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First published online July 23, 2003

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Aerodynamic force generation and power requirements in forward flight in a fruit fly with modeled wing motion

Mao Sun^* and Jiang Hao Wu

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

View larger version (19K): [in a new window]   Fig. 1. Sketches of the reference frames and wing motion. OXYZ is an inertial frame, with the XY plane in the horizontal plane. o'x'y'z' is another inertial frame, with the x'y' plane in stroke plane. oxyz is a frame fixed on the wing, with the x axis along the wing chord, and the y axis along the wing span. , positional angle of the wing; min and max, minimum and maximum positional angle, respectively; , angle of attack of the wing; ß, stroke plane angle; V, free-stream velocity; and R, wing length. CL and CT, coefficients of lift and thrust, respectively; Cl and Cd, coefficients of wing lift and wing drag, respectively; Cd', x' component of Cd..

View larger version (31K): [in a new window]   Fig. 5. (A-H) Vorticity plots at half-wing length at various times during one cycle (advance ratio J=0.27). is 60°, non-dimensional time; c is 60°, non-dimensional period of one cycle; , angle of attack of wing. Solid and broken lines indicate positive and negative vorticity, respectively. The magnitude of the non-dimensional vorticity at the outer contour is 1 and the contour interval is 1. (A-D), downstroke; (E-H), upstroke.

View larger version (21K): [in a new window]   Fig. 2. Comparison of the calculated and measured lift (CL) and drag (Cd) coefficients. The experimental data are reproduced from fig. 3C,D of Sane and Dickinson (2001). (A,B) The midstroke angle of attack m is 50° and stroke amplitude h is 60°. (C,D) The midstroke angle of attack m is 50° and stroke amplitude h is 180°. , non-dimensional time; c, non-dimensional period of one flapping cycle.

View larger version (28K): [in a new window]   Fig. 3. Non-dimensional angular velocity of pitching rotation and azimuthal rotation (A), lift coefficient CL (B), thrust coefficient CT (C), wing lift coefficient C1 (D), wing drag coefficient Cd (E) and x' component of wing drag coefficient Cd' (F) versus time during one cycle for five advance ratios. J. c, non-dimensional period of one flapping cycle; , non-dimensional time (midstroke angle of attack m and stroke plane angle ß vary with flight speed; stroke amplitude h=150°).

View larger version (33K): [in a new window]   Fig. 4. (A-H) Vorticity plots at half-wing length at various times during one cycle (advance ratio J=0). , non-dimensional time; c, non-dimensional period of one cycle; , angle of attack of wing. Solid and broken lines indicate positive and negative vorticity, respectively. The magnitude of the non-dimensional vorticity at the outer contour is 1 and the contour interval is 1. (A-D), downstroke; (E-H), upstroke.

View larger version (32K): [in a new window]   Fig. 6. (A-H) Vorticity plots at half-wing length at various times during one cycle (advance ratio J=0.53). is 60°, non-dimensional time; c is 60°, non-dimensional period of one cycle; , angle of attack of wing. Solid and broken lines indicate positive and negative vorticity, respectively. The magnitude of the non-dimensional vorticity at the outer contour is 1 and the contour interval is 1. (A-D), downstroke; (E-H), upstroke.

View larger version (81K): [in a new window]   Fig. 7. Sectional streamline plots at half-wing length at various times during one cycle (advance ratio J=0). , non-dimensional time; c, non-dimensional period of one cycle; , angle of attack of wing (the spatial interval of the incoming streamlines can be seen from the left or right of a plot). (A-C), downstroke; (D-F), upstroke.

View larger version (80K): [in a new window]   Fig. 8. Sectional streamline plots at half-wing length at various times during one cycle (advance ratio J=0.27). , non-dimensional time; c, non-dimensional period of one cycle; , angle of attack of wing (the spatial interval of the incoming streamlines can be seen from the left or right of a plot). (A-C), downstroke; (D-F), upstroke.

View larger version (80K): [in a new window]   Fig. 9. Sectional streamline plots at half-wing length at various times during one cycle (advance ratio J=0.53). , non-dimensional time; c, non-dimensional period of one cycle; , angle of attack of wing (the spatial interval of the incoming streamlines can be seen from the left or right of a plot). (A-C), downstroke; (D-F), upstroke.

View larger version (15K): [in a new window]   Fig. 10. Aerodynamic torque coefficients for translation CQ,a,t (A) and for rotation CQ,a,r (B) and inertial torque coefficients for translation CQ,i,t (C) and for rotation CQ,i,r (D) versus time in one cycle for various advance ratios J. , non-dimensional time; c, non-dimensional period of one cycle.

View larger version (22K): [in a new window]   Fig. 11. Coefficients of power for translation CP,t (A) and for rotation CP,r (B) versus time in one cycle for various advance ratios J. , non-dimensional time; c, non-dimensional period of one cycle (midstroke angle of attack m and stroke plane angle ß vary with flight speed; stroke amplitude =150°).

View larger version (14K): [in a new window]   Fig. 12. Body-mass-specific power P* versus advance ratios J. m, midstroke angle of attack; ß, stroke angle; , stroke amplitude; n, stroke frequency.

View larger version (27K): [in a new window]   Fig. 13. Non-dimensional angular velocity of pitching rotation and azimuthal rotation (A), lift coefficient CL (B), thrust coefficient CT (C), wing lift coefficient Cl (D), wing drag coefficient Cd (E) and x' component of wing drag coefficient Cd' (F) versus time during one cycle for five advance ratios J. c, non-dimensional period of one flapping cycle; , non-dimensional time (stroke amplitude and stroke plane angle ß vary with flight speed; midstroke angle of attack m=46.5°; stroke frequency n=240 s-1).

View larger version (21K): [in a new window]   Fig. 14. Coefficients of power for translation CP,t (A) and for rotation CP,t (B) versus time in one cycle for various advance ratios J. , non-dimensional time; c, non-dimensional period of one cycle (stroke amplitude and stroke plane angle ß vary with flight speed; midstroke angle of attack m=46.5°; stroke frequency n=240 s-1).

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