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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
Hydrodynamic performance of the minke whale (Balaenoptera acutorostrata) flipper
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
* Author for correspondence (e-mail: l.noelle.cooper{at}gmail.com)
Accepted 1 April 2008
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) depending on testing
speed. When the leading edge was rotated ventrally, loss in lift occurred
around –18° regardless of speed. Range of mobility in the
fresh limb was approximately 40% greater than the range of positive
lift-generating angles of attack predicted by wind tunnel data (+14°
). Video footage, photographs and observations of swimming, engulfment
feeding and gulping minke whales showed limb positions corresponding to low
drag in wind tunnel tests, and were therefore hydrodynamically efficient.
Flippers play an important role in orienting the body during feeding maneuvers
as they maintain trim of the body, an action that counters drag-induced torque
of the body during water and prey intake.
Key words: Cetacea, forelimb, flipper, wind tunnel, hydrodynamics, feeding, control surface, engulfment, lunge
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONReferences |
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;
Fish, 2004). Cetacean pectoral
flippers are composed of the bony elements plesiomorphic to those of tetrapods
(humerus, radius, ulna, carpals, metacarpals and digits), all encased in dense
connective tissues, creating a stiffened flipper
(Fig. 1). Flippers, once
deployed, manipulate flow around the body by altering angle of attack and
sweep angle to aid in steering, but do not oscillate and do not generate
propulsion or thrust during rectilinear locomotion.
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;
Lauder and Drucker, 2004;
Fish and Lauder, 2006) by
actively controlling fin curvature, displacement and fin area via
contractions of muscles that insert on the rays embedded within the fins
(Lauder, 2005;
Fish and Lauder, 2006). Shark
pectoral fins are stiff, but function to alter body pitch via changes
in the fin trailing edge (Lauder and
Drucker, 2004). Cetacean flippers are stiffened as in sharks, but
unlike sharks and rays, retain several bones within the flipper, manipulate
flow via coordinated contraction of muscles housed mostly within the
body wall, and little deformation has been reported in the flippers in most
cetaceans (Cooper et al.,
2007b).
Role of the cetacean flipper during feeding
Balaenopterid whales, including minke whales, employ engulfment feeding, in
which a whale will approach a patch of aggregated prey at a high speed and
engulf thousands of liters of water and prey, causing an enlarged ventral
throat pouch to distend (Lambertsen et
al., 1995; Goldbogen et al.,
2006,
2007). While the mouth closes,
water is pushed through the baleen
(Lambertsen et al., 1995),
forcing prey to be captured by fringes of baleen along the lingual sides of
baleen plates. Although the function of the balaenopterid feeding apparatus
has been the subject of anatomical (e.g.
Lambertsen et al., 1995;
Lambertsen and Hintz, 2004)
and experimental (e.g. Goldbogen et al.,
2006) studies, no experiments have tested flipper function
associated with gulping and engulfment feeding behaviors. This study aims to
expand understanding of the hydrodynamic performance of the flipper and its
role during feeding maneuvers.
Studies addressing the functional role of the balaenopterid forelimb have
either hypothesized the function based on anatomical observations (e.g.
Howell, 1930;
Benke, 1993;
Fish and Battle, 1995;
Woodward et al., 2006), or
placed synthetic models of flippers in wind tunnels to explore the behavior of
air over the surface of the model
(Miklosovic et al., 2004). No
tests in water have been conducted.
This study integrates anatomical, observational and experimental data to report on the hydrodynamic performance of the cambered minke whale (Balaenoptera acutorostrata Lacépède 1804) flipper, and addresses the functional role of the flipper during feeding maneuvers. A cast of a fresh minke whale flipper was constructed and used for wind tunnel testing of lift, drag and stall behavior. Objectives of this study were to identify the functional range of the minke whale forelimb, angles and speed at which the model stalls, and optimal angles of attack for hydrodynamic efficiency. These data were then integrated to address the hydrodynamic performance of the minke whale flipper during engulfment maneuvers.
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MATERIALS AND METHODS |
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) was
determined through manipulation of the flipper to the most extreme possible
angle. Digital images and videos documented this range of motion. No data were
gathered regarding negative angles of attack as the laboratory architecture
did not allow the scapula to be secured while manipulating the limb in
negative angles of attack.
Three dimensional architecture of the limb was observed both via
computed axial tomography (CT) scans and anatomical dissection. The entire
flipper was scanned using a GE Light Plus CT Scanner. CT images of the flipper
were then compiled and visualized with Amira 4.1 (Mercury Computer Systems,
Carlsbad, CA, USA; Fig. 1).
Detailed osteological and soft tissue descriptions of this flipper are
published elsewhere (Cooper et al.,
2007a; Cooper et al.,
2007b).
Locomotion observations
Observations of dwarf minke whale locomotion were based on the television
documentary `Mystery of the Minkes'
(Natural History New Zealand,
2002) and photos (Arnold et
al., 2005), which showed exceptional footage of the dwarf minke
whale swimming and engaging in non-feeding gulping behavior. Furthermore,
observations of surface-lunge feeding maneuvers supplemented these data
(Kot, 2005). Although it was
not possible to reliably gather quantitative data on forelimb position and
range of motion, qualitative data of forelimb position during swimming,
gliding and gulping behaviors were gathered. Also, based on still photos of
engulfing and feeding balaenopterid whales, further insight was added to
standard orientations of flippers during different engulfing maneuvers.
Wind tunnel experiments
A mold and cast (Fig. 2)
were made of the flipper of a fresh neonatal stranded specimen of minke whale
(Balaenoptera acutorostrata, COA no. 020717Ba;
Fig. 1). The rubber mold of the
flipper was made by wrapping the fresh limb in thin plastic and using a
mixture of RTV silicone and accelerator. A hard mother mold was made using
plaster (Silicast casting urethane; Silpak, Pomona, CA, USA) and Hydrocal
FGR-95 gypsum cement with 10 mm thick monofilament fiberglass. The flipper
cast was then created by filling the mold with plaster casting urethane
(Fig. 2). Before the urethane
dried, a metal rod was embedded along the longitudinal axis for attachment to
the yaw plate of the wind tunnel (Fig.
2). Remnants of skin folds in the axillary region of the cast were
sanded and then smoothed with aluminium tape. The model had a maximum
thickness of 6.5 cm, tip thickness of 0.3 cm, and total length of 70 cm
(Fig. 2). The average model
thickness was 3.5 cm, with an average chord length of 18.0 cm
(Fig. 2).
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), and the trailing edge of the fresh flipper had a thin
layer of skin that probably deformed with water flow.
Wind tunnel tests were performed in the low speed, single return, closed jet, continuous flow wind tunnel at the San Diego State University, Department of Aerospace Engineering and Engineering Mechanics. Airflow was generated by a 150HP electric motor driving a variable pitched, four-blade propeller. The test section was 1149 mm wide, 819 mm high and 1727 mm long. The model was mounted on a computer-controlled turntable with a 0.01 degree resolution.
To match swimming speeds and wind tunnel speeds, two Reynolds number
equations were used: one equation with values specific for air flow behavior,
and a second with values for sea water flow behavior. Experiments were
conducted at a range of Reynolds numbers
(Table 1;
Re=1.7x105–5.9x105), using
the equation Re=(
lU)/µ, where refers to fluid
density (air=1.29 kg m–3), l is the length of
the object in the direction of flow, in this case the chord length (0.129 m),
U is the swimming speed (m s–1), and µ is the
dynamic viscosity (Ns m–2)
(Reynolds, 1883;
Vogel, 1994).
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). The
model was rotated from –40 to +40° , in two degree increments
yielding a total of 40 angle measurements at each testing speed
(Fig. 3). A cruising minke
whale has been observed with a speed of 3.25 m s–1
(Blix and Folkow, 1995). A
total of six wind tunnel speeds/whale swimming speeds were examined during our
experiments (Table 1): 17.4 m
s–1/0.7 m s–1 (N=3, Re=171
002), 25.9 m s–1/1.7 m s–1 (N=3,
Re=254 100), 30.4 m s–1/2.3 m s–1
(N=2, Re=298 249), 34.4 m s–1/2.9 m
s–1 (N=3, Re=337 492), 45.6 m
s–1/5.1 m s–1 (N=4, Re=447
373), and 60.4 m s–1/8.9 m s–1
(N=3, Re=592 574). This testing range both exceeds and falls
well below reported swimming speed.
As with standard aero/hydrodynamic measurements, the flipper cast was
positioned with its base against the flat base of the wind tunnel
(Miklosovic et al., 2004),
which is functionally analogous to a wall. This configuration approximated the
junction between the flipper and the body of the whale which has a relatively
low curvature at the base chord of the flipper
(Stewart and Leatherwood,
1985). As the mid-chord of the flipper base was located at
approximately 0.26 of body length from the rostrum tip
(Stewart and Leatherwood,
1985), drag due to the interference between the body and flipper
was comparatively small (Hoerner,
1965). Interference drag is at a maximum when a wing is located at
the largest diameter of a fuselage, but is lowest toward the nose. The lift
produced by a wing on a fuselage has a slightly higher lift than a wing alone,
although a wing canted at an angle would exhibit a slightly lower lift
(Hoerner and Borst, 1985).
Lift and drag were measured for the minke whale flipper at various angles of
attack and therefore provided a reasonable approximation for the actual forces
on the flipper, and are consistent with previous wind tunnel experiments based
on cetacean flipper models (Miklosovic et
al., 2004).
Force and moment data, from the mounted flipper model in the wind tunnel, were gathered through a six-component, load cell, strain-gauge type balance system. The signals from the strain gauges in the balance, which typically produce in the order of 4.5 mV N–1, were amplified using Pacific Model 8655 transducer conditioning amplifiers. These amplifiers, which utilize a low-pass filter with a cut-off frequency of 10 Hz, were set to a gain of 200. Extensive calibration of the balance system demonstrated negligible interaction between the six components (lift, drag, and side force, yaw, pitch and roll) for single axis loadings up to the load limits. Interaction was less than 1% under any combination of loading up to 75% of the load limits. The amplified and filtered signals were then routed to, and acquired in, a standard personal computer equipped with a LabView AT-MIO-16E-2 data acquisition board. A LabView VI (virtual instrument) program, written especially for the San Diego State University low speed wind tunnel, converted the strain gauge signals to engineering units and stored them for subsequent analysis.
Drag and lift values depend on the object's size and speed relative to the
fluid's viscosity and density (Vogel,
1994). Therefore, lift (L) and drag (D) values
were expressed as dimensionless coefficients [coefficient of lift,
CL=(2L)/(ApU2)
and coefficient of drag,
CD=(2D)/(AsU2)
where Ap is the planar surface area of a flipper, and
As is the total area of a flipper] that are a function of
the Reynolds number (Reynolds,
1883; Vogel,
1994).
To visualize flow, tufts (air stream indicators) were attached via
smoothed aluminium tape to both the dorsal and ventral surfaces of the model.
Tufts allow identification of laminar or linear flow along the boundary layer,
turbulent flow along the boundary layer, and complete boundary layer
separation from the surface of the model. Visual identification the model
orientations at which the boundary layer separates was essential as it
indicated when flow interacts with outer flow, and is creating a broader wake
and increasing drag (Fish and Lauder,
2006). During turbulent flow, the boundary layer is still attached
to the surface of the model but is not linear. Complete boundary layer
separation occurs when air around the surface of the model is shedding
vortices. Digital photos and video recordings were used to examine the flow
behavior over the surface of the model at various combinations of speed and
angles of attack.
Resulting lift and drag data were then used in a full-body model of a minke
whale to estimate the magnitude of forces created by the flippers
versus those created by the body during engulfment maneuvers. Based
on illustrations from Stewart and Leatherwood
(Stewart and Leatherwood,
1985), the center of mass of a minke whale was located at 46% of
the body length, and the flippers were located well anterior to this at
approximately 27% of the body length (4.8 m). The drag created by an open
mouth was positioned at the centroid of the triangular lower jaw in frontal
view, and was calculated from the equation,
Drag=0.5ACdU2, where is the
density of sea water, A is the frontal area of the lower jaw (0.376
m2), Cd is the drag coefficient, based on a
hollow half sphere (Vogel,
1994), and U was the swimming speed of 2.3 m
s–1. The drag torque was calculated as the product of the
drag, lever arm (2.2 m; dashed blue line; distance from the point of
application of the drag to the center of mass), and sine of the angle between
the lever arm and horizontal line. The lift produced by the flippers was
calculated from the equation,
Lift=0.5AfClV2,
where Af is the combined planar area of the flippers
(0.184 m2) and Cl is the maximum lift
coefficient (1.5). The lift torque was calculated as the produce of the lift
and the lever arm (1.3 m; distance from flippers to center of mass).
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during passive manipulation in which only the
angles of attack were altered. Detailed anatomical descriptions of this
specimen are published elsewhere (Cooper et
al., 2007a; Cooper et al.,
2007b). Results of the three-dimensional (3D) visualization of the minke whale flipper (B. acutorostrata, COA no. 020717Ba) are shown in Fig. 1. These data show the flipper forms a hydrofoil with a rounded leading edge and a tapered trailing edge (Fig. 1C–E). The flipper is dorsoventrally flattened (Fig. 1B), and rather than displaying symmetry, each of the flipper cross sections illustrate the cambered nature of the flipper (Fig. 1C–E).
This elongated flipper is supported throughout its length by both cartilaginous and bony elements. The flipper protrudes out of the body wall at the level of the mid-humerus, and the leading edge is supported by an elongated radius and ulna that compose approximately 45% of the flipper length (Fig. 1A,B,E). The wrist consists of five bony carpal elements immersed in cartilage, and together these structures make up 9% of the flipper length (Fig. 1A). Along the trailing edge of the wrist is the cartilaginous anlage of the pisiform bone, which creates a trailing edge extension of the wrist (Fig. 1A). Both the metacarpals and phalanges are arranged into four digital rays that with cartilaginous joints that account for 41% of the total flipper length (Fig. 1A). The radius and ulna and the metacarpals and phalanges therefore account for approximately equal amounts of the flipper length. Rather than being broad and paddle-like, the flipper is narrow, with the greatest chord lengths corresponding to two trailing edge extensions of the flipper, the olecranon process of the ulna, and the pisiform cartilage of the wrist (Fig. 1A). The three digital rays closest to the leading edge are closely appressed with little interdigital space (Fig. 1A,D), and the radius, located nearest the leading edge, appears to be of a larger diameter than the caudally placed ulna (Fig. 1A,E).
Locomotion observations
Observations of flipper movements in swimming minke whales showed flippers
were typically held in one of three general positions. During vertical ascents
and descents, the flipper was typically held flush to the body wall, thus
increasing the streamlined nature of the body by reducing drag. While
swimming, or cruising, the minke whales held their flippers swept back at
approximately 45° and near zero angles of attack. During non-feeding
gulping maneuvers, the flipper was held perpendicular to the longitudinal axis
of the body, with a sweep angle near zero
(Arnold et al., 2005), and with
angles of attack near 0°. During gulps, the body moved forward
via propulsion from the tail, and as the mouth opened, the rostrum
was raised (Arnold et al.,
2005). The flippers were then rotated forward to approximately
0° sweep, and 0° . While the mouth was closing, flippers were
returned to the swept-back position associated with cruising and sometimes
held flush against the body wall.
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) for each testing speed and these raw
data were then averaged and plotted as the average CL
vs (Fig. 4),
and reported in Table 1. A near
linear relationship was found between CL and for a
total range of 32° at the slowest speed (17 m
s–1) and 26° at the highest speeds (46 and 60 m
s–1; Fig. 4).
This near linear slope of 0.11 for all speeds indicated flow was attached to
the model surface, and stall did not occur during those flow states
(Fig. 4). The
y-intercept (=0) of all trials occurred between approximately
0.4 and 0.6 CL (Fig.
4).
A substantial loss in lift indicates flow separation, or stall, along a
large part of the surface of the model. While testing in the range of positive
(raising the leading edge of the model) at 17 m s–1,
a drop in CL occurred most dramatically at +12° , with a
31% drop in CL (Fig.
4, Table 1). During
the 26, 30 and 34 m s–1 trials, between +12° and +14°
, there was a slight drop in CL (1% drop), and at
+16° , the CL reached a maximum at 1.49
(Fig. 4,
Table 1). At greater
than +16°, CL declined, indicating a separation of the
boundary layer over the dorsal surface of the model
(Fig. 4,
Table 1). The 45.6 m
s–1 trial showed an initial slight loss of
CL at 8° (Fig.
4, Table 1). This
initial loss in lift was followed by a plateau until +14° where
the lift gradually declined. The 60 m s–1 trial indicated an
initial drop in CL from 6–8° . At 12°
, the CL was constant until 16° , and
then gradually declined (Fig.
4, Table 1).
Contrary to the more abrupt losses in lift in the positive angles of
attack, all loss of lift along the negative angles of attack was gradual up to
–25° (Fig.
4). Beginning at –18° , testing speeds of
26–60 m s–1 showed a similar value of
CL (Fig.
4). Different experimental speeds could be distinguished by their
differing CL levels at each plateau with 17 m
s–1 having the lowest CL (–1.6;
Fig. 4) and 60 m
s–1 displaying the value closest to positive
CL (–1.2; Fig.
4). Within the negative range, data indicated distinct
CL values for 26, 30 and 34 m s–1. At 26
m s–1, the negative tail of the curve reached a plateau at
approximately –1.6 CL, compared to –1.56 for
30 m s–1, and –1.4 for 34 m s–1
(Fig. 4).
In all speed trials, there was a steady increase in drag at angles of
further away from 0°, and the lowest drag was found at low
positive angles of attack (Fig.
5). The angles for which the drag was lowest indicates the flipper
orientations that would be most hydrodynamically efficient at generating lift.
The lowest drag was found usually in a four degree range for each tested
speed, between 0° and +4°
(Fig. 5, Tables
1 and
2). However at speeds of 60 m
s–1, a narrower window of low drag was found between 0°
and +2° . At 17 m s–1 the least amount of drag was
found between +2° and +4° (CD=0.02). The
least amount of drag, at 26 m s–1, was found between +2°
(CD=0.04) and +4°
(CD=0.05; Fig.
5, Table 1).
Compared to other data, the minimum CD range at 30 m
s–1 was noted at a larger , and displayed the lowest
values at +2° (CD=–0.01) and +6°
(CD=–0.001). Both 34 m s–1
and 46 m s–1 showed a CD minimum of 0.04
at +2° . The minimum range of the average CD
was the most narrow for the 60 m s–1 trial, and spanned only
two degrees [0° (CD=0.059) to +2°
(CD=0.056); Fig.
5, Table 1]. Ratios
of CL to CD were calculated and the
higher the ratio, the more theoretically efficient the flipper would be at
generating lift, and the more efficient the limb orientation would be for
cruising. Data indicate the greatest efficiency at 0° at 26 m
s–1 (CL:CD of 641),
+2° at 34.4 m s–1
(CL:CD of 381), and +6° at
26 m s–1 (CL:CD of
148). The inflated ratio value at 0° , is a result of drag values
near zero. Negative drag values are theoretically impossible as this would
imply the flipper was being sucked forward, and these values may have been
caused by the tip of the model being close to the wind tunnel boundaries, thus
creating interference in the model and wind tunnel boundary layers.
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Tufts placed along both the dorsal and ventral surfaces of the model
identified areas of laminar and turbulent boundary layer flow and complete
separation of the boundary layer over the surface of the model
(Fig. 6). Laminar flow was
found along most of both surfaces of the model at 17 m s–1,
+10° (Fig. 6A), as
indicated by the near linear slope of the CL in the wind
tunnel data (Fig. 4). At
positive angles of attack beyond the near linear slope range of
CL, turbulent flow or complete separation should occur
mostly on the dorsal surface of the model. Tufts placed along the dorsal
surface of the model showed that flow separation began first along the
trailing edge of the flipper, and then spread to the base and tip, and finally
the entire dorsal surface indicating stall
(Fig. 6A–D). At positive
angles of attack, an ideal flipper model should retain laminar flow over the
entire ventral surface of the model. However in the axillary region, near the
ventral surface base, a small pocket of flow separation was found along the
trailing edge of the model at low speeds (17 m s–1 and 30 m
s–1; Fig.
6A,B). At higher speeds, flow separation occurred along the
trailing edge of most the model (46 m s–1 and 60 m
s–1; Fig.
6C,D).
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Modeling drag and lift forces on a feeding minke whale indicate that the lift torque generated by the flippers was slightly larger than the drag torque created by the open mouth (Fig. 7). The lift and lift coefficient of the flippers were found to be 747.0 N and 1.5, whereas the drag and drag coefficient of the lower jaw were 1449.1 N and 1.42. Similarly, the torque of the flippers (N m) was found to be 664.9 N m, whereas the torque of the lower jaw was found to be 579.8 N m.
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Besides the cross-sectional dimensions of the flipper, three other
characteristics are essential for creating a limb that acts as a hydrofoil:
the flipper needs to be long, stiff and webbed. Elongation increases area that
will manipulate flow around the body, and is achieved by increasing the number
of bones in the limb and changing limb allometry. Most mammals have retained
or reduced the plesiomorphic phalangeal count of 2/3/3/3/3, but cetaceans are
the only mammals that have increased the number of phalanges, a morphology
termed hyperphalangy (Fig.
1A,B) (for a review, see
Howell, 1930). By evolving
hyperphalangy, cetaceans change limb allometry by increasing manus length
relative to limb length. Minke whale digital rays account for about 40% of the
flipper length (Fig. 1A,B),
whereas in some dolphins (i.e. Risso's dolphin) the digital rays account for
65% of flipper length. Some mysticetes have also elongated the radius and ulna
(Fig. 1A,B), which can account
for approximately half of the flipper length (45% of the flipper length in the
minke whale), but most odontocetes have reduced the length of these bones.
Cetaceans reduced flipper deformation by evolving several stiffening
structures throughout the limb. Alterations to joint structure have greatly
reduced skeletal mobility throughout the limb. The elbow (or cubital) joint is
immobilized as bony constraints lock the joint, and the wrist is mostly
immobilized by closely appressed carpal elements that lack the ability to
glide relative to another (Fig.
1A). Surrounding the digits is a thick and dense layer of
connective tissue that minimizes movements of the digits, and this connective
tissue continues along the length of the flipper to stiffen the wrist, and
support the radius and ulna (Fig.
1). In some cases, the connective tissue layer alone is thicker
than the digits. By increasing limb stiffness, the flipper functions as a
hydrofoil in which flow is manipulated by active contractions of limb
musculature, but passive movements of the limb do not effect flow
(Fish and Lauder, 2006). This
flipper stiffness is in strong contrast to the highly flexible fins of some
fish. Fish fins do not act as hydrofoils as they readily deform due to both
active contractions of the fin musculature and deformations caused by fluid
loads (Fish and Lauder,
2006).
Unlike most mammals, cetaceans do not have digits that are anatomically separate from one another – they are webbed together in a single flipper (Fig. 1). By retaining tissues between the digits, a smooth contour is created along the chord of the flipper (the distance between the leading and trailing edges; Fig. 1). This smooth contour facilitates laminar flow and boundary layer adhesion to the surface of the flipper, and is therefore essential for lift generation.
The flipper is simply deployed as a stiff hydrofoil, rather than being used
as an oscillator to generate propulsion. The magnitude of lift and drag forces
on a given wing or flipper are affected by the spanwise and radial flow
pressure differences at the tip and those vortices that are being shed at the
tip (Ellington et al., 1996;
Birch and Dickinson, 2001;
Bandyopadhyay et al., 2008).
For flapping motions, such as in the case of the wings of insects and the
pectoral fins of some fishes, the spanwise flow helps to stabilize flow over
the lifting surface and maintain lift in unsteady conditions. In contrast to
this, the flippers of minke whales, when extended perpendicular to the
longitudinal axis of the body, would experience a comparatively steadier flow
and less spanwise flow. Indeed, the tapered planform shape of the flippers
would limit pressure differences at the flipper tip and decrease the magnitude
of tip vortices, which are associated with induced drag. van Dam
(van Dam, 1987) showed that a
tapered wing planform with crescent cross-sectional shape could reduce the
induced drag by 8.8% compared to a wing with an elliptical planform. Minimal
induced drag is fostered by a swept wing planform with a root chord (proximal
chord) greater than the chord at the tips giving a triangular shape
(Küchermann, 1953;
Ashenberg and Weihs, 1984).
This optimal shape approximates the planform of the minke whale flipper.
Taken together, it appears that the cetacean flipper is a complex structure in which several skeletal and soft tissue structures create a hydrofoil-shaped limb that is capable of generating lift and acting as a control surface to manipulate fluid flow around the body.
Efficacy of the model
Data gathered from wind tunnel testing of lift and drag parameters, and
stall behavior provided insight into the efficacy of the minke whale flipper
model. A total of six wind tunnel speeds/whale swimming speeds were examined
during our experiments (Table
1): 17.4 m s–1/0.7 m s–1
(N=3, Re=171002), 25.9 m s–1/1.7 m
s–1 (N=3, Re=254100), 30.4 m
s–1/2.3 m s–1 (N=2,
Re=298249), 34.4 m s–1/2.9 m s–1
(N=3, Re=337492), 45.6 m s–1/5.1 m
s–1 (N=4, Re=447373) and 60.4 m
s–1/8.9 m s–1 (N=3,
Re=592574). Stall, or the point in which the boundary layer along the
surface of the model sheds vortices, was abrupt at +12° at 17 m
s–1 (Fig. 4).
However, only partial stall was observed at high positive angles of attack for
the middle testing speeds (26, 30 and 34 m s–1) because
laminar flow was retained in the middle of the flipper dorsal surface (Figs
4,
6). At higher speeds (46 and 60
m s–1) flow visualization showed the entire dorsal surface of
the model had complete separation of the boundary layer
(Fig. 6C,D), indicating
complete stall. Contrary to this visual identification of stall
(Fig. 6C,D), averaged data from
the wind tunnel measurements indicated only a slight loss in lift over a broad
range of , suggesting incomplete flow separation
(Fig. 4). At negative angles of
attack, the ventral surface failed to have complete flow separation, and
therefore only reached partial stall (Fig.
6E–H). Near –18° for all tested speeds,
similar CL values were maintained over a broad range of
angles of attack (Fig. 4)
rather than a consistent loss of lift with decreasing angles of attack. In
this case, the observed tuft behavior (Fig.
6A–H) was consistent with measured flow behavior suggested
by coefficient of lift parameters (Fig.
4).
A possible explanation for the variation between flow data and observations could be that unexpected turbulent flow along the model surfaces obscured accurate readings. Because of this discrepancy, flow visualization was considered essential for accurately interpreting air flow behaviors suggested by the wind tunnel data, and also served as a means to hypothesize possible sources of measurement error. Visualizations (Fig. 6) showed that patches of turbulent flow were found on surfaces that would ideally have been completely laminar. The cast was made from a swept back, fresh and articulated flipper and scapula and to retain the full length of the leading edge, the axillary region had to be reconstructed, and this area of the model consistently shed vortices (Fig. 6E–G). Therefore, the axillary reconstruction may have caused perturbations in the data, but those discrepancies were isolated to the axillary region.
This is the first study to employ a biologically real cast of a flipper, rather than an idealized or known aerodynamic model. Although some perturbations were found in flow over the axillary region, flow over the model predicted general hydrodynamic principles (e.g. stall angles, lift-generating angles) that can be used to address the performance of the minke whale flipper. In an ideal study, replicas of actual flippers could be made based on three dimensional scans, but until these studies are undertaken, this study furthers our understanding of a flipper with a shape like that of an actual balaenopterid flipper.
Performance of the minke whale flipper
Results of the wind tunnel data taken together with locomotion observations
and tests of the range of motion provide a broad picture of the possible
functional attributes of the minke whale flipper. Unlike other marine mammals
that oscillate their flippers to generate propulsion [e.g. pinnipeds, otariids
(for a review, see Fish,
2002)], mysticetes deploy flippers into one of three general
positions (swept back, flush to the body wall and perpendicular to flow) and
alter the angle of the flippers from their stationary positions.
Balaenopterids engulf large amounts of water while feeding, creating a net
downward body torque. If this torque was not counteracted, the anterior aspect
of the body would pitch downward (ventrally). Whales counteract drag induced
by the engorged ventral pouch by several mechanisms. First, locomotion data
indicated one or both of the flippers was extended during ventral pouch
expansion. Extended flippers were held at low angles of attack, near 0°,
which is a hydrodynamically efficient posture corresponding to greatest lift
and least drag values (Figs 4,
5). Second, during pouch
expansion and forward motion, the palate was raised
(Arnold et al., 2005) and
experienced dorsally and posteriorly directed forces that probably
counteracted body torque. Third, flukes generate both thrust and lift as
whales accelerate into prey aggregations, and are probably the most effective
at countering body torque. Lastly, some whales arched the vertebral column
such that the caudal half of the body was relatively straight but the cranial
third of the body was raised to an angle of 15°
(Arnold et al., 2005), which
would also counteract drag-induced torque. However, field observations show
that engulfment can sometimes occur without this spinal movement. By altering
flipper and palate orientations, fluking, and sometimes arching the spine,
whales are probably able to maintain a positive body pitch, which would
facilitate the engulfment of water in the ventral pouch. These data are
significant, as feeding in minke whales requires the integration of multiple
body parts (i.e. feeding apparatus, body and palate orientation and flipper
position) in order to maintain body position during feeding maneuvers.
Previous studies have not hypothesized the functional role of the flipper
during these behaviors.
Although minke whales may prefer to hold flippers at low angles of attack
during engulfment maneuvers, manipulation of a fresh limb indicated a +27°
range of motion. However, experimental results indicated the
lift-generating angles of attack between –18° and +12° ,
and outside of this range drag exceeded lift (Figs
4,
5). Drag also plays an
important role in flipper function. Bottlenose dolphins (Tursiops
truncatus) slowed forward motion by pronating both flippers and
generating drag (Bloodworth and Marshall,
2005). If flippers are asymmetrically oriented, the body will turn
in the direction of the flipper creating the greatest drag. Surface feeding
minke whales extend one flipper perpendicular to flow while the other is held
flush against the body wall, creating a `pirouette' behavior. Therefore,
besides generating lift, cetaceans also orient flippers to induce drag and
slow forward motion and steer.
By comparing lift, drag and torque forces in a feeding minke whale model, results indicated that even the seemingly tiny flippers of a minke whale generated a slightly larger torque than the drag torque created by an open mouth (Fig. 7). These data imply that deployment of the flippers to a position extended perpendicular to body flow may in fact generate enough lift to counteract drag induced by the open mouth, and that the flippers can function to stabilize body position during feeding maneuvers.
Results of this analysis can be compared to a previous study of a
generalized whale flipper, and an idealized humpback whale (Megaptera
novaeangliae) flipper. A NACA 0200 airfoil with known aerodynamic
parameters, with a shape superficially similar to the minke whale flipper
model tested here, stalled near +12° for testing speeds from
17–34 m s–1
(Miklosovic et al., 2004),
which was consistent with the results of this study. A NACA 0200 with a
scalloped leading edge simulated leading edge tubercles in humpback whales
(Fish and Battle, 1995;
Miklosovic et al., 2004). The
scalloped flipper exhibited a 40% increase in the angle of stall compared to
both the NACA 0200 and the minke whale model. Humpback whale flippers appear
to be more hydrodynamically efficient at generating and maintaining lift.
Minke whales are the smallest balaenopterid mysticetes with body
proportions similar to all nine species of non-humpback balaenopterids
(Horwood, 1990). Minke whale
flippers are similar in shape and dimensions to all non-humpback
balaenopterids, and can be considered representative of the standard
balaenopterid flipper. Flippers of other balaenopterid taxa may display
similar hydrodynamic properties and stall behaviors.
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References |
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