hovering, the unstable oscillatory mode needs to be stabilized and the slow subsidence mode needs stability augmen- tation. The former can be accomplished by feeding back horizontal velocity (or pitching rate) to produce ,~¢ or ,~o~2; the latter by feeding back vertical velocity to produce ,~d~ or hal. Only two controls (,~d~ and ,~¢, or hal and ha2, or ,~d~ and ha2, or hal and ,~¢) being required means that the stabilization control can be relatively simple.

6055 We, 08:30-08:45 (P29) Dynamics of f lapping f l ight control: birds v e r s u s insects G.K. Taylor. Oxford University, Department of Zoology, Oxford, UK

Flapping poses both difficulties and opportunities from the perspectives of flight stability and control. The oscillatory nature of the forces means that flapping fliers must contend with stabilising a forced oscillation rather than a steady equilibrium, but this in turn makes it possible to initiate a manoeuvre by temporarily destabilising the system and making use of the transient excited by the forcing to initiate a turn. The importance of forcing in the body dynamics will depend on how their natural timescales compare to those of the wingbeat, so allometry in the their scaling is expected to lead to fundamental and systematic differences in the mechanics of flight stability and control across the range of size from insects to birds. Recent experimental work has begun to shed light on the dynamics of insect flight, for which the aerodynamic forces can be measured either directly in tethered flight or indirectly on appropriately scaled mechanical flapping models. Expressing the measured forces as functions of the instantaneous state of the wing and/or body then allows the flight dynamics to be described empirically using equations of motion. Neither experimental approach is currently possible with birds, which cannot ethically be tethered and which have wing kinematics too complex to model mechanically on account of their intrinsic musculature. An alternative approach is to exploit the large size of birds by getting them to carry an array of sensors (magnetometers, gyroscopes and accelerometers) providing information on free-flight body kinematics. These free-flight data

17.4. Swimming and Flying S357

can then be used to parameterise the equations of motion using system identification techniques. Force measurements in tethered flight and system identification in free flight are complementary approaches to the same problem, and allow us to address the same questions of stability and control for birds and insects. Here I discuss new experimental techniques and results associated with these two approaches, with the aim of shedding new light on the contrasting mechanisms of flight stability and control used by birds and insects.

5260 We, 08:45-09:00 (P29) Determination of vortex structures in the wake of swimming and flying animals

1 2 J. Peng 1 , J. Dabiri 1,2. Bioengineering & Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA, USA

Swimming and flying animals are able to generate locomotive forces by transferring momentum to surrounding fluid in the form of vortices. Dabiri (2005) introduced a model to deduce swimming and flying forces from wake measurements. The application of this model is contingent on quantitative determination of wake vortex structure. In this study, a method is proposed to determine vortex boundaries. Using a novel experiment technique, the trajecto- ries of many particles tracked in the fluid were measured. A numerical scheme was developed to reconstruct the entire flow field by interpolating the measured trajectories. From the measured and the interpreted trajectories, finite-time Lyapunov exponents (FTLE) were calculated to determine the separatrices which separate fluid particles that recirculate inside the vortices from fluid particles that are redirected around the vortices. The separatrices are called Lagrangian Coherent Structures (LCS) and are in correspondence with the vortex boundaries. As an application, the structure of a propagating vortex ring pair generated by a mechanical piston-cylinder apparatus was revealed using the method and was consistent with previous studies. The method proposed in this study is different from the previously reported techniques that estimate vortex boundaries using digital particle image ve- Iocimetry (DPIV). By directly measuring the Lagrangian trajectories of fluid particles instead of calculating them from Eulerian vector fields measured by DPIV, the method used here has the advantage of not only higher order of accuracy but also simpler experiment setup and reduced computation cost. The application of this method to the quantitative determination of vortex structures in the wake of swimming and flying animals will enable the estimation the locomotive forces.

7430 We, 09:00-09:15 (P29) Study of osci l latory lift-based propulsion by f lapping airfoil with flexible trail ing edge

S.Y. Shinde, J.H. Arakeri. Indian Institute ef Science, Bangalere, India

The interface between biology and fluid mechanics is a broad and interesting field. Our interest lies in external biofluiddynamics, especially of lunate fish propulsion. Many swimming and flying creatures use the principle of oscillatory lift based propulsion. Often the flapping element is flexible, totally or partially. The flow dynamics because of a flexible flap is thus of considerable interest. The present work investigates the effect of trailing-edge flexibility on the flow field. A flexible flap with negligible mass and stiffness is attached at the trailing edge of NACA0015 airfoil. The airfoil oscillates and at the same time it moves in a circular path in stationary water. The parameters varied are frequency, amplitude of oscillation and forward speed. The Strouhal number is kept around 0.3, which falls in the gamut of Strouhal numbers for maximum propulsive efficiency. We visualize the flow with dye and particles and measure velocities using PIV. We study flap motion, flow around the flap, wake width, energy left in the wake (which is measure of propulsion efficiency), wake structure in terms of vortex spacing, evolution of vortices, etc. We compare the wakes of the airfoil with and without flap. A flexible trailing edge induces multiple vortices while in case of a rigid trailing edge; one vortex is shed per half cycle. The wake of airfoil with flexible flap dies out faster (because of multiple vortices) compared to the wake of the airfoil without flap. Although wake widths for airfoil with flexible as well as rigid trailing edge are of the same order, wake width would be much larger with a rigid flap. For the same Strouhal number, wake is almost momentumless (i.e. thrust=drag) for rigid trailing edge while for flexible trailing edge it is not momentumless. Thus addition of flap alters the Strouhal number for maximum efficiency. Large flap deflections and curvatures are observed. The deflections of flap tip and airfoil trailing edge are of the same order. A phase difference exists between trailing edge and flap tip deflections. The flap tip deflections and phase difference remain nearly the same for all the frequencies studied for given amplitude. The interaction of the separated flow with flap is quite interesting and will be studied in detail.