Aquatic turning performance by the whirligig beetle: constraints on maneuverability by a rigid biological system
1 Department of Biology, West Chester University, West Chester, PA 19383,
USA
2 Department of Physics, West Chester University, West Chester, PA 19383,
USA
* Author for correspondence (e-mail: ffish{at}wcupa.edu)
Accepted 24 February 2003
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Summary |
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Key words: whirligig beetle, Dineutes, maneuverability, turning rate, flexibility
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Introduction |
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Arthropods have bodies constrained by a cuticle exoskeleton. Despite this
perceived disadvantage, these animals are able to execute rapid maneuvers with
higher efficiency than elicited by flexible vertebrates
(Webb, 1979).
The body form of aquatic insects exhibits variation that is associated with
a compromise between maneuverability and speed
(Nachtigall, 1974;
Ribera et al., 1997
). The
flexible body of damsel-fly larvae permits these insects to produce
rapid-flexure maneuvers similar kinematically and hydrodynamically to the
C-starts of fish (Brackenbury,
2002
). These insects, like other aquatic larvae, are elongate with
multiple flexion joints along the abdomen and no constraining wings or elytra,
permitting extensive bending (Nachtigall,
1974
; Brackenbury,
2002
).
Whirligig beetles (Coleoptera: Gyrinidae) have a fixed exoskeleton
thatrenders the body rigid and firm
(Nachtigall, 1974). The
majority of the dorsum is composed of the paired elytra, which flex only at
the anterior jointwith the thorax. The body has an oval design that is
considered unstable and extremely maneuverable both at and below the water
surface. The beetle propel themselves by drag-based strokes of the paddle-like
middle and hind legs (Bendele,
1986
). High-speed turning in tight circles is a
characteristicbehavior of whirligig beetles. These beetles turn to capture
prey, avoidpredators and perform territorial displays
(Humphries and Driver, 1967
;
Newhouse and Aiken, 1986
;
Fitzgerald, 1987
). Typical
circular turns have a radius of less than twice the length of the beetle
(Fitzgerald, 1987
). The turns
are so tight that the beetle appears to be rotating with an axis extending
vertically through the body.
The ability of beetles to turn at high speed suggests that maneuverability is not constrained by a rigid body. To investigate the maneuvering performance by whirligig beetles, high-speed videography was used to quantify the spatial (i.e. radius) and rate (i.e. angular velocity) characteristics of turning. Comparisons were made with available data from the literature onturning performance by animals with flexible and rigid bodies.
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Materials and methods |
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Beetles were examined individually in a test arena. The arena was constructed from a 46 mm section of white PVC pipe with an internal diameter of 115 mm. The floor of the arena was constructed from clear acrylic plastic. Tapwater filled the arena to a depth of approximately 30 mm. Water temperature was 22°C. Swimming trials for each beetle lasted no longer than 2 min.
Data analysis
Beetles were videotaped at 500 frames s1 and 1000 frames
s1 with a Kineview high speed video system (Model 1256P;
United Technologies Adaptive, Optics Associates, Cambridge, MA, USA) equipped
with a Fujinon-TV zoom lens (1:1.2/12.575; F=5.6; Fuji Photo Optical
Co., Saitama, Japan) and videorecorder (Panasonic SVHS AG-7400). The
resolution of the camera was 640 pixelsx 480 pixels. The camera was
positioned approximately 0.2 m below the floor of the swimming arena. A
plastic 65 mm scale was floated on the water surface and videotaped prior to
the swimming trials. Lighting was supplied with a single 1000 W halogen
photographic light (Model 750-SG; Smith-Victor Corp., Griffith, IN, USA).
Video records were analyzed frame-by-frame with a video recorder (Panasonic
AG-7300). Only those records in which the animal's body remained within a
horizontal plane through the turn (i.e. no change in depth during swimming
sequence) were used. The sequential positions of the leading edge of the head
were recorded onto transparencies from the video monitor (Panasonic
CTJ-2042R). The center of rotation of the turn was determined
geometrically(Youm et al.,
1978). Turning radius, R, and mean speed, U,
were measured in m and m s1, respectively. Turns measured at
theleading edge of the beetle were assumed to be equivalent to turns
trackedatthe center of mass because of the rigid body. For comparison with the
turning performance by other animals, relative values of R and
U were calculated by dividing by L. Centripetal
acceleration, ac, as a multiple of gravitational
acceleration (g=9.8 m s2) was computed
according to:
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To examine the maximal turning performance by the beetles, data were
expressed as maximum and minimum values, means ± 1 S. D. and the means
of the extreme 20% of values (i.e. minimum radius, maximum turn rate). Choice
of the extreme 20% of values was considered arbitrary but was used previously
for comparisons of turning performance
(Webb, 1983;
Gerstner, 1999
).Statistical
comparisons by t-test were made using Data Desk version 3.0, and
regression equations and correlation coefficients were computed using Cricket
Graph version 1.3 software. Results were considered significantat the
=0.05 level.
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Results |
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Swimming patterns
Whirligig beetles performed spontaneous rapid turning maneuvers in the test
arena. A total of 119 turns were analyzed. Beetles swimming at the surface
accounted for 86.5% of all turns. In one case, turning was performed
underwater while the beetle had rolled 90° so that its venter was tilted
into the turn, but the animal remained in the horizontal plane. In many cases,
the turns were made as circles or as continuously decreasing spirals
(Fig. 1). Such circles and
spirals could be maintained for approximately 35 cycles. All curved
trajectories by the beetles were executed as powered turns, whereby
thrust-generating actions were continuous throughout the maneuver. Generally,
asymmetrical rowing of the midlegs and hindlegs on the outboard side (i.e. the
side facing away from the center of the turn) of the beetle powered the
maneuver. Both contralateral sets of legs were observed to stroke through the
turn. However, the outboard legs completed the power phase of the stroke cycle
more rapidly than the inboard legs. In addition, turns were effected when the
foreleg on the inboard side was extended. The foreleg acted as a brake and
allowed the beetle to pivot through the turn.
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Turns also were observed by winged-swimming
(Fig. 2). Winged-swimming was
performed by sculling using a single wing
(Fig. 2). This means of turning
was initiated by abduction (i.e. movement away from the midline of the body)
of the elytra on the inboard side (i.e. side facing the center of the turn) of
the beetle to a position perpendicular to the longitudinal body. Asthe elytra
was abducted, the underlying wing was unfolded to its full span.The elytra on
the outboard side was only slightly abducted and its underlying wing was never
unfolded and deployed. The inboard wing was oscillated inthe space between the
body and elytra at a frequency of 47.14±3.21 Hz. The distal apical half
of the inboard wing acted as if jointed like a two-way hinge to the proximal
part of the wing (Fig. 3). This
joint midway alongthe wing was believed to correspond with the folding pattern
of the wing (Wooton, 1981,
1992
). Oscillations of the
wing were synchronized with turningmovements. Throughout the turn, the body
showed a rotational oscillation around its center of mass. The wing was
collapsed as the elytra was adducted at the end of the turn. The beetle was
capable of moving in complete circles during winged-swimming.
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Turning performance
Summary data on turning performance of the whirligig beetles, which
wasmeasured at the beetle's leading edge, are presented in
Table 1. Turning bywinged
propulsion was not significantly different (t-test;
d.f.=117;P>0.05) from legged propulsion for any variable of
turning performance. Data for winged-swimming and legged propulsion were
combined. Swimmingspeeds varied from 0.06 m s1 to 0.55 m
s1 with a mean of 0.22±0.09 m s1.
This range represented lengthspecific speeds of 4.744.5 L
s1. Turning radius was weakly associated (r=0.336;
d.f.=117; P<0.05) with swimming velocity
(Fig. 4) for all data according
to the equation:
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Discussion |
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Territorial behaviors, characteristic of each sex of whirligig beetle, use
turning maneuvers. Spurts are typical of male whirligig beetles
(Fitzgerald, 1987). A spurt is
a rapid maneuver in which the beetle accelerates quickly, turns abruptly at an
acute angle and then drifts. Females more commonly use whirls, which are
defined by large circular or spiral trajectories.Extremely tight circular
paths (<2 L), known as pivots, are used byboth males and females
in territorial displays (Fitzgerald,
1987
).
Typical turning maneuvers in whirligig beetles were shown to be poweredby
asymmetrical paddling of the paddle-like legs. The middle leg can paddlewith a
frequency of up to 25 Hz and the hind legs stroke twice as fast
(Bendele, 1986). The water
beetles Acilius and Dytiscus similarlysteer with
asymmetrical paddling (Nachtigall,
1974
). Acilius turns with hind legs swept through greater
amplitudes and frequencies. Dytiscus turns by varying the phase
relationship between contralateral legs
(Hughes, 1958
). For rapid
turns, Dytiscus can extend one hind leg to act simultaneously as a
brake and pivot, while the opposite leg paddles.
The whirligig beetles of the genus Dineutes can reach speeds of
0.53 m s1 (Tucker,
1969), although speeds of up to 1.0 m s1 have
been reported for the related genus Gyrinus
(Nachtigall, 1974
). The
maximum U measured in this study was in agreement with the results
reported by Tucker (1969
) but
was lower than the maximum speed reported by Nachtigall
(1974
). Higher speeds may have
been recorded if rectilinear swimming was measured and the beetles were
allowed to be heated above ambient temperature. Pond-dwelling
Dineutes favor sunny areas,where they presumably warm themselves by
basking (Fitzgerald, 1987
).
Higherinternal temperatures can increase muscle output and locomotor
performance.
The increase in with decreasing R occurred because, over
an equivalent range of U, beetles would traverse similar arc
lengths.With smaller-radius turns, beetles would move through a greater number
of degrees than during larger-radius turns.
approaches an asymptote as
the beetles cannot increase U further. This limit is dependent on
energetic constraints associated with the drag on the beetle and
inefficienciesof the paddling mode. At high U, the beetles would
experience high drag from displacement of half their body mass in water and
surface tension at the water surface
(Tucker, 1969
). Furthermore,
paddling is inefficient at high U because the speed differential
between the body and the paddle becomes smaller with less propulsive force
being generated(Blake, 1986
;
Fish, 1996
).
The winged-swimming of the whirligig beetle is a unique style of locomotion
that has not previously been reported for any insect. The results reported
here are the first description for an insect of winged-swimming with single
wing deployment as a unique mechanism for turning. Although insects can swim
using legged-propulsion or skim the water surface while in flight
(Nachtigall, 1974;
Marden and Kramer, 1994
),
winged-swimming of insects is rare and has not been analyzed. Adult female
Hydrocampa nymphaeata (Lepidoptera) swim by a combination of wings
and legs (Nachtigall, 1974
).
Minute aquatic Hymenoptera, including Polynema,Hydrophylax,
Limnodytes and Caraphractus, swim using the wings solely
(Lubbock, 1863
;
Matheson and Crosby, 1912
).
Caraphractus cinctus was described to swim rapidly with a jerky
motion that corresponded to awingbeat cycle of 2 Hz
(Matheson and Crosby, 1912
).
Implicit in the descriptions of winged-swimming in insects is that both wings
are deployed simultaneously.
The mechanics of winged-swimming for turning the whirligig beetle can be modeled as a combination of drag and vectored thrust (Fig. 3). In this conceptualization, the sculling by the wing could act to generate thrust at an acute angle to the longitudinal axis of the body. Both the body and the abducted elytra can generate drags. Compared with the streamlined cross-sectional profile of the body, the elytra could generate an asymmetrically larger drag on the inboard side of the beetle. Such an asymmetry of forces could generate a torque about the center of mass. Thus, in this model, the sum of all torques derived from the thrust and imbalance of drags from the body and the elytra relative to the center of mass would result in a circular motion of small radius.
Why winged-swimming is used for turns in deference to leg paddling is
unknown. Wing-swimming confers no advantage in turning performance compared
with paddling. The smallest radius and highest rate for a winged turn was 0.4
L and 3130.4 degrees s1, respectively. Theses
valueswere not equivalent to the minimum R and maximum for
paddling,although they were in the extreme 20% of values.
Turning mechanisms
Turning is effected by dynamic forces. These forces include unsteady
inertial forces and steady non-inertial forces. Inertial forces include body
internal dynamics (i.e. redistribution of body mass) and fluid inertial
reaction (i.e. pulsed jet), whereas steady non-inertial forces include lift
and drag. In the aquatic maneuvering systems of most animals, the non-inertial
forces dominate.
Animals can use an asymmetrically applied drag from their appendages toproduce a pivot point in water to rotate the center of mass of the body around it. This mechanism is analogous to using a single oar to turn a rudderless rowboat. If the rowboat has forward momentum, the inboard oar can act as a brake and develop the turning drag by being held stationary in the water. The posteriorly oriented drag is applied to the distal end of the oar creating torque to turn the boat. Alternatively, the rowboat can be turned byactive paddling of the outboard oar. Sweeping the outboard oar posteriorly produces a forward directed drag at the blade, which produces a net torque to angularly accelerate the boat.
Animals that maneuver with appendages modified as paddles work well in
conditions dictated by low speed and precise control
(Webb, 1997). However,precise
turns should be less effective in conditions of rapid movement withhigh speed.
In instances where the inboard paddle is held stationary, the consequence of
using such a drag-based maneuver is a dramatic reduction in speed because the
appendage, which is typically used for propulsion, becomesa braking device
without producing thrust. The energy cost of turning in this manner will be
high as the animal must accelerate to restore its original speed. Speed can be
maintained if the outboard appendages are continuously paddled through the
turn. In this case, the active paddling motion produces the turn. This
mechanism has distinct advantages when U=0, as thepaddles induce
their own speed and hydrodynamically derived drag without movement of the body
(Blake, 1986
). Turns can be
performed in limited spaces,and turns can be composed of pure rotational
movements with no body translation
(Walker, 2000
).
Lift-based maneuvering systems have the advantage of producing a
centripetal force to effect turning without incurring a large decelerating
drag (Watts, 1961). This is
the primary system used by ships, fish, penguins and marine mammals
(Manning, 1930
;
Howland, 1974
;
Hoerner and Borst, 1975
;
Weihs, 1981
; Webb,
1983
,
1997
;
Hui, 1985
;
Marchaj, 1988
;
Fish and Battle, 1995
;Fish,
1997
,
2002
). Lift-based maneuvers
work best with high aspect ratio appendages used as control surfaces. The
effectiveness of lift-based mechanisms varies with speed
(Marchaj, 1988
). Lift used by
the control surfaces to create destabilizing moments varies in proportion to
U2. However, lift-based turning is independent of speed
(Webb, 1997
). As speed
decreases, the lift also decreases relative to the required force necessary to
turn so that maneuvering is more difficult at low U.
Despite the apparent advantages of lift-based versus drag-based
systems with regard to high speed turns, the use of rowing appendages can be
beneficial for continuous turning. Propulsion is curtailed during small-radius
turning maneuvers using extreme body flexibility in combination with lifting
surfaces (Fish, 2002). During
these turns, the lifting surfaces abandon their function as propulsive
surfaces and are used as control surfaces. The turn becomes unpowered, and the
duration of the turn is dependent on the momentum of the animal at the start
of the maneuver. Thus, these unpowered turns are limited in duration, as
frictional drag on the body causes a loss of momentum. To generate more
momentum to continue a turn, flexible animals using lift-based systems would
have to dispense with the unpowered turn and revert to a powered turn with its
comparatively larger turning radius (Fish,
2002
). Only by alternating bouts of powered and unpowered turns
could a position be held and the turn sustained (i.e. circular motion).
Adjustments between the powered and unpowered turns will reduce the
effectiveness of the maneuver. With rowing, the appendages can continue to
generate thrust to maintain the minimum turning radius for a prolonged period.
Although propulsion by paddling is less efficient than oscillating a hydrofoil
(Blake, 1986
; Fish,
1993
,
1996
), maintenance of a stable
circular turn could make paddling more efficient for circular maneuvers.
Comparison of turning performance
Compared to animals with flexible bodies, the relative turning radii of
whirligig beetles are constrained by a rigid body morphology. Expressed as a
proportion of body length, the minimum turning radius is 0.000.47
L for fish, 0.24 L for penguins, 0.110.17 L
for cetaceans and 0.090.16 L for sea lions
(Hui, 1985; Domenici and
Blake, 1991
,
1997
;
Blake et al., 1995
;
Fish, 1997
;
Gerstner, 1999
;
Walker, 2000
). The highest
minimum turning radius for fish (0.47 L) was found for the tuna
(Blake et al., 1995
). These
fish are thick-bodied and relatively stiff, having specialized for rapid
cruising (Webb, 1984
). Squids,
which keep the mantle stiff, cannot produce turns of less than 0.5 L
(Foyle and O'Dor, 1988
). The
shelled Nautilus can, at best, negotiate a turn of 2 L
(Chamberlain, 1990
). Submarines
with inflexible hulls have turning radii of 23 L
(Maslov, 1970
). Encased by a
carapace of thickened, suture bony plates, the boxfish Ostracion is
not limited by stiffness. Boxfish display a minimum R of 0.0005
L (Walker, 2000
),
which is due largely to rotation. The ability to rotate or spin is dependent
on the position of multiple propulsors located about the center of mass.
Limitations in turning performance because of body inflexibility would not
appear to extend to . Whirligig beetles demonstrate a maximum
that is equivalent to the maximum
for some flexible-bodied fishes
(Webb, 1983
). However, turning
rate is inversely proportional to L
(Fig. 7); thus, larger animals
turn at a slower speed than do smaller animals. From this perspective, fish
demonstrate superior performance with respectto
, because they can
produce a maximum
that is equal to that ofthe beetle (which is
3.520 times the size). In Fig.
7, which compares
over a range of body lengths, inflexible
bodies are represented by the whirligig beetle and the experimental submarine
USS Albacore at the extremes of the size range. If a line is drawn between
these two rigid-bodied swimmers, flexible-bodied swimmers are shown to have
higher turning rates with respect to their size. The tuna approaches the line
and falls far below turning rates for similarly sized fish. Meanwhile, the
boxfish and squid fall to the left of the line, suggesting performance
constraint due to stiffness.
|
Higher ac are generated by flexible-bodied organisms
compared with rigid bodies for equivalent levels of
(Fig. 8). Thisis largely a
consequence of the tighter turning radius of flexible organisms. For these
animals that turn using lifting surfaces, the high ac is
necessary to generate sufficient centripetal force for theturn. However, high
ac are not required by the beetles.The drag-based paddling
and vectored thrust mechanisms can effect turns with a pivoting action that
permits a higher turning rate but with lower ac. These
mechanisms allow the beetles to turn continuouslywithout deceleration. This
enhances their ability to escape predation from animals with tighter but less
sustained turning ability.
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Acknowledgments |
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