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First published online January 31, 2006
Journal of Experimental Biology 209, 590-598 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02034

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Dynamics of the aerial maneuvers of spinner dolphins

Frank E. Fish^1,*, Anthony J. Nicastro² and Daniel Weihs³

¹ Department of Biology
² Department of Physics, West Chester University, West Chester, PA 19383, USA
³ Faculty of Aerospace Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel

View larger version (11K): [in a new window]   Fig. 1. Illustration of the method by which the moment of inertia of a control appendage is calculated. This figure shows an example using the dorsal fin. The vertical z-axis represents the axis of rotation, which runs longitudinally through the center of the dolphin. The horizontal R-axis measures the distance from the axis of rotation. In this example for the model dorsal fin, an isosceles triangular shape is adopted whose height is 0.16 m and base is 0.42 m in length, and is 0.15 m from the axis of rotation. The equations of the canted edges of the dorsal fin are indicated. For our calculations, the area mass density of the control surfaces was taken to be 30 kg m-2 (F. E. Fish, unpublished data).

View larger version (10K): [in a new window]   Fig. 2. Regression of the spin index against the number of aerial spins by spinner dolphins. The regression line is described by the equation: spin index=2.00+0.18 aerial spins.

View larger version (23K): [in a new window]   Fig. 3. Relationship between the angular speed (A) while corkscrewing necessary to execute various numbers of complete spins (N) over a range of swimming speeds (vs). The dotted diagonal lines indicate a realistic approximation of the spinning performance of the dolphin, where the angular speed is directly proportional to the swim speed (i.e. A=Rvs). The black dotted line is based on the observation of spinning rate from Lagenorhynchus obliquidens of R=1.5 rad m-1. The red dotted line is for R=3 rad m-1 in order to achieve seven aerial spins, which is the maximum number of spins observed for Stenella longirostris (Norris et al., 1994).

View larger version (26K): [in a new window]   Fig. 4. Diagram summarizing the four stages of a spinning leap. (A) Animal is completely submerged while corkscrewing, (B) pectoral fins emerge, (C) the dorsal fin emerges, and (D) the flukes emerge and the animal is freely spinning while airborne. The relationship is shown between rotation speed of the dolphin body and resistive (red) and drive (blue) torques developed underwater. Arrowheads indicate the direction of the opposing torques. The surface of the water is indicated by the light blue line and the magnitude of the rotational speed by the size of the green ovals.

View larger version (67K): [in a new window]   Fig. 5. Time sequence of photographs from video of the underwater corkscrewing motion of a Pacific striped dolphin (Lagenorhynchus obliquidens). The corkscrewing motion is characterized by a balance of the anterior drive torque at the pectoral flippers and the posterior drive torque produced at the flukes. Any anterior-posterior imbalance would generate a systematic, continual torsion of the anterior half with respect to the posterior half (Dynamic Balance Condition 2). This torsion would be indicated by a helical twisting in the dorsal/ventral line of coloration discontinuity. This sequence of images of the corkscrewing dolphin shows no discernable torsion in the body. This orientation demonstrates the balance in torques that the animal achieves in order to execute corkscrewing motion at a uniform rotational rate. A uniform rate of rotation around the longitudinal axis itself is indicative of a balance of resistive torques and drive torques (Dynamic Balance Condition 1). Image 6 shows the dorsal fin canted due to the resistive torque in rotational motion.