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DOI: 10.1126/science.
Science 325 , 1549 (2009);
John Young, et al.
Efficiency
Enhance Aerodynamic Function and Flight
Details of Insect Wing Design and Deformation
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here, either directly or that we used as modeling templates. The full list of these proteins is provided in the supporting online material. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institute of General Medical Sciences (NIGMS). This work was supported by the NIH PSI grants P20 GM076221 (JCCM) and U54 GM074898 (JCSG) from the NIGMS; grant DE-FG02-08ER64686 from the Office of Science (Biological and Environmental Research), U.S. Department of Energy; and the Gordon and Betty Moore Foundation CAMERA project. Supporting Online Material www.sciencemag.org/cgi/content/full/325/5947/1544/DC Materials and Methods Figs. S1 to S Tables S1 to S References Metabolic reconstruction in SMBL and MATLAB formats 8 April 2009; accepted 22 July 2009 10.1126/science.
Details of Insect Wing Design and
Deformation Enhance Aerodynamic
Function and Flight Efficiency
John Young,^1 Simon M. Walker,^2 Richard J. Bomphrey,^2 Graham K. Taylor,^2 Adrian L. R. Thomas^2 *
Insect wings are complex structures that deform dramatically in flight. We analyzed the aerodynamic consequences of wing deformation in locusts using a three-dimensional computational fluid dynamics simulation based on detailed wing kinematics. We validated the simulation against smoke visualizations and digital particle image velocimetry on real locusts. We then used the validated model to explore the effects of wing topography and deformation, first by removing camber while keeping the same time-varying twist distribution, and second by removing camber and spanwise twist. The full-fidelity model achieved greater power economy than the uncambered model, which performed better than the untwisted model, showing that the details of insect wing topography and deformation are important aerodynamically. Such details are likely to be important in engineering applications of flapping flight.
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nsects achieve remarkable flight perform- ance with a diverse range of complex wing designs ( 1 , 2 ). Computational fluid dynam- ics (CFD) offers an opportunity to identify the features underpinning the aerodynamic perform- ance of insect wings. By comparing numerical simulations of different designs, it is possible to test the effects of modifications that may be outside the natural range of variation. Unfortu- nately, a lack of detailed measurements of insect wing kinematics has limited previous numerical studies of insect flight to two-dimensional (2D) models ( 3 – 6 ) or to 3D models in which the wings are modeled as rigid flat plates ( 7 – 11 ) or as rigid sections with constant camber and twist ( 12 ). Such simplifications can dramatically change the conclusions drawn about flow struc-
ture ( 13 ), and no model has yet been validated experimentally against flow visualizations from a real insect. We used the most detailed set of insect wing kinematics published to date ( 2 ) to develop the first 3D CFD model of an insect with de- forming wings. We validated the results of our CFD simulations against qualitative and quanti- tative flow visualizations of real locusts. We then used progressive simplifications of the wing kinematics to analyze the aerodynamic conse- quences of the measured twist and camber. We modeled a typical wingbeat of the desert locust Schistocerca gregaria ( 14 ) by averaging the kinematics of four consecutive wingbeats from one of the individuals described in ( 2 ). These kinematics were obtained by using four high-speed digital video cameras to track more than 100 natural features and marked points on the wings, which were then used to reconstruct the deforming surface topography of the wings with a mean spatial error of 0.11 mm ( 15 ). We fitted cubic splines to the wing outline and veins, and we interpolated these spatially to give the surface mesh for the CFD simulations, which we
then interpolated temporally to give up to 800 time steps per wingbeat ( 14 ). We gave the modeled wings a nominal constant thickness of 0.05 mm based on published cross-sections of the wing veins and membrane ( 16 ). We did not attempt to model variations in thickness due to wing vena- tion. Folding of the hindwing against the thorax could not be modeled exactly, and we instead modeled the hindwing as if it were joined to the thorax along its chord ( 14 ). We solved the unsteady incompressible Navier-Stokes equations assuming laminar flow using a commercial CFD package ( 14 ). We con- structed the CFD grid for the locust kinematics in multiple parts by using commercial software, and we incorporated the wing motions via a look-up table prescribing the kinematics ( 14 ). The wings and body were meshed with a tri- angular surface grid and surrounded with a thin boundary-layer grid to provide adequate resolu- tion of velocity gradients normal to the surface. These were then surrounded with stationary outer regions representing the wind tunnel, and a deforming inner region in which the wings and boundary layer grids moved. A symmetry plane running through the sagittal plane of the insect was used. Aerodynamic forces on the wings and body were calculated by integrating pressure and viscous shear stress over the surfaces. Starting transients in the calculated aerodynamic forces vanished rapidly within the first wingbeat, with very close agreement between wingbeats there- after, so we allowed the simulation to run for four repeated wingbeats. Aerodynamic power requirements were calculated by integrating the inner product of the local pressure and viscous forces with the local wing surface velocity in a coordinate system fixed to the insect’s body. We validated our CFD method against an independent CFD algorithm ( 17 ) by using our method to replicate published force computations for a simple model of a flapping dragonfly wing in hover ( 11 , 14 ). The predicted instantaneous vertical force coefficients from the two algo- rithms were in excellent agreement, with a linear
(^1) School of Engineering and Information Technology, Univer- sity of New South Wales, Australian Defence Force Academy, Canberra, Australian Capital Territory 2600, Australia. 2 De- partment of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, UK. *To whom correspondence should be addressed. E-mail: [email protected]
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Both simplified kinematics models preserve the gross changes in projected and wetted wing area that result from corrugation and folding of the hindwing ( 2 ). The wetted area of the hindwing in the full-fidelity model varies by as much as 14%, which reflects folding of the wing against the thorax. The wetted area of the hindwing in the untwisted model varies by as much as 19%, and the 5% difference here reflects the fact that the untwisted wing does not corrugate, because it is modeled as a flat plate. The computed surface pressure field for the full-fidelity model shows no evidence of leading- edge separation, with the locally varying camber ensuring that the leading edge is well aligned with the oncoming flow at all times (Fig. 3A). In contrast, the untwisted kinematic model shows massive separation on the hindwing mid- downstroke, when the downward velocity of the wing is maximal, as evidenced by a low-pressure region extending over much of the wing’s upper surface at this time (Fig. 3C). The uncambered model also shows evidence of separation, but with the low-pressure region confined to the basal part of the hindwing (Fig. 3B). The 2D flow fields plotted in the bottom row of Fig. 3 confirm
that flow separation is present in the two sim- plified models. Flow reversal is clearly visible over the hindwing for both the uncambered (Fig. 3B) and untwisted (Fig. 3C) models, but there is no evidence of flow reversal with the full-fidelity kinematics (Fig. 3A). This difference is present despite the hindwing angle of attack being iden- tical among simulations in the 2D plane shown in Fig. 3, and it must therefore result from a com- bination of 3D effects and camber. We compared the computed aerodynamic forces and aerodynamic power requirement for the full-fidelity, uncambered, and untwisted kin- ematics models (Fig. 4). The aerodynamic force is resolved into a lift component normal to the free stream and a thrust component parallel to it. The uncambered wings generate less lift and thrust during the downstroke than the full-fidelity wings do, because of the absence of the positive camber present on the real wings. The uncam- bered wings generate a similar amount of lift to the full-fidelity wings through most of the up- stroke, however, which is presumably because the real wings flatten and feather on the upstroke and are therefore better approximated by the un- cambered model. The same features are reflected
in the aerodynamic power requirement, with the uncambered wings requiring slightly less power than the full-fidelity wings on the downstroke but needing similar aerodynamic power on the upstroke. The pattern is more complicated for the untwisted wings, which nevertheless produce less lift and thrust than the full-fidelity model does and require greater aerodynamic power to do so. The aerodynamic advantages of the full- fidelity wing kinematics are clearly revealed by comparing the total power economy of the dif- ferent models, defined as the ratio of time- averaged total force to time-averaged total power. The total power economies in the uncambered (0.98 N W−^1 ) and untwisted (0.84 N W−^1 ) models are 7% and 15% lower, respectively, than the total power economy of the full-fidelity mod- el (1.06 N W−^1 ). This lower efficiency of mo- mentum transfer is attributable partly to the leading-edge separation that occurs on the hind- wings in the simplified models. In addition, the simplified wing kinematics cause the resultant force to have a less favorable direction, as can be seen from the large decrements in lift and thrust in Fig. 4. This results in an even greater reduction in lift power economy, defined as the ratio of time-averaged lift to time-averaged total power: The lift power economy of the uncambered wings (0.78 N W − 1 ) is 12% lower than that of the full-fidelity model (0.88 N W−^1 ), whereas the lift power economy of the untwisted wings (0.51 N W−^1 ) is 35% lower. In summary, wing deformation in locusts is important both in en- hancing the efficiency of momentum transfer to the wake and in directing the aerodynamic force vector appropriately for flight. The high-lift aerodynamics of insect flight are typically associated with massive flow separation and large leading-edge vortices ( 19 – 21 ). How- ever, when high lift is not required, attached-flow aerodynamics can offer greater efficiency. The aerodynamic power efficiency of locusts appears to derive from their ability to reduce flow separa- tion and the associated loss of energy as vortical motion in the wake. Simple heaving or flapping flat plates can generate high lift with stable leading-edge vortices ( 21 , 22 ), but designing robust lightweight wings that can also support efficient attached flow aerodynamics is likely to be much more difficult. Our results show that the secret to doing so lies in building a wing that undergoes appropriate aeroelastic deformation through the course of the wingbeat. We have shown previously that the shape and structure of a locust’s hindwing are tuned so that it twists appropriately to maintain a constant angle of attack across the wing during the downstroke ( 2 ). Our CFD simulations demonstrate furthermore that time-varying wing twist and camber are essential to the maintenance of attached flow. Implementing such tailored deformations in an engineered system is a difficult problem and may demand an evolutionarily optimized solution in order even to approach the elegance of an insect.
Fig. 3. Computed sur- face pressure maps from the CFD simulations using full-fidelity kinematics (A), uncambered kinemat- ics (B), and untwisted kin- ematics (C). The same four consecutive stages of the wingbeat are shown as in Fig. 1, beginning with the start of the downstroke. There is an extensive area of low pressure over the hindwing in the untwisted model, indicative of leading- edge separation. A more limited separation is visi- ble near the root of the hindwing in the uncam- bered model. There is no clear evidence of separa- tion with the full-fidelity kinematics. The plots at the bottom of the figure show the corresponding 2D flow fields for the stage of the downstroke when the hindwing is horizon- tal, for the same vertical plane as in Fig. 1. The variation in flow separa- tion between the three kinematics models is dem- onstrated in these images by the reversed flow over the top surface of the uncambered and untwisted wings, even though the hindwing angle of attack is identical in all three simulations in these sections. The reduction in the extent of flow separation between the uncambered and untwisted wing must be due to wing twist and associated 3D flow effects. The lack of reversed flows with the full-fidelity kinematics is presumably due to the curvature of the wing section and the reduced local angle of attack at the leading edge. Figure S shows the effects on the computed 2D flow field through the wingbeat.
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References and Notes
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- The research leading to these results has received funding from the Engineering and Physical Sciences Research Council (EPSRC) under grant GR/S23049/01 to A.L.R.T. and from the European Research Council (ERC) under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 204513 to G.K.T. J.Y. was supported by the Merit Allocation Scheme on the National Facility of the
Australian National Computing Infrastructure (NCI-NF) and gratefully acknowledges the Rector of the University of New South Wales at the Australian Defense Force Academy for the award of a sabbatical scholarship to perform this work. R.J.B. holds an EPSRC Career Acceleration Fellowship. G.K.T. is a Research Councils UK Academic Fellow and Royal Society University Research Fellow. We gratefully acknowledge the EPSRC Instrument Loan Pool and thank N. J. Lawson for advice and the loan of equipment for the DPIV measurements.
Supporting Online Material www.sciencemag.org/cgi/content/full/325/5947/1549/DC Materials and Methods SOM Text Figs. S1 to S References Movie S
6 May 2009; accepted 24 July 2009 10.1126/science.
D-Amino Acids Govern Stationary Phase
Cell Wall Remodeling in Bacteria
Hubert Lam,^1 * Dong-Chan Oh,^2 *† Felipe Cava,^1 * Constantin N. Takacs, 1 ‡ Jon Clardy, 2 Miguel A. de Pedro, 3 Matthew K. Waldor 1 §
In all known organisms, amino acids are predominantly thought to be synthesized and used as their L-enantiomers. Here, we found that bacteria produce diverse D-amino acids as well, which accumulate at millimolar concentrations in supernatants of stationary phase cultures. In Vibrio cholerae, a dedicated racemase produced D-Met and D-Leu, whereas Bacillus subtilis generated D-Tyr and D-Phe. These unusual D-amino acids appear to modulate synthesis of peptidoglycan, a strong and elastic polymer that serves as the stress-bearing component of the bacterial cell wall. D-Amino acids influenced peptidoglycan composition, amount, and strength, both by means of their incorporation into the polymer and by regulating enzymes that synthesize and modify it. Thus, synthesis of D-amino acids may be a common strategy for bacteria to adapt to changing environmental conditions.
I
n all kingdoms of life, cells predominantly use L-amino acids. In most bacteria, the only D-amino acids produced in significant quan- tities are D-Ala and D-Glu, which are incorporated
into peptidoglycan (PG) ( 1 ). PG is a strong and elastic polymer of the bacterial cell wall that is syn- thesized and modified by penicillin-binding pro- teins (PBPs). PG counteracts the cell’s osmotic
Fig. 4. Instantaneous lift-generated, thrust- generated, and aerody- namic power required in the CFD simulations using full-fidelity kinematics (A), uncambered kine- matics (B), and untwisted kinematics (C). Solid and dashed lines denote the lift or power components for the hindwing and fore- wing, respectively. The wingbeat shown begins at the start of the hind- wing downstroke and ends at the point denoted by the vertical line. For the lift and thrust plots, the shading shows the decre- ment (red) or increment (green) in instantaneous force for the simplified kinematics as compared to the full-fidelity model. For the power plots, the shading shows the equiv- alent increment (red) or decrement (green) in in- stantaneous power required.
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