Cormorants are water birds that forage by submerged swimming in search and pursuit of fish. Underwater they swim by paddling with both feet simultaneously in a gait that includes long glides between consecutive strokes. At shallow swimming depths the birds are highly buoyant as a consequence of their aerial lifestyle. To counter this buoyancy cormorants swim underwater with their body at an angle to the swimming direction. This mechanical solution for foraging at shallow depth is expected to increase the cost of swimming by increasing the drag of the birds. We used kinematic analysis of video sequences of cormorants swimming underwater at shallow depth in a controlled research setup to analyze the swimming gait and estimate the resultant drag of the birds during the entire paddling cycle. The gliding drag of the birds was estimated from swimming speed deceleration during the glide stage while the drag during active paddling was estimated using a mathematical`burst-and-glide' model. The model was originally developed to estimate the energetic saving from combining glides with burst swimming and we used this fact to test whether the paddling gait of cormorants has similar advantages.

We found that swimming speed was correlated with paddling frequency(r=0.56, P<0.001, N=95) where the increase in paddling frequency was achieved mainly by shortening the glide stage(r=–0.86, P<0.001, N=95). The drag coefficient of the birds during paddling was higher on average by two- to threefold than during gliding. However, the magnitude of the drag coefficient during the glide was positively correlated with the tilt of the body(r=0.5, P<0.003, N=35) and negatively correlated with swimming speed (r=–0.65, P<0.001, N=35), while the drag coefficient during the stroke was not correlated with tilt of the body (r=–0.11, P>0.5, N=35) and was positively correlated with swimming speed(r=0.41, P<0.015, N=35). Therefore, the difference between the drag coefficient during the glide and during propulsion diminished at lower speeds and larger tilt. The mean drag of the birds for a single paddling cycle at an average swimming speed of 1.5 m s–1 was 5.5±0.68 N. The burst-and-glide model predicts that energy saving from using burst-and-glide in the paddling cycle is limited to relatively fast swimming speeds (>1.5 m s–1), but that as the birds dive deeper (>1 m where buoyancy is reduced), the burst-and-glide gait may become beneficial even at lower speeds.

Hydrodynamic drag is a primary force in determining the performance of aquatic animals (Alexander,1968). In a simplified form, it is the force (due to dynamic pressure differences over the body and skin friction) that causes the resistance to motion through the water. It sets limits to the maximum swimming speed achieved by the animal and has a direct effect on the energy expenditure during swimming (Bilo and Nachtigall,1980; Hedenstrom and Liechti,2001; Hui, 1988; Lovvorn, 2001; Lovvorn et al., 1991, 2001; Prange and Schmidt-Nielsen,1970; Skrovan et al.,1999; Stelle et al.,2000; Stephenson,1994; Thomas,1996; Videler and Weihs,1982; Webb, 1971; Weihs, 2002). At high Reynolds numbers Re (Re=Ul/υ, where U is swimming speed, l is the length of the swimmer and υ is kinematic viscosity of water, ∼10–6 m2s–1), drag is proportional to size (area) and to the square power of the swimming speed (Hoerner,1965). Drag is also dependent on shape. The latter is represented in the equation of drag in the form of a non-dimensional drag coefficient(Cd). The relation between Cd and drag force (at Re>104) is described as:
\[\ C_{\mathrm{d}}=2D{/}{\rho}AU^{2},\]
(1)
where D is drag, ρ is density of water (∼103 kg m–3) and A is a characteristic area.

Cd has been measured for different animals from models and carcasses in a water or air tunnel(Fish, 1984; Hui, 1988a; Lovvorn et al., 2001; Maybury and Rayner, 2001) or by using trained animals towed behind a boat(Williams and Kooyman, 1985). An indirect approach is to measure drag from the deceleration of live animals as they glide (Bilo and Nachtigall,1980; Clark and Bemis,1979; Miller et al.,2004; Stelle et al.,2000; Williams and Kooyman,1985). This technique uses the fact that during the glide no thrust is being produced, hence the deceleration results directly from drag. By measuring the deceleration of the body, the drag force can be calculated from Newton's second law (F=Ma, where F=force, M=mass and a=acceleration). However, some correction is required for the added mass of water that is accelerated with the body(Vogel, 1994). The advantage of this technique is that the estimate is derived from animals swimming voluntarily, cruising at preferred speeds so that the shape and orientation of body parts is realistic. However, unlike with rigid objects, Cd of live animals changes during swimming. The swimming motions (undulations, flapping, rowing and paddling) increase the drag significantly beyond that of a motionless animal at the same swimming speed(Weihs, 1974; Schultz and Webb, 2002; Vogel, 1994). None of the above-mentioned techniques considers the elevated drag during active swimming and the drag measured is thus termed `parasite drag' (for models and carcasses where the propelling appendages are removed) or `passive drag' (for gliding animals). A different approach that does allow the estimation of the drag for active swimming is to model the thrust from the kinematics of the propelling appendages. Once thrust is estimated, then during swimming at constant speed,drag should equal thrust (Fish,1993; Vogel,1994). However, since estimation of passive drag from glides is relatively simple, it would be beneficial if active drag could be estimated directly from passive drag using simple kinematics. We explore this option using the swimming behavior termed `burst-and-glide' (described by Weihs, 1974) that has been shown to exist in fish, marine mammals, penguins, water birds, lobsters,plankton and numerous aerial flyers (Haury and Weihs, 1976; Hove et al.,2001; Lovvorn,2001; Sato et al.,2003; Spanier et al.,1991; Van Dam et al.,2002; Videler and Weihs,1982; Webb and Fairchild,2001; Weihs, 2002, 2004).

Swimming animals that use burst-and-glide can reduce the total energetic cost of swimming (Weihs, 1974;see Appendix). With this strategy, instead of swimming continuously at a constant speed, the swimmer accelerates to a final speed(Uf) above the desired average speed and then glides(decelerates) until reaching the initial speed (Ui). The energetic saving from such behavior is calculated as the ratio (R)between the energy required to burst-and-glide and the energy required to swim at the same average speed but at constant speed. R can be calculated directly from the burst-and-glide model using easily obtained kinematic data(see, for example, Videler and Weihs,1982). However, the model requires knowledge of the parameterα, which is the ratio of drag during active swimming and drag during gliding. For example, the α used by Weihs(1974) for fish was 3, based on evidence that the drag of active swimming fish (dace and trout) is about three times the drag during passive gliding(Lighthill, 1971; Webb, 1971). A similar value of α was reported later for dolphins(Fish, 1993).

Cormorants propel their body underwater by stroking (paddling) with both feet simultaneously while the wings are tightly folded against the body(Lovvorn, 1991; Schmid et al., 1995). However,when swimming on the surface, cormorants employ alternate paddling, stroking with one foot at a time (Lovvorn,1991; Ancel et al.,2000). Kinematic data on cormorants (Phalacrocorax carbo sinensis Blumelbach) swimming underwater(Ribak et al., 2004) showed that the paddling cycle is divided into three distinct successive stages: a stroke stage, where both feet move backward and generate the thrust; a glide stage, where the feet have no motion relative to the body; and a recovery stage, where the feet move forward relative to the body, in preparation for the next stroke. The glide stage lasts for approximately 50% of the entire paddling cycle duration (Ribak et al.,2004). The combination of a short power stage, where the birds accelerate, with a long glide stage, where the birds decelerate, resembles the burst-and-glide swimming pattern described above.

Submerged cormorants are positively buoyant(Lovvorn and Jones, 1991) so that the birds need to invest energy to remain submerged. Most of the buoyancy of water birds is due to air volumes in the plumage and in the airsacs(Lovvorn and Jones, 1991; Wilson et al., 1992), and their buoyancy therefore depends on diving depth. As the birds dive deeper,the hydrostatic pressure compresses the gas volumes, making the birds less buoyant. During shallow horizontal dives, cormorants swim with the midline of the body at an angle to the swimming direction (pitch, head pointing down,tail pointing up). This angle-of-attack generates hydrodynamic lift to help offset the positive buoyancy of the birds. This tilt of the body is highest during the stroke and recovery stages(Ribak et al., 2004). Using lift to counter buoyancy by tilting the body allows the birds to forage underwater at shallow depths where their buoyancy is maximal, but this behaviour should result in elevated drag during submerged swimming.

The drag coefficient (Cd) of the Brandt's cormorant Phalacrocorax pencillatus was measured by Lovvorn et al.(2001) by towing frozen, dead birds and a smooth featherless model. The values they obtained (based on the surface area as the characteristic area, A) were about 0.008 and 0.022 for the model and carcasses, respectively (at Re=106; figs 6 and 7 in Lovvorn et al., 2001). However, these values are applicable only for gliding birds at depths where buoyancy is negligible (≫20 m; Wilson et al., 1992), since the towed birds were aligned in the direction of the flow and were not performing swimming motions. Great cormorants are shallow divers, mostly diving to depths <11 m(Grèmillet et al., 1999; Johansgard, 1993). Therefore,a method to estimate the drag during active paddling while taking into account the influence of buoyancy at shallow depths will provide a more realistic evaluation of the mechanical constraints on swimming for these waterbirds.

The problem of increased drag resulting from propulsive motions is a general issue confronting all animals that move in fluid media (air, water,biological fluids) and different species have found various ways of coping. Here we examine the adaptations of the cormorant, a flyer and also an adept swimmer. We use the long glide stage between the stroke and recovery stages in the paddling cycle of the cormorant to measure the passive drag of the birds from their deceleration. Then, we employ the `burst-and-glide' model to calculate the drag of the bird during active swimming and to evaluate the energetic benefit of adding glides to the paddling cycle.

Morphometric measurements

The calculation of Cd from deceleration requires a typical area (A, in Eqn 1) and added mass coefficients for the body of great cormorants Phalacrocorax carbo sinensis Blumelbach. We used volume V to the 2/3 power (V2/3) for area, by calculating the volume of each bird from its body mass, and from the average density (810 kg m–3) reported for cormorant carcasses(Ribak et al., 2004). An earlier study on parasite drag of cormorants reported drag coefficients based on surface area (Lovvorn et al.,2001), so we measured this area as well, to allow comparison (see below). Five carcasses of adult cormorants that were shot over fishing ponds during a wildlife management program were obtained fresh and stored frozen(–20°C) until processing after completely defrosting at room temperature (∼15°C). The carcasses were used to estimate the added mass, surface area and general shape of the birds in three dimensions. This was done by folding the wings to their normal position during swimming, and securing them in place with tape. Each carcass was laid with its neck stretched on a 0.5 cm thick, 1×0.1 m plate, with markings every 1 cm along the long side of the plate. The tip of the bill, the tip of the tail and the center of the body were secured to the plate with tape. The plate with the bird was then advanced, 1 cm at a time, through a measuring device consisting of two perpendicular metal rods, sliding orthogonally with respect to each other (Fig. 1A). Each rod was scaled using a measuring tape (±1 mm), allowing the simultaneous measurement of height and width of the carcass each centimeter along the long axis of the body. The body is covered with soft plumage and has some flexibility, thus the measured height and width may change with the pressure applied by the measuring tool. To minimize this error, prior to each measurement the rods were pressed lightly onto the carcass and then released gently to allow the plumage and body tissues to push the rods back to normal position. The set of measurements from each carcass thus included diameters of 1 cm thick transverse `slices' of the birds(Fig. 1B). The volume of each slice was calculated from the area of both sides of the slice, using the area of an ellipse (area = π yz, where y is half the height measurement and z is half the width measurement). Then, the area of both sides was averaged and multiplied by the thickness of the slice (1 cm) to obtain volume. The volumes of all the slices were summed to yield the total volume of the carcass. Similarly, surface area was measured from the perimeters of each side of the slices using the equation for an ellipse:
\[\ \mathrm{Perimeter}=2{\pi}\sqrt{\frac{y^{2}+z^{2}}{2}}.\]
(2)
The surface area of each slice was assumed to be the average of both perimeters, multiplied by the slice thickness (1 cm). Then, all areas along the length of the bird were summed to yield the surface area of the whole bird. We divided the quantity V2/3 of the carcasses by the measured surface area and used this ratio to convert Cdcalculated based on V2/3 to Cdcalculated based on surface area in the live birds.
Fig. 1.

Shape of the cormorant's body in three dimensions. (A) Schematic illustration (not to scale) of the apparatus used to measure the diameters of the cormorant carcass along the body's main axis.(B) Diameter of the width(lateral axis, solid rectangles) and height (dorso–ventral axis, empty circles). The x-axis represents the position along the body's main axis in % of body length (total body length = 85 cm). The diameters were used to calculate surface area, volume and added mass coefficients. The broken vertical lines mark the definition of the body excluding the neck and tail(trunk).

Fig. 1.

Shape of the cormorant's body in three dimensions. (A) Schematic illustration (not to scale) of the apparatus used to measure the diameters of the cormorant carcass along the body's main axis.(B) Diameter of the width(lateral axis, solid rectangles) and height (dorso–ventral axis, empty circles). The x-axis represents the position along the body's main axis in % of body length (total body length = 85 cm). The diameters were used to calculate surface area, volume and added mass coefficients. The broken vertical lines mark the definition of the body excluding the neck and tail(trunk).

The added mass is the mass of water that is accelerated with a body and is proportional to the volume of the body(Denny, 1993). The exact magnitude of the Cd calculated from decelerations depends slightly on the estimation of the added mass. Underestimation of the added mass will result in a lower calculated value of the drag coefficient and vice versa. To be as accurate as possible we estimated the added mass directly from the size and shape of the birds and accounted for the angle-of-attack θ of the body and tail. The added mass coefficient is the volume of the added mass divided by the volume of the body. An infinitely long cylinder moving parallel to its long axis has an added mass coefficient close to zero while the same cylinder moving perpendicular to its length will have an added mass coefficient of 1 (Lamb,1945). Similarly the added mass of the body of the cormorant depends on whether it moves aligned in the direction of swimming (parallel to the length of the body) or if the body's main axis is tilted at an angle to the flow. Since the birds in our experiment were always gliding with their body at an angle-of-attack to the flow (tail pointing up) we obtained two added mass coefficients: once for the cormorant moving lengthwise and a second time for motion perpendicular to the longitudinal axis of the bird(θ=90°). The values of both were combined to estimate the added mass coefficient for a specific angle-of-attack. For the sake of this analysis we disregarded the neck, which contributes less than 10% to the volume of the entire body (9.5±1%, N=5), does not orient as the rest of the body, and therefore resembles a cylinder aligned with the direction of flow. We thus focused on estimating the added mass of the body (trunk) and tail. For the added mass coefficient relevant for lengthwise motion(Cax) of the body we used 0.122, which is the theoretical value for a prolate spheroid with fineness ratio (length/diameter) of 3 (p. 155 in Lamb, 1945). For motion perpendicular to the flow (downwards) we used Cay=1.339(Table 1) for the body, which was the average calculated from our carcasses [standard error of mean(s.e.m.)=0.045, N=5] using elongated body theory (see, for example, Lighthill, 1970, 1960). The theory states that the added mass of each cross section of a slender body moving broadside to the flow is approximately the volume of a cylinder with a circular cross section that encompasses the diameter of the body at the specific cross section. Thus using the diameters of the body measured at each 1 cm along its length(excluding the neck and tail), we calculated the volume of encompassing cylinders (1 cm long) and integrated all volumes to achieve the volume of added mass when the body is tilted at θ=90°.

Table 1.

Volume and surface area of great cormorant carcasses

CarcassBody mass (kg)V × 10-3 (m3)Aw (m2)V2/3/AwCay
G022 2.220 3.105 0.158 0.134 1.298 
G020 2.376 3.181 0.162 0.134 1.220 
G019 2.028 2.816 0.155 0.128 1.480 
G017 2.178 2.924 0.160 0.128 1.397 
G016 2.159 2.810 0.155 0.129 1.299 
Mean ± s.e.m. 2.192±0.056 2.97±0.07 0.158±0.0013 0.131±0.001 1.339±0.045 
CarcassBody mass (kg)V × 10-3 (m3)Aw (m2)V2/3/AwCay
G022 2.220 3.105 0.158 0.134 1.298 
G020 2.376 3.181 0.162 0.134 1.220 
G019 2.028 2.816 0.155 0.128 1.480 
G017 2.178 2.924 0.160 0.128 1.397 
G016 2.159 2.810 0.155 0.129 1.299 
Mean ± s.e.m. 2.192±0.056 2.97±0.07 0.158±0.0013 0.131±0.001 1.339±0.045 

V, volume; Aw, surface area; N=5.

The measurement of volume was used to estimate the added mass coefficient and the surface area was used to calculate a conversion ratio between Cd based on V2/3 and Cd based on surface area(V2/3/Aw).

Cay is the added mass coefficient of the body (trunk)for motion perpendicular to its longitudinal axis (θ=90°) calculated from elongated body theory (see text).

The volume of added mass was then divided by the actual volume of the bird to yield the added mass coefficient for motion perpendicular to the flow(Cay). The specific added mass coefficient for a givenθ was assumed to be the sum of the projections of the two added mass coefficients (Cax and Cay) on the direction of swimming:
\[\ C_{\mathrm{a}({\theta})}=C_{\mathrm{ax}}{\,}\mathrm{cos}{\,}{\theta}+C_{\mathrm{ay}}{\,}\mathrm{sin}{\,}{\theta}.\]
(3)
The same approach was used for the tail, treating it as a flat plate with trapezoid shape and dimensions of 2 cm and 8.6 cm at the bases and 13.8 cm as the length (data taken from Ribak et al.,2004, which described the planform area of tails of cormorants during swimming). For such a plate Cax is negligible(Cax=0) and Cay is the volume of a truncated cone with radii 1 cm and 4.3 cm at the bases and height 13.8 cm(=3.44×10–4 m3) divided by the volume of the bird. The added mass coefficient Ca(θ), for the tail is calculated as in Eqn 3 but using the angle-of-attack of the tail (the angle between the upper surface of the tail and the direction of swimming). Calculating separate added mass coefficients for the body and tail enabled us to account for changes in the added mass of the bird due to changes in the angle-of-attack of the body and of the tail when the two were not the same. Finally the added mass coefficient Ca of the entire bird(body and tail) is the sum of the coefficients(Ca(θ)) for the tail and for the body.

Body length (tip of bill to tip of tail) of the live birds used to calculate the Reynolds number was measured from scaled images of the birds swimming with their neck stretched.

Swimming sequences

Video sequences were obtained from 5 male and 5 female adult (age >3 years) great cormorants swimming in an experimental setup described previously(Ribak et al., 2004). The birds were filmed swimming inside a straight, 7 m-long metal mesh channel,with a rectangular 0.5 m×0.5 m profile, placed on the floor of a 1 m-deep pool. A 2 m-long section in the tunnel, starting 3.5 m away from the entrance, was used as a testing section. It was equipped with a mirror (2 m×0.7 m) angled at 45° above the tunnel. The birds were filmed swimming in the test section using a CCTV video camera (VK-C77E, Hitachi,Tokyo, Japan; 752×582 effective pixels, shutter speed 1/50s), inside an underwater housing, and connected to a S-VHS video (HR-S7600AM, JVC, Tokyo,Japan). The camera was positioned 0.5 m above bottom, 2 m away from the middle of the testing section, and covered most of the testing section and the mirror(2.3 mm/pixel in the side view 2.7 mm/pixel in the upper view,0.0030–0.0036 body length/pixel, respectively), thus allowing simultaneous lateral and dorsal (through the mirror) views of the swimming bird while using a single camera. The video sequences (each containing one complete paddling cycle) were converted to consecutive video fields (50 fields s–1, i.e. time resolution was ±0.02 s) using a video editing system (Edit 6, Autodesk Inc., San Rafael, CA, USA).

The position of the test section along the tunnel was chosen to allow sufficient distance for the birds to develop a repeated burst-and-glide cycle at given average swimming speed in a straight path prior to the measurement of swimming parameters. The tunnel was positioned along the floor at the center of the pool, at least 1 m away from the nearest wall. We calculated the ground effect (Hoerner, 1975) on the cormorants and found it to be negligible beyond a distance of one body thickness (maximum distance between dorsal and ventral sides of the body) from the floor (at Re>106) and hence only used runs that were >10 cm distant from the floor. The upper 0.5 m height limitation of the tunnel ensured that the birds were swimming away from the surface, at a distance of more than 4 times the body thickness. Hence, no surface waves formed by the swimming bird were measured and the resulting added drag can be assumed to be negligible (approaching zero at depth >3 times the body thickness; fig. 289 in Hertel,1966).

Only a few minutes each time (<10 min) were required to obtain 5–8 video sequences from each bird in a series of 4 sampling days. The short duration of the experiments ensured that changes in buoyancy due to time-dependant plumage wettability would be small(Ribak et al., 2005).

Kinematic analysis

In each sequence, stride length was defined as the horizontal distance traversed during the paddling cycle. The cycle duration was calculated from the number of video fields per cycle and paddling frequency was defined as(cycle duration)–1. The average swimming speed for the entire cycle was defined as stride length divided by cycle duration. Each paddling cycle was divided into three distinct stages: stroke, glide and recovery,based on the motion of the feet as described above and in Ribak et al.(2004). The changes in gait during swimming were analyzed by testing for correlation between the duration of each of the three stages with paddling frequency.

The upper view (through the mirror) in each video field was used to measure the instantaneous speed of the birds. This was done by measuring in each video field the position of a small, round (1.5 cm in diameter) tag glued to the feathers on the back of the birds. The momentary horizontal swimming speed was calculated as the first derivative (∂x/∂t) of the function describing the change in position along the x (horizontal)axis with time, using a Lagrange 3-points numerical equation(Hildebrand, 1956). In each paddling cycle, the birds had slight vertical deviations (∼2 cm) from the horizontal direction (Ribak et al.,2004). However, the descent and ascent angles (measured from the side view) were sufficiently small (∼4°) that the horizontal component of the measured speed represents over 99% of the two-dimensional speed. The angle-of-attack of the body during the glide was defined as the angle between the longitudinal midline of the body (base of neck to base of tail) and the instantaneous direction of swimming in the side view.

The velocity profiles, each comprising one complete paddling cycle(Fig. 2), were used for analysis of drag and burst-and-glide. During the stroke, the body accelerates,and during the glide and recovery it decelerates. Following Weihs(1974), we defined a parameter Uf as the maximum instantaneous speed of the body during the stroke, and Ui as the minimum speed at the start of the stroke. The time interval between them was defined as the power stage(tp, see Fig. 2) to differentiate it from the stroke stage, which is a more robust kinematic definition based solely on the motion of the feet. The speed at the start of the recovery stage was defined as Ur and tg was defined as the duration of the deceleration from Uf to Ur. tr was the duration of the recovery stage. We measured Lp, Lg and Lr as the horizontal distances traversed during the power (tp), glide(tg) and recovery (tr) stages,respectively(Lp+Lg+Lr=stride length).

Fig. 2.

Variation in velocity during one paddling cycle. The plot was obtained from one video sequence (Bird 5) and smoothed by a stepwise 5-point moving average for easy viewing. The plot shows the kinematic parameters defined by Weihs(1974) for the burst-and-glide model (L1, L2, Ui, Uf), and the additional parameters defined in the present study (Lp, Lg, Lr, Ur, tp, tg, tr); see List of symbols for the description of each parameter. The bottom bar indicates the division of the paddling cycle into three stages based on the motion of the feet relative to the body (stroke,glide and recovery). Average swimming speed for this cycle was 1.72 m s–1. Note that the bird did not swim at a constant speed but rather accelerated during the power stage and decelerated during the glide and recovery stages in a burst-and-glide swimming pattern.

Fig. 2.

Variation in velocity during one paddling cycle. The plot was obtained from one video sequence (Bird 5) and smoothed by a stepwise 5-point moving average for easy viewing. The plot shows the kinematic parameters defined by Weihs(1974) for the burst-and-glide model (L1, L2, Ui, Uf), and the additional parameters defined in the present study (Lp, Lg, Lr, Ur, tp, tg, tr); see List of symbols for the description of each parameter. The bottom bar indicates the division of the paddling cycle into three stages based on the motion of the feet relative to the body (stroke,glide and recovery). Average swimming speed for this cycle was 1.72 m s–1. Note that the bird did not swim at a constant speed but rather accelerated during the power stage and decelerated during the glide and recovery stages in a burst-and-glide swimming pattern.

Stride length, paddling frequency and average swimming speed were measured from all the sequences available (95 sequences from 10 birds). However, for the calculation of the drag coefficients we used only the best 35 sequences(from 10 birds) that had the same speed at the start and at the end of the cycle and the smoothest velocity profiles, with distinct acceleration and deceleration. In a few cases, data smoothing, using 3 or 5 point stepwise moving averages, was necessary to determine the exact point of transition between tp and tg, on the velocity profiles. The sequences used were the ones where the birds were swimming as straight as possible (no sideslips and minimal vertical deviations of the center of mass).

Estimation of drag

The instantaneous speed profiles from each of the 10 birds were used to evaluate the drag coefficients of the birds, both when actively swimming and during gliding. We assumed that during the glide and recovery stages, the body moves due to inertia, and thrust is not added to the system so that the Cd of the glide and recovery can be calculated directly from the deceleration of the birds. This assumption is trivial for the glide stage, but in the recovery stage, the forward motion of the feet may presumably add some forward thrust (from inertia). Here we assume that this thrust is negligible since it is likely cancelled by the increased drag on the feet, as they move against the swimming direction. The velocity profiles indicate that the birds indeed decelerated during the recovery stage(Fig. 2).

For the calculation of the drag coefficient during the glide stage we used the technique suggested by Bilo and Nachtigall(1980), based on the average linear slope (C) of the inverse instantaneous speed(U–1) vs time:
\[\ C_{\mathrm{d}}=\frac{2Cm}{{\rho}A}.\]
(4)
where C is the slope of the least-square linear regression between U–1 and time (obtained from the glide data), m is the virtual mass of the birds (bird mass + added mass; Stelle et al., 2000), A is taken as volume of the bird to the 2/3 power, and ρ is water density (103 kg m–3). Virtual mass (m) is calculated from the mass of the bird (M) in kg, the added mass coefficient calculated for the bird in the mean angle-of-attack during the glide (Ca,, see morphometric measurements) and the volume of the bird (V) in m3. It is thus calculated as:
\[\ m=M+{\rho}VC_{\mathrm{a}}.\]
(5)
The calculations of Cd were made once for the glide stage(Cd,glide) and then for the combined glide + recovery stage (Cd,glide+recovery). After Cd,glide and Cd,glide+recovery are calculated, the Cd for the recovery stage(Cd,recovery) can be isolated either directly from the kinematic data of the deceleration during the recovery, or arithmetically,treating the Cd,glide+recovery as the mean contribution of the Cd,glide and the Cd,recovery combined:
\[\ C_{\mathrm{d},\mathrm{glide}+\mathrm{recovery}}=C_{\mathrm{d},\mathrm{glide}}\left(\frac{L_{\mathrm{g}}}{L_{\mathrm{g}}+L_{\mathrm{r}}}\right)+C_{\mathrm{d},\mathrm{recovery}}\left(\frac{L_{\mathrm{r}}}{L_{\mathrm{g}}+L_{\mathrm{r}}}\right),\]
(6)
where Cd,glide+recovery and Cd,glidewere calculated from Eqn 4 above, and the distances Lg and Lr are taken from the kinematic data.
We can now use the burst-and-glide model to calculate Cd for the burst (power) stage(Cd,stroke). The burst-and-glide model is based on a two-stage swimming behavior. It defines L1 as the distance traveled during the acceleration (burst) and L2 as the distance traveled during the deceleration and provides equations to calculate each of them from Ui and Uf (see Appendix). We used the fact that L1 and L2 can be measured directly from the kinematic data to solve these equations for α in the burst-and-glide model. The factorα is the ratio between the drag coefficient during the burst stage and the drag coefficient during the glide. We replaced L2 in the original calculation with our Lg+Lr and used Lpinstead of the original L1. The modified equations are therefore:
\[\ \frac{L_{\mathrm{g}}+L_{\mathrm{r}}}{L_{\mathrm{p}}}=\frac{{\alpha}{\,}\mathrm{ln}(U_{\mathrm{f}}{/}U_{\mathrm{i}})}{\mathrm{ln}(\mathrm{cosh}{\,}B+\overline{U_{\mathrm{i}}}{\,}\mathrm{sinh}{\,}B)},\]
(7)
where
\[\ B=\mathrm{tanh}^{-1}\frac{\overline{U_{\mathrm{f}}}-\overline{U_{\mathrm{i}}}}{1-\overline{U_{\mathrm{f}}}{\,}\overline{U_{\mathrm{i}}}},\]
(8)
where i=Ui/Ue and f=Uf/Ue; Ue is a reference velocity, chosen, for convenience, to be larger than the highest measured velocity so that the normalized values are always <1. Weihs (1974)called this speed the maximum achievable sustained swimming speed.
The factor α may now be isolated from Eqn 7 and solved using the values of Lp, Lg, Lr, Ui, Uf and Ue. Except for the latter, all parameters are available from the kinematic data. For Ue we used the value 2.5 m s–1, which was slightly higher than the maximum Uf observed in our data (2.41 m s–1). Once α is obtained, the Cd of the power stage(Cd,stroke) can be obtained from the definition ofα:
\[\ {\alpha}=\frac{C_{\mathrm{d},\mathrm{stroke}}}{C_{\mathrm{d},\mathrm{glide}+\mathrm{recovery}}},\]
(9)
where Cd,glide+recovery was obtained from Eqn 4.
We now have the drag coefficient for each of the stages (stroke, glide and recovery). To calculate the instantaneous drag force (at Re>105) from the drag coefficients at any point in time along the cormorant paddling cycle, one needs to substitute the appropriate Cd and instantaneous speed (U) into Eqn 1 and isolate D as:
\[\ D=\frac{1}{2}{\rho}C_{\mathrm{d}}AU^{2}.\]
(10)
The average drag for the entire paddling cycle is the integral of Eqn 10 over time, divided by the paddling cycle duration:
\[\ D=\frac{1}{2}{\rho}A\left(\frac{{{\int}_{0}^{t_{\mathrm{p}}}}C_{\mathrm{d},\mathrm{stroke}}U^{2}\mathrm{d}t+{{\int}_{t_{\mathrm{p}}}^{t_{\mathrm{p}+}t_{\mathrm{g}}}}C_{\mathrm{d},\mathrm{glide}}U^{2}\mathrm{d}t+{{\int}_{t_{\mathrm{p}+}t_{\mathrm{g}}}^{t_{\mathrm{p}+}t_{\mathrm{g}+}t_{\mathrm{r}}}}C_{\mathrm{d},\mathrm{recovery}}U^{2}\mathrm{d}t}{t_{\mathrm{p}}+t_{\mathrm{g}}+t_{\mathrm{r}}}\right),\]
(11)
where tp, tg and tr are the durations of the power glide and recovery stages, respectively (Fig. 2).
The burst-and-glide model was developed to evaluate the energetic advantage of using burst-and-glide. If we continue to solve the original model we can obtain the energetic advantage (R) of combining glides in the paddling cycle, as opposed to constant paddling at constant swimming speed,from the following equations (modified from Videler and Weihs, 1982; see Appendix):
\[\ \overline{U_{\mathrm{c}}}=\frac{{\alpha}{\,}\mathrm{ln}(U_{\mathrm{f}}{/}U_{\mathrm{i}})+\mathrm{ln}(\mathrm{cosh}{\,}B+\overline{U_{\mathrm{i}}}{\,}\mathrm{sinh}{\,}B)}{B+{\alpha}(1{/}\overline{U_{\mathrm{i}}}-1{/}\overline{U_{\mathrm{f}}})},\]
(12)
\[\ R=\left(\frac{1}{\overline{U_{\mathrm{c}}}^{2}}\right){\times}\left(\frac{1}{1+[(L_{\mathrm{g}}+L_{\mathrm{r}}){/}L_{\mathrm{p}}]}\right).\]
(13)
R is the ratio of the energy expended during burst-and-glide vs the energy expended for swimming constantly at the same average speed. In the case where there is no benefit in gliding R=1, and as R becomes smaller, the energetic advantage in burst-and-glide, as opposed to swimming at constant speed, will be greater. However, in our specific case, simply solving for R will result in an exaggerated value. This is because we combined the recovery stage with the glide for the drag estimation. The α value that we calculated above (as a means to find Cd,stroke) considers only the stroke stage as `active swimming', while in practice, the recovery stage is part of the active swimming as well. To find α that is relevant for the calculation of the energetic advantage in combining glides into the paddling cycles that contain only stroke and recovery, we repeated the analysis, this time with the recovery included in the burst stage of the burst-and-glide model.
We defined a new drag coefficient for the stroke + recovery stages(Cd,propulsion) and recalculated α (Eqn 7), this time replacing L1 with(Lp+Lr), and Uiwith Ur (the velocity at the beginning of the recovery stage). The above mentioned Eqn 7 and 8 then become:
\[\ \frac{L_{\mathrm{g}}}{L_{\mathrm{p}}+L_{\mathrm{r}}}=\frac{{\alpha}{\,}\mathrm{ln}(U_{\mathrm{f}}{/}U_{\mathrm{r}})}{\mathrm{ln}(\mathrm{cosh}{\,}B+\overline{U_{\mathrm{r}}}{\,}\mathrm{sinh}{\,}B)},\]
(14)
and
\[\ B=\mathrm{tanh}^{-1}\frac{\overline{U_{\mathrm{f}}}-\overline{U_{\mathrm{r}}}}{1-\overline{U_{\mathrm{f}}}{\,}\overline{U_{\mathrm{r}}}},\]
(15)
where =Ur/Ue.
The new α obtained is defined as:
\[\ {\alpha}=\frac{C_{\mathrm{d},\mathrm{propulsion}}}{C_{\mathrm{d},\mathrm{glide}}}.\]
(16)
We then continue to use the burst-and-glide model, replacing L1 in the original model with(Lp+Lr), and Uiwith Ur. Thus, Eqn 12 and 13 above become:
\[\ \overline{U_{\mathrm{c}}}=\frac{{\alpha}{\,}\mathrm{ln}(U_{\mathrm{f}}{/}U_{\mathrm{r}})+\mathrm{ln}(\mathrm{cosh}{\,}B+\overline{U_{\mathrm{r}}}{\,}\mathrm{sinh}{\,}B)}{B+{\alpha}(1{/}\overline{U_{\mathrm{r}}}-1{/}\overline{U_{\mathrm{f}}})},\]
(17)
and
\[\ R_{\mathrm{p}}=\left(\frac{1}{\overline{U_{\mathrm{c}}}^{2}}\right){\times}\left(\frac{1}{1+[L_{\mathrm{g}}{/}L_{\mathrm{p}}+L_{\mathrm{r}})]}\right).\]
(18)
This Rp is the energetic saving, adjusted for the special case of three-stage paddling. It gives the ratio of the energy required for a paddling cycle including a glide vs the energy needed to swim constantly at the same average swimming speed, with a paddling cycle that includes only stroke and recovery.

Data analysis

Thirty five sequences (from ten different birds) were fully analyzed for the drag coefficients and burst-and-glide parameters (R,Rp) while a larger sample size was used to analyze gait,paddling frequency and stride length (95 sequences). Statistical significance for correlations between variables was tested using Statistica (StatSoft,Tulsa, OK, USA). To ensure no bias from pseudo-replications or the unequal number of trials per bird, statistical significance of all correlations that are reported here for all the trials were tested a second time using mean values per bird (N=10 birds). Similarly, the mean values reported throughout this work are the means of all birds (N=10), calculated by averaging all values from sequences from a single bird and then averaging for all birds. Values of statistical variation quoted in the text and figures are thus standard error of mean (s.e.m.) where N=10 birds. Tables 2and 3 are an exception. These tables present the means of each bird calculated from small and unequal sample size. We therefore chose to present variance in these tables as the standard deviation (s.d.).

Table 2.

Kinematic data from the swimming sequences of the great cormorant

BirdU (m s-1)NLp (m)Lg (m)Lr (m)Ui (m s-1)Uf (m s-1)Ur (m s-1)tp (s)tg (s)tr (s)
1.43±0.169 0.186±0.009 0.585±0.072 0.164±0.040 1.28±0.39 1.69±0.099 1.13±0.129 0.17±0.048 0.35±0.118 0.17±0.020 
1.75±0.182 0.229±0.069 0.541±0.016 0.217±0.081 1.29±0.43 2.13±0.266 1.87±0.284 0.12±0 0.25±0.014 0.15±0.042 
1.31 0.191 0.472 0.216 0.55 1.98 1.37 0.12 0.24 0.24 
1.68±0.092 0.224±0.020 0.549±0.164 0.262±0.029 1.42±0.12 1.98±0.232 1.48±0.237 0.13±0.034 0.205±0.030 0.2±0.023 
1.62±0.230 0.207±0.029 0.685±0.098 0.158±0.026 1.41±0.27 1.89±0.330 1.52±0.284 0.14±0.046 0.38±0.071 0.14±0.022 
1.71±0.027 0.237±0.009 0.868±0.049 0.142±0.015 1.34±0.10 2.09±0.132 1.49±0.250 0.13±0.023 0.48±0.026 0.11±0.011 
1.47±0.047 0.195±0.010 0.314±0.159 0.009±0.525 1.32±0.21 1.65±0.092 1.55±0.136 0.14±0.02 0.19±0.081 0.15±0.012 
1.40±0.064 0.163±0.539 0.567±0.133 0.184±0.09 0.90±0.22 1.61±0.200 1.19±0.159 0.14±0.017 0.40±0.121 0.20±0.080 
1.30±0.058 0.170±0.010 0.578±0.233 0.152±0.049 0.97±0.08 1.37±0.308 1.09±0.172 0.15±0.026 0.45±0.126 0.15±0.026 
10 1.62±0.008 0.209±0.002 0.509±0.046 0.198±0.029 1.15±0.11 2.15±0.242 1.58±0.177 0.12±0 0.24±0 0.15±0.014 
BirdU (m s-1)NLp (m)Lg (m)Lr (m)Ui (m s-1)Uf (m s-1)Ur (m s-1)tp (s)tg (s)tr (s)
1.43±0.169 0.186±0.009 0.585±0.072 0.164±0.040 1.28±0.39 1.69±0.099 1.13±0.129 0.17±0.048 0.35±0.118 0.17±0.020 
1.75±0.182 0.229±0.069 0.541±0.016 0.217±0.081 1.29±0.43 2.13±0.266 1.87±0.284 0.12±0 0.25±0.014 0.15±0.042 
1.31 0.191 0.472 0.216 0.55 1.98 1.37 0.12 0.24 0.24 
1.68±0.092 0.224±0.020 0.549±0.164 0.262±0.029 1.42±0.12 1.98±0.232 1.48±0.237 0.13±0.034 0.205±0.030 0.2±0.023 
1.62±0.230 0.207±0.029 0.685±0.098 0.158±0.026 1.41±0.27 1.89±0.330 1.52±0.284 0.14±0.046 0.38±0.071 0.14±0.022 
1.71±0.027 0.237±0.009 0.868±0.049 0.142±0.015 1.34±0.10 2.09±0.132 1.49±0.250 0.13±0.023 0.48±0.026 0.11±0.011 
1.47±0.047 0.195±0.010 0.314±0.159 0.009±0.525 1.32±0.21 1.65±0.092 1.55±0.136 0.14±0.02 0.19±0.081 0.15±0.012 
1.40±0.064 0.163±0.539 0.567±0.133 0.184±0.09 0.90±0.22 1.61±0.200 1.19±0.159 0.14±0.017 0.40±0.121 0.20±0.080 
1.30±0.058 0.170±0.010 0.578±0.233 0.152±0.049 0.97±0.08 1.37±0.308 1.09±0.172 0.15±0.026 0.45±0.126 0.15±0.026 
10 1.62±0.008 0.209±0.002 0.509±0.046 0.198±0.029 1.15±0.11 2.15±0.242 1.58±0.177 0.12±0 0.24±0 0.15±0.014 

Listed are the parameters used as input in the burst and glide model (see List of symbols and Fig. 2 for descriptions of the parameters). Each parameter is the mean ± s.d. of all the sequences analyzed from the same bird (N =number of sequences per bird).

Table 3.

The calculated drag coefficient for each stage of the paddling cycle of the great cormorant and the resulting average drag per cycle

BirdMass (kg)Length (m)Re×106RpRCd,glideCd,recoveryCd,strokeDrag cycle-1
1.99 0.74 1.04 1.22±0.16 0.62±0.21 0.176±0.145 0.030±0.353 0.339±0.041 4.3±0.14 
2.30 0.82 1.41 0.73±0.20 0.55±0.27 0.101±0.031 0.476±0.230 0.711±0.233 10.6±2.05 
1.89 0.73 0.94 1.04 1.26 0.180 0.565 0.394 5.2 
2.10 0.79 1.32 1.01±0.20 0.50±0.13 0.120±0.043 0.201±0.097 0.556±0.418 7.4±4.35 
2.40 0.77 1.24 0.80±0.15 0.49±0.16 0.124±0.026 0.183±0.103 0.480±0.164 6.0±2.02 
2.18 0.77 1.31 0.62±0.12 0.43±0.04 0.091±0.017 0.122±0.104 0.411±0.135 4.7±1.06 
2.00 0.76 1.11 1.31±0.19 0.80±0.23 0.166±0.087 0.189±0.085 0.287±0.211 4.07±2.90 
1.48 0.72 1.00 1.22±1.24 0.82±0.22 0.180±0.041 0.423±0.256 0.373±0.104 3.2±0.55 
1.80 0.71 0.92 1.16±0.32 0.74±0.58 0.171±0.025 0.343±0.289 0.325±0.083 3.5±0.9 
10 1.90 0.75 1.21 0.79±0.02 0.57±0.03 0.119±0.061 0.194±0.243 0.441±0.007 5.6±1.00 
Mean ± S.D. 2.004±0.263 0.76±0.03 1.12±0.172 0.99±0.242 0.68±0.246 0.143±0.035 0.273±0.171 0.432±0.126 5.5±2.16 
BirdMass (kg)Length (m)Re×106RpRCd,glideCd,recoveryCd,strokeDrag cycle-1
1.99 0.74 1.04 1.22±0.16 0.62±0.21 0.176±0.145 0.030±0.353 0.339±0.041 4.3±0.14 
2.30 0.82 1.41 0.73±0.20 0.55±0.27 0.101±0.031 0.476±0.230 0.711±0.233 10.6±2.05 
1.89 0.73 0.94 1.04 1.26 0.180 0.565 0.394 5.2 
2.10 0.79 1.32 1.01±0.20 0.50±0.13 0.120±0.043 0.201±0.097 0.556±0.418 7.4±4.35 
2.40 0.77 1.24 0.80±0.15 0.49±0.16 0.124±0.026 0.183±0.103 0.480±0.164 6.0±2.02 
2.18 0.77 1.31 0.62±0.12 0.43±0.04 0.091±0.017 0.122±0.104 0.411±0.135 4.7±1.06 
2.00 0.76 1.11 1.31±0.19 0.80±0.23 0.166±0.087 0.189±0.085 0.287±0.211 4.07±2.90 
1.48 0.72 1.00 1.22±1.24 0.82±0.22 0.180±0.041 0.423±0.256 0.373±0.104 3.2±0.55 
1.80 0.71 0.92 1.16±0.32 0.74±0.58 0.171±0.025 0.343±0.289 0.325±0.083 3.5±0.9 
10 1.90 0.75 1.21 0.79±0.02 0.57±0.03 0.119±0.061 0.194±0.243 0.441±0.007 5.6±1.00 
Mean ± S.D. 2.004±0.263 0.76±0.03 1.12±0.172 0.99±0.242 0.68±0.246 0.143±0.035 0.273±0.171 0.432±0.126 5.5±2.16 

Cd,glide, Cd,recovery and Cd,stroke are the drag coefficients during the glide,recovery and stroke stages, respectively (see text for the description of the stages).

Also listed are the dimensions of the birds: mass used to estimate the area of the birds (V2/3) and length used in the calculation of the Reynolds number (Re) for the swimming cycle, Re=(length×U)/ν, where U is the average swimming speed for a paddling cycle. Rp and R are the energy ratios in the burst and glide model, where Rpis calculated with the recovery stage as part of the burst stage and R is calculated with the recovery stage as part of the glide stage.

Values listed are the means for each bird ± s.d. The sample size for each bird is as listed in Table 2.

The morphometric measurements performed on carcasses are summarized in Table 1.

The swimming speed of the cormorants in the video sequences was 1.51±0.058 m s–1 (N=10 birds). Mean swimming speed calculated for each bird in the experiment(Fig. 3) was correlated with the bird's body mass (r=0.75, P<0.015, N=10) and body length (r=0.87, P<0.015, N=10). The paddling frequency was positively correlated with swimming speed(r=0.56, P<0.001, N=95 sequences). This was achieved mainly by shortening the duration of the glide stage as the paddling frequency increased (r=–0.86, P<0.001, N=95 sequences) while the duration of the stroke and recovery stages remained unaffected (stroke: r=0.009, P>0.93; recovery: r=0.035, P>0.74) (Fig. 4A). Taking this into account, the relation between the duration of the glide stage and the paddling frequency suggests a maximal paddling frequency of approximately 2.7 Hz when glide duration is zero(Fig. 4A,B).

Table 2 summarizes the kinematic data used for the drag estimation and Table 3 summarizes the various drag coefficients, R and Rp, calculated from the model. The Re for each bird, based on body length and average speed(Table 3), ranged between 0.9×106 and 1.4×106 (mean=1.12×106±5.92×104). The average Cd,glide calculated for each bird, using V2/3 as a reference area, was 0.143±0.011(N=10 birds), but ranged between a minimum of 0.091 to a maximum of 0.180. The Cd,glide calculated for each sequence was negatively correlated with the Re and mean swimming speed calculated for the same sequence (r<–0.62, P<0.001, N=35 in both cases). When the average Cd,glidefor each bird was compared with the average Re (or the average speed)for the same bird (giving equal weight to all birds) the correlation improved(r<–0.93, P<0.001, N=10). Each Cd,glide obtained from a video sequence was positively correlated with the average angle-of-attack of the body during the glide in that sequence (r=0.50, P<0.003, N=35). A similar relation between the average angle-of-attack during the stroke and Cd,stroke was not significant (r=–0.11, P>0.54, N=35 sequences). The average angle-of-attack during the glide was negatively correlated to the average swimming speed(r=–0.65, P<0.001, N=35), so while swimming faster the birds were swimming at smaller angle-of-attack and vice versa. The average angle-of-attack during the stroke stage was not significantly correlated to the average swimming speed(r=–0.29, P>0.09, N=35) or to the average swimming speed during the stroke phase (r=–0.21, P>0.22, N=35). Cd,stroke was positively correlated with the average swimming speed (r=0.41, P<0.015, N=35).

Fig. 3.

The average swimming speed observed for each cormorant in the experiment relative to body length. Each point is the mean swimming speed obtained from 5–10 sequences taken of the same bird (values are ± s.e.m.).

Fig. 3.

The average swimming speed observed for each cormorant in the experiment relative to body length. Each point is the mean swimming speed obtained from 5–10 sequences taken of the same bird (values are ± s.e.m.).

The average Cd,recovery and the Cd,stroke were 0.273±0.054 and 0.432±0.040 respectively (N=10 birds). The average Cd,recovery and Cd,stroke for each bird were 2.6±0.71- and 3.2±0.57-fold higher, respectively, than Cd,glide of the same bird (N=10). The average drag for the entire paddling cycle (as calculated from Eqn 11) for each bird was 5.5±0.68 N (N=10). The drag was highest during the stroke,then decreased considerably during the glide, and increased slightly during the recovery stage (Fig. 5). The burst-and-glide model predicts an average Rp value of 0.99±0.077 and a R value of 0.68±0.078(Table 3). Thus, when the recovery stage is considered as part of the glide, the average energetic gain of the birds from the non-constant swimming speed is 32%. However, if the recovery is considered as part of the burst stage, then on average there is no energetic saving from using burst-and-glide. The values of R and Rp were negatively correlated with the average swimming speed (r<–0.68; P<0.001; N=35 for both R and Rp), suggesting that the faster birds were gaining more from burst-and-glide while the slower birds were actually losing from it relative to an idealized constant swimming(Fig. 6A). The αcalculated from the burst-and-glide model (using Eqn 7 or 14) increased non-linearly with the increase in swimming speed(Fig. 6B). At low speeds,α was close to 1 and then increased sharply up to 8 in the fastest birds.

Fig. 4.

The duration of each stage in the paddling cycle of the great cormorant (A)and the proportion of the power (burst) and deceleration (glide + recovery)stages in the paddling cycle (B) in relation to paddling frequency. Note that the glide duration decreased with the increase in paddling frequency. At a paddling frequency of 2.7 Hz, the duration of the glide phase was diminished to almost zero so that the power and recovery stages each occupy ∼50% of the paddling cycle duration.

Fig. 4.

The duration of each stage in the paddling cycle of the great cormorant (A)and the proportion of the power (burst) and deceleration (glide + recovery)stages in the paddling cycle (B) in relation to paddling frequency. Note that the glide duration decreased with the increase in paddling frequency. At a paddling frequency of 2.7 Hz, the duration of the glide phase was diminished to almost zero so that the power and recovery stages each occupy ∼50% of the paddling cycle duration.

The present study shows that in order to swim faster, cormorants shorten their paddling cycle by shortening the duration of the glide stage within each cycle. Clark and Bemis (1979)reported a similar trend in penguins and suggested that this either allows the propelling muscles to operate at maximum efficiency over a range of swimming speeds or allows an energy saving from burst-and-glide swimming. In the case of the cormorant, an additional advantage is derived from the fact that the recovery stage occurs when the speed of the body is minimal. Thus, the increase in the drag coefficient during the recovery stage is compensated for by the lower swimming speed at the end of the paddling cycle, maintaining a relatively low drag (Fig. 5).

During the glide, the body is at the smallest angle-of-attack, the neck is aligned with the swimming direction, and the feet are trailing behind the body. At this posture, the bird can optimally use its momentum to keep moving at relatively low drag. During propulsion (stroke and recovery), the tilt of the body is increased and the feet are moved from their posterior position under the tail. This results in an increase in the drag coefficient, and thus the drag of active swimming is higher than during gliding. The duration of the paddling cycle is determined by the length of the glide stage. When paddling frequency increases, propulsion occupies a more significant portion of the paddling cycle (Fig. 4B) and this affects the drag of the bird. Therefore, the ability to calculate a drag coefficient for each stage of the swimming cycles, using simple kinematics,allows the more accurate calculation of the drag during swimming for a wide range of paddling cycles that combine glides and propulsion.

While the drag coefficient for the glide stage was lower than the drag coefficient for the recovery and stroke stages, its value was affected by the need to counter buoyancy. Cormorants are positively buoyant and use hydrodynamic lift to counter their tendency to float while swimming underwater(Ribak et al., 2004). The magnitude of the lift force is dependent on swimming speed and on the angle-of-attack of the body. We show here that the birds that were swimming slower had higher drag coefficients for the glide stage. This is because the slower birds tilted their body at a larger angle-of-attack to compensate for the reduced speed and achieve sufficient lift to counter their buoyancy. This tilt increased their drag coefficient, as evident from the significant correlation between Cd,glide and the tilt of the body. Thus, the actual drag encountered by cormorants swimming at shallow depths is greatly affected by the need to counter buoyancy. Buoyancy is considered the primary mechanical constraint of diving water birds, but this constraint is depth-dependent (Wilson et al.,1992; Lovvorn and Jones,1991). Here we show that although the birds have managed to cope with the mechanical constraint of buoyancy during shallow submerged swimming,there exists an energetic trade-off in which the birds are required either to swim faster or swim at a larger angle-of-attack, increasing the drag in either case and thus making shallow foraging more costly.

Fig. 5.

The distribution of the momentary drag along an average paddling cycle of the great cormorant. Momentary drag is calculated using the Cd average for each of the paddling stages. To average all the analyzed sequences despite the differences in cycle duration, the x-axis is the proportion of the cycle duration that is normalized by dividing the period of each stage (stroke, glide and recovery) by the mean duration of that stage. To allocate equal weight to all birds, the sequences of each bird were first averaged and then means ± s.e.m. of all birds were calculated.

Fig. 5.

The distribution of the momentary drag along an average paddling cycle of the great cormorant. Momentary drag is calculated using the Cd average for each of the paddling stages. To average all the analyzed sequences despite the differences in cycle duration, the x-axis is the proportion of the cycle duration that is normalized by dividing the period of each stage (stroke, glide and recovery) by the mean duration of that stage. To allocate equal weight to all birds, the sequences of each bird were first averaged and then means ± s.e.m. of all birds were calculated.

Unlike in the glide stage the Cd,stroke was not statistically correlated with the average angle-of-attack of the body during the stroke. This may be due to the fact that the angle-of-attack changes throughout the stroke stage while our Cd,stroke is an average for the entire stage. Another explanation is that during the stroke the tail changes orientation and the feet move beneath the body, thus changes in the drag coefficient during propulsion are not limited to the increase in the angle-of-attack. Cd,stroke was, however, positively correlated with the average swimming speed. Thus as swimming speed increased, Cd,glide decreased while Cd,strokeincreased, and this resulted in the increase in α observed here(Fig. 6B).

The birds in our study differed only slightly in body length(0.71–0.82 m), and to a greater extent in average swimming speed(1.3–1.75 m s–1). Hence the variation in Rebetween birds was mainly due to the difference in swimming speeds. Rewas negatively correlated with Cd,glide. Such a relation may be due to a reduction in the thickness of the boundary layer(Hoerner, 1965). In our case,however, it is more likely that the decrease in Cd,glidewith speed is due to the above-mentioned need to tilt the body further during slow swimming. Regardless of the precise reason for the decrease in Cd,glide at higher Re, this relationship explains why each of our birds had a fairly distinct swimming speed(Fig. 3) that was correlated with body size. The average thrust for a complete cycle, developed by each bird, should equal its drag. If we assume that the thrust developed by each bird during the paddling is proportional to the bird's size (i.e. thrust/A=constant), then the birds should glide at similar values of Cd,glideU2. Multiplying the square of the average swimming speed and the average Cd,glide obtained for each bird yields a constant value (0.309±0.0089; N=10)that was not significantly correlated with the length of the birds or with their body mass (r<0.24, P>0.5, N=10 for both cases). Thus, the observed variation in swimming speeds among birds was a consequence of the birds' drag coefficients during the glide.

Fig. 6.

The `burst-and-glide' parameters R or Rp (A)and α (B) in relation to the average swimming speed of the great cormorant in each paddling cycle. Open symbols denote calculated values when the recovery is treated as part of the burst stage and full symbols are calculated values when the recovery is treated as part of the glide stage (see text). Solid horizontal lines mark the proportion of 1, where the energetic cost of burst-and-glide is exactly the same as for swimming at constant speed. Broken vertical lines in A mark the threshold average speed where the least square regression of the points (broken line for Rp, solid line for R) intersects with the value of 1. At this swimming speed the energetic benefit from burst-and-glide changes from gain (R<1)into loss (R>1). In B, values ≤1 imply that the drag coefficient for passive drag is as high as or higher than the coefficient for active swimming. Note that the open symbols represent a more conservative approach for estimating the energetic advantage from burst-and-glide.

Fig. 6.

The `burst-and-glide' parameters R or Rp (A)and α (B) in relation to the average swimming speed of the great cormorant in each paddling cycle. Open symbols denote calculated values when the recovery is treated as part of the burst stage and full symbols are calculated values when the recovery is treated as part of the glide stage (see text). Solid horizontal lines mark the proportion of 1, where the energetic cost of burst-and-glide is exactly the same as for swimming at constant speed. Broken vertical lines in A mark the threshold average speed where the least square regression of the points (broken line for Rp, solid line for R) intersects with the value of 1. At this swimming speed the energetic benefit from burst-and-glide changes from gain (R<1)into loss (R>1). In B, values ≤1 imply that the drag coefficient for passive drag is as high as or higher than the coefficient for active swimming. Note that the open symbols represent a more conservative approach for estimating the energetic advantage from burst-and-glide.

The average Cd,glide reported here is intermediate between the values calculated for a model and for carcasses of the Brandt's cormorant (P. pencillatus) towed in a water tunnel by Lovvorn et al.(2001). Our value for Cd,glide at Re=1.12×106 using surface area as a reference (see Table 1 for the conversion factor) was 0.0186±0.0014. This value is higher than that reported for a featherless model, but slightly lower than the value reported for a frozen carcass (∼0.008 and ∼0.022,respectively, at Re=106; data taken from figs 6 and 7 in Lovvorn et al., 2001). Drag measurements on carcasses of birds tend to overestimate the drag coefficient due to feather fluttering (Pennycuick et al., 1988; Tucker,1990). The featherless model, on the other hand, underestimates the true drag of the birds during the glide by measuring drag at zero lift(θ=0).

Our original application of the burst-and-glide model was to calculate drag coefficients and drag for the entire paddling cycle of the cormorants. However, the model also provides a tool with which to explore the energetic benefit (if existing) of the paddling cycle of these birds. The values of Rp and R that were calculated in our case are rather hypothetical because the burst-and-glide model was designed for animals such as fish that can develop constant thrust. In the original model, the energy required for a fish to overcome water resistance during swimming is compared between swimming at constant speed and swimming at periodically varying speeds oscillating around the same average swimming speed. The paddling of the cormorant, with both feet moving together, is different from this scenario due to existence of the recovery stage. Cormorants can never truly swim at constant speed since the body decelerates during the recovery stage. Therefore, the R and Rp we obtained from the model is the energetic saving from the burst-and-glide swimming pattern relative to the energy required for swimming at constant speed, which is only theoretical. Another difference is the fact that although the recovery is a continuation of the glide (since the body continues to decelerate), it is also part of the burst stage, since without it there is no constant paddling. To deal with these special characteristics of paddling we included the recovery stage in the burst, and therefore compared the energetic saving from combining glides with propulsion, as opposed to paddling constantly at the same average speed.

The values we found for Rp(Table 3, Fig. 6A) suggested that most of our birds were gaining little from combining glides with the paddling cycle. As the average swimming speed became increasingly lower than Ue, the energetic advantage from burst-and-glide diminished to a point where, according to the model, the birds that would propel constantly would save more energy than the birds that added glides to their paddling cycle (Rp>1). The inverse relation between swimming speed and Rp is predicted by the burst-and-glide model. Weihs(1974) has shown that for a given α, R increases (energy saving decreases) when the average swimming speed is reduced with respect to Ue. Therefore,for each value of α there is a minimum average swimming speed where burst-and-glide becomes inefficient. Swimming below this threshold speed will result in R>1. In addition to this the threshold speed decreases as α becomes higher. This way, birds with a higher α benefit from burst-and-glide even at slower swimming speeds. The slower birds in our experiments had the lowest values of α due to the fact that their Cd,glide was relatively higher. This elevated Cd,glide was due to the need to counter buoyancy at shallow depths. It follows that at deeper depths, where buoyancy of the birds is reduced, Cd,glide will decrease (due to a decrease in the angle-of-attack). Cd,stroke does not seem to be related to buoyancy as Cd,glide, and if this is indeed the case then α should increase with depth, making burst-and-glide more beneficial. This conjecture can be validated by Eqn 7 and 14 above. If we assume that birds swim with the same Ui and Uf but at deeper depth so that their buoyancy is reduced,and also Cd,glide, then the birds deceleration during the glide stage should reduce as well. Since Ui and Uf remain the same, the birds glide for longer to decelerate from Uf to Ui (or from Uf to Ur), thereby traversing a larger distance of Lg. Since Lg is the numerator in Eqn 7 and 14, the larger Lg for the same set of Ui and Uf results in a largerα. Therefore, the ineffective burst-and-glide observed here(Rp≥1) may prove beneficial at larger depths where buoyancy of the birds is lower.

Fig. 6 shows that the transition from benefit to loss (Rp=1) from adding glides to the paddling cycle occurs at an average swimming speed of about 1.5 m s–1, which is identical to the mean swimming speed observed in our birds. Therefore, only birds that swim at high speeds may gain from adding a glide to their paddling cycle, relative to constant paddling. Yet,all the birds were adding glides to all paddling cycles, regardless of their average speed. The reason is that Rp is a conservative estimate. As mentioned above, the recovery stage is part of the propulsion, on one hand, but it is also part of the deceleration, on the other. When we add the recovery to the stroke stage, we reduce the average acceleration during the burst stage, lower the average drag coefficient for the burst stage(Cd,propulsion), lengthen the burst stage, and shorten the deceleration stage. This makes paddling less costly relative to gliding(α becomes smaller) and hence the gain in gliding diminishes. However,during the recovery stage the bird continues to move forward(Lr) at a lower drag coefficient and without adding thrust. If the model is rearranged, with the recovery stage added to the glide stage, then the burst stage shortens, it has a higher drag coefficient and the deceleration stage is longer. The R calculated this way (Eqn 7–13) is mostly below 1, and the threshold swimming speed shifts to∼1.0 m s–1 (Fig. 6). This speed is similar to the minimal average swimming speed observed from our birds (1.154 m s–1; bird 8). The true energetic benefit and threshold swimming speed are somewhere in between these extreme values for R and U.

The R and Rp values express the energy savings from using burst-and-glide vs swimming at constant speed. A hypothetical scenario where cormorants are able to swim at constant speed is one where the birds will use alternate paddling underwater. Cormorants only use alternate paddling while swimming on the surface and use synchronized strokes only underwater (Ancel et al.,2000; Lovvorn,1991). It is thus interesting to note that the transition between alternate paddling and synchronized strokes should occur at a swimming speed of 1.0–1.5 m s–1, which is similar to the findings that surface-swimming Brandt's cormorants switch from surface swimming to submerged swimming at a speeds of about 1.3 m s–1(Ancel et al., 2000). The birds dive primarily to avoid the higher work against drag at the surface, but the point of transit from surface swimming to submerged swimming also encompasses a change in gait, from alternate paddling to synchronized strokes, and this point of transit fits well with the energy saving threshold found in the present study. However, further research is needed to test the suggestion that in paddlers the shift from alternate to synchronized paddling occurs in agreement with burst-and-glide predictions. If the cormorant has indeed a higher α when swimming at the same swimming speed but at deeper depths,then the associated shift of the threshold swimming speed to slower speeds (as predicted by the burst-and-glide model; Weihs, 1974; Fig. 6A) will ensure that burst-and-glide will have a higher benefit with depth making alternate paddling underwater inefficient in practical swimming speeds. The closely related anhinga, however, is similar to the cormorant in shape but has a different foraging strategy. Due to unusual plumage wettability it relies on hydrostatic mechanisms to become neutrally buoyant underwater(Johansgard, 1993). This allows it to swim very slowly underwater and stalk pray (unlike the active pray chasing in the cormorant). Alternate paddling underwater as well as synchronized strokes have been reported for anhingas(Owre, 1967), and this raises the question whether this behavior is associated with burst-and-glide efficiency, as discussed above. If the bird is neutrally buoyant its αshould remain constant with depth and so should the trade-off speed. Therefore during slow swimming, anhingas may profit from shifting to alternate paddling when burst-and-glide is no longer effective. Unfortunately this suggestion cannot be evaluated at present due to lack of observations on the relationship between paddling gait and horizontal swimming speed at various depths in anhingas and cormorants.

     
  • a

    acceleration

  •  
  • A

    area (general)

  •  
  • α

    ratio between the Cd for active swimming and Cd for gliding

  •  
  • Aw

    surface area

  •  
  • C

    average linear slope of the inverse instantaneous swimming speed vs time

  •  
  • c

    components of drag that are not speed dependant(0.5ρACd)

  •  
  • Ca

    added mass coefficient (general)

  •  
  • Ca(θ)

    added mass coefficient when the body is tilted at an angle of attack=θ

  •  
  • Cax

    added mass coefficient for motion parallel to the length of a body

  •  
  • Cay

    added mass coefficient for motion perpendicular (vertical) to the length of a body

  •  
  • Cd

    drag coefficient (general)

  •  
  • Cd,glide+recovery

    average drag coefficient during the glide + recovery stage

  •  
  • C

    d,glide drag coefficient during the glide stage

  •  
  • Cd,propulsion

    average drag coefficient during the power + recovery stage

  •  
  • C

    d,recovery drag coefficient during the recovery stage

  •  
  • C

    d,stroke drag coefficient during the power (acceleration)stage

  •  
  • D

    hydrodynamic drag force

  •  
  • ρ

    density of water (103 kg m–3)

  •  
  • F

    force (general)

  •  
  • l

    body length

  •  
  • L1

    distance traversed during the burst in the original burst-and-glide model

  •  
  • L2

    distance traversed during the glide in the original burst-and-glide model

  •  
  • Lg

    distance traversed during the glide stage

  •  
  • Lp

    distance traversed during the power (acceleration) stage

  •  
  • Lr

    distance traversed during the recovery stage

  •  
  • M

    mass

  •  
  • m

    virtual mass (mass of the body + added mass of water)

  •  
  • R

    relative energetic saving from burst-and-glide (in the case of the cormorant: when the recovery stage is considered as part of the glide)

  •  
  • Re

    Reynolds number

  •  
  • Rp

    relative energetic saving from burst-and-glide when the recovery stage is considered as part of the burst

  •  
  • tg

    duration of the glide stage

  •  
  • tp

    duration of the power stage

  •  
  • tr

    duration of the recovery stage

  •  
  • θ

    angle-of-attack

  •  
  • U

    speed (general)

  •  
  • c

    average swimming speed in the burst-and-glide model divided by Ue

  •  
  • Uc

    average swimming speed in the burst-and-glide model

  •  
  • Ue

    maximum achievable swimming speed

  •  
  • f

    instantaneous speed at the end of the burst stage divided by U

  •  
  • Uf

    instantaneous speed at the end of the burst stage

  •  
  • i

    instantaneous speed at the start of the burst stage divided by Ue

  •  
  • Ui

    instantaneous speed at the start of the burst stage

  •  
  • r

    instantaneous speed at the start of the recovery stage divided by Ue

  •  
  • Ur

    instantaneous speed at the start of the recovery stage

  •  
  • V

    volume

  •  
  • V2/3

    volume of the bird to the 2/3 power (representing area)

  •  
  • y

    half the body height measurement at a point along the body's length

  •  
  • υ

    kinematic viscosity of fresh water (at 20°C=∼10–6 m2s–1)

  •  
  • z

    half the body width measurement at a point along the body's length

The `burst-and-glide' model summarized in brief from Weihs(EF481974)

Burst-and-glide is an energy saving locomotion strategy where, instead of swimming at a constant speed, an animal accelerates from an initial velocity Ui to a final velocity Uf during a short stage termed `burst'. It then glides passively (without producing thrust), decelerating until it reaches the initial velocity Ui (glide stage). During this cycle the animal travels at an average swimming speed Uc. To evaluate when burst-and-glide is energetically efficient, the energy expended from this swimming strategy is compared to the energy expended during swimming at constant speed Uc. This is done by calculating the energy ratio R, which is the ratio between the energy needed to burst-and-glide vs the energy needed to swim constantly, where in both cases the average swimming speed is Uc. Weihs(1974) showed that Rcan be calculated from Ui and Uf,(which are obtained directly from observations) if two additional parameters, Ue and α, are known. Ue is the maximum sustained velocity achievable during maximum thrust. It is used to normalize all speeds to a value ≤1. The parameter α is the factor describing the increment in drag when an animal perform swimming motions as oppose to gliding passively (rigid body). In his analysis, Weihs(1974) developed equations for the distances traversed (L1 and L2)and the time period (t1 and t2) during the burst and the glide stages, respectively, and for Uc. In final form these equations are listed below.

The distance traveled during the burst stage (eqn 21 in Weihs, 1974):
\[\ L_{1}=\frac{m}{{\alpha}c}\mathrm{ln}\left[\mathrm{cosh}{\,}B+\left(\frac{U_{\mathrm{i}}}{U_{\mathrm{e}}}\right)\mathrm{sinh}{\,}B\right].\]
(A1)
The distance traveled during the glide stage (eqn 24a in Weihs, 1974):
\[\ L_{2}=\left(\frac{m}{c}\right)\mathrm{ln}\left(\frac{U_{\mathrm{f}}}{U_{\mathrm{i}}}\right).\]
(A2)
The duration of the burst stage (eqn 22 in Weihs, 1974):
\[\ t_{1}=\frac{1}{(\frac{{\alpha}cU_{\mathrm{e}}}{m})}\mathrm{tanh}^{-1}\frac{(\frac{U_{\mathrm{f}}}{U_{\mathrm{e}}}-\frac{U_{\mathrm{i}}}{U_{\mathrm{e}}})}{(1-\frac{U_{\mathrm{f}}U_{\mathrm{i}}}{U_{\mathrm{e}}^{2}})}.\]
(A3)
The duration of the glide stage (eqn 24b in Weihs, 1974)
\[\ t_{2}=\frac{m}{cU_{\mathrm{e}}}\left(\frac{U_{\mathrm{e}}}{U_{\mathrm{i}}}-\frac{U_{\mathrm{e}}}{U_{\mathrm{f}}}\right).\]
(A4)
The average swimming speed (eqn 25 in Weihs, 1974)
\[U_{\mathrm{c}}=U_{\mathrm{e}}\frac{{\alpha}{\,}\mathrm{ln}(\frac{U_{\mathrm{f}}}{U_{\mathrm{i}}})+\mathrm{ln}[\mathrm{cosh}{\,}B+(\frac{U_{\mathrm{i}}}{U_{\mathrm{e}}})\mathrm{sinh}{\,}B]}{B+{\alpha}(\frac{U_{\mathrm{e}}}{U_{\mathrm{i}}}-\frac{U_{\mathrm{e}}}{U_{\mathrm{f}}})}\]
and
\[\ B=\mathrm{tanh}^{-1}\frac{(\frac{U_{\mathrm{f}}}{U_{\mathrm{e}}}-\frac{U_{\mathrm{i}}}{U_{\mathrm{e}}})}{(1-\frac{U_{\mathrm{i}}U_{\mathrm{f}}}{U_{\mathrm{e}}^{2}})}.\]
(A5)
m is the virtual mass (mass + added mass of water accelerated with the body) and c is the component of drag that is not dependant on speed (from the drag term D=0.5ρACdU2=cU2c=0.5ρACd). Both are unknown but will not be required for the final calculation of R, as explained below.
The energy ratio R is (eqn 18 in Weihs, 1974):
\[\ R=U_{\mathrm{e}}^{2}\frac{t_{1}(t_{1}+t_{2})}{(L_{1}+L_{2})^{2}},\]
(A6)
which can be rearranged using Eqn A3, A4 to be an expression including only velocities and distances (see Videler and Weihs, 1982).
\[\ R=\frac{1}{(\frac{U_{\mathrm{c}}}{U_{\mathrm{e}}})^{2}(1+\frac{L_{2}}{L_{1}})}\]
(A7)
(eqn 15 in Videler and Weihs,1982).
This solution has an advantage in the calculation since using the ratio L2/L1 both m and ccancel out and the final equation can be calculated using only Ui, Uf, Ue andα. Thus:
\[\ \frac{L_{2}}{L_{1}}=\frac{(m{/}c)\mathrm{ln}(U_{\mathrm{f}}{/}U_{\mathrm{i}})}{(m{/}{\alpha}c)\mathrm{ln}[\mathrm{cosh}{\,}B+(U_{\mathrm{i}}{/}U_{\mathrm{e}})\mathrm{sinh}{\,}B]}=\frac{{\alpha}{\,}\mathrm{ln}(U_{\mathrm{f}}{/}U_{\mathrm{i}})}{\mathrm{ln}[\mathrm{cosh}{\,}B+(U_{\mathrm{i}}{/}U_{\mathrm{e}})\mathrm{sinh}{\,}B]}.\]
(A8)
R is the ratio between the energy required for burst-and-glide and the energy required for constant swimming at Uc. For values of R<1, burst-and-glide saves energy relative to constant swimming and when R>1, constant swimming is more energetically efficient.

This research was funded by the Israeli Ministry of Science and Technology under contract no. 3920. We are grateful for the assistance of Ohad Agranat,Ruth Almon, Shani Set and Shoshana Goldenberg in the experiments. Comments from two anonymous reviewers greatly improved this manuscript. The Video Department of the Technion provided technical support.

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140
,
179
-200.