Wing Design in Flies: Properties and Aerodynamic Function
<p>Characteristics of fly wings. (<b>a</b>) Detached wing of the blowfly <span class="html-italic">Calliphora vomitoria</span>, mounted to a steel holder. (<b>b</b>) Deformation of a blowfly wing (green) during loading by a ~64 µN point force (white dot) applied normal to the ventral wing side (arrow) [<a href="#B75-insects-11-00466" class="html-bibr">75</a>]. Grey, surface profile without load. (<b>c</b>–<b>e</b>) Spanwise and chordwise wing profiles along the axes of rotation in three differently-sized fly species (<span class="html-italic">Drosophila melanogaster</span>, <span class="html-italic">Musca domestica</span>, <span class="html-italic">Calliphora vomitoria</span>). The wing profiles are superimposed on natural wing models (grey). The profiles separately show wing camber (Cam) and wing corrugation (Cor). Both wing components were numerically extracted from the natural wing shape (Nat) according to a procedure outlined in Engels et al. [<a href="#B83-insects-11-00466" class="html-bibr">83</a>]. The out-of-plane component (z) is exaggerated by a factor of 2 for better clarity.</p> "> Figure 2
<p>Ideal distribution of spanwise lift in translating and revolving wings. Distribution of vertical downwash velocity during translation in an (<b>a</b>) rectangular and (<b>b</b>) elliptical insect wing. At constant forward flight velocity, the inflow towards the wing is uniform. The ideal elliptical wing shape spreads spanwise vorticity that produces maximum span and Rankine–Froude efficiencies. (<b>c</b>) In a revolving wing, the non-uniform inflow requires adjustments in wing shape for maximum efficiency. (<b>d</b>) Distribution of spanwise circulation in an elliptical wing according to Prandtl [<a href="#B109-insects-11-00466" class="html-bibr">109</a>], Betz [<a href="#B110-insects-11-00466" class="html-bibr">110</a>] and Goldstein [<a href="#B111-insects-11-00466" class="html-bibr">111</a>]. (<b>e</b>) Ideal wing shape for maximum span efficiency in a revolving wing according to Prandtl–Betz and Goldstein (see <a href="#app1-insects-11-00466" class="html-app">Supplementary Materials</a>).</p> "> Figure 3
<p>Aerodynamics of revolving wings. (<b>a</b>–<b>c</b>) Upper row: aerodynamic characteristics of three flat, continuously revolving wings (rectangular wing, ideal wing for rotation, wing of a blowfly). Middle row: data show iso-surface with vorticity magnitude of 75 s<sup>−1</sup> (grey) superimposed on a vorticity iso-surface with 150 s<sup>−1</sup> (red). The flow is shown after ~0.4 revolutions after motion onset. Lower row: pressure difference (Δp *) between dorsal and ventral wing sides, and normalized to the uniform wing loading pressure. The latter value is equal to body weight divided by the surface area of two wings. (<b>d</b>,<b>e</b>) Time evolution of vertical lift in <span class="html-italic">d</span> and aerodynamic power in <span class="html-italic">e</span>. After motion onset (grey, left), lift and power stabilize approximately after 0.3 revolutions (grey, right). Dots are mean values calculated from ~0.32–~0.5 revolutions (grey, right). Wing length and area are identical in all wings. For numerical modeling see [<a href="#B83-insects-11-00466" class="html-bibr">83</a>]. Orange, rectangular wing; blue, wing of <span class="html-italic">Calliphora vomitoria</span>; and red, ideal-shaped wing.</p> "> Figure 4
<p>Evolution of vorticity in a flapping rectangular (left) and blowfly (right) wing. (<b>a</b>–<b>g</b>) Vorticity distribution at the beginning of the 3rd flapping cycle (t = 0–1) after motion onset. Vorticity of a flapping wing of <span class="html-italic">Calliphora vomitoria</span> slightly differs from the flow in the rectangular wing. Data show iso-surface with vorticity magnitude of 75 s<sup>−1</sup> (semi-transparent grey) superimposed on a vorticity iso-surface with 150 s<sup>−1</sup> (red). LEV, leading edge vortex; TEV, trailing edge vortex; TIV, wing tip vortex. For performance data and wing kinematics confer to <a href="#insects-11-00466-t001" class="html-table">Table 1</a> and a previously published study [<a href="#B83-insects-11-00466" class="html-bibr">83</a>], respectively. Wing length and area are identical in both wings.</p> "> Figure 5
<p>Flow pattern produced by natural wing models of three fly species. Color-coded instantaneous streamlines in (<b>a</b>) <span class="html-italic">Drosophila</span>, (<b>b</b>) <span class="html-italic">Musca</span>, and (<b>c</b>) <span class="html-italic">Calliphora</span>. Snapshots are taken at 1.3 (<span class="html-italic">Drosophila</span>) and 3.3 stroke cycle (<span class="html-italic">Musca, Calliphora</span>) after motion onset in natural wings [<a href="#B83-insects-11-00466" class="html-bibr">83</a>]. Streamlines were computed from particles released in the corrugation valleys of the dorsal (upper) wing surface near the leading wing edge. Data show little spanwise vorticity inside the corrugation valley near the surface (arrows) and leading-edge vortex suction pulls the virtual particles away from the surface.</p> ">
Abstract
:1. Introduction
2. Aerodynamic Properties of Root-Flapping Rectangular Wings
3. The Aerodynamic Benefits of an Ideal Planform
4. Functional Relevance of Three-Dimensional Wing Shape
5. Wing Stiffness and Benefits of Elastic Wing Deformation
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Kinematics | Property | Rectangular Wing | Ideal Wing | Fly Wing |
---|---|---|---|---|
Revolving 1 | Vertical force (μN) | 471 | 215 | 431 |
Revolving 1 | Paero (μW) | 1696 | 724 | 1434 |
Revolving 1 | Efficiency | 0.22 | 0.16 | 0.23 |
Flapping 2 | Vertical force (μN) | 479 | n.a. | 458 |
Flapping 2 | Paero (μW) | 2340 | n.a. | 2361 |
Flapping 2 | Efficiency | 0.27 | n.a. | 0.25 |
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Krishna, S.; Cho, M.; Wehmann, H.-N.; Engels, T.; Lehmann, F.-O. Wing Design in Flies: Properties and Aerodynamic Function. Insects 2020, 11, 466. https://doi.org/10.3390/insects11080466
Krishna S, Cho M, Wehmann H-N, Engels T, Lehmann F-O. Wing Design in Flies: Properties and Aerodynamic Function. Insects. 2020; 11(8):466. https://doi.org/10.3390/insects11080466
Chicago/Turabian StyleKrishna, Swathi, Moonsung Cho, Henja-Niniane Wehmann, Thomas Engels, and Fritz-Olaf Lehmann. 2020. "Wing Design in Flies: Properties and Aerodynamic Function" Insects 11, no. 8: 466. https://doi.org/10.3390/insects11080466