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First published online June 13, 2008
Journal of Experimental Biology 211, 2014-2025 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.016931

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Wing kinematics measurement and aerodynamics of hovering droneflies

Yanpeng Liu^* and Mao Sun

Institute of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100083, People's Republic of China

View larger version (6K): [in this window] [in a new window]   Fig. 1. Model of trinocular stereo vision system. (XW YW ZW), the world coordinate system; (XC1 YC1 ZC1), (XC2 YC2 ZC2) and (XC3 YC3 ZC3), the camera coordinate systems of cameras 1, 2 and 3, respectively; (u1 v1), (u2 v2) and (u3 v3), image coordinate systems of camera 1, 2 and 3, respectively. P, an arbitrary point; p1, p2 and p3, the projective points and f1, f2 and f3, the focal length of cameras 1, 2 and 3, respectively.

View larger version (59K): [in this window] [in a new window]   Fig. 2. (A) Wing model. (B) Example of frames recorded by the three cameras. See text for details.

View larger version (63K): [in this window] [in a new window]   Fig. 3. Definitions of morphological parameters of wing and body. h1, distance from wing-root axis to long-axis of body; l1, distance from wing-root axis to body center of mass; lr, distance between two wing roots; lb, body length.

View larger version (23K): [in this window] [in a new window]   Fig. 4. A portion of the computation grid of the dronefly wing.

View larger version (10K): [in this window] [in a new window]   Fig. 5. Definitions of the angles of a flapping wing that determine the wing orientation. (X Y Z), coordinates in a system with its origin at the wing root and with Z-axis points to the side of the insect and X–Z plane coincides with the stroke plane. , the positional angle; , geometrical angle of attack; , deviation angle.

View larger version (39K): [in this window] [in a new window]   Fig. 6. Instantaneous wing kinematics of DF1 in hovering. , the positional angle; , geometrical angle of attack; , deviation angle.

View larger version (19K): [in this window] [in a new window]   Fig. 7. Wing kinematics of DF1. , positional angle; , geometrical angle of attack; , deviation angle; , non-dimensional time.

View larger version (14K): [in this window] [in a new window]   Fig. 8. Time courses of the computed force and moment coefficients in one cycle. , non-dimensional time; CV and CH, vertical and horizontal force coefficients, respectively; CM, coefficient for pitching moment about the center of mass; CL and CD, wing lift and drag coefficients, respectively.

View larger version (21K): [in this window] [in a new window]   Fig. 9. Vorticity plots at 2 at various times during one cycle. Solid and broken lines indicate positive and negative vorticity, respectively. The magnitude of the non-dimensional vorticity at the outer contour is 2 and the contour interval is 3. , non-dimensional time.

View larger version (9K): [in this window] [in a new window]   Fig. 10. Time courses of power. CP, non-dimensional power; Cp,a and Cp,j, non-dimensional aerodynamic and inertial power, respectively.

View larger version (4K): [in this window] [in a new window]   Fig. 11. (A) Wing-tip trajectory of DF1; (B) that of a fruit fly [plotted using data from Fry et al. (Fry et al., 2005)] (B). , the positional angle; , deviation angle.

View larger version (25K): [in this window] [in a new window]   Fig. 12. Wing kinematics data. (A–C); fruit fly (data from Fry et al., 2005). (D–F); dronefly DF1. , the positional angle; , geometrical angle of attack; , deviation angle; , non-dimensional time

View larger version (4K): [in this window] [in a new window]   Fig. 13. Vertical force of fruit flies over the course of a stroke cycle (Fry et al., 2005).

View larger version (7K): [in this window] [in a new window]   Fig. 14. Time course of power [plotted using data from Fry et al. (Fry et al., 2005)]; red solid line, total mechanic power; blue broken line, aerodynamic power component; green broken dot line, inertial power component.

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