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First published online October 17, 2008
Journal of Experimental Biology 211, 3478-3489 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.017590
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Kinematics of slow turn maneuvering in the fruit bat Cynopterus brachyotis

José Iriarte-Díaz1,* and Sharon M. Swartz1,2

1 Department of Ecology and Evolutionary Biology, Brown University, Providence, RI 02912, USA
2 Division of Engineering, Brown University, Providence, RI 02912, USA


Figure 1
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  		Fig. 1. Diagram showing two types of turning mechanisms. (A) A banked turn, in which a bat rolls into the turn. By banking the body, a bat tilts the dorsal component of the net aerodynamic force (NAFdorsal) produced during downstroke towards the center of the turn; the lateral component of the NAFdorsal corresponds to the centripetal force (CF). (B) A crabbed turn, in which a bat yaws into the turn. The yawing of the body will reorient the forward component of the net aerodynamic force (NAFforward) produced during downstroke towards the center of the turn; the lateral component of the NAFforward corresponds to the centripetal force.

 

Figure 2
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  		Fig. 2. Superior view of turning portion of the flight corridor, indicating the position of the calibrated space and the high-speed cameras. Three cameras were placed on the floor pointing upward to capture the ventral side of the bat body and wing. As the bat passed through the calibrated volume, the position of several anatomical markers were tracked in the global coordinate system XgYgZg. Figure not to scale.

 

Figure 3
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  		Fig. 3. Schematic representation of marker positions on the ventral side of a bat. Prefixes R and L refer to right and left, and pvs, ch, wst, d3 and d5 to pelvis, chest, wrist, end of the third digit and end of the fifth digit, respectively.

 

Figure 4
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  		Fig. 4. Orientation and body angles used in the present study. The heading angle ({psi}) was defined as the angle between the projection of the longitudinal axis of the body on the horizontal plane (Xg–Yg) and the Xg axis; the elevation angle ({theta}) was defined as the angle between the longitudinal axis of the body and the horizontal plane (Xg–Yg); and the bank angle ({phi}) was defined as the angle between the line connecting both chest markers and the horizontal plane (Xg–Yg) (see inset). Body angles were defined as the deviation around the body-fixed axes in a body coordinate system. Arrows define the positive rotation direction of the body angles. Rotations about the body-centered XbYbZb axes were designated roll, pitch and yaw, respectively. XbYbZb, dynamic, body-based coordinate system, centered on the hip.

 

Figure 5
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  		Fig. 5. Schematic of the mass distribution model used to calculate the center of mass (CoM) of the bat. The thick, solid lines represent the modeled masses of the bone. The shaded triangle patches represent the base triangles of the skin mass model, and insets show detailed subdivisions of bone and skin masses (mi) and individual triangular elements (Ti) of the model.

 

Figure 6
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  		Fig. 6. Dorsal view of a flying bat showing the relationship between bearing angle (Formula) and heading angle ({psi}) in the global coordinate system for a bat at three time points during the turn. Bearing angle is calculated from the horizontal component of the body velocity vector (Vb,xy, orange arrows) obtained as the derivative of the position vector of the center of mass (CoM). The heading angle ({psi}) was defined as the angle between the projection of the longitudinal axis of the body on the horizontal plane (Xg–Yg) and the Xg axis.

 

Figure 7
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  		Fig. 7. Lateral (A) and dorsal view (B) of a flapping bat, indicating vertical ({gamma}v) and horizontal ({gamma}h) stroke plane angle in the body coordinate system. Dotted line corresponds to an actual trace of the right wingtip (d3 marker) throughout a representative stroke cycle.

 

Figure 8
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  		Fig. 8. Plot of the orientation angles (heading, bank and elevation; A) and body angles (yaw, pitch and roll; B) for a representative right turn. Bearing angle (orange line) was included to the orientation angles plot for comparison of body attitude with the changes in flight direction. Shaded bars correspond to downstroke periods.

 

Figure 9
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  		Fig. 9. Angle, angular velocities and angular accelerations for the orientations angles (heading, elevation and bank) (A–C) and the body angles (yaw, pitch and roll) (D–F). The width of the traces represents the means ± s.e.m. Shaded bars correspond to downstroke periods. Because bats performed both right and left turns, all turns were standardized to a right turn, and both heading and yaw angles started at zero degrees. Body angles were obtained as the cumulative sum of the body angular velocities obtained from the angular velocities of the Euler angles. For pitch and roll angles, the cumulative sum was added to the initial elevation and bank angle, respectively, for each trial.

 

Figure 10
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  		Fig. 10. Angle and angular velocity for heading (blue trace) and bearing(orange trace) throughout a stroke cycle measured in a global coordinate system. Shaded bars correspond to downstroke periods. The width of the traces represents the means ± s.e.m.

 

Figure 11
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  		Fig. 11. Speed of wingtip marker (A), wrist marker (B) in the body coordinate system, angle of attack (C) and wrist angle (D) over a standardized wingstroke. Red, blue and grey traces represent the inside and the outside wing and the difference between them, respectively. The width of the traces corresponds to the 95% CI (confidence interval). Shaded bars correspond to downstroke periods.

 

Figure 12
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  		Fig. 12. Relationship between heading angular velocity (A) and bank angle (B) with the bearing angular velocity.

 

Figure 13
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  		Fig. 13. Effect of bank angle and heading on the estimation of the expected centripetal acceleration due to the banked orientation of the body. (A) Posterior view of a bat performing a right turn. The net aerodynamic force (green vector) was estimated based on the bank angle ({phi}), the total vertical acceleration produced by the bat (ACoM,z), and assuming that the net aerodynamic force is produced perpendicular to the bank angle. (B) Superior view of a bat performing a right turn. Because the heading orientation of the body (blue line) does not necessarily match the direction of flight (orange vector), the centripetal acceleration due to the bank (Ac,bank) must be corrected by the difference between heading and bearing angle ({psi}–Formula). (C) Observed (Ac,total, red trace) and the estimated centripetal acceleration from bank (Ac,bank, blue trace) throughout a standardized wingstroke. Gray trace corresponds to the difference Ac,total–Ac,bank. The width of the traces represents the means ± 95% CI (confidence interval) (N=32) and the shaded bar corresponds to the downstroke period.

 

Figure 14
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  		Fig. 14. Distance of the wingtip to the midline of the body in the horizontal plane Xg–Yg, and red, blue and gray traces correspond to the inside (in) and the outside (out) wing and the difference between them (out–in), respectively. The width of the traces corresponds to the 95% CI (confidence interval). Shaded bar corresponds to the downstroke period.

 

Figure 15
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  		Fig. 15. Forward velocity profiles for the wingtip (A) and wrist markers (B) in a global coordinate system that has been rotated in the Zg axis to align the X-axis component to the bearing velocity vector and, thus, the forward velocity represents the marker velocity in the direction of flight. This rotation maintains the elevation and bank orientation of the body. The width of the traces represents the means ± 95% CI (confidence interval). Shaded bars correspond to downstroke periods. In, inside of the wing; out, outside of the wing; out–in, difference between outside and inside wing.

 

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© The Company of Biologists Ltd 2008