West Chester University
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Biology Faculty Publications
Biology
4-2015
Estimation of shape of the sea lion for
hydrodynamic analysis. Response to 'Cambered
profile of a California sea lion's body'
Frank E. Fish
West Chester University of Pennsylvania, [email protected]
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Recommended Citation
Fish, F. E. (2015). Estimation of shape of the sea lion for hydrodynamic analysis. Response to 'Cambered profile of a California sea
lion's body'. Journal of Experimental Biology, 218(8), 1271-1272. http://dx.doi.org/10.1242/jeb.117572
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© 2015. Published by The Company of Biologists Ltd | The Journal of Experimental Biology (2015) 00, 1-3
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CORRESPONDENCE
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Cambered profile of a California sea lion’s body
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Anwar Ul-Haque1, *, Waqar Asrar1, Ashraf A. Omar2, Erwin Sulaeman1 and J. S. Mohamed Ali1
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Department of Mechanical Engineering, International Islamic University Malaysia (IIUM), Kuala Lumpur 50728, Malaysia.
Department of Aeronautical Engineering, University of Tripoli, P.O. Box 13154, Tripoli, Libya.
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*Author for correspondence ([email protected])
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More than 100 research articles have referred to an experimental
study by Feldkamp (1987) on the California sea lion, which
mentions that its body resembles a symmetric airfoil NACA 66018.
We believe that perhaps an over simplification has been made in this
paper. This conclusion may be arrived at by shifting the leading and
trailing edges of the contour of the sea lion in order to move the chord
line in the upward direction, such that the maximum thickness of the
selected airfoil is close to that of a sea lion’s body. It is pertinent to
highlight that most of the research articles on different species of sea
lions (Cheneval, 2005; Suzuki et al., 2014; Fish, 1998; Stelle et al.,
2000) are related to its hydrodynamic drag and lift generated by its
flippers. However, the effect of assuming resemblance to a
symmetric airfoil reduces the additional hydrodynamic lift and the
induced drag generated by the body.
If one closely observes the sketch used by Feldkamp (1987), it
is obvious that a sea lion’s upper and lower contours are different
(Fig. 1A); this feature is unique to any cambered airfoil. In order
to elaborate it further; this sketch was used as a baseline sketch
and graphically digitized for unit length (L) by defining the
maximum thickness (d ) equal to 18% of unit length (Fig. 1B). The
upper and lower contour lines were generated by using a 4th order
polynomial fit and the camber line is also plotted to show the
difference between a symmetric and a cambered airfoil. Feldkamp
(1987) did not specifically mention the maximum diameter (d ) of
the body. The only known information is the lateral view of the
body resembling a NACA 66-018 airfoil. Hence the maximum
thicknesses of 18% of the chord length and fineness ratio equal to
5.5, Fig. 1A are used in the present work for defining a suitable
cambered airfoil.
In order to select a cambered airfoil that best fits the shape of the
sea lion at its nose, upper and lower contours and meet the
requirements of maximum thickness and its location, RONCZ 1082
and FX S 03-182 were randomly chosen. These are two standard
cambered airfoils which have maximum thickness of 18% at 40%
chord and 18.2% at 40.2% chord, respectively (Airfoil Tools, 2014).
Once the profile of these airfoils were plotted on the sketch used
by Feldkamp (1987), it was observed that the lateral view of the
California sea lion’s body cannot fully resemble any engineering
application airfoil (Fig. 1C). Although its body is streamlined, the
lower contour of its body is somewhat bulkier, whereas the upper is
elongated.
Unfortunately, complete geometric details of the sea lion
required to compare with different airfoils are still missing in the
open literature. However because of the difference between the
upper and lower contour in lateral view, the body of the sea lion
partially resembles a cambered or un-symmetric airfoil. The
same also holds true for a sea lion lying on the ground, as
observed at Zoo Negara, Kuala Lumpur, Malaysia (Fig. 1D).
Also, it is well known that most of the terrestrial vertebrates have
a vaulted dorsum which makes the body appear in the lateral
view as a cambered airfoil. Based on the discussion above, it may
be concluded that the sea lion’s body resembles a cambered
airfoil.
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Acknowledgements
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The support of the Ministry of Science, Technology and Innovation (MOSTI),
Malaysia, under the grant 06-01-08-SF0189 is gratefully acknowledged. Authors are
grateful to the management of Zoo Negara, Kuala Lumpur for providing the
opportunity to closely observe the shape of the California sea lion.
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Fig. 1. Sketches and images of the California sea lion body shape compared with airfoil cross-sections. (A) Sketch used by Feldkamp (1987) in which the
dotted line shows the profile of airfoil NACA 66018. (B) Sketch drawn to show the camber in lateral view of the sea lion (black data points and plotted black line).
Red and blue lines indicate………., respectively. (C) Geometric comparison of sea lion outline sketch (red) with NACA 66018 and cambered airfoils.
(D) Pictorial view of California sea lion, taken in Zoo Negara, Kuala Lumpur.
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CORRESPONDENCE
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References
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Airfoil Tools (2014). Available at: http://airfoiltools.com
Cheneval, O. (2005). Biomechanics of turning manoeuvres in Steller sea lions. PhD
Thesis, University of British Columbia, Vancouver, BC.
Feldkamp, S. D. (1987). Swimming in the California sea lion: morphometrics, drag
and energetics. J. Exp. Biol. 131, 117-135.
Fish, F. (1998). Imaginative solutions by marine organisms for drag reduction.
In: Proceedings of the International Symposium on Seawater Drag Reduction,
pp. 443-450. Newport, Rhode Island.
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The Journal of Experimental Biology (2015) 00, 1-3
Hertel, H. (1966). Structure-Form-Movement. New York: Reinhold Publishing
Corp.
Stelle, L. L., Blake, R. W. and Trites, A. W. (2000). Hydrodynamic drag in steller sea
lions (Eumetopias jubatus). J. Exp. Biol. 203, 1915-1923.
Suzuki, I., Sato, K., Fahlman, A., Naito, Y., Miyazaki, N. and Trites, A. W. (2014).
Drag, but not buoyancy, affects swim speed in captive Steller sea lions. Biol. Open
3, 379-386.
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Estimation of shape of the sea lion for hydrodynamic analysis.
Response to ‘Cambered profile of a California sea lion’s body’
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Frank E. Fish
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Department of Biology, West Chester University, West Chester, PA 19383, USA.
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[email protected]
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To understand the complexity of aero- and hydrodynamic effects
related to the morphology of animals, the shape of the organism is
often simplified. Researchers used engineered foils to approximate
the geometry of aquatic animals (Hertel, 1966; Aleyev, 1977;
Feldkamp, 1987; Fish and Battle, 1995; Weber et al., 2009).
The advantage of this substitution is that the performance (lift,
drag, moment) of these idealized shapes was well characterized
and documented. Using these quantitative data, the design of
different animal body shapes in a flow can be quantitatively
assessed. The results of this first-order analysis were used to
examine morphological differences, propulsive efficiency and the
energetics of locomotion. A potential problem with this approach is
how an appropriate engineered foil is selected to mimic the real
animal. The choice was based on a catalog of known foils (Abbott
and von Doenhoff, 1959; Airfoil Tools, 2014). The appropriate foil
to mimic an animal is dependent on similarities of shape parameters
including fineness ratio (length/maximum thickness), relative
position of maximum thickness, and camber. However, the
choice was still subjective as the geometry of the animal and that
of the foil section were not an exact match. In effect, it is the
equivalent of placing a square peg in a round hole.
Despite its relatively smooth contours, the California sea lion
(Zalophus californianus) has a complex geometry. Feldkamp
(1987) performed the first hydrodynamic analysis of the sea lion.
His analysis simplified the shape of the animal by considering it
to be equivalent to a streamlined body of revolution with a NACA
66-018 profile. The NACA profile, like the sea lion, had a fineness
ratio of 5.5 and maximum diameter of 40% of the body length.
Comparison of the sea lion’s shape with the streamlined spindle
indicated that the drag for the animal was lower due to differences in
flow structure.
Anwar Ul-Haque et al. (2015) call into question Feldkamp’s
(1987) use of a symmetrical profile as an equivalent to the shape of
the sea lion. For Ul-Haque and his colleagues, the profile of the sea
lion is more similar to cambered airfoils. Indeed, the profile of sea
lions gliding in water displays an asymmetry in the sagittal plane
(Feldkamp, 1987). In general, mammals have asymmetrical profiles
due to the distribution of body mass, prominence of the thoracic
trunk and curvature of the spine. The asymmetry of the sea lion is
even more exaggerated when the animal is lying down on solid
ground (Ul-Haque et al., 2015). For these reasons Ul-Haque et al.
(2015) argued that the profile of the sea lion in water was better
described by cambered airfoils, RONCZ 1082 and FX S 03-182
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(Airfoil Tools, 2014). These foils have similar dimensions to the sea
lion as described by Feldkamp (1987).
Although Ul-Haque et al. (2015) provided more realistic shapes
as a proxy for the geometry of the sea lion, their choice was still as
subjective as that of Feldkamp (1987). The cambered foil designs
approximated the midsection of the sea lion, but were dissimilar to
the anterior and posterior portions of the animal. The pointed
rostrum, tapering neck and expanded hind flippers are not emulated
in the design of the foil sections. Furthermore, the profiles only
describe a two-dimensional shape and do not consider the threedimension aspects of the animal. It is the very shape of the sea lion
that best examines the hydrodynamic implications of that specific
morphology. Previously, modeling the exact shape of a biologically
complex design with any fidelity was not possible. Airfoil sections
that closely resembled an organism therefore were used as
acceptable alternatives. More recently, the use of computational
geometry, digital photography, computed tomography scanning and
three-dimensional scanning allows the reconstruction of the surface
geometry of highly complex shapes. This digital reconstruction can
be used with computational fluid dynamic programs (e.g. panel
code, RANS, LES) to examine the flow structure or to use rapid
prototyping, 3D printers to create physical models that can be testing
in wind and water tunnels. Such modeling procedures provide more
accurate estimates of hydrodynamic parameters. A foil section with
a similar geometry to the organism can still be used as a baseline for
comparison.
But what is the importance of camber for the body of the sea lion?
The major criticism by Ul-Haque and his colleagues was that
Feldkamp (1987) did not use a cambered profile to compare with the
sea lion. However, the correspondence by Ul-Haque et al. (2015)
failed to actually consider the hydrodynamic implications of
cambering. Camber on a wing increases the lift generated. For the
sea lion, an increase in lift on the body could aid in surfacing when
negatively buoyant or decrease the rate of sinking when gliding
underwater. However, camber can also change the drag on the body.
Feldkamp (1987) found that the symmetrical NACA 66-018 foil had
a drag coefficient that was 1.18 times the drag coefficient calculated
for a gliding sea lion. The drag coefficients for the camber foils,
RONCZ 1082 and FX S 03-182, are 1.89- and 1.79-times greater
than for the sea lion, respectively (Airfoil Tools, 2014). The drag
coefficients for the cambered profiles were measured at a Reynolds
number (1×106), which was slightly lower than values for the sea
lion (2.03×106–2.87×106). The implication of the difference in drag
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CORRESPONDENCE
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coefficients is that there is still an imperfect match between the
animal and the engineered shapes.
While it is instructive to match the shape of biological forms to
engineered designs as a first-order approximation of performance,
tools are now available to more precisely copy and measure the
intricacies of biological design. As a result of past limitations in
replicating anatomical features, the physics of how biology worked
relied on simplified engineered models. Understanding of
complexity and performance attributes of morphology can now be
more directly addressed. As a result, new engineering concepts are
being developed from the integration of biological capabilities and
designs with existing technologies (Bar-Cohen, 2012).
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Acknowledgements
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I would like express my gratitude to John Beneski and Anthony Nicastro for their
helpful comments on the manuscript.
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The Journal of Experimental Biology (2015) 00, 1-3
References
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Abbott, I. H. and von Doenhoff, A. E. (1959). Theory of Wing Sections. New York:
Dover.
Airfoil Tools (2014). Available at: http://airfoiltools.com
Aleyev, Y. G. (1977). Nekton. The Hague: Junk.
Ul-Haque, A., Asrar, W., Omar, A. A., Sulaeman, E. and Ali, J. S. M. (2014).
Cambered profile of a California sea lion’s body. J. Exp. Biol. 218, xxx-xxx.
Bar-Cohen, Y. (2012). Biomimetics: Nature-Based Innovation. Boca Raton, FL:
CRC.
Feldkamp, S. D. (1987). Swimming in the California sea lion: morphometrics, drag
and energetics. J. Exp. Biol. 131, 117-135.
Fish, F. E. and Battle, J. M. (1995). Hydrodynamic design of the humpback whale
flipper. J. Morphol. 225, 51-60.
Hertel, H. (1966). Structure, Form, Movement. New York: Reinhold.
Smith, H. C. (1992). Illustrated Guide to Aerodynamics. Blue Ridge Summit, PA:
McGraw-Hill.
Weber, P. W., Murray, M., Howle, L. E. and Fish, F. E. (2009). Comparison of real
and idealized cetacean flippers. Bioinspir. Biomim. 4, 046001.
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