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First published online June 6, 2005
Journal of Experimental Biology 208, 2303-2318 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01612

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The aerodynamics of hovering flight in Drosophila

Steven N. Fry^1,*, Rosalyn Sayaman² and Michael H. Dickinson²

¹ Institute of Neuroinformatics, University/ETH Zürich, Switzerland
² California Institute of Technology, Mail Code 138-78, Pasadena, CA 91125, USA

View larger version (50K): [in a new window]   Fig. 1. Measurement of kinematics and forces. (A) 3D high speed videography. Three orthogonally aligned high speed cameras were used to film flies as they entered a small volume (wire-frame) next to a visual target (black cylinder). (B) Examples of frames recorded simultaneously by the three cameras. Body and wing kinematics were measured by matching markers for the head and abdomen, as well as the right (red) and left (yellow) wing in all three images. Arrows show the subsequently measured aerodynamic force projected back onto the images. (C) Wing position in body centered polar coordinates are defined by three angles: Stroke position (0° lateral, downstroke positive), stroke deviation (upward positive) and angle of attack (rotation around wing span, 0° leading edge up, positive rotation brings leading edge forward), following previously used conventions (Sane and Dickinson, 2001). (D) Dynamically scaled robotic wing. Each wing was controlled by three servo motors via coaxial drive shafts. Most of our data were acquired using a single-wing configuration. (E) Wing sensor and aerodynamic force. Forces were measured in a plane orthogonal to the wing span. For the analysis, the forces needed to be scaled and transformed into fixed frame coordinates, as shown in B. For further details on the setup refer to Materials and methods. A more detailed description of the robotic wing is given in Dickson and Dickinson (2004).

View larger version (29K): [in a new window]   Fig. 2. Instantaneous wing kinematics and flight forces. (A) Body and wing kinematics measured during a slow vertical ascent. The body is pitched up by 45° (top, black trace) and the fly ascends at a constant velocity of about 0.12 m s–1. The kinematics of the right (red) and left (blue) wing in the body frame (compare to Fig. 1C; the reference plane is inclined by 45° with respect to the long axis of the fly's body) are given below. Forward thrust and lift are shown at the bottom. (B) Average wing motion and instantaneous aerodynamic forces (red arrows) for the same data sample. Black lines indicate the position of the wing chord at 25 temporally equidistant points during the stroke cycle, with dots marking the leading edge. Green arrows show the direction of wing motion. The axes indicate a vertical range of stroke position between –90° to 90° horizontally and –10° to 10° vertically. The inset shows the mean downstroke and upstroke forces (red arrows), together with the average over the entire stroke (green arrow). (C) Quasi-steady analysis. The total aerodynamic force measured using the robotic wing (red trace) is compared with the flight force predicted by the model (black trace), which is composed of a translational (blue) and a rotational component (green). Calculations were performed using the model and code provided by W. B. Dickson (also see Dickson and Dickinson, 2004).

View larger version (27K): [in a new window]   Fig. 3. Aerodynamic forces and torques during free hovering flight. (A–C) Translational forces over the course of the stroke cycle (abscissa). Red and blue traces show the forces generated by the right and left wing, respectively. The total force generated by the wings is shown in black, together with the S.D. (gray shaded area). The mean force over the duration of a stroke cycle is shown as a red dot on the ordinate. (A) Vertical force component, (B) forward thrust, (C) sideways thrust. (D–F) Torques. The same notation is used as in A–C. (D) Yaw torque, (E) roll torque, (F) pitch torque.

View larger version (17K): [in a new window]   Fig. 4. Comparison between free and tethered flight. (A) Wing kinematics. Red, green and blue traces show the time course of stroke position, stroke deviation and angle of attack, respectively, over the course of a stroke cycle. Solid and broken lines show data from free and tethered flight, respectively. For comparison, data from a previous study using phase-reconstruction of separate stroboscopic images (Zanker, 1990a) are shown as dotted lines. Small differences of the coordinate systems used to measure wing position in this study may account for the discrepancy between the tethered flight measurements. (B) Wing motion and aerodynamic forces during free flight. For clarity, (mean) downstroke and upstroke forces are shown in blue and green, respectively. For details refer to the legend of Fig. 2B. (C) Same analysis as in B, except that data from tethered flies were used.

View larger version (24K): [in a new window]   Fig. 5. Aerodynamic forces and torques during tethered flight. Refer to legend of Fig. 3 for details.

View larger version (23K): [in a new window]   Fig. 6. Instantaneous specific flight power. (A) Flight power during free flight. Traces show total mechanical power, P*Mech (black) and its aerodynamic (P*Aero, red) and inertial (P*acc, blue) components. Shaded areas show standard deviation. (B) Flight power during tethered flight.