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First published online April 23, 2004
Journal of Experimental Biology 207, 1887-1901 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.00969

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A computational study of the aerodynamic forces and power requirements of dragonfly (Aeschna juncea) hovering

Mao Sun^* and Shi Long Lan

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

View larger version (23K): [in a new window]   Fig. 1. Sketches of the model wings, the flapping motion and the reference frames. FW and HW denote fore- and hindwings, respectively. OXYZ is an inertial frame, with the X and Y axes in the horizontal plane; oxyz is another inertial frame, with the x and y axes in the stroke plane; o'x'y'z' is a frame fixed on the wing, with the x' axis along the wing chord and y' axis along the wing span. ß, stroke plane angle; , positional angle; , angle of attack; R, wing length.

View larger version (103K): [in a new window]   Fig. 2. Some portions of the moving overset grids.

View larger version (16K): [in a new window]   Fig. 3. Comparison between numerical and analytical solutions of a starting sphere. (A) Drag coefficient (Cd) vs non-dimensional time (s). (B) Azimuthal velocity (u) vs non-dimensional radial distance (r/2a).

View larger version (20K): [in a new window]   Fig. 4. Comparison of the calculated and measured lift and drag forces. The experimental data are reproduced from fig. 3C,D of Sane and Dickinson (2001). (A,B) The midstroke angle of attack is 50° and stroke amplitude is 60°; (C,D) the midstroke angle of attack is 50° and stroke amplitude is 180°.

View larger version (19K): [in a new window]   Fig. 5. Non-dimensional angular velocity of flip rotation () and azimuthal rotation () of (A) hindwing and (B) forewing; (C) time courses of total vertical force coefficient (CL) and (D) total thrust coefficient (CT) in one cycle.

View larger version (17K): [in a new window]   Fig. 6. (A) Time courses of vertical force coefficients of forewing (CL,f) and hindwing (CL,h) and (B) thrust coefficients of the forewing (CT,f) and the hindwing (CT,h) in one cycle.

View larger version (17K): [in a new window]   Fig. 7. (A) Time courses of lift coefficients of forewing (Cl,f) and hindwing (Cl,h) and (B) drag coefficients of the forewing (Cd,f) and the hindwing (Cd,h) in one cycle.

View larger version (15K): [in a new window]   Fig. 8. (A) Time courses of vertical force coefficients of forewing (CL,f) and single forewing (CL,sf); (B) thrust coefficients of the forewing (CT,f) and single forewing (CT,sf); (C) vertical force coefficients of the hindwing (CL,h) and single hindwing (CL,sh) and (D) thrust coefficients of the hindwing (CT,h) and single hindwing (CT,sh) in one cycle.

View larger version (47K): [in a new window]   Fig. 9. (A–F) Iso-vorticity surface plots at various times in one cycle (single hindwing). Note that the X axis is along the body of the dragonfly and the XZ plane is the plane of symmetry of the insect. , non-dimensional time. The magnitude of the non-dimensional vorticity is 1.

View larger version (41K): [in a new window]   Fig. 10. Velocity vectors in a vertical plane parallel to and 0.6R from the plane of symmetry at various times in one cycle (single hindwing). The horizontal arrow at the top left represents the reference velocity (U). , non-dimensional time.

View larger version (70K): [in a new window]   Fig. 11. Iso-vorticity surface plots at various times in one cycle (fore- and hindwings). Note that the X axis is along the body of the dragonfly, and the XZ plane is the plane of symmetry of the insect. , non-dimensional time. The magnitude of the non-dimensional vorticity is 1.

View larger version (211K): [in a new window]   Fig. 12. Velocity vectors in a vertical plane parallel to and 0.6R from the plane of symmetry at various times in one cycle (fore- and hindwings). The horizontal arrow at the top left represents the reference velocity (U). , non-dimensional time.

View larger version (14K): [in a new window]   Fig. 13. Time courses of aerodynamic torque coefficients for translation (CQ,a,t) and rotation (CQ,a,r) of (A) forewing and (B) hindwing in one cycle; (C) time courses of inertial torque coefficient for translation (CQ,i,t) in one cycle.

View larger version (23K): [in a new window]   Fig. 14. Time courses of power coefficients of forewing (A) and hindwing (B) in one cycle. Cp, power coefficient; Cp,a, coefficient of power due to aerodynamic force; Cp,i, coefficient of power due to inertial force.