Quantification of wing and body kinematics
in connection to torque generation during damselfly yaw turn

Samane Zeyghami; Ayodeji T. Bode-Oke; HaiBo Dong

doi:10.1007/s11433-016-0302-5

SCIENCE CHINA Physics, Mechanics & Astronomy

SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 60, Issue 1: 014711(2017) https://doi.org/10.1007/s11433-016-0302-5

Quantification of wing and body kinematics in connection to torque generation during damselfly yaw turn

Samane Zeyghami, Ayodeji T. Bode-Oke, HaiBo Dong

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ReceivedJul 28, 2016
AcceptedOct 8, 2016
PublishedNov 10, 2016

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Abstract

This study provides accurate measurements of the wing and body kinematics of three different species of damselflies in free yaw turn flights. The yaw turn is characterized by a short acceleration phase which is immediately followed by an elongated deceleration phase. Most of the heading change takes place during the latter stage of the flight. Our observations showed that yaw turns are executed via drastic rather than subtle changes in the kinematics of all four wings. The motion of the inner and outer wings were found to be strongly linked through their orientation as well as their velocities with the inner wings moving faster than the outer wings. By controlling the pitch angle and wing velocity, a damselfly adjusts the angle of attack. The wing angle of attack exerted the strongest influence on the yaw torque, followed by the flapping and deviation velocities of the wings. Moreover, no evidence of active generation of counter torque was found in the flight data implying that deceleration and stopping of the maneuver is dominated by passive damping. The systematic analysis carried out on the free flight data advances our understanding of the mechanisms by which these insects achieve their observed maneuverability. In addition, the inspiration drawn from this study can be employed in the design of low frequency flapping wing micro air vehicles (MAV’s).

Funded by

C. Y. Li and Z. Ning for acquiring the insects and videotaping their flights.

we thank Y. Ren

National Natural Science Foundation(CEBT-1313217)

Acknowledgment

This work was supported by the National Natural Science Foundation (Grant No. CEBT-1313217), and Air Force Research Laboratory (Grant No. FA9550-12-1-007). We thank W. Zhang and E. L. Mitchell for their help in 3D surface reconstruction of the flight videos. Also, we thank Y. Ren, C.Y. Li and Z. Ning for acquiring the insects and videotaping their flights.

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Figure 1
(Color online) Three species of damselfly. (a) A representative of each one of the three species of damselfly in this experiment are shown side by side for comparison. Damselfly #1-Hetaerina Americana, Damselfly #2-Argia Apicalis, Damselfly #3-Calopteryx Maculata. The wings are artificially dotted for the tracking purpose (refer to methods section for details). Species name is shown next to the corresponding picture; (b) an image of a left fore and hind wing of each species is shown. The dots are the marker points placed on the wing for tracking the wing motion.
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Figure 2
(Color online) Definition of the wing and body coordinate systems and validation of quasi-steady model. (a) x′y′z′ coordinate system is fixed on the wing and moves with it. xyz-axes is fixed to the body; (b) angle of attack of the wing is the angle between the wing chordline and direction of incoming velocity. Leading edge of the wing is shown by a closed circle. This angle can be altered by either pitching the wing or changing the direction of incoming velocity to the wing; (c) validation of the quasi-steady model used in this study in comparison to CFD results.
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Figure 3
(Color online) Morphology of three damselfly species. (a) Body length was found to be strongly correlated to the body mass; (b) the length of the wing increases directly with the length of the body; (c) the actual area of the wing is strongly correlated with the product of the wing length and the maximum wing chord for both fore and hindwings.
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Figure 4
(Color online) Damselfly body motion during an aerial yaw turn. (a) Sequence of images of the yaw turn of damselfly #3. The selected images were recorded by downward facing camera. The body orientation is shown at the beginning and end of each flapping stroke of the forewings. Radius of turn, r, is shown on the figure; (b) body kinematics of the representative turn of each species is shown versus normalized time which is the ratio of actual time to the maneuver duration. The maximum yaw velocity is indicated by a star symbol.
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Figure 5
(Color online) Wing kinematics of damselflies yaw turn. Kinematics of the fore and hind wings is shown in separate plots with solid and dashed lines, respectively. The inner and outer wings kinematics is indicated by red and blue. The instantaneous difference between Euler angles of the bilateral wings is shown in solid black. In this plot flap angle is positive when wing moves forward. The positive direction for deviation and pitch angles are moving up and pitching up, respectively. Gray shadings mark the downstrokes of the forewings.
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Figure 6
(Color online) Wing tip trajectory in the body fixed coordinate system for damselfly #2. (a) and (b) respectively show the perspective and back view of the wing tip trajectories. The fore and hind wings’ trajectories are shown by black and purple lines. The initial position of the wing tip is shown by a sphere. It is evident that the wing trajectory is not periodic and varies significantly during the yaw turn.
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Figure 7
(Color online) Correlation between the kinematics of bilateral wings. The half-stroke-averaged kinematics of the outer wings is plotted against the inner wings for all three flights. For clarity the data points form damselflies #1, #2 and #3 are indicated by black, purple and green, respectively. The linear regression line is shown in solid black. (a) The flapping amplitudes of the inner and outer wings were correlated, with inner wings having slightly higher amplitude than the outer wings. Similarly, the average magnitude of the deviation and the pitch angles of the inner wings were found to be higher than that of the outer wings; (b) the rates of change in all three Euler angles of the wings were bilaterally correlated, as well. The data also shows that the velocity of the inner wings is in general higher than that of the outer wings.
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Figure 8
(Color online) Aerodynamic yaw torque. The aerodynamic yaw torque generated by each wing (a) as well as the total generated torque (b) is shown for all three flights. Torque is non-dimensionalized by the damselfly’s body weight and body length. The peak value of the torque is higher at the first stage of the maneuver. The downstrokes of the forewings and hindwings are marked by gray and purple arrows, respectively. The sign of the yaw torque generated by the outer wings were reflected to achieve consistency in the data. Since the sign difference in the yaw torque generated by left and right wings is due to the respective location of the wing with respect to the center of mass, it is independent of the wing kinematics. Therefore, this adjustment does not affect the accuracy of our analysis.
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Figure 9
(Color online) Mechanism of torque generation in damselfly yaw turns. For clarity the data points form damselflies #1, #2 and #3 are indicated by black, purple and green, respectively. The linear regression line is shown in solid black. (a) The half-stroke-averaged yaw torque is plotted against the half-stroke averaged angle of attack of the wings for all three flights together. A strong correlation was found between these two variables which suggest that the damselflies adjust the wing angle of attack to regulate the yaw torque. The half-stroke-averaged wing angle of attack of the wing is plotted against the half-stroke-averaged geometric angle of attack of the wing (b) and the ratio of wing’s angular velocity about y and z axes, $ω_{y} / | ω_{z} |$ (c). The correlation between the angle of attack and $ω_{y} / | ω_{z} |$ was significantly stronger the correlation between this variable and the geometric angle of attack of the wing. These results imply that rather than manipulating the wing orientation, a damselfly alters the wing velocity to control the angle of attack.

Table 1 Morphological data for three damselfly species in this experiment. Values are reported as mean±SD.

Species	Sample size	Body mass (mg)	Body length (mm)	Forewing span (mm)	Hindwing span mm)	Forewing chord (mm)	Hindwing chord (mm)	Forewing area (mm²)	Hindwing area (mm²)
Hetaerina Americana	7	86±5	45±2	30±1	28±1	6±1	6±1	136±13	126±13
Argia Apicalis	4	22±6	35±1	23±1	23±1	4±0	4±0	65±2	65±3
Calopteryx Maculata	4	66±4	44±1	30±2	29±2	9±1	10±1	190±29	188±35

Table 2 Kinematics of damselflies’ body in yaw maneuver. The data for two consecutive turns of damselfly #3 is provided in two separate rows

Species	Turn amplitude (°)	Maneuver duration (s)	Maneuver duration (wingbeats)	Max yaw velocity (10³ °/s)	Avg turn radius (body length)	Average yaw velocity (°/wingbeat)
Species	Turn amplitude (°)	Maneuver duration (s)	Maneuver duration (wingbeats)	Max yaw velocity (10³ °/s)	Avg turn radius (body length)	Accel. phase	Decel. phase
Damselfly #1	160	0.185	5	1.2	0.17	25	31
Damselfly #2	170	0170	5	1.7	0.65	33	38
Damselfly #3	55	0140	2	0.5	0.90	28	32
Damselfly #3	110	0.170	3	0.8	0.43	25	44

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47.11.Fg	Finite element methods
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.55.nb	Capillary and thermocapillary flow

Quantification of wing and body kinematics in connection to torque generation during damselfly yaw turn

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