© 2001 by The Society for Integrative and Comparative Biology
Upstroke Thrust, Drag Effects, and Stroke-glide Cycles in Wing-propelled Swimming by Birds1
1 Department of Zoology, University of Wyoming, Laramie, Wyoming 82071
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A number of bird species swim underwater by wing propulsion. Both among and within species, thrust generated during the recovery phase (upstroke) varies from almost none to more than during the power phase (downstroke). More uneven thrust and unsteady speed may increase swimming costs because of greater inertial work to accelerate the body fuselage (head and trunk), especially when buoyant resistance is high during descent. I investigated these effects by varying relative fuselage speed during upstroke vs. downstroke in a model for wing-propelled murres which descend at relatively constant mean speed. As buoyant resistance declined with depth, the model varied stroke frequency and glide duration to maintain constant mean descent speed, stroke duration, and work per stroke. When mean fuselage speed during the upstroke was only 18% of that during the downstroke, stroke frequency was constant with no gliding, so that power output was unchanged throughout descent. When mean upstroke speed of the fuselage was raised to 40% and 73% of mean downstroke speed, stroke frequency declined and gliding increased, so that power output decreased rapidly with increasing depth. Greater inertial work with more unequal fuselage speeds was a minor contributor to differences in swimming costs. Instead, lower speeds during upstrokes required higher speeds during downstrokes to maintain the same mean speed, resulting in nonlinear increases in drag at greater fuselage speeds during the power phase. When fuselage speed was relatively higher during upstrokes, lower net drag at the same mean speed increased the ability to glide between strokes, thereby decreasing the cost of swimming.
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INTRODUCTION |
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For birds that swim underwater by wing propulsion, thrust during the recovery phase (upstroke) can be negligible to even greater than during the power phase (downstroke) (Hui, 1988
; Rayner, 1995). Relative thrust during the upstroke vs. downstroke varies between species depending on whether the wings, skeleton, and muscles are adapted for downstroke-based aerial flight as in alcids, diving-petrels, and some seaducks, or lack constraints of aerial flight as in penguins (Stettenheim, 1959; Snell, 1985; Raikow et al., 1988; Hui, 1988; Bannasch, 1994). Within species, penguins apparently increase upstroke thrust to offset buoyancy during horizontal swimming near the surface, just as birds flying in air must offset gravity with more thrust on the downstroke (Hui, 1988). In alcids that fly both in air and underwater, thrust during swimming is sometimes much greater during the downstroke than upstroke, resulting in quite unsteady speed during strokes (Fig. 1A; Rayner, 1995; Lovvorn et al., 1999). However, murres appear to vary the degree of upstroke thrust, generating substantial upstroke lift under some conditions during horizontal swimming (Fig. 1B), and especially when descending against high buoyancy at shallow depths (National Geographic Society, 1995; see also Rayner et al., 1986). Thus, because the wings, skeleton, and muscles of alcids are also adapted to flying in air, their fuselage speeds during swimming strokes appear to be more variable than in penguins, and in some cases may approach the unsteadiness seen in some foot-propelled divers at shallow depths (Lovvorn et al., 1991).
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Thrust by wings or foreflippers can have both drag-based and lift-based components (Feldkamp, 1987
; Wyneken, 1988), and these mechanisms become less distinct in unsteady circulation theory of hydrofoils (Dickinson, 1996). If forward speeds are high enough and stroke periods long enough for flow development, thrust can be generated with less energy (greater propeller efficiency) by lift-based than by drag-based mechanisms (Weihs and Webb, 1983; Daniel and Webb, 1987). However, my arguments here about greater costs of less steady speeds during strokes are based not on the fluid mechanics of propulsive limbs, but on the net thrust needed to overcome forces (drag, buoyancy, inertia) acting on the body fuselage (head and trunk excluding propulsive limbs). More variable instantaneous speeds of the fuselage during strokes result in greater inertial work. Also, because drag of the body fuselage increases nonlinearly with increasing speed (Lovvorn et al., 2001), greater speed during the downstroke to offset lower speed during the upstroke may also increase the cost of swimming at the same mean speed.
If the same mean speed can be achieved with less work per stroke when thrust and speed are more evenly distributed between power and recovery phases, the bird might be able to glide more between strokes. It has been shown empirically in marine mammals (Skrovan et al., 1999; Williams et al., 2000) and by modeling for murres (Lovvorn et al., 1999) that gliding between strokes increases as the buoyancy of air spaces decreases during descent, resulting in substantial energy savings. Thus, changes in the frequency and duration of gliding may be an important consequence of varying relative thrust on the upstroke vs. downstroke.
In this paper, I investigate effects of varying thrust and speed during the recovery phase in a model of swimming by thick-billed murres (Uria lomvia) during descent. Relative upstroke speed (RU = mean fuselage speed during upstroke ÷ mean fuselage speed during downstroke) was varied from 0.73 to 0.40 to 0.18. As buoyant resistance declined with depth, the model varied stroke frequency and glide duration to maintain constant mean descent speed, stroke duration, and work per stroke. The results showed how work against drag and inertia were affected by relative upstroke thrust to alter the frequency and duration of gliding as buoyancy changed during descent.
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SWIMMING SPEED, MUSCLE EFFICIENCY, AND STROKING IN MURRES |
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During dives to over 80 m to feed on epibenthic prey, thick-billed murres near Coats Island, Nunavut, Canada appeared to descend almost vertically, so that data from time-depth recorders approximated actual swimming speeds (Croll et al., 1992
; Lovvorn et al., 1999). During descent, an instrumented murre typically reached a constant speed of about 1.52 m/sec within 10 m of the water surface, and maintained that speed throughout direct descent. This speed corresponded to the speed of minimum drag coefficient as determined from drag measurements of a frozen murre carcass (Fig. 2). This pattern of relatively constant speed during direct descent to the bottom at deep depths has also been observed in foot-propelled divers such as blue-eyed shags (Phalacrocorax atriceps) and king cormorants (P. albiventer) (Croxall et al., 1991; Kato et al., 1996).
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(where 
AswU2 (where For the murre, buoyant resistance changed dramatically during descent, so maintaining constant mean speed required it either to decrease muscle contraction speed and/or work per stroke, or else to maintain the same contraction speed and work per stroke while substituting glide periods to regulate mean speed (Lovvorn et al., 1999
). There appear to be important reasons to regulate speed via gliding while keeping contraction speed and work per contraction the same. Fiber-type composition and metabolic capacity of muscles are typically adapted to a relatively narrow range of contraction speeds and loads, and power output and efficiency [work/(work + heat)] decrease at either higher or lower values (Fig. 3; Pennycuick, 1991, 1992). This generality is especially true of muscles composed mostly of a single fiber type, as are the pectoral muscles of fast-flapping aerial fliers like ducks and alcids (see refs. in Lovvorn et al., 1999). Thus, the instrumented murre at Coats Island not only maintained constant swimming speed during descent despite changes in buoyancy, but probably also regulated its speed by alternate stroking and gliding.
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METHODS |
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Mechanical forces and swimming speed
During descent and ascent, diving birds must overcome three main mechanical forces on the body fuselage: drag, buoyancy (positive or negative depending on depth), and inertial resistance to accelerational stroking (Lovvorn et al., 1991
). For an animal of given shape and surface roughness, drag of the body fuselage (head and trunk excluding propulsive limbs) increases nonlinearly with speed (Lovvorn et al., 2001). Buoyancy results mostly from air volumes in the respiratory system and plumage, which vary greatly with hydrostatic pressure at shallower depths (Lovvorn and Jones, 1991, 1994; Wilson et al., 1992). Buoyancy can be manipulated somewhat at shallow depths by altering these air volumes (Lovvorn, 1991), but buoyancy changes little below depths at which most compression of air has already occurred (
20 m, Fig. 4; Lovvorn and Jones, 1991; Lovvorn et al., 1999). Inertial work depends on (a) the "virtual mass" (body mass plus "added mass" of water entrained in the boundary layer (Daniel, 1984)), and (b) variability in speed during a stroke as affected by propulsive mode and resistance by drag and buoyancy (Lovvorn et al., 1991, 1999). Body mass does not change with depth, although added mass (which depends on body volume) may change slightly with compression of the plumage air layer.
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Thus, swimming speed (work against drag) and its variability during strokes (inertial work) are the main factors birds can regulate for deep dives. If drag and buoyant resistance are small enough to allow gliding between strokes, drag can sometimes be reduced by a "flap-and-glide" ("burst-and-coast") strategy (Clark and Bemis, 1979
; Blake, 1983); however, buoyancy is typically too high for this gait during steep descent at depths less than 10–15 m. Otherwise, to maximize mechanical efficiency during steady stroking, birds should swim at the mean speed of lowest drag coefficient, while minimizing unsteadiness due to unequal thrust during power and recovery phases (Lovvorn et al., 1999).
Drag and buoyancy
In this paper I use a quasi-steady modeling approach, in which drag of the fuselage at a given instant during the stroke is assumed to be the same as drag at that speed under steady conditions. Drag of a frozen common murre (Uria aalge) with wings removed was measured in a tow tank (Fig. 2). Drag of the body fuselage without wings does not account for drag of the propulsive limbs. In this modeling approach (Lovvorn et al., 1991, 1999), drag of oscillating propulsors is subsumed by the aerobic efficiency coefficient (
a = mechanical power output ÷ aerobic power input). This coefficient, best derived from mechanical modeling and respirometry under the same conditions, is used to calculate aerobic energy requirements from estimates of the mechanical power needed for propulsion (in this case to propel the body fuselage). This approach is similar to that often used in naval engineering, in which the drag of a hull is matched with a propulsive system of given net efficiency. For animal swimming, this method avoids the need to develop and verify complex models of fluid vorticity around oscillating propulsors with time-varying shape, size, and rotation (see Dickinson, 1996). I do not apply an aerobic efficiency coefficient to results in this paper, because I am interested only in mechanical forces acting on the body fuselage.
Buoyancy of body tissues was calculated from body composition, and volumes of air in the respiratory system and plumage were estimated from equations in Lovvorn et al. (1999). No measurements of air loss from the plumage during deep dives have been made, so I did not correct buoyancy for loss of plumage air during dives. Owing to compression of air spaces, buoyancy decreased rapidly with depth, becoming negligible below about 20 m and negative below 62 m (Fig. 4).
Stroke acceleration curves, inertial work, and summation of work components
For changes in fuselage speed throughout swimming strokes, I used the curves proposed for murres by Lovvorn et al. (1999). According to these curves, relative upstroke speed (RU = mean fuselage speed during upstroke ÷ mean fuselage speed during downstroke) ranged from 0.73 to 0.40 to 0.18 (Fig. 5). These curves were applied to the mean swimming speed during direct descent of a thick-billed murre fitted with a time-depth recorder at Coats Island: 1.52 m/sec (Lovvorn et al., 1999).
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To model work during a swimming stroke, I first calculated the linear distance moved by the body fuselage during 0.01-sec intervals, according to the fractional speeds in Figure 5 and mean speed during a stroke at the given depth (see below). Work during these 0.01-sec intervals was calculated by multiplying the drag and buoyancy at the given depth by displacement, and then adding the inertial work done to accelerate the fuselage and the added mass of entrained water (see Lovvorn et al., 1991
). In a quasi-steady approach, work during all intervals was then integrated over the entire stroke to yield total work during the stroke.
Constant work per stroke throughout descent was assumed to be the same as that calculated for the first stroke of the dive, according to the stroke speed curve used (Fig. 5). In subsequent strokes throughout descent, at each time step of one stroke duration (0.357 sec, Lovvorn et al., 1999), the model calculated the work against drag, buoyancy, and inertia for the mean stroke speed of the preceding stroke. If total work for the new stroke was less than the constant work per stroke, speed of the fuselage during that stroke was increased until the total work to generate that speed was equal to the constant value (only fuselage speed and not contraction speed of propulsors was increased). If the net mean speed of the fuselage during the new stroke (averaged over the stroke and any preceding glide) exceeded the mean steady descent speed (1.52 m/sec), the bird did not execute the stroke during that time step. This algorithm was repeated until the net speed of the fuselage averaged over the stroke and any preceding glide was less than the mean steady descent speed, in which case the bird executed the stroke. Speed and distance moved during a glide (non-stroking) time step was calculated based on the speed of the fuselage at the end of the last stroke and the drag and buoyant resistance at that depth.
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RESULTS |
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Relative upstroke speed (RU = mean fuselage speed during upstroke ÷ mean fuselage speed during downstroke) had dramatic effects on stroke-glide cycles, mechanical power output, and total mechanical work of diving (Fig. 6). When RU was only 0.18, there was no gliding at all. For RU = 0.40, duration of gliding increased to one and then two time steps per stroke during descent. For RU = 0.73, gliding after single strokes increased to three time steps as buoyancy declined to negligible levels at about 20 m depth (Fig. 4), and then increased gradually to 19 time steps (6.8 sec) before the last stroke at 61 m (buoyancy went negative at 62 m, below which the bird descended to 80 m by gliding only). As stroke frequency decreased and gliding increased, net stroke power (including a single stroke and subsequent glide) and total dive cost correspondingly decreased (Fig. 6).
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When fuselage speed during the upstroke was a larger fraction of downstroke speed (RU = 0.73 or 0.40), work against drag and buoyancy depended strongly on the number of glide steps (Fig. 7). During glide steps, speed, distance moved, and resulting drag work were much lower than during actual strokes—drag increases with speed (Fig. 2) and drag work = drag x distance. As predicted, inertial work from accelerating the body fuselage during strokes was much higher for the lowest relative upstroke speed (0.18). However, work against drag dwarfed inertial work for all upstroke patterns, and this difference was greatest by far for lower relative upstroke speeds (Fig. 7).
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The reason drag was more important was revealed by changes in work components throughout individual strokes at different depths (Fig. 8). Although inertial work of accelerating the body fuselage was quite large, this work was recaptured as momentum during deceleration over the latter halves of the upstroke or downstroke. Recapturing inertial work resulted in relatively low net work against inertia for all upstroke patterns, although it was higher at greater depths when reduced buoyancy required higher speeds during strokes to maintain constant work per stroke. This effect was magnified as relative upstroke speed RU of the fuselage decreased, requiring even greater speed during the downstroke to maintain constant work per stroke and constant mean descent speed. Because fuselage drag increased nonlinearly with speed (Fig. 2), drag increased nonlinearly with increased instantaneous speed during the downstroke. Thus, the much higher costs of diving when relative upstroke speed was low (Fig. 6) resulted not from greater inertial work, but from higher fuselage drag at higher speeds during the downstroke. Regardless of the mechanism, total work still increased greatly with less steady fuselage speeds throughout a stroke cycle.
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According to the model, how is gliding related to steadiness of fuselage speed throughout strokes? With the intent of maximizing physiological efficiency, stroke duration (contraction speed) and work per stroke (load) were held constant. Although fuselage speed during the downstroke can be increased to offset low upstroke speed, downstroke speed can increase only so much until resulting nonlinear increases in drag exceed the constant work restriction. As a result of this nonlinear drag effect, the mean fuselage speed during the stroke can never be as high for the same work per stroke as when relative upstroke speed RU is greater. Because overall mean speed during a stroke is lower for lower RU, there is less chance that a glide step can be inserted while maintaining the constant mean descent speed. Therefore if work per stroke stays constant, enhanced drag resulting from greater fuselage speed during the downstroke limits mean stroke speed, and thus the potential for gliding after a stroke.
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DISCUSSION |
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Caveats to the modeling approach
Model results reported here depend on two key assumptions: constant stroke duration and constant work per stroke. As explained earlier, these assumptions are based on the premise that maximum muscle efficiency is achieved over a limited range of contraction speeds (stroke duration) and loads (work per contraction) (Fig. 3). I am unaware of direct measurements of the efficiency of flight muscles of any bird for different contraction speeds and loads, but these principles are supported by a variety of studies of isolated muscles and exercising endotherms (Pennycuick, 1991, 1992
). The model presented here has shown that the flap-and-glide strategy not only reduces drag (Figs. 7, 8; Clark and Bemis, 1979; Blake, 1983), but is also a way to conserve the physiological efficiency of muscle (Lovvorn et al., 1999). By interspersing glides, murres in the model were able to regulate their mean descent speed without altering muscle contraction speed or load.
Another important issue is that the quasi-steady approach assumes that fuselage drag at speeds over short time increments (0.01 sec) is the same as if speed were steady during those increments. This assumption is incorrect to the extent that fully developed flow does not occur instantaneously. Most work on unsteady flow during locomotion in fluids has focused on flapping propulsors, and verifications of the theory have necessarily focused on rigid robotic limbs under carefully controlled conditions (see Dickinson, 1996; Dickinson et al., 1999). The current state and complexity of theory for unsteady (vs. quasi-steady) flow makes it difficult to apply to diverse bird species under varying field conditions. Despite shortcomings, the quasi-steady approach used here has helped reveal how variable fuselage speed during strokes affects locomotor costs of animals with different gaits, independently of the fluid mechanics of propulsive limbs.
Critical to the quasi-steady approach is a description of instantaneous speed throughout a stroke cycle (Fig. 5). Although high-speed films (e.g., 100 frames/sec) are quite desirable for this purpose (see Lovvorn et al., 1991), there are serious limits to the generality of such data obtained under tractable controlled conditions. For high-speed films to be properly lighted and registered in space, equipment currently available to researchers typically requires that a bird swim under very bright illumination within a predetermined field perhaps 50 cm deep. Because of high film speed, the camera must be turned on instantaneously in anticipation of a bird swimming through the specified field, and usually only a few sequences can be captured before the film must be changed. Thus, one must be in a position to film a bird at close range, to turn the camera on and off for sequences lasting only a fraction of a second, and to do so without disturbing the bird's swimming patterns by flashing strobes under low light conditions at depth. The birds quite possibly modulate their relative upstroke speed throughout dives (cf., Rayner et al., 1986; Skrovan et al., 1999), so such films would have to be obtained at a gradient of depths to perhaps over 100 m. Stroke frequencies throughout deep dives have been measured with video cameras mounted on the bodies of marine mammals (Williams et al., 2000), but cameras currently available are much too large for birds. Given the technical limitations to filming, probably a more fruitful approach would be to develop accelerometers and electronic dataloggers that could measure not only stroke frequency, but also speeds throughout strokes in free-ranging birds under ambient conditions. Some progress with such instruments is being made by both Japanese and European researchers (Y. Watanuki and R. P. Wilson, personal communication).
Importance, determinants, and consequences of upstroke function
Rayner et al. (1986) suggested that in both bats and birds flying in air, wingbeat gaits (the cyclic pattern of wing movements) are in fact defined by upstroke function, which varies with wing morphology. They noted that flapping gaits are not species-specific, but that upstroke use and effect vary in the same species depending on conditions. In bats and birds in air, lift (and thrust) is generated by the upstroke at high flight speeds, but not at low speeds (Rayner et al., 1986). However, in films of murres underwater (National Geographic Society, 1995), relative upstroke speed and thrust appear (without kinematic analysis) to be greater during vertical descent against high buoyancy than during horizontal swimming. As mean speeds of murres are generally greater during horizontal swimming (mean 2.18 m/sec, Swennen and Duiven, 1991) than during direct descent against buoyancy (1.5–1.8 m/sec, Lovvorn et al., 1999), it appears that mean fuselage speed is not the only or even principal determinant of upstroke use and effect in underwater flight by alcids. Analyses here suggest that potential for gliding—as affected by buoyant resistance, body size (inertia), and desired speed relative to drag—may have strong influence on upstroke function and gaits selected (see Clark and Bemis, 1979).
These principles may extend to other modes of swimming. In bottlenose dolphins (Tursiops truncatus), Skrovan et al. (1999) found that adjustment of glide frequency and duration as buoyancy changed with depth was an important strategy to reduce costs of descent and ascent. These dolphins were positively buoyant (above 90 m) throughout most of the 100-m dives studied. In dolphins thrust differs appreciably between upstroke and downstroke (Videler and Kamermans, 1985), so kinematic analyses of speed throughout strokes might reveal that changes in stroke-glide patterns with depth also vary with relative upstroke speed.
The model presented here indicates that birds swimming with their wings underwater should keep fuselage speeds during upstroke and downstroke as similar as possible. This is apparently no problem for penguins, which may generate even more thrust on the upstroke than downstroke if conditions warrant (Hui, 1988). However, for alcids and diving-petrels that also fly in air, forelimb joint mobility is much lower than in penguins, probably due to constraints of aerial flight (Raikow et al., 1988). Kinematic studies are needed to examine the occurrence and limits to upstroke thrust in non-penguins, and the extent to which upstroke capabilities of different bird species affect their relative swimming costs.
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ACKNOWLEDGMENTS |
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I thank Randi Weinstein for inviting me to this symposium. I especially acknowledge C. J. Pennycuick whose work provided important ideas and inspiration, and G. A. Liggins for his expertise and dedication during long hours at the drag tank. D. R. Jones, S. M. Calisal, G. N. Stensgaard, A. Akinturk, and M. MacKinnon provided financial support, equipment, laboratory space, and technical assistance; and G. V. Byrd and A. L. Sowls collected the murre used for drag measurements. This work was supported by National Science Foundation, Office of Polar Programs grant OPP-9813979 to J.R.L.
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FOOTNOTES |
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1 From the Symposium Intermittent Locomotion: Integrating the Physiology, Biomechanics and Behavior of Repeated Activity, presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 4–8 January 2000, at Atlanta, Georgia.
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