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Measuring wing kinematics, flight trajectory and body attitude during forward flight and turning maneuvers in dragonflies

Hao Wang^1,*, Lijiang Zeng¹, Hao Liu² and Chunyong Yin¹

¹ State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China
² Computer and Information Division, The Institute of Physical and Chemical Research (RIKEN), Japan

View larger version (40K): [in a new window]   Fig. 1. PCFL system based on the global coordinate system (OXYZ). The measurement and reference fringes come from points W1 and W2, respectively. The global coordinate is defined as follows: the XOY plane is at the lowest position; the Z-axis is the optical axis of the high-speed camera; the X-axis is perpendicular to the fringes and the Y-axis is parallel to the fringes. A calibration plane (CP) perpendicular to the optical axis of the high speed camera (HCCD) was used to calibrate the system. PC, personal computer; FPP, fringe pattern projector.

View larger version (21K): [in a new window]   Fig. 2. (A) Landmarks on forewing and hindwing of a dragonfly; (B) definition of the local body-centered coordinate system and yaw, pitch and roll angles. Arrows define the positive rotation directions. The local body-centered coordinate system O'X'Y'Z' is based on four wingbases (B1, B2, B3 and B4), where points B1 and B2 are wingbases of the forewing, and B3 and B4 those of the hindwing. The midpoint KF of B1 and B2 is the origin of the local body-centered coordinate. The Y'-axis is along the line KFKH that joins points KF and the midpoint of B3 and B4, KH. The plane X'O'Y' is constructed by points KF, KH and B1. The Z'-axis is perpendicular to the X'O'Y' plane and upward.

View larger version (18K): [in a new window]   Fig. 3. Wing kinematics. The figure illustrates the parameters of the left forewing; those of the other three wings are defined by the same way. (A) Definition of flapping angle . Point B1 represents the wingbase of the left forewing, point T1 the wingtip of that. The line B1-T1 denotes the leading edge of the wing. The stroke plane is defined by three points: the wingbase B1, and the wingtip at the maximum and minimum angular positions (T1H and T1L) in a flapping cycle based on the local body-centered coordinate system. (Note that the stroke plane of the left wing is generally different from that of the right wing without any assumption of kinematic symmetry, i.e. the stroke planes with respect to the left and right wing are not in one plane.) The line L1 represents the intersection of the plane X'—O'—Y' and the stroke plane. The flapping angle is defined as the angular position of the wing in the stroke plane, measured from dorsal reversal (start of downstroke) to ventral reversal (start of upstroke). =0 for the leading edge in the plane X'—O'—Y'. (B) Definition of the angle of attack, the torsional angle and camber deformation. The plane , which is normal to the leading edge and at a spanwise position of 50% of the total wing length, is defined as the mid-span chord plane. The intersection arch of the wing surface and the plane is the mid-span arch . The mid-span chord vector MN is corresponding to the arch , whose direction definition is from the wing trailing edge (M) to leading edge (N). The line L is the intersection of the plane and the stroke plane , which denotes the tangent of the wing's trajectory. The line L' is the perpendicular of the line L. The angle of attack is defined as the included angle between the vector MN and the line L and the torsional angle is defined as the included angle between the vector MN and the line L'. Note that and are complementary angles. When MNL, =0; =+90° (if downstroke) or =-90° (if upstroke). The two-dimensional coordinate system (o', x', y') is established in the plane with the x-direction from N to M, the y-direction from the lower surface to the upper surface of the wing and the origin in the leading edge. The camber deformation [UNK] is defined as the ratio of the maximum arch rise Hmax to the mid-span chord length MN|.

View larger version (57K): [in a new window]   Fig. 4. Three-dimensional (3-D) reconstruction of the four wings of the flight dragonfly. (A) An original digital image of a dragonfly, and its 3-D reconstruction observed from the same perspective (overhead view). (B) The 3-D reconstruction observed from different viewpoints, represented by two parameters, azimuth or horizontal rotation (as AZ) and vertical elevation (as EL), both in degrees. AZ is positive as the viewpoint is rotated clockwise, while positive values of elevation correspond to movement above the object. Notice that the three orthogonal short arrows represent the body-centered coordinate system.

View larger version (68K): [in a new window]   Fig. 5. Flight trajectories of two typical flight behaviors. The flight trajectories of forward flight and turning maneuvers are expressed by lines with open squares and open circles, respectively, and the flight trajectories projected onto the plane XOY by the solid and dotted lines, respectively. The interval of the vertical projection line is 1/955 s.

View larger version (26K): [in a new window]   Fig. 6. Attitude of two flight behaviors: (A,C,E,G,I) for forward flight; (B,D,F,H,J) for turning maneuvers. (A,B) The flight trajectory, velocity and acceleration. The position of the dragonfly is drawn at an interval of 1/955 s. The solid and dotted lines are with respect to the velocity v and acceleration a vectors, starting from the body position, denoted by crosses (the vector arrow is neglected). In forward flight, the maximum and minimum velocities are 1.71 m s-1 and 1.22 m s-1, and the maximum and minimum accelerations are 129.8 m s-2 and 16.7 m s-2; and in turning maneuvers, these are 2.01 m s-1 and 1.26 m s-1, 101.5 m s-2 and 39.1 m s-2, respectively. (C,D) Flight trajectories projected on the X, Y and Z axes. The filled circles, measured data. The curves are fitted by cubic regression functions as follows. For forward flight, and for turning maneuvers, where the time t is ms, and coordinates X, Y and Z in mm. (E,F) Attitude of the dragonfly expressed by orientation angles; filled square, filled circle and filled triangle denote roll, pitch and yaw, respectively. To calculate the angular velocity and acceleration, these raw data are also fitted using cubic regression functions, denoted by solid, broken and dotted lines for roll, pitch and yaw, respectively. For forward flight, and for turning maneuvers, where the time t is ms, and attitude angle is degrees. (G,H) Angular velocities; (I,J) angular accelerations.

View larger version (39K): [in a new window]   Fig. 7. Wing kinematics for two flight behaviors: (A,C,E) for forward flight; (B,D,F) for turning maneuvers. The middle of the error bar is the actual data point. (A,B) Flapping angle. The smooth curves are fitted by the Fourier series as Equation 1, with the parameter k=1. The value of the error bar is the standard error of fitting expressed as equation 2, with the parameter P=4. The flapping angles of right and left hindwing and right and left forewing are represented by the symbols rh, lh, rf and lf, respectively. For forward flight, and for turning maneuvers, where the time t is ms, and flapping angle in degrees. (C,D) Torsional angle at the 50% spanwise positions. The smooth curves are fitted by the Fourier series as Equation 1 with k=3. The value of the error bar is the standard error of fitting expressed as Equation 2 with P=8. The torsional angles of right and left hindwing and right and left forewing are represented by the symbols rh, lh, rf and lf, respectively. For forward flight, and for turning maneuvers, where the time t is ms, and torsional angle in degrees. (E,F) Camber deformation (the ratio of the maximum arch rise to the mid-span chord length). The smooth curves are fitted by B-spline function. The value of the error bar is determined from the ratio of measurement error of any point on the distorted fringe to the mid-span chord length.

View larger version (45K): [in a new window]   Fig. 8. A computational fluid dynamic study of unsteady aerodynamics of a two-dimensional (2-D) model of the right forewing in forward flight. (A) A systematic diagram of the 2-D computational model. The geometric model is a flat-plate airfoil with the same length as the mid-span chord length and a thickness approximately 2% of the chord length. The angle of stroke plane is defined as the included angle of the stroke plane and the plane X'O'Z' plane of the body-centered coordinate system. The kinematic model consists of a translational motion and a rotational motion. (B) Plots of time-varying force coefficients in a complete beating cycle with and without camber deformation. The force coefficients Cy and Cz represent the time-variations of drag and lift, respectively. LPCD, large positive camber deformation; NCD, negative camber deformation. (C,D) Flow patterns at zero flapping angle during downstroke with (C) and without (D) camber deformation. Velocity vectors and pressure contours are drawn to visualize the flow patterns about the airfoil; and blue in the color map denotes low pressure and red is high pressure.