QUICK SEARCH:   [advanced] Author: Keyword(s):
Home     Help     Feedback     Subscriptions     Archive     Search     Table of Contents

First published online October 27, 2003

This Article Summary Full Text Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Sane, S. P. Search for Related Content PubMed PubMed Citation Articles by Sane, S. P.

The aerodynamics of insect flight

Sanjay P. Sane

Department of Biology, University of Washington, Seattle, WA 98195, USA

View larger version (24K): [in a new window]   Fig. 1. Conventions and terminology. (A) Sketch of an insect. The wing section is depicted by a segment drawn perpendicular to a line joining the wing base and wing tip. This segment, representing the wing chord, connects the leading edge (filled circle) to the trailing edge. (B) Sectional view of the insect wing. The free-stream velocity is denoted by U, and downwash velocity is denoted by U' (written in bold to signify their vector nature). The geometric angle of attack () is the angle that the wing section makes with U. The aerodynamic angle of attack (') is given by the angle between the wing section and the free-stream velocity deflected as a result of the downwash. (C) Phases of insect wing kinematics. Wing pronation occurs dorsally as the wing transitions from upstroke to downstroke, and wing supination occurs ventrally at the transition from downstroke to upstroke. (D,E) Linear vs flapping translation. In a linearly translating wing (D), both wing tip and base translate at the same velocity, whereas in a flapping translating wing (E), the tip rotates around an axis fixed at the base.

View larger version (6K): [in a new window]   Fig. 2. Kutta condition and circulation. The Kutta condition arises from a sum of the flow around an airfoil placed in an inviscid fluid (A) to additional circulation arising from the presence of viscosity (B) to yield a smooth, tangential flow from the trailing edge (C). When satisfied, the Kutta condition ensures that the vorticity generated at the trailing edge is zero. For the inviscid case, the net force on the airfoil (blue arrow) acts perpendicular to the free stream.

View larger version (15K): [in a new window]   Fig. 3. Wagner effect. The ratio of instantaneous to steady circulation (y-axis) grows as the trailing edge vortex moves away from the airfoil (inset), and its influence on the circulation around the airfoil diminishes with distance (x-axis). Distance is non-dimensionalized with respect to chord lengths traveled. The graph is based on fig. 35 in Walker (1931). The inset figures are schematic diagrams of the Wagner effect. Dotted lines show the vorticity shedding from the trailing edge, eventually rolling up into a starting vortex. As this vorticity is shed into the wake, bound circulation builds up around the wing section, shown by the increasing thickness of the line drawn around the wing section.

View larger version (19K): [in a new window]   Fig. 4. Section schematic of wings approaching each other to clap (A–C) and flinging apart (D–F). Black lines show flow lines, and dark blue arrows show induced velocity. Light blue arrows show net forces acting on the airfoil. (A–C) Clap. As the wings approach each other dorsally (A), their leading edges touch initially (B) and the wing rotates around the leading edge. As the trailing edges approach each other, vorticity shed from the trailing edge rolls up in the form of stopping vortices (C), which dissipate into the wake. The leading edge vortices also lose strength. The closing gap between the two wings pushes fluid out, giving an additional thrust. (D–F) Fling. The wings fling apart by rotating around the trailing edge (D). The leading edge translates away and fluid rushes in to fill the gap between the two wing sections, giving an initial boost in circulation around the wing system (E). (F) A leading edge vortex forms anew but the trailing edge starting vortices are mutually annihilated as they are of opposite circulation. As originally described by Weis-Fogh (1973), this annihilation may allow circulation to build more rapidly by suppressing the Wagner effect.

View larger version (19K): [in a new window]   Fig. 5. Polhamus' leading edge suction analogy. (A) Flow around a blunt wing. The sharp diversion of flow around the leading edge results in a leading-edge suction force (dark blue arrow), causing the resultant force vector (light blue arrow) to tilt towards the leading edge and perpendicular to free stream. (B) Flow around a thin airfoil. The presence of a leading edge vortex causes a diversion of flow analogous to the flow around the blunt leading edge in A but in a direction normal to the surface of the airfoil. This results in an enhancement of the force normal to the wing section.

View larger version (17K): [in a new window]   Fig. 6. A comparison of 2-D linear translation vs 3-D flapping translation. (A) 2-D linear translation. As an airfoil begins motion from rest, it generates a leading and trailing edge vortex. During translation, the trailing edge vortex is shed, leading to the growth of the leading edge vortex, which also sheds as the airfoil continues to translate. This motion leads to an alternate vortex shedding pattern from the leading and trailing edges, called the von Karman vortex street. This leads to a time dependence of the net aerodynamic forces (blue arrows) measured on the airfoil. (B) 3-D flapping translation. As in A, when an airfoil undergoing flapping translation starts from rest, it generates a leading and trailing edge vortex. However, as the motion progresses, the leading edge vortex attains a constant size and does not grow any further. Because no new vorticity is generated at the leading edge, there is no additional vorticity generated at the trailing edge and the airfoil obeys the Kutta condition. When established, the Kutta condition ensures that there is a net change in the direction of momentum resulting in a reactive aerodynamic force on the airfoil (black arrows; mvi signifies initial momentum, mvf signifies final momentum and mv signifies the difference between initial and final momenta). After establishment of the Kutta condition, the measured net aerodynamic forces (blue arrows) stay stable over a substantial period during translation and do not show time dependence. For Reynolds numbers of 100, this force acts normally to the wing and can be decomposed into mutually orthogonal lift and drag components (green arrows). Ultimately, however, the net downward momentum imparted by the airfoil to the fluid causes a downwash that slightly lowers the constant value of the net aerodynamic force on a steadily revolving wing.

View larger version (13K): [in a new window]   Fig. 7. Stable attachment of the leading edge vortex. As the flapping wing translates, a span-wise velocity gradient interacts with the leading edge vortex, causing the axial flow to spiral towards the tip. The axial flow transports momentum out of the vortex, thus keeping it stably attached. The vortex detaches at about three-quarters of the distance to the wing tip and is shed into the wake. Thick black arrows indicate downwash due to the vortex system generated by the wing in its surrounding fluid. Figure adapted from VandenBerg and Ellington (1997).

View larger version (10K): [in a new window]   Fig. 8 A hypothesis for wing–wake interactions. Parts A–F depict a wing section as it reverses stroke. As the wing transitions from a steady translation (A) phase and rotates around a chordwise axis in preparation for a stroke reversal, it generates vorticity at both the leading and trailing edges (B). These vortices induce a strong velocity field (dark blue arrows) in the intervening region (C,D). As the wing comes to a halt and then reverses stroke (D,E), it encounters this jet. As the wing interacts with its wake, a peak is registered in the aerodynamic force record (light blue arrows), which is sometimes called wake capture or wing–wake interaction. U, free-stream velocity.

View larger version (24K): [in a new window]   Fig. 9. Polar plot comparisons of data from different studies of insect flight. Dotted lines signify coefficients for flapping translation and continuous lines for non-flapping translation. The values in parentheses signify the upper and lower limits of travel in chord lengths within which values were averaged. Values at the beginning and end of each plot signify the angle of attack in degrees. These data are derived from the following studies: Tipula oleracea (Re=1500; orange; Nachtigall, 1977), Schistocerca gregaria (Re=2000; light blue; Jensen, 1956), Bombus (Re=2500; black; Dudley and Ellington, 1990b), Manduca sexta (Re=7300; purple; Willmott and Ellington, 1997a), Drosophila virilis (Re=200; grey; Vogel, 1967), 2-D model Drosophila wings (Re=200; dark blue; Dickinson and Götz, 1993), model flapping Drosophila (Re=150; red; Dickinson et al., 1999), model flapping Manduca (Re=8000; green; Usherwood and Ellington, 2002a). Please note that the Reynolds number (Re) values are approximate and broadly representative of the aerodynamic regime. CD, coefficient of drag; CL, coefficient of lift.