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First published online December 3, 2004
Journal of Experimental Biology 207, 4707-4726 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.01319

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The fluid dynamics of flight control by kinematic phase lag variation between two robotic insect wings

Will J. Maybury and Fritz-Olaf Lehmann^*

Department of Neurobiology, University of Ulm, Albert-Einstein-Allee 11, 89081 Ulm, Germany

View larger version (28K): [in a new window]   Fig. 1. Wing beat kinematics of a dragonfly, set-up of the robotic wing hinge, and mechanical properties of the model wings as used in this study. (A) Diagram showing wing tip path of fore- (green) and hindwing (purple) and orientation of a freely flying dragonfly with near vertical thrust vector. Body orientation, location of the wing hinges and wing tip path were plotted after data published by Wakeling and Ellington (1997). In this kinematic study advance ratio, defined as the ratio between forward and wing flapping speed, was 0.44. Due to the steep body angle with respect to the horizontal, the wing hinges are aligned almost vertically and thus similar to the alignment of the robotic wing hinges shown in (B). (B) Schematic diagram of the robotic dragonfly setup, modeling aerodynamic characteristics on one side of the functionally four-winged insect with the forewing and hindwing wingtip trajectories of our generic dragonfly kinematics superimposed (see Materials and methods for details). The kinematics used during fore- and hindwing motion is identical in all experiments, yielding 100° stroke amplitude and symmetrical wing rotation at dorsal and ventral stroke reversal. Kinematic phase shift is the temporal offset between fore- and hindwing motion. (C) The shape of the robotic forewing and hindwing used. The wings are driven by servo motors mounted in a gear box that controls back/forth, up/down and rotational wing motion. Forces and moments acting on the wing during motion are measured on the surface mid point of the force sensor (blue circle). The center of gravity of the wing including the mass of the wing's holder is indicated by a red circle, respectively. lx, length of the horizontal moment arm for the wing's center of gravitiy; ly, length of the vertical moment arm between the wing's center of gravitiy and the wing's rotational axis. (D) Wing deflection due to bending moments under static load of the plexiglas model forewing (orange, red, black) and hindwing (cyan, green, blue). Deflection during load was measured at two distinct positions on the wing at two-third wing length (orange, cyan) and the wing tip (red, black, green, blue). To load the wing, small metal weights were placed on the upper wing surface either at two-third distance from the wing base (**, red, green, cyan, orange) or on the wing tip (*, black, blue). The vertical gray line indicates approximately mean force (0.3 N) measured throughout one complete stroke cycle on the wings during flapping motion. Horizontal gray area shows the range of deflections for fore- and hindwing, assuming the wing is loaded with mean force. The pictogram illustrates the measurement procedure showing wing holder and the wing seen parallel to the wing's surface.

View larger version (28K): [in a new window]   Fig. 2. Inertial forces during wing flapping due to wing mass (A) and added mass (virtual mass) of the wing (B). For kinematic details, see traces in B (bottom) and explanations given in the text. (A) Top: unfiltered raw force trace of lift (black) and drag (red) measured during a single stroke of the dragonfly model hindwing. Bottom: wing inertia in the horizontal (drag, red) and vertical (lift, black) calculated from the acceleration profile during translational and rotational wing motion of a complete stroke cycle. Total wing mass is equal to the mass of the wing and the holder attached to it. Note the different force scales. (B) Top: unfiltered total forces measured during wing motion of the model hindwing (red) within one flapping cycle with superimposed added mass inertia (black) calculated according to the equation given in the text. The blue trace shows the measured forces after subtracting added mass inertia. Bottom: kinematic pattern used for calculations of inertia. Traces show the angular position of the wing within the horizontal stroke plane (red) and the wing's angle of attack (black) throughout the entire stroke cycle.

View larger version (29K): [in a new window]   Fig. 3. Alterations in total lift and lift-to-drag ratio of the model fore- and hindwing in response to changes in kinematic phase shift between both wings. (A) Negative phase-shift values indicate that the forewing leads wing motion (red) throughout the entire stroke cycle whereas positive phase-shift values indicate that the hindwing leads wing motion (blue). Kinematic pattern of both wings is the same (cf. Fig. 4C). (B-D) Lift averaged over an entire stroke cycle (closed red circles) and lift-to-drag ratio (closed blue circles) are shown for the forewing flapping on top of the hindwing (B), the hindwing (C) and the combined performance of both fore- and hindwing (D) during various kinematic phase relationships. Performances of single wings flapping without wake-wing interaction are shown as solid lines in the respective color. Data are presented for the robotic wings vertically separated by 1.3 (closed circles) and 5.0 (open circles) mean forewing chord lengths, measured as the distance between the rotational axis of the two wings (cf. Fig. 1C). For an explanation of L, see text.

View larger version (46K): [in a new window]   Fig. 4. Maximum modulation in lift performance throughout a stroke cycle occurs during the second quarter of each half stroke. (A) Time history of lift forces in the robotic dragonfly hindwing during the stroke cycle are shown for stroke conditions in which the hindwing (red) or the forewing (blue) leads by a quarter stroke cycle. Lift of the hindwing free from forewing wake interference is plotted in black. (B) Lift enhancement on the hindwing calculated from the difference in performance between the hindwing with and without forewing wake interference (difference between colored and black line shown in A). Red (blue) line indicates lift enhancement when the hindwing (forewing) leads by a quarter stroke cycle. Asterisks *1 (15% stroke cycle) and *2 (35% stroke cycle) indicate the position in the stroke cycle when DPIV analysis was performed in Figs 7 and 8. (C) Translational (purple) and rotational (green) velocities of the wing (measured at the wing's second moment of area). The three translational plots represent the velocity profiles for the best (hindwing leads by 25% stroke cycle), zero (both wings move in-phase) and worst (forewing leads by 25% stroke cycle) kinematic patterns. T, stroke cycle.

View larger version (138K): [in a new window]   Fig. 5. (A-L) Time sequence of the wake produced by a tandem dragonfly model wing moving in a horizontal plane and highlighted by air bubbles in the mineral oil. The bubbles are illuminated by conventional fiber optics that intersect the wake at approximately 50% distance from the wing base and normal to the wing surface at mid half stroke. The red lines in each graph indicate inclination of the visible chordwise wing element as it appears on the video images; the upper and lower lines show wing motion of the forewing and hindwing, respectively. Leading wing edge is indicated by a red dot. (A-F) Complete half stroke (upstroke) of the forewing moving from left to right. (G-L) Complete half stroke (downstroke) of the forewing moving from right to left. The time sequence shows the wake while the forewing leads hindwing motion by a quarter stroke cycle. In all images yellow pictograms indicate the location and spin of vortices either shed in the wake (vortex core is marked by a cross) or attached to the wing (leading edge vortex). Only when clearly visible in the fluid, the vortices' spin and location were reconstructed from the video by eye and within the illuminated plane of the wake. Note: vortices that were masked by other flow structures or moving outside the imaging plane are not shown in this reconstruction. The stroke period for flapping motion is 0.96 s and stroke amplitude is 100°. See text for more details on stroke kinematics. Images were taken using a conventional 50 Hz video camera (Sony, TRV120E, Cologne, Germany).

View larger version (137K): [in a new window]   Fig. 6 (A-L) Time sequence of the wake produced by a tandem dragonfly wing moving in a horizontal plane. In contrast to Fig. 5, the time sequence shows the wake while the hindwing leads wing motion by a quarter stroke cycle. Wing kinematics and experimental techniques are similar to those mentioned in the legend for Fig. 5. The vortex that is indicated by the broken yellow line in I appeared to break down in the video image or moved outside the image plane.

View larger version (86K): [in a new window]   Fig. 7. Analysis of flow field velocities around the hindwing using DPIV techniques reveals the elaborate flow structures. The wing sections (white lines) are viewed at 50% distance between the wing base and tip, and have a geometric angle of attack of 45°. The direction of wing translation is from left to right in the hindwing (lower wing in panels) and, where present in the images, from right to left for the forewing (upper wing). The rotational axis for the fore- and hindwing is 0.33 and 0.22 chord widths, respectively. The DPIV images show wake velocity fields at two different times within the stroke cycle (A-C, 15% of stroke cycle; D-F, 35% of stroke cycle) when the hindwing flaps free from forewing downwash (A,D), when both wings flap but the forewing (B,E) or the hindwing (C,F) leads wing motion by a quarter stroke cycle. White open boxes in A-F indicate the region, located between the lower surface of the wing and the free stream, from which downwash flow velocities and angles were measured (see text for details). T, stroke cycle.

View larger version (52K): [in a new window]   Fig. 8. Vorticity contours near the hindwing with superimposed velocity vectors at 35% of stroke cycle when hindwing lift is enhanced or attenuated maximally (*2 in Fig. 4). Vorticity and velocity vectors for the kinematic condition in which (A) hindwing lift is attenuated maximally (worst condition; forewing leads by a quarter stroke cycle), and (B) hindwing lift exceeds lift production of a single hindwing flapping free of forewing downwash interference (best kinematic pattern; hindwing leads by a quarter stroke cycle). Square white boxes indicate the regions from which circulation of the leading edge vortex was measured. The wing sections (white lines) are viewed at 50% distance between the wing base and tip, and have a geometric angle of attack of 45°. The direction of wing translation is from left to right. T, stroke cycle.

View larger version (25K): [in a new window]   Fig. 9. Schematic reconstruction of vortices and local flow conditions at two different kinematic phase relationships between fore- and hindwing and at two different times within the stroke cycle. Hindwing lift depends on LEV strength and the velocity and angle of the oncoming fluid (local flow). Local flow conditions (black vector) on the wing segment (grey oval) are calculated from the velocity and angle of the combined fore-hindwing downwash determined in a region below the wing's surface in a single PIV image plane (green vector, see white box in Fig. 7), and the translational velocity of the hindwing section (grey vector). Blue arrows, lift attenuation; red arrow (F), lift enhancement of the hindwing compared to a wing flapping free of forewing downwash. Vortical circulation (cm2 s-1) in the hindwing's leading edge vortex is shown in square brackets close to the LEV icon. The different strengths of starting and leading edge vorticies are indicated approximately by the size of the plotted `vortex' icons. Effective angle of attack for the hindwing section (degrees, left value) and local flow velocity (m s-1, right value) are shown respectively in parentheses under the vector diagram. (A-F) The flow characteristics for a flapping hindwing free from forewing downwash (single wing flapping) at (A) 15% and (B) 35% of stroke cycle; when the forewing (upper wing) leads wing motion by a quarter stroke cycle (C) at 15% and (D) 35% of stroke cycle; when the hindwing (lower wing) leads by a quarter stroke cycle (E) at 15% and (F) 35% of stroke cycle. A detailed description of vortex development and local flow is given in the text. In all diagrams, the motion of the hindwing (lower wing) is from left to right. White arrows indicate the direction of motion of the forewing. T, stroke cycle.

View larger version (29K): [in a new window]   Fig. 10. Modulation of hindwing lift depends on the vertical distance between fore- and hindwing wing hinges. The traces show lift modulation similar to Fig. 3C for various distances between the wings measured in mean chord width c, while phase lag systematically varied between -50% (forewing leads by a half stroke cycle) and 50% (hindwing leads by a half stroke cycle). Aspect ratio of the two identical wings=2.7, stroke amplitude=120°, flapping frequency= 666 mHz, wing rotation symmetrical, Re=137.