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First published online May 30, 2008
Journal of Experimental Biology 211, 1859-1867 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.014134
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Hydrodynamic performance of the minke whale (Balaenoptera acutorostrata) flipper

Lisa Noelle Cooper1,2,*, Nils Sedano3, Stig Johansson4, Bryan May5, Joey D. Brown6, Casey M. Holliday7, Brian W. Kot8 and Frank E. Fish9

1 Department of Anatomy, Northeastern Ohio Universities College of Medicine, Rootstown, OH 44201, USA
2 School of Biomedical Sciences, Kent State University, Kent, OH 44242, USA
3 Air Force Research Laboratory, Liquid Rocket Engines Branch, 4 Draco Drive, Edwards Air Force Base, CA 93524, USA
4 Department of Aerospace Engineering and Engineering Mechanics, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182, USA
5 2217 Burrough Street, Unit #1, San Diego, CA 92111, USA
6 NASA Jet Propulsion Laboratory, 4800 Oak Grove Drive M/S T1723-118, Pasadena, CA 91109, USA
7 Department of Anatomy and Pathology, Joan C. Edwards School of Medicine, 1542 Spring Valley Drive, Huntington, WV 25704, USA
8 Department of Ecology and Evolutionary Biology, University of California, Los Angeles, Box 1606, 621 Charles E. Young Drive South, Los Angeles, CA 90095-1606, USA
9 Department of Biology, West Chester University, 750 S. Church Street, West Chester, PA 19383, USA


Figure 1
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  		Fig. 1. Minke whale (Balaenoptera acutorostrata) flipper in (A) dorsal view and (B) leading edge view. Bones colored red, cartilage colored blue. Dotted lines indicate planes of section. (C–E) Flipper cross-sections along the (C) distal end of the flipper, (D) metacarpals and (E) distal radius and ulna. The cambered nature of the flipper is shown in D and E as the ventral surface of the flipper is more convex than the dorsal surface. The tapered trailing edge of the flipper was partially deformed during packaging for CT scanning, but normally would be in line with the chord axis. c, carpals; ct, dense connective tissue; h, humerus; mc, metacarpals; ol, olecranon process of the ulna; ph, phalanges; ps, cartilaginous anlage of the pisiform bone; r, radius; s, scapula; u, ulna. Scale bar, 5 cm.

 

Figure 2
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  		Fig. 2. Minke whale (Balaenoptera acutorostrata) flipper model, cast from a fresh flipper. After removal of skin folds from the model, aluminium tape was used to smooth the base of the model. This model was used for wind tunnel testing of lift, drag and stall behaviors. (A) Dorsal view, (B) ventral view. Scale bar, 10 cm.

 

Figure 3
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  		Fig. 3. Orientation of the flipper model in the wind tunnel as seen from above. Data were collected every 2° as the model was rotated between +40 and –40 angle of attack ({alpha}).

 

Figure 4
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  		Fig. 4. Averaged lift data for the minke whale flipper model. Averaged wind tunnel measurements of the lift coefficient, CL, shown as a function of the angle of attack, {alpha}, on the x-axis at 17 m s–1 (yellow), 26 m s–1 (pink), 30 m s–1 (green), 34 m s–1 (light blue), 46 m s–1 (indigo) and 60 m s–1 (black).

 

Figure 5
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  		Fig. 5. Averaged drag data for the minke whale flipper model. Averaged wind tunnel measurements of the drag coefficient, CD, shown as a function of the angle of attack, {alpha}, on the x-axis at 17 m s–1 (yellow), 26 m s–1 (pink), 30 m s–1 (green), 34 m s–1 (light blue), 46 m s–1 (indigo) and 60 m s–1 (black).

 

Figure 6
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  		Fig. 6. Air flow behavior over the model based on movements of tufts (air stream indicators) attached to the surface of the model during wind tunnel testing. The model is outlined in black, with areas of laminar flow in white, turbulent flow in gray and complete boundary layer separation in black. (A) Flow behavior at +10° {alpha} at 17 m s–1, (B) +12° {alpha} at 30 m s–1, (C) +12° {alpha} at 46 m s–1, (D) +14° {alpha} at 60 m s–1, (E) –16° {alpha} at 17 m s–1, (F) –18° {alpha} at 26 m s–1, (G) –22° {alpha} at 34 m s–1 and (H) –18° {alpha} at 60 m s–1.

 

Figure 7
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  		Fig. 7. Model of forces (drag, lift) resulting in the development of torque to stabilize a feeding minke whale. The features shown are: the center of mass of the whale (blue circle); drag (straight black arrow) from the open mouth, which is positioned at the centroid of triangular lower jaw in frontal view; drag torque (curved black arrow); drag lever arm (dashed blue line); and lift torque (curved red arrow). The lift torque was found to be slightly larger than the drag torque created by the open mouth.

 

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© The Company of Biologists Ltd 2008