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Drag and energetics of swimming in Steller sea lions (Eumetopias jubatus) Stelle, Lei Lani 1997

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D R A G AND ENERGETICS OF SWIMMING IN STELLER SEA LIONS (EUMETOPIAS JUBATUS) by LEI LANI STELLE B.A., University of California, Santa Cruz A THESIS SUBMITTED IN PARTIAL FULFILMENT OF i THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE F A C U L T Y OF GRADUATE STUDIES (Department of Zoology) We accept this thesis as conforming to the required^andard THE UNIVERSITY OF BRITISH COLUMBIA July 1997 © Lei Lani Stelle, 1997 in presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, ) agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada Da,e DE-6 (2/88) ABSTRACT This thesis presents the first hydrodynamic investigation of swimming in Steller sea lions (Eumetopias jubatus). Passive drag was calculated from "deceleration during glide" measurements. A total of sixty-six glides from six juvenile sea lions yielded an average drag coefficient (referenced to total wetted surface area) of 0.0056 at an average Reynolds number of 5.5 x 106. The drag values indicate that the boundary layer is largely turbulent at these Reynolds numbers, which are past the point of transition from laminar to turbulent flow. The position of maximum thickness (average = 0.344) was lower than for a "laminar" profile, and supports the idea that there is little laminar flow. Steller sea lions in this study were characterized by an average fineness ratio of 5.55; the streamlined shape helps to delay flow separation, which reduces total drag. In addition, turbulent boundary layers are more stable than laminar, thus separating further back on the animal. The average glide velocity of the individual sea lions ranged from 2.9-3.4 m/s, or 1.2-1.5 body lengths/s. These speeds are very close to the predicted swim velocity of 1.4 body lengths/s, based on the minimum cost of transport for California sea lions (Zalophus californianus). Efficiencies of swimming were calculated based on drag data and preliminary metabolic measurements. Aerobic efficiencies were calculated to reach 13-17% at a swimming velocity of 3.6 m/s. Metabolic costs of swimming were also predicted based on the power required to overcome the measured drag, with assumed efficiencies from literature values. Both approaches yielded very similar metabolic rates and aerobic efficiencies. The metabolic rate was determined to be approximately 29 ml CVmin kg for a Steller sea lion swimming at 2.0 m/s, and 45 ml 0 2/min kg at a velocity of 3.5 m/s. Drag measurements provide a means to estimate the energetic costs ii of swimming over a range of natural velocities. This approach has applications for the modeling of pinniped energy budgets which are a necessary component of research projects aimed at investigating the decline of the endangered Steller sea lions. iii TABLE OF CONTENTS ABSTRACT " LIST OF TABLES vi LIST OF FIGURES vii ACKNOWLEDGEMENTS viii DEDICATION ix CHAPTER 1: GENERAL BACKGROUND 1 Introduction 1 Why study Steller sea lions? 2 Hydrodynamic Principles 4 Aquatic Swimmers 6 Otariid Swimming 12 CHAPTER 2: DRAG FORCES... . 19 INTRODUCTION 19 MATERIALS AND METHODS 21 Study Animals 21 Morphometries 22 Glide Filming 24 Video Analysis 24 RESULTS 26 Drag 26 Morphometries 37 DISCUSSION 40 Sources of Error 40 Drag 41 Morphometries 45 Conclusions 48 CHAPTER 3: ERROR ANALYSIS AND COMPARISON OF METHODS 49 INTRODUCTION 49 METHODS AND RESULTS 51 Comparison of Approaches 51 Experimental Error 52 DISCUSSION 53 Conclusions 58 CHAPTER 4: EFFICIENCIES AND METABOLIC REQUDREMENTS OF SWIMMING 60 iv Steller Sea Lion Decline 60 Measurement of Swimming Costs 61 Swimming Efficiencies 63 Predicted metabolic rates 68 Assesment of drag values 75 Conclusions "78 REFERENCES 80 v LIST OF TABLES Table 2.1: Average drag coefficients, associated velocities and Reynolds numbers for each sea lion 29 Table 2.2: Parameters for all glides analyzed in determining drag coefficients 30 Table 2.3: Morphometric data for each of the six Steller sea lions 38 Table 2.4: Drag coefficients determined from glides for a variety of marine animals 42 Table 4.1: Comparison of metabolic rates and efficiency values calculated for Tag from drag data and metabolic measurements in the swim flume 65 Table 4.2: Comparison of metabolic rates and efficiency values calculated for Sugar from drag data and metabolic measurements in the swim flume 66 Table 4.3: Metabolic requirements to swim at a range of speeds, calculated from the average drag (Cd A = 0.0056) 70 Table 4.4: Metabolic requirements to swim at a range of speeds, calculated from the minimum drag (Cd A = 0.0025) 71 Table 4.5: Metabolic requirements to swim at a range of speeds, calculated from the maximum drag (Cd A = 0.0098) 72 Table 4.6: Metabolic rates calculated from drag data for high swimming speeds 74 Table 4.7: Maximum velocities possible based on a range of active drag values 76 vi L I S T O F F I G U R E S Figure 1.1: The influence of fineness ratios on the drag acting on a streamlined body 7 Figure 1.2: The effect of Reynolds number on the friction drag coefficient for a flat plate with a laminar, transitional, and turbulent boundary layer 8 Figure 1.3: The dramatic reduction in pressure drag at Reynolds numbers in the transition region 9 Figure 1.4: Drag for attached versus separated flow on a streamlined body with laminar, transitional, and turbulent boundary layers 10 Figure 1.5: Schematic diagram of the forces acting on a sea lion's foreflippers during the recovery and power phase of a stroke cycle 14 Figure 1.6: Drag coefficients for California sea lions determined from tow measurements, adjusted by glide drag 15 Figure 1.7: Metabolic rates of California sea lions as a function of swimming speed 17 Figure 2.1: An example of a linear regression used to calculate the coefficient of drag for a decelerating glide 27 Figure 2.2: Coefficients of drag for Steller sea lions as a function of Reynolds number, measured from glides 34 Figure 2.3: Drag as a function of swimming velocity 35 vii A C K N O W L E D G E M E N T S I would like to acknowledge my thesis advisor, Dr. Robert W. Blake for his support and interest in this project. Other researchers were also very helpful. Dr. Andrew W. Trites generously allowed me access to the sea lions at the aquarium and included me in the Steller research group. Dr. John M. Gosline was always available to answer questions and provided the digitizing equipment. Dr. Dave A. S. Rosen was very accommodating of my research needs, and generously provided his preliminary metabolic rate measurements to be used in this thesis. I would also like to thank Russ D. Andrews for sharing his swimming speed measurements of wild Steller sea lions. I would like to acknowledge the Vancouver Aquarium for providing research facilities, and the staff for their help. I especially appreciate the assistance of Todd Shannon, Chris Porter, and Dennis Christen with their handling of the sea lions during my experiments. I would also like to thank the members of the Gosline lab for their input and willingness to share lab equipment. I am very grateful to William Megill, Jennifer Haywood-Farmer, Tara Law, and Mario Kasapi for their assistance with this project. This work was partially funded by grants to the North Pacific Universities Marine Mammal Research Consortium from the North Pacific Marine Science Foundation. Lastly, I would like to acknowledge my family and friends. I am especially grateful to my parents for their continual support and encouragement. viii Dedicated to Shane M. Keena and Kiko for their loving support CHAPTER 1: GENERAL BACKGROUND Introduction Pinnipeds live in both aquatic and terrestrial environments, feeding and traveling in water, and reproducing and often resting on land. Their body design reflects these dual requirements, such as flippers that can function for locomotion in both environments (English, 1976). The three subfamilies of the Order Pinnipedia: Phocidae (true seals), Otariidae (sea lions and fur seals), and Odobenidae (walruses), demonstrate different locomotor strategies but their bodies are similarly designed for efficient swimming. Pinnipeds rely on swimming to travel and forage; thus energetics research should include a focus on their swimming adaptations and abilities. In biomechanical studies to date, otariids have been represented by only one species, the California sea lion (Zalophus californianus). Feldkamp (1987b) concluded that these sea lions have a very low drag coefficient, which is partially due to an optimally streamlined body form. In addition, their propulsive and aerobic efficiencies are among the highest reported for marine mammals (Fish, 1992), and increase with swimming speed despite a curvilinear increase in metabolic rate with velocity. Studies on California sea lions have generated valuable information, but until other otariid species are investigated it will remain uncertain whether their impressive swimming performance is unique. This thesis investigates the hydrodynamic drag and metabolic requirements of swimming in another otariid species, the Steller sea lion (Eumetopias jubatus). 1 Why study Steller sea lions? In the last thirty years there has been a drastic and rapid decline of pinniped populations in regions of the North Pacific. The Steller sea lions have suffered the most, with an overall decline of more than 70% since the mid 1970's (Trites and Larkin, 1996). The greatest decline has occurred in the Aleutian Islands. Populations in the Central and Western Gulf of Alaska are also declining while those in Canada and Southeastern Alaska appear stable (Trites and Larkin, 1996). In 1990 the Steller sea lions were listed as threatened under the U.S. Endangered Species Act. Recently, the population in the Gulf of Alaska and the Aleutian Islands was reclassified as endangered while the remaining U.S. population has maintained its threatened listing. The reasons for the decline are unknown, but possible causes include disease, predation, parasitism, pollution, incidental and intentional kills, entanglement in debris, and nutritional stress. Although it is unlikely that just one factor is entirely responsible for the decline, the food-limited hypothesis is currently considered the most probable explanation. An altered prey base may not be able to provide for the Steller sea lions' energetic demands, reducing the survival chances of the nutritionally stressed animals. Populations of northern fur seals (Callorhinus ursinus) and harbor seals (Phoca vitulina) have also experienced declines in the same regions as the Steller sea lions, within a similar period of time (Pitcher, 1990). The build up of commercial fishing is consistent with the timing of all three species' declines. These species also exhibit an overlap of diet, and their common decline in the Aleutian islands supports the idea that lower food availability in this area is a major factor in the decline of all three pinniped species. There are various possible causes of food depletion. through ecosystem changes, in response to a combination of commercial fishing and environmental factors. The commercial 2 fisheries and pinnipeds may be competing directly for fish. Steller sea lions are opportunistic feeders with a diet composed mainly of fish and invertebrates, although they will also occasionally eat other pinnipeds (Riedman, 1990). The fisheries target some pinniped prey: pollock, salmon, capelin, and previously herring, yet these commercial species may only account for about one-third of the pinniped diet (based on scat samples, A. Trites, personal communication). Large scale environmental changes in the region may also have affected the productivity and ecosystem structure (Alverson, 1992), resulting in indirect competition between pinnipeds and the fisheries for the finite ocean productivity (A. Trites, personal communication). Changes in the ecosystem have altered the food resources available to pinnipeds, and subsequently their diet. In the past, the preferred prey of Steller sea lions were schooling fish such as herring, capelin, rockfishes, sand lance, and flatfish (Fiscus, 1966). There is now a reliance on walleye pollock, a low quality, non-schooling fish. Alverson (1992) hypothesizes that the major diet shift to pollock, which have less caloric value and are more energetically costly to catch, has contributed to the dietary deficiency. This idea is supported by the fact that the decline in pinnipeds coincides with an increase in pollock. However, this hypothesis is confounded by the fact that pollock is now also a major prey item of healthy Steller sea lion populations (A. Trites, unpublished data). There is some evidence that Steller sea lions are nutritionally stressed. Studies have noted that Steller sea lions were physically smaller in the mid 1980s compared to the 1970s, which may indicate that they were not obtaining adequate nutrition (Calkins et al, in press). Yet, a study of Steller sea lion pups concluded they were healthy and did not show any indication of starvation (Castellini et al, 1993). York (1994) used a population model to determine that the principal cause of the Steller sea lion decline is a decreased juvenile survival of 10-20%. It is likely that the mothers are investing most of their reserves in their pups, therefore the young are not severely 3 affected by depleted fish stocks until they become juveniles, and starvation would not show up until after weaning. The weaned juveniles may have trouble successfully feeding on their own since their swimming, diving, and thus foraging abilities are likely not equivalent to those of an adult (Merrick and Loughlin, in press). Population management and fisheries conflicts can only be resolved with knowledge of the quantitative relationships between predator and prey, and an understanding of the energy flow in the system (Lavigne et ai, 1982). Information on the activity budgets of free ranging animals, combined with experimental data, allows accurate energetics models to be generated. Steller sea lions spend a large portion of their time swimming, thus it may be a major energetic cost. Therefore, it is essential to determine the costs of this activity. Hydrodynamic data on drag, along with an analysis predicting the metabolic rates of swimming in Steller sea lions, are presented in this thesis. Hydrodynamic Principles Animals that rely on swimming for locomotion must propel themselves through water, a dense and viscous medium. This causes a backwards acting drag force that resists forward motion. Blake (1983) provides a comprehensive review of the principles of fluid dynamics that apply to aquatic swimmers. Due to viscosity, the fluid in immediate contact with a solid boundary has the same velocity as the boundary, resulting in a no-slip condition. The region of velocity increase, from the zero velocity at the body surface to the point where the final velocity approximates that of a free stream, is termed the boundary layer. Boundary layer flow can be 4 either laminar or turbulent; laminar is smooth and steady while turbulent is unsteady and eddying. Turbulent boundary layers are associated with greater friction drag forces than laminar flow. Reynolds Number is a non-dimensional index that expresses the relative importance of the inertial and viscous forces acting on a submerged body. The behavior of boundary layer flow around a body is dependent on the fluid's viscosity (u) and density (p), or kinematic viscosity (v = u/p), velocity (U), and the body's characteristic length (1), these factors are represented by the Reynolds number, Re: Re = lU (1) v The drag acting on a body varies with the Reynolds number and is described by the equation: Drag = 1/2 pSCdU 2 (2) with S referring to a designated surface area and Cd the coefficient of drag. The total drag force acting on a swimmer is composed of pressure, friction, interference, and induced drag (Blake, 1983). The modified pressure distribution due to the boundary layer causes pressure drag, while the tangential stress in the boundary layer results in friction drag. The addition of an appendage, such as a fin, to a streamlined body causes an additional interference drag term due to the interaction of the flow around the two body parts. Also, when fins produce lift there is downward momentum of the fluid that flows over the section, and an induced drag force is associated with this deflection. The importance of drag in an aquatic environment is demonstrated by the convergence of body design exhibited by widely differing animals. To reduce pressure drag, most swimmers have a streamlined body form with a ratio of maximum length to maximum diameter (Fineness Ratio) 5 of between 2 to 6, with an optimum value of 4.5 (Figure 1.1). At a certain Reynolds number (between 5x l0 5 and 5xl0 6), termed the critical value, flow in the boundary layer changes from laminar to turbulent, increasing the friction drag (Figure 1.2) while causing a sudden decrease in the pressure drag (Figure 1.3). Transition from laminar to turbulent flow tends to occur at the point of maximum thickness on the body. This location is also where pressure gradients in the boundary layer often cause a reversal of flow which leads to separation from the body, and the formation of an extensive wake. For bodies swimming at high Reynolds Numbers (Re >103), the overall drag force is largely due to the underpressure in the wake; this can be reduced by delaying boundary layer separation until a point near the rear of the body (Blake, 1983). Streamlining accomplishes this by having a profile with a slowly tapering tail, thus reducing total drag. Also, turbulent boundary layers are more stable than laminar because they have greater momentum which allows the fluid to flow farther against the adverse pressure gradient before separating. Turbulent boundary layers are thus able to delay flow separation, resulting in substantially lower pressure drag than for separated laminar flow. The total drag for a separated boundary layer with turbulent flow is actually lower than with laminar flow (Figure 1.4), therefore animals swimming at high Reynolds numbers are still able to decrease drag. Aquatic Swimmers Animals that use swimming for their locomotion must generate thrust which propels them by giving the fluid backward momentum; to obtain steady velocities the thrust must be of equal magnitude to the drag (Alexander and Goldspink, 1977). There are a variety of propulsive designs observed in aquatic animals, including the utilization of undulatory body waves. 6 ,. 1. ' I : I L 0 1 2 3 4 5 F i n e n e s s r a t i o Figure 1.1: The influence o f fineness ratio on the drag acting on a streamlined body. A value o f 4.5 is op t imum, but there is less than a 10% difference in drag for fineness ratios from 2 to 7. (Mod i f i ed from Blake 1983) 7 F i g u r e 1.2: The effect of Reynolds number on the friction drag coefficient for a flat plate with a laminar boundary layer (line 1), with transitional flow (line 2), and with a turbulent boundary layer (line 3). (Modified from Blake 1983) 8 0 X X X X 1 X 1 2 3 4 5 6 R e y n o l d s n u m b e r ( R e ) (x 10s) Figure 1.3: The dramatic reduction in pressure drag at Reynolds numbers in the transition region from laminae to turbulent flow. Line 1- ellipsoid with a ratio of major to minor axis of 1:1.8 (major axis parallel to flow), line 2- sphere, line 3- ellipsoid with a ratio of major to minor axis of 1:0.75 (major axis normal to flow). (Modified from Blake 1983) 9 laminar p a r t l y turbulent l a m i n a r a t t a c h e d 1 1 1 • W///V//A partly turbulent laminar separated Figure 1.4: Drag for attached versus separated flow on a streamlined body with laminar, transitional, and turbulent boundary layers. Hatched areas represent frictional drag and clear areas pressure drag. (Webb 1975) 10 undulatory fins, or oscillatory fins. Oscillatory fin swimmers can be divided into those that are propelled by a drag based (rowing) principle and those that are propelled by a lift based mechanism (Blake, 1983). Sea lions swim by combining these methods, oscillating their hydrofoil shaped foreflippers to generate lift, and paddling at the end of the stroke to produce drag based thrust (English, 1976; Feldkamp 1987a). Locomotion is often a major energetic requirement, but animals are able to modify their swimming behavior to reduce costs. Williams (1987) discusses the different speeds required by marine mammals for maximizing dive duration, escaping predators, foraging, migrating, and traveling between haul outs and food patches. The cost of transport (COT) defines the amount of energy to move a unit mass a unit distance, and can be used to determine optimum speeds for these various activities. The minimum COT occurs at the velocity that allows an animal to cover the greatest distance with the least energy output. It has been shown that the average swimming speeds of otariids in the wild (Ponganis et al, 1980) are close to the velocity of their minimum COT (Feldkamp, 1987b). Although much of the research on swimming biomechanics has focused on fish, studies have also investigated the swimming of marine mammals, semi-aquatic mammals, and birds. Most of these animals display convergence in their streamlined body forms (Howell, 1930), but they employ a variety of swimming modes. Phocids undulate the posterior of their body in horizontal motions similar to carangiform fish, while minks (Williams, 1983) and ducks (Baudinette and Gill, 1985) use the less efficient drag based paddling for locomotion. Propulsion can also be achieved through appendage generated lift. Cetaceans utilize their large aspect ratio flukes (Fish, 1993b; Darren et al, 1994), penguins their wings (Baudinette and Gill, 1985; Culik et al, 1994), and sea 11 lions their foreflippers (Gordon, 1983; Feldkamp, 1987a) in this manner. Odobenids utilize a form combining the posterior undulations of seals and the foreflipper oscillations of sea lions. Studies have revealed some consistent trends in the swimming of marine animals, even among different vertebrate classes and swimming modes. The hydrodynamic drag equation predicts a proportional relationship to velocity2 at high Reynolds numbers. This curvilinear increase in drag with speed has been shown experimentally in sea lions (Feldkamp, 1987b), seals (Williams and Kooyman, 1985), penguins (Baudinette and Gill, 1985), ducks (Baudinette and Gill, 1985), and minks (Williams, 1983). Hydrodynamic models of the thrust generated by actively swimming animals have revealed the same curvilinear increase with velocity (Fish et al, 1988; Fish, 1993b). To meet these greater energetic demands of high speed swimming, oxygen consumption increased curvilinearly with velocity in sea lions (Feldkamp, 1987b; Williams et al, 1991), seals (Davis et al, 1985; Williams et al., 1991), and minks (Williams, 1983). With information on hydrodynamics and metabolic requirements, the efficiency of a swimmer can also be determined. Studies of sea lions (Feldkamp, 1987b) and minks (Williams, 1983) have shown an increase in efficiency with swimming speed, but no relationship was found for dolphins (Fish, 1993b) or seals (Fish el al, 1988). Otariid Swimming The otariid swimming mode enables the animal to achieve rapid swimming speeds and precise underwater maneuvering (Feldkamp, 1987a). Their foreflippers are used as wings to generate lift, while their hindflippers act as rear stabilizers and play, an essential role in turning (Ray, 1963; Gordon, 1983; Godfrey, 1985). Steller sea lions are the largest of the otariids, and 12 they exhibit pronounced sexual dimorphism in size, with the males weighing up to 1 ton (Ray, 1963). It is thus expected that they should be able to swim faster than smaller species because drag increases with body length squared, while the available power increases with the cube of body length (Aleyev, 1977). Feldkamp (1987a) described three segments in the propulsive cycle of California sea lions, lift based recovery and power phases (Figure 1.5), along with a paddle phase. From observations it was concluded that although thrust was generated from lift in both the recovery and power phases, it was actually the drag based paddle phase that generated the majority of the thrust. The time to complete the recovery phase was about one half the stroke cycle, with the remainder of the time split evenly between the power and paddle phases. The thrust generated per stroke was not a constant but varied with changes in the angle of attack, amplitude, and velocity of the foreflipper. Swimming is a comparatively inexpensive means of transport for California sea lions, and body shape is an important contribution to their swimming performance (Feldkamp, 1987b). In Feldkamp's (1987b) study the sea lions' average fineness ratio was 5.5, and their maximum thickness was located at 40% of total body length, characteristics of a well streamlined form. The coefficient of drag (CdA) averaged about 0.0042-0.0039 at Reynolds numbers ranging from 2.03-2.87 x 106. Reynolds numbers in this range represent the transitional zone between laminar and turbulent flow. The drag values determined for the California sea lions are slightly lower than for a similarly shaped spindle at the same Reynolds numbers with a completely turbulent boundary layer (Figure 1.6). It appears that the California sea lion's streamlined body shape allows laminar flow in the anterior body region, with the transition to turbulence delaying the point of separation to reduce drag forces. 13 A i I B ) P O W E R Figure 1.5: A schematic diagram of the forces acting on a sea lion's foreflippers during the (a) recovery and (b) power phase of a stroke cycle. Vectors are labelled as follows: Vi = incident water velocity, V N = normal water velocity encountered by the flipper as it travels vertically through the fluid, and V R = resultant water vector. The resultant force (F) can be divided into thrust (T) and normal lift (L) components during each phase. (Feldkamp 1987a) 14 ° 3 P A R T I A L L Y T U R B U L E N T I J _l I j . I i 1 2 . 3 4 .5 6 Re x. 1 0 6 Figure 1.6: Drag coefficients for California sea lions determined from tow measurements, adjusted by glide drag. ' For comparison, the upper line represents the drag coefficients for a similarly shaped spindle with a fully turbulent boundary layer and the lower curve is for the same spindle with a partially laminar, partially turbulent boundary layer. (Feldkamp 1987b) 15 The success of this body design and swimming mode is reflected in relatively low energetic costs and high efficiencies of swimming. Feldkamp (1987b) measured the metabolic rates of California sea lions at actual swimming speeds of 1.3 m/s, and drag simulated speeds up to 2.7 m/s. The metabolic rate increased curvilinearly with velocity (Figure 1.7), reflecting the increase in power required for propulsion which is proportional to the velocity cubed. The minimum cost of transport of 0.12 ml 0 2/kg m at a relative speed of 1.4 body lengths/s was 2.5 times the predicted value for a similar sized fish. The resting metabolic rate was 1.4 times the predicted rate by the Kleiber mass relationship (Feldkamp 1987b). Unlike terrestrial animals, the intercept of the V 0 2 curve versus speed for the sea lions accurately predicted their resting metabolic rate. Feldkamp (1987b) determined that the sea lions expend less energy in locomotion than similar sized terrestrial mammals. This was suggested to be due to neutral buoyancy, which eliminates the need to support the body or move the center of mass against gravitational forces. The California sea lions' aerobic efficiency (r)a) averaged 15%, and the mechanical efficiency (rip) of foreflipper propulsion reached a plateau around 80% (maximum value = 90%) at the highest velocities. Williams et al. (1991) reported a maximum aerobic efficiency of 30% for California sea lions at a velocity of 3 m/s. These efficiencies are similar to values obtained for phocids (Williams and Kooyman, 1985; Fish et ai, 1988; Williams et al., 1991) but are substantially higher than for minks (Williams, 1983), ducks, and penguins (Baudinette and Gill, 1985). The explanation for such high efficiencies is likely their swimming mode, which produces thrust throughout the entire stroke cycle, and their well designed bodies. The aim of this thesis is to provide information on the swimming requirements of Steller sea lions. Passive drag was measured from decelerating glides, providing data on drag coefficients over a limited range of natural swimming speeds. Information on metabolic rates 16 35-30— CD * 2 5-1-CM 20^-O CM o-10-r 0. 0 0 . c 7 o o 7 4. 4 t 1 I 2 V E L O C I T Y (M/S.EC3 3 F i g u r e 1.7: Metabolic rates (mass specific) of California sea lions as a function of swimming speed. The lower curve is from measurements of two animals at a water temperature of 26°C and the upper curve is from one animal at a temperature of 18°C. (Feldkamp 1987b) 17 during swimming at slow speeds was combined with the drag data to calculate efficiencies, and provide estimates of the additional drag due to active swimming. Metabolic rates at higher swimming speeds were also estimated, based on the energetic requirements necessary to overcome the measured drag. The results from this study are compared to what is known regarding the swimming of other aquatic vertebrates, and otariids in particular. The biomechanical data to date has relied on California sea lions, and this study provides the opportunity to assess the similarities and differences between California and Steller sea lions. In addition, it is the first investigation of the largest otariid representative, thus providing experimental data to examine some theoretical ideas regarding the influence of size on swimming performance. The information from this study can be used to predict the costs of swimming for wild animals, which allows estimates of their energy and thus food requirements. Combining the data from this study with that from field research projects on the diet, location of available prey, and activity budgets of Steller sea lions, should assist research into the nutritional stress hypothesis. 18 C H A P T E R 2: D R A G F O R C E S INTRODUCTION The energetics of swimming are a function of the hydrodynamic forces encountered by an animal. Characteristics of flow in the boundary layer will strongly influence the total cost of swimming, and knowledge of drag forces provides information on these flow patterns adjacent to the body surface. Metabolic rate measurements during swimming provide valuable information on energetic costs but are difficult to measure, and when available are often limited to slow swimming speeds for larger animals. Determination of the drag forces acting on a gliding animal often provides a more practical means of estimating the minimum power requirements of swimming at high speeds. This method has the additional advantage that the drag can be measured with little interference by the experimenter; the reduced stress on the animals should lead to more normal behavior and natural swimming speeds. Studies focusing on the energetics of marine mammals should therefore include research into the hydromechanics of swimming to estimate the power output. Many hydrodynamic investigations of swimming rely on the "rigid body analogy", assuming thrust is equal to the drag of gliding or towed animals. During active swimming, the drag forces are greater than this minimum (passive) drag due to undulatory body motions (Blake 1983). Active drag has yet to be directly determined experimentally, but hydromechanical models (Lighthill, 1971; Chopra and Kambe, 1977; Yates, 1983) have been applied to swimming seals and dolphins. The increased power requirements were estimated to be on the order of 2-7 times greater than values based on passive drag (Fish et al, 1988; Fish, 1993b). Unlike these undulatory body swimmers, sea lions swim with an essentially rigid body and move only their 19 foreflippers to generate thrust. Therefore, passive drag estimates should provide a reasonable estimate of the drag for an actively swimming sea lion. A variety of methods have been used to determine the passive drag for animals ranging from fish to large whales. Often it is assumed that drag coefficients can be based on a flat plate, or a body of revolution with a shape similar to the subject animal (Blake, 1983). This approach tends to underestimate drag and also requires assumptions about the characteristics of the boundary layer flow. Some studies have used dead animals or models to measure drag (e.g. Mordinov, 1972; Williams, 1983; Culik et al, 1994), but these methods also have limitations. The body of a live animal undergoes natural deformations that may affect the drag and can not be accounted for with models (Williams, 1987); also dead animals often "flutter", increasing drag (Blake, 1983). Towing of live animals can provide drag data for a large range of swimming speeds, but this approach tends to overestimate the passive drag because animals attempt to stabilize their position with flipper movements (Feldkamp, 1987b; Williams and Kooyman, 1985). To accurately determine the minimum drag encountered by a gliding animal, video or film records of the deceleration during glide provide the best method. Drag is estimated based on the principle that the only force acting on a passively gliding animal is the drag force of the medium. Thus, by measuring the rate of deceleration the total passive drag can be calculated. This approach allows the animals to swim at their preferred speed and activity level, providing a better indication of free-ranging behavior than in other captive research. Studies using this approach often calculate the deceleration from the change in velocity measured at two points (e.g. Williams and Kooyman, 1985; Feldkamp, 1987b) or from an unspecified average velocity change (e.g. Clark and Bemis, 1979; Videler and Kamermans, 1985). Bilo and Nachtigall (1980) proposed a more accurate method that involves determining 20 the velocity frequently along the course of the glide, and plotting the reciprocal velocity against time to provide the rate of change for calculating the drag coefficient. These approaches assume that drag coefficients are constant over the range of Reynolds numbers characterizing the glide (Bilo and Nachtigall, 1980). Also, the changes in velocity must be extremely small so that the drag equations are valid (Williams, 1987). To measure passive drag, it is important that the animals remain in a gliding position without changing their posture or moving their appendages. Fortunately, small fluctuations in deceleration from body movement will be smoothed by using the method of Bilo and Nachtigall (1980). This method has been employed in this study to determine the drag acting on Steller sea lions, providing a comprehensive data set on drag coefficients for six individuals. The drag forces and swimming behavior of the Steller sea lions are discussed in relation to their body morphology, and compared to what is known regarding California sea lions. M A T E R I A L S AND M E T H O D S Study Animals This research was conducted at the Vancouver Public Aquarium in British Columbia, Canada. Six juvenile Steller sea lions were used; three females (Kiska, Sade, and Sugar) and three males (Adak, Tag, and Woody). The animals were held outdoors, with access to both ambient sea water and haul out areas. Their normal diet consisted of thawed herring (Clupea harengus) supplemented with vitamin tablets (5M26 Vitazu tablets, Purina Test Diets, Richmond, IN). Glide data were collected from May, 1996 to April, 1997. 21 Morphometries Lengths and weights were collected weekly by trainers at the aquarium. The animals were weighed on a U M C 600 digital platform scale, accurate to +/- 0.05 kg. The maximum length was measured from nose to the end of the hindflippers, and standard length from nose to tip of tail. The fineness ratio, FR, was calculated as the maximum length divided by the diameter of the maximum girth. The position of maximum thickness, C, was calculated as the distance from the nose to the location of maximum girth divided by maximum body length. The coefficients of drag were referenced to (i.e. divided by) three different body areas: total wetted surface area, frontal surface area, and volume273. A series of body measurements, necessary to determine these reference areas, were made for each individual at two separate times since the juvenile animals were still growing. Measurements were taken once in August 1996, and again in March, 1997, when the majority of the glides were filmed. Trainers measured girths at seven places along the body (a-g): the neck, directly in front of the foreflippers, directly behind the foreflippers, two along the trunk region, the hips, and the last where the body and hindflippers meet. The perpendicular distances between successive girths (1-7) were also measured. To determine total wetted surface area, the formula for the surface area of a truncated cone was applied to each increment; example: Surface Area = girth (a) + girth (b) x hypotenuse of distance 2 (1) 2 The measured perpendicular distances were adjusted to a hypotenuse length by considering the shape to be a trapezoid. To determine the surface area of the flippers, the left foreflipper and hindflipper of each animal were videotaped with a reference grid in view. A measurement software program (SigmaScan/Image, version 2.01, Jandel Scientific) was then used to determine the surface area of each flipper, by calibrating with a reference grid. The surface area obtained 22 from one side of a flipper was multiplied by two to get entire flipper surface area (top and bottom), and both the left and right flippers were assumed to have the same surface area. The surface areas calculated for the seven body cones and 4 flippers were summed for total wetted surface area. The foreflipper span (maximum length) and maximum chord (width) were also measured from the video images. The average chord was calculated as the surface area divided by the span. The aspect ratio was calculated as the square of the flipper's span divided by the surface area of one side. Frontal surface area was calculated as the cross-sectional area of the body at its point of maximum width, based on the girth measurement made directly anterior to the foreflippers and assuming a circular shape. To determine total body volume, the girth and distance measurements discussed previously were used to calculate the volume of the same series of cones. The volume of a truncated cone is given by the following sample equation: Volume = 1/3 71 x perpendicular 2 x ((radius a x radius b) + (radius a)2 + (radius b) 2) (2) The equation for calculating the volume of the flippers: Volume = span x average chord x average thickness (3) requires determining the average thickness of the flipper. To determine a reasonable estimate of this varying thickness, the volume of one subject's foreflipper was measured by water displacement. The average thickness of this flipper was then calculated based on its measured span and chord. With the assumption that thickness varied consistently with span, the relationship found for the foreflipper was then used to calculate the average thickness of the other sea lion's foreflippers based on their own spans. The hindflippers of each individual animal were then assumed to have the same average thickness as their foreflippers, and their volume calculated in the same way. The volume of both sets of flippers was included in the total 23 body volume. The density of each animal was also calculated as a check on the volume estimates; since sea lions tend to be neutrally buoyant their density should be close to the surrounding medium. The densities averaged 0.968 kg/1 (± 0.0839, 1 std. dev.), which is similar to the density of sea water, 1.03 kg/1 at 10°C (CRC handbook). Glide Filming Glides were recorded when the sea lions were swimming individually in a seawater tank, measuring approximately 20 m length x 8 m width. They were filmed from outside the tank through a window, which was divided into five panels (110 cm wide each) separated by metal columns (10 cm wide each). The window's height was much higher than the water surface, and the water depth at the window was approximately 105 cm. A Canon ES2000 Hi-8 camcorder (60 Hz) was set on a tripod 4.3 m from the window. The field of view included about half of the first window panel, and the entire next three panels. Animals were filmed gliding past the window under the direction of trainers. They were directed to swim a straight distance from a rock outside the viewing area to rocks past the far right of the window. Although the sea lions started the movement with a flipper stroke (outside of the field of view), they glided the rest of the distance to their target. A meter stick was taped in the vertical position on the far right window divider, with visible marks delineating every 10 cm, to provide stationary reference points. Video Analysis The Hi-8 video was transferred to Super VHS tape with a S VHS VCR (Panasonic A G -1960); a digital counter (Panasonic) which showed elapsed time to 0.01 seconds was 24 simultaneously recorded onto the tape. The following criteria were used to select glides for analysis: no movement of flippers and their placement near the animal's sides, no obvious horizontal movement, only gradual changes in depth (if any), and a minimum glide duration of one second. Individual glides were digitized on a PC with a Matrox PIP frame grabber (V software for Dos, version 1.0, Digital Optics Ltd). To evaluate the extent of parallax, a three meter stick marked every 10 cm was placed horizontally in the water at approximately the same position as the average glides. Measurements of the 10 cm intervals using the V program revealed no distortion in the field of view except at the extreme ends which were therefore not included in the analysis of glides. The sea lion's apparent maximum length was measured at the beginning, middle, and end of each glide record. These lengths (in pixels) were averaged and divided by the animal's true length (in cm) to calibrate the measurements. This method corrected for the air/water distortion and the distance of each glide from the window. Every third frame (0.05 s apart) was used for analysis. Two reference points were marked on each frame to determine distance traveled; an interval mark on the meter stick was the constant point (approximately horizontal to the glide), and the sea lion's nose acted as the moving point. The measurements for each glide were then analyzed using a spreadsheet (Microsoft Excel 5.0). The method of Bilo and Nachtigall (1980) was used to calculate the coefficient of drag (Cd). The equation: Cd = c(2(Mb+Ma) (4) Area x p requires the value of the slope of the deceleration equation (c), the sea lion's body mass (Mb) and additional mass due to the entrained water (Ma), the reference area, and the seawater density (p). The most recently measured mass value and the added mass coefficient for the fineness ratio of the individual based on an equivalent three-dimensional body of revolution (Landweber, 25 1961) were used in the calculations for each glide. The appropriate density and kinematic viscosity of seawater for the temperature on the day of the glide (CRC handbook) were used in each calculation. Instantaneous velocities were averaged to describe the mean glide speed and for calculation of Reynolds numbers. When frames were skipped because the reference point was blocked by the window divider, missing values were filled in by linear interpolation. A modification of Bilo and Nachtigall's (1980) method was used in this study; a running average (every three analyzed frames) was applied to the measurement values to reduce scatter. Then the smoothed position measurements were subtracted to determine the distance moved between frames. These distances were divided by the time between each frame (0.05 s) for instantaneous velocity (m/s). A linear regression was fitted with the least squares method to the graph of time versus inverse velocity (Figure 2.1). Glides were only included in the data set if the slope of the line, c, was significantly different from zero (P value less than or equal to 0.05 and a power greater than or equal to 0.80). Al l statistical analyses in this study were performed with SigmaStat (for Windows, version 1.0, Jandel Scientific), and the significance level was set at a probability < 5%. RESULTS Drag A total of 66 glides from 6 individual sea lions were analyzed to determine the drag forces. The coefficient of drag was calculated for each glide and referenced to the animal's total wetted J 0.20 co > 0.10 0.00 0.0 0.0 0.2 0.3 0.4 0.5 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Time (s) F i g u r e 2.1: An example of a linear regression (y = 0.0505x + 0.2758, R 2 = 0.6903) for a decelerating glide. The slope of this line was used to calculate the coefficient of drag. 27 surface area (Cd A), frontal area (CaV), and volume (Cdv). The average Cd values for each animal are shown in Table 2.1, which also includes the average Reynolds number and average velocity (in m/s and body lengths/s) for each individual. There were no significant differences between the average C d A values for individual sea lions (Kruskal-Wallis one way A N O V A on ranks; H=6.86, df=5, p=0.2311), therefore the data sets were pooled. Table 2.2 lists all of the Cd values, the average body depth below the surface during the glide, Reynolds numbers, velocities, and the regression equation with the slope used to calculate Cd. There were significant differences between individuals in their average CdF, (one way A N O V A ; F=3.19, df=5, p=0.0128, power=0.6755 with an alpha=0.05) but not in their average C d v (Kruskal-Wallis one way A N O V A on ranks; H=6.92, df=5, p=0.2268). The C d A values appear to decrease slightly with increasing Reynolds numbers (Figure 2.2), but the slope was not significantly different from zero. Theoretical drag values based on a similarly shaped spindle with a completely turbulent boundary layer, are also plotted on the graph for comparison. The majority of the values from this study lie above this predicted line, and are greater by an average of 49%. The coefficient of drag values show natural variability, the overall range of C d A is from 0.0025 to 0.0098 with an average of 0.0056 (± 0.0016), the C d v range from 0.029 to 0.094 with an average of 0.053 (± 0.016), and the C d F range from 0.049 to 0.19 (Table 2.2). Drag forces calculated from the C d A values increased with glide velocity (Figure 2.3), but the relationship was not well described by the expected power regression relationship. There was a lot of scatter around the linear regression (equation: y = 18.7x + 15.7, R 2 = 0.0445) with a minimum drag of 27 N and a maximum of 130 N. Most of the drag values for the sea lions were also greater than the theoretical values based on a completely turbulent boundary layer (Figure 2.3). 28 Table 2 . 1 : Average drag coefficients (± one standard deviation), and associated velocities and Reynolds numbers for each sea lion. The number of glides (n) is indicated next to the sea lion's name. The coefficients of drag are referenced to all 2/3 three areas as follows: C d A - total wetted surface area, Cd F - frontal surface area, and Cdv - volume . Sea Lion (n) Adak (11) Kiska (10) Sade (17) Sugar (5) Tag (10) Woody (13) Average C d A 0.0058 0.0046 0.0055 0.0074 0.0055 0.0055 (0.0017) (0.00086) (0.0014) (0.0015) (0.0024) (0.0014) Average C d F 0.10 0.080 0.12 0.13 0.11 0.10 (0.030) (0.015) (0.031) (0.022) (0.047) (0.028) Average C d v 0.054 0.044 0.052 0.070 0.053 0.052 (0.016) (0.0080) (0.013) (0.014) (0.023) (0.013) Reynolds Number 5.2 5.5 5.6 5.0 5.06 6.1 (x 1 0 6 ) (0.33) (0.080) . (0.43) (0.53) (0.12) (0.31) Average Velocity 2.9 3.4 3.2 2.9 2.9 3.2 (m/s) (0.19) (0.049) (0.17) (0.33) (0.071) (0.26) Average Specific 13 1.5 1.5 1.3 1.2 1.3 Velocity (L/s) (0.084) (0.021) (0.081) (0.13) (0.030) (0.070) Table 2.2: Al l glides analyzed to determine drag coefficients. The linear regression equation and P value are listed for each glide. The average depth (referenced to body diameter), velocity, and Reynolds number (Re) of each glide is also included. C d A - total wetted surface area, CdF - frontal surface area, and Cdv - volume273. SEA L ION E Q U A T I O N D E P T H (h/d) V E L O C I T Y (m/s) Re (x 106) C d A C d F Cdv Adak y=0.0481x + 0.337 N A 2.74 4.88 0.00549 0.0974 0.0514 Adak y=0.0677x + 0.295 N A 2.98 5.30 0.00773 0.137 0.0723 Adak y=0.0552x +0.333 1.90 2.74 4.87 0.00630 0.112 0.0589 Adak y=0.0481x +0.325 2.48 2.90 5.15 0.00549 0.0974 0:0514 Adak y=0.0819x + 0.316 2.07 2.72 4.84 0.00935 0.166 0.0874 Adak y=0.0507x +0.332 N A 2.76 4.90 0.00579 0.103 0.0541 Adak y=0.0476x + 0.302 1.95 3.10 5.51 0.00544 00964 0.0508 Adak y=0.0298x + 0.292 2.29 3.26 5.79 0.00340 0.0604 0.0318 Adak y=0.0574x + 0.286 1.91 3.14 5.58 0.00656 0.116 0.0613 Adak y=0.0400x + 0.306 2.22 3.04 5.40 0.00457 0.0810 0.0427 Adak y=0.034x +0.310 2.16 3.03 5.38 0.00388 0.0689 0.0363 Kiska y=0.0562x + 0.267 2.34 3.44 5.57 0.00638 0.110 0.0598 Kiska y=0.0409x+.0.278 2.59 3.32 5.39 0.00464 0.0800 0.0435 Kiska y-0.0276x + 0.276 2.86 3.43 5.56 0.00313 0.0538 0.0293 Kiska y=0.0408x + 0.276 2.68 3.33 5.39 0.00463 0.0795 0.0434 Kiska y=0.0464x + 0.264 2.65 3.44 5.58 0.00526 0.0904 0.0493 Table 2 .2 : continued SEA L I O N E Q U A T I O N D E P T H (h/d) V E L O C I T Y (m/s) Re (x 106) C d A C d F C d v Kiska y=0.0349x + 0.269 2.56 3.45 5.59 0.00396 0.0680 0.0371 Kiska y=0.0370x + 0.268 2.85 3.45 5.59 0.00420 0.0721 0.0393 Kiska y=0.0386x +0.270 2.76 3.44 5.57 0.00438 0.0752 0.0410 Kiska y=0.0448x + 0.270 2.76 3.37 5.46 0.00508 0.0873 0.0476 Kiska y=0.0426x + 0.268 2.49 3.42 5.54 0.00483 0.0830 0.0453 Sade , y=0.0874x + 0.286 3.06 3.14 5.74 0.00844 0.190 0.0795 Sade y=0.0507x + 0.285 2.71 3.28 6.00 0.00489 0.110 0.0461 Sade y=0.0851x + 0.275 2.54 3.21 5.81 0.00761 0.171 0.0717 Sade y=0.0684x+ 0.272 2.71 3.32 6.01 0.00612 0.137 0.0576 Sade y=0.0503x + 0.292 2.52 3.11 5.62 0.00450 0.101 0.0424 Sade y=0.0425x + 0.273 2.49 3.43 6.20 0.00380 0.0854 0.0358 Sade y=0.0567x + 0.289 2:21 3.15 5.70 0.00507 0.114 0.0478 Sade y=0.0505x + 0.276 2.21 3.30 5.98 0.00452 0.102 0r0426 Sade y=0.0626x + 0.249 1.48 3.63 6.56 0.00560 0.126 0.0528 Sade y=0.0405x +0.319 2.42 2.95 5.33 0.00362 0.0814 0.0341 Sade y=0.0480x + 0.277 2.70 3.35 5.52 0.00455 0.102 0.0428 Sade y=0.0658x + 0.282 2.25 3.22 5.31 0.00624 0.140 0.0587 Sade y=0.0375x +0.289 1.64 3.22 5.32 0.00352 0.0790 0.0331 Sade y=0.0748x + 0.302 1.63 2.90 4.80 0.00701 0.158 0.0660 Table 2 .2 : continued SEA LION EQUATION DEPTH (h/d) VELOCITY (m/s) Re (x 106) Cd A C d F Cdv Sade y=0.0611x + 0.278 1.92 3.22 5.33 0.00573 0.129 0.0540 Sade y=0.0663x + 0.270 2.86 3.19 5.26 0.00628 0.141 0.0592 Sade y=0.0666x + 0.286 2.73 3.18 5.23 0.00631 0.142 0.0595 Sugar y=0.0636x + 0.260 3.28 3.50 5.88 0.00738 0.131 0.0695 Sugar y=0.0809x + 0.323 2.65 2.76 4.64 0.00939 0.166 0.0884 Sugar .y=0.0578x + 0.318 N A 2.88 4.84 0.00671 0.119 0.0631 Sugar y=0.0703x +0.314 3.12 2.90 4.87 0.00816 0.145 0.0768 Sugar y=0.0488x+ 0.358 3.19 2.64 4.57 0.00551 0.109 0.0524 Tag y=0.0512x +0.298 2.37 3.01 5.18 0.00624' 0.121 0.0598 Tag y=0.0499x + 0.307 1.89 2.98 5.12 0.00608 0.118 0.0583 Tag y=0.0791x +0.304 N A 3.01 5.18 0.00978 0.190 0.0938 Tag y=0.0430x + 0.322 N A 2.88 4.95 0.00532 0.103 0.0510 Tag y=0.0753x + 0.311 2.63 2.91 5.02 0.00931 0.181 0,0892 Tag y=0.0267x + 0.324 2.56 2.93 5.04 0.00330 0.0642 0.0316 Tag y=0.0204x + 0.343 . N A 2.79 4.81 0.00252 0.0490 0.0242 Tag y=0.0350x +0.316 N A 2.94 5.06 0.00433 0.0842 0.0415 Tag y=0.0419x + 0.313 N A 3.02 5,21 0.00518 0.101 0.0497 Tag y=0.0276x +0.321 N A 2.95 5.08 0.00336 0.0654 0.0322 Woody y=0.0559x + 0.354 1.90 2.65 5.29 0.00572 0.118 0.0530 Table 2 . 2 : continued SEA L I O N E Q U A T I O N D E P T H (h/d) V E L O C I T Y (m/s) Re (x 1 0 6 ) C d A C d F C d v Woody y=0.0466x + 0.300 1.76 3.12 6.24. 0.00477 0.0981 0.0442 Woody y=0.0394x + 0.302 2.13 3.06 6.11 0.00403 0.0830 0.0374 Woody y=0.0734x + 0.292 2.06 3.09 6.18 0.00751 0.154 0.0697 Woody y=0.0592x + 0.285 1.63 3.19 6.38 0.00606 0.125 0.0562 Woody y=0.0549x + 0.296 1.29 3.15 6.30 0.00562 0.116 0.0521 Woody y=0.0407x +0.261 1.57 3.59 6.45 0.00509 0.0861 0.0484 Woody y=0.0606x+ .0.288 2.02 3.18 5.72 0.00730 0.124 0.0694 Woody y=0.0505x+ 0.272 1.87 3.42 6.15 0.00631 0.107 0.0600 Woody y=0.0590x + 0.267 1.85 3.42 6.14 0.00730 0.124 0.0694 Woody y=0.0349x + 0.272 1.92 3.45 6.20 0.00421 0.0712 0.0400 Woody y=0.0266x + 0.266 1.81 3.55 6.38 0.00321 0.0543 0.0305 Woody y=0.0358x + 0.276 2.14 3.39 6.09 0.00432 0.0731 0.0410 0.010 0.008 0.007 ^ 0.006 5 0.005 $ , 0.004 O 0.003 I 0.002 O CJ 0.001 0.000 4e+6 5e+6 6e+6 Reynolds number (log Re) 7e+6 8e+6 Figure 2 .2 : Results from the glide drag experiments. The coefficient of drag (Cd A , closed circles) for all Steller sea lions does not vary with the Reynolds number of the glide. The theoretical drag for a spindle with the same fineness ratios and a completely turbulent boundary layer is indicated with the open circles. It was calculated from the equation: Cd = Cf (l + 1.5 (d/1)15 + 7 (d/1)3), with Cf = 0.072 Re"" 5, d = diameter and 1 = length (Hoerner 1958). The linear regression of each relationship is shown. 34 Figure 2.3: Drag forces (closed circles) calculated from the C d A values are plotted against the average velocity of the glide. The lower curve represents the drag for a spindle with a turbulent boundary layer (open circles), calculated from the theoretical Cd values in Figure 2. 35 Reynolds numbers characterizing the glides ranged from 4.6 x 106 to 6.6 x 106 (Table 2.2). The average Reynolds numbers characterizing each individual's glides were significantly different between sea lions (one way A N O V A ; F=14.2, df=5, p<0.0001, power=1.0 with an alpha=0.05), but the range of the individual's averages (5.0-6.lx 106) were similar to the overall range. The average velocities of the glides were significantly different between individuals, both when measured in meters per second (m/s) (one way A N O V A ; F=7.16, df=5, p<0.0001, power=0.9952 with an alpha=0.05) and also when referenced to maximum body length (L/s) (Kruskal-Wallis one way A N O V A on ranks; H=32.9, df=5, p<0.0001). Average velocities for individual sea lions ranged from 2.9 to 3.4 m/s (Table 2.1), and overall there was a slightly larger range from 2.6 to 3.6 m/s (Table 2.2). When converted to body lengths per second, the average velocity for individuals was limited to 1.2 to 1.5 L/s but the overall range was slightly greater, extending from 1.1 to 1.6 L/s. The viewing window did not extend to the bottom of the pool, therefore the depth of the filmed glides was limited. Depth of the glide was reported as the number of body diameters submerged (h/d) by measuring the distance from the water surface to the mid point on the animal's body and dividing by the maximum body diameter. The analyzed glides had depths ranging from 1.3 to 3.3 h/d, with an average depth of 2.3 h/d. The coefficient of drag values appeared to be unaffected by differences in these depths, the average C d A of glides 2.7 h/d and deeper was not significantly different (t-test; t=-0.357, df=64, p=0.7223, power=0.05 with alpha=0.05) from the average C d A of the shallower glides. 36 Morphometries The morphometric data for each of the six sea lions from both measurement periods is presented in Table 2.3. The animals grew over the course of the study, with an average weight gain of 19.2% (range 12.8-27.1%) and an average increase in maximum length of 4.8% (range 2.2-6.7%). Their frontal surface area increased by an average of 19.6%, with a minimum increase of 6.25% and a maximum of 29.5%. Total wetted surface area showed considerably more variation, from a decrease of 0.40% to an increase of 16%, with an average increase of 4.3%. Changes in total body volume also varied; the average increase was 5.4%, but the range included a decrease of 3.3% and an increase of 27%. The fineness ratio was relatively consistent for each individual over the course of the study, and although it did decrease for all animals, the average change was only 5.11%. Overall, the fineness ratios ranged from 4.77 to 6.04, with an average from all measurements of 5.55. There were no consistent changes in the position of maximum thickness with age; the maximum decrease was 17.4%, and there was an increase of 11.7%. Despite these changes the position was relatively similar between all individuals, with an average of 0.34, and an overall range of 0.31 to 0.38. Foreflipper aspect ratios also showed no substantial difference between individuals; the average was 3.37. With age, the change in aspect ratios varied, with a decrease of 11.9% and an increase of 17.0%, but on average there was an increase of 5.20%. To calculate drag, morphological parameters measured on the date closest to the day of the glide were always used. 37 Table 2.3: Morphometric data for each of the six Steller sea lions, Summer measurements were taken in August, 1996 and the winter in March, 1997. SA refers to surface area, max is for maximum, and avg is for average. Sea Lion Adak Kiska Sade Sugar Tag Woody Summer Winter Summer Winter Summer Winter Summer Winter Summer Winter Summer Winter Age (years) [Birth yearj Mass (kg) Maximum Length (m) Standard Length (m) 3 3 1/2 3 3 1/2 2 2 1/2 3 3 1/2 3 3 1/2 3 3 Vi [1993] [1993] [1994] [1993] [1993] [1993] 158 185 1 12 128 107 136 104 132 140 158 154 180 2.23 2.37 2.28 2.33 2.27 2.33 2.15 2 27 2.25 2.40 2.42 2.55 2.01 2.06 1.88 1.95 1.90 1.97 1.81 1.92 1.99 2.03 2.05 2.08 Total wetted SA 2.91 3.01 2.29 2.35 2.49 2.48 2.08 2.42 2.64 2.66 2.94 3.03 (m2) Frontal SA (m2) 0.164 0.194 0.120 0.136 0.111 0139 0.105 0.136 0.128 0.136 0.143 0.179 Volume (L) 173 180 119 125 136 133 102 130 151 146 178 180 Fineness Ratio 4.88 4.77 5.82 5.59 6 04 5.54 ' 5.87 5.44 5.94 5.76 5.67 5.34 Table 2.3: continued Sea Lion Adak Kiska Sade Sugar Tag Woody Summer Winter Summer Winter Summer Winter Summer Winter Summer Winter Summer Winter Position of max 0.359 0.350 0.382 0.343 0.379 0.313 0.307 0.343 0.351 0.329 0.347 0.325 thickness SA of Fore- \ 0.447 0.481 0.377 0.374 0.426 0.400 0.372 0.406 0.406 0.435 0.472 0.582 flippers (m2) Foreflipper 0.586 0.614 0.556 0.594 0.596 0.571 0.537 0.590 0.568 0.636 0.668 0.696 Span (m) Foreflipper Avg 0.191 0.196 0.170 0.157 0.178 0.175 0.173 0.172 0.179 0.171 0.177 0.209 Chord (m) Foreflipper Max 0.266 0.279 0.220 0 233 0.23 9 0.220 0.220 0.215 0.232 0.240 0.240 0.269 Chord (in) Foreflipper 3.07 3.14 3.27 3.78 3.34 3.26 3.10 3.43 3.18 3.72 3.78 3.33 Aspect Ratio DISCUSSION Sources of Error Swim studies in enclosed tanks are not exact simulations of free swimming in the wild because of wave interference with the walls, shallow depths, and restricted distances. It is predicted that an animal swimming near the surface of the water will encounter additional drag forces from the formation of wave drag (Hertel, 1963). This drag augmentation is greatest at 0.5 body diameters depth, and the effect decreases until it is negligible at 3 body diameters below the surface. An experimental study on harbor seals and humans showed this increase in drag when the subjects were towed at the surface compared to submerged tows (Williams and Kooyman, 1985). In this study on Steller sea lions, there was no apparent effect of depth on the drag coefficients. This is likely because the average depth of the glides was 2.3 h/d, and the expected augmentation in that region is small (Hertel, 1963). Although the glides appear to have been sufficiently deep enough to reduce surface drag, there could still be drag increases due to interference with the surrounding tank walls. This effect can not be quantified, but most glides appeared to be greater than one body diameter from the wall. Therefore any augmentation would be minimal. The total experimental error in the drag coefficients from this study is estimated to be approximately 18% due to errors in the digitizing process and reference area measurements (see Chapter 3). Although this may seem high it is less than the natural variability displayed by the animals in this study. 40 Drag Drag coefficients determined for the Steller sea lions are comparable to values obtained for other marine species (Table 2.4). The C d A values based on "deceleration during glide" measurements in the literature range from a minimum of 0.0021 for emperor penguins (Clark and Bemis, 1979) to a maximum of 0.018 for bottle-nosed dolphins (Videler and Kamermans, 1985) at Reynolds numbers of approximately 106. The overall average C d A for the Steller sea lions in this study of 0.0056 at an Re of 5.5 x 106 is slightly higher than the average C d A of 0.0042 at an Re of 2.0 x 106 reported by Feldkamp (1987b) for California sea lions. Drag coefficients of Steller sea lions, and most other marine mammals, are not substantially higher than the theoretical values for a streamlined body (Fish 1993a). Ideal streamlined shapes are not hindered by natural protuberances or body movements, suggesting that the animals actually have quite low drag coefficients. The measured drag coefficients show a range of values (Figure 2.2). This natural variability may reflect slight differences in body configuration during glides, or changing water currents generated in the tank by their swimming. Since these same factors can affect the movements of free ranging animals it is important to acknowledge that the energetic costs of swimming in the wild will also vary with changing conditions. The majority of the drag coefficients measured in this study were greater than the theoretical values for a completely turbulent boundary layer, indicating that the flow on the Steller sea lions is largely turbulent. This contrasts with Feldkarnp's (1987b) suggestion that California sea lions are able to maintain a partially laminar boundary layer. Boundary layer flow is expected to be laminar for a streamlined body at an Re up to 5 x 105, turbulent above Re of 5 x 106', and transitional between these values (Blake, 1983). The Steller sea lions were swimming at Reynolds numbers (Re > 4 x 106) where turbulence would be expected, while the California 41 Table 2.4: Drag coefficients determined from glides for a variety of marine animals. If more than one value was provided for a species, the minimum Cd (of the individuals' averages) was listed, along with the associated velocity and Reynolds number (Re). C d A - total wetted surface area, CdF - frontal surface area, and C d v - volume273. Asterisks indicate values calculated from information provided, NR refers to parameters that were not reported. Species Mass Velocity Velocity Re CdA Cd F Cd v Method Source (m/s) (L/s) (glide drag) Steller sea lion 128 3.41 1.46 5.52 0.0046 0.080 0.044 deceleration: This study (Eumetopias jubatus) x 106 instantaneous rates California sea lion 37.5 2.36 1.62 2.87 0.0039 0.046 0.032* deceleration: Feldkamp (1987) (Zalophus califomianus) x 106 two points Harbor seal 33 1.8 1.4* 1.6 0.004 0.038 NR deceleration: Williams and (Phoca vitulina) x 106 two points Kooyman (1985) Bottle-nosed dolphin 232 1.89 0.76* ~106 0.012 NR NR deceleration: Videler and (Tursiops truncatus) average rate Kamermans (1985) Estuary dolphin 85 2.45 0.98* ~106 0.004 NR NR deceleration: Videler and (Sotalia guianensis) average rate Kamermans (1985) Gentoo penguin 5 NR NR ~106 0.0044 0.07 0.031 deceleration: Nachtigall and (Pygoscelis papua) instantaneous Bilo(1980) rates Emperor penguins 30 1.63 1.72* 1.25 0.0021 NR NR deceleration: Clark and Bemis (Aptenodytes forsteri) x 106 average rate (1979) sea lions were swimming at Reynolds numbers (Re < 5 x 106) in the transition region. Drag coefficients vary with speed, decreasing with increasing Reynolds number until after the transition point when they tend to stabilize (see Figure 1.2). The Steller sea lions' C d A values were relatively constant over the Reynolds number range of this study (Figure 2.2), again implying that the animals were swimming at Reynolds numbers associated with turbulent boundary layers. Theoretically, the drag values should show a slight decrease with Reynolds numbers in this range. The expected slope is very small though, which would make it difficult to statistically demonstrate this relationship with measured values. If the Steller sea lions had been swimming with a transitional boundary layer, the drastic decrease in drag would be obvious with the amount of variance in these measured values. Many marine mammals do swim at Reynolds numbers in the transition region, but studies on pinnipeds and cetaceans (e.g. Innes, 1984; Videler and Kamermans, 1985; Williams and Kooyman, 1985) have also concluded that they swim with a largely turbulent boundary layer at Reynolds numbers greater than 106. Turbulent boundary layers are associated with higher frictional drag forces than laminar boundary layers but have the advantage of delaying the point of separation (Vogel, 1981; Blake, 1983). Separation of flow results in a dramatic increase in pressure drag, reduced lift production, and unsteadiness in the flow that can cause buffeting of the body (Blake, 1983). Pennycuick et al. (1988) suggests that there exists a region of Reynolds numbers below the transition level where the flow around an animal is laminar but detached, with greater associated drag than for turbulent flow at higher speeds. Therefore, total drag for a separated boundary layer with turbulent flow is lower than with laminar flow (Figure 1.4), because of the delayed onset of separation. It has been suggested that protuberances on the body such as eyelids and the rostrum induce turbulence for the purpose of preventing separation of the flow (Walters, 1962). Flow 43 visualization studies on seals and dolphins have shown that the flow can remain attached along almost the entire body length (Williams and Kooyman, 1985; Rohr et al., in press). Much less energy is then lost to wake formation, greatly reducing total drag. Partially laminar flow is associated with the lowest drag forces for separated boundary layers. It is possible that if the Steller sea lions were swimming at slower speeds, the lower Reynolds numbers (velocity « 2m/s, Re < 4 x 106) would allow maintenance of laminar flow along the anterior portion of the animal's body. At the higher Reynolds numbers, however, laminar flow would be difficult to maintain without separation. Therefore, it is likely that by swimming with a turbulent boundary layer, separation of the flow is delayed, and the total drag is reduced Drag is dependent on the square of velocity; thus it should increase curvilinearly with swimming speed. In this study, drag actually had more of a linear response with increasing speeds (Figure 2.3), but this can probably be attributed to the limited range of swimming velocities over which drag was measured. If a broader range of swimming velocities had been investigated, the drag would be expected to show a curvilinear response similar to what was found for California sea lions (Feldkamp, 1987b) and harbor seals (Williams and Kooyman, 1985). The coefficients of drag were greater than predicted for a completely turbulent boundary layer, therefore the drag forces were also greater than the theoretical values by an average of 50%. Experimental design in this study allowed the animals to swim at speeds of their choice. This limited the range of drag data, but provided an opportunity to evaluate their preferred swimming speeds. These speeds are likely to vary in the wild, but results from this study do give an indication of the swimming velocities attainable by Steller sea lions. The average glide velocities of individuals ranged from 2.9 to 3.4 m/s; these values are higher than the averages 44 found for gliding California sea lions of 2.0 to 2.4 m/s (Feldkamp, 1987b). It is expected that Steller sea lions should swim faster than their smaller relatives because although drag increases with the square of velocity, the available power rises with the cube of the body length (Aleyev, 1977). Yet when glide velocity is converted from meters to body lengths per second, the average speeds for the Steller sea lions of 1.2 to 1.5 L/s are lower than for the California sea lions (1.6 to 1.8 L/s, Feldkamp, 1987b). This reduced specific speed (velocity referenced to body length) for larger animals has also been observed in cetaceans (Webb, 1975). The minimum cost of transport (COT), or the amount of energy required to move a unit of mass a given distance (Schmidt-Nielsen, 1972), predicts the velocity at which the greatest distance can be traveled with the least energetic costs (Williams, 1987). The preferred swimming speed should thus match the speed of minimum COT, which has been demonstrated in animals ranging from ducks to sea lions (Prange and Schmidt-Nielsen, 1970; Feldkamp, 1985; respectively). Feldkamp (1987b) determined that the minimum COT occurred at 1.8 m/s or 1.4 L/s for California sea lions, a specific speed very similar to that chosen by the Steller sea lions in this study. Ponganis et al. (1990) recorded the velocities of otariids in the wild, and showed that the average speeds of the smaller species were consistent with predictions based on the minimum COT (Feldkamp, 1987b) while the larger animals tended to dive slower than expected. Morphometries The streamlined body forms of most marine animals represent a prime example of convergent evolution in their design to minimize drag for locomotion in the water (Howell, 1930). At high Reynolds numbers streamlining provides an effective means of drag reduction by delaying the point of boundary layer separation (Vogel, 1981; Blake, 1983). Fineness ratios are 45 a measure of streamlining, and values from 2 to 6 result in reduced drag, with an optimum at 4.5 (Blake, 1983). The average FR of the Steller sea lions in this study was 5.55, which is similar to other marine mammals including seals, dolphins, and whales (Fish, 1993a). For a similarly streamlined body gliding at the same Reynolds numbers, theoretical equations predict that about 85% of the total drag is due to skin friction with the remainder made up of pressure drag. The position of maximum thickness is another indicator of the magnitude of drag; larger values prevent separation of the boundary layer over a greater portion of the body surface thus decreasing overall drag (Mordinov, 1971). Boundary layer separation is expected to occur at this position, and has been observed on a model dolphin (Purves et al., 1975). Yet, studies on freely swimming seals and dolphins show no separation of the flow until near the end of the body (Williams and Kooyman, 1985; Rohr et al., in press). The position of maximum thickness (C) is also important because it is often the point where boundary layer flow switches from laminar to turbulent (Vogel, 1981; Blake, 1983). By placing this region farther back there is a greater region of laminar flow and therefore lower overall drag. Steller sea lions in this study had an average C of 0.34. This is slightly lower than the values of 0.40 for California sea lions (Feldkamp, 1987b) and 0.34-0.45 for dolphins (Fish and Hui, 1991), and much lower than the range of 0.5-0.6 for phocid seals (Aleyev, 1977; Innes, 1984). The position of maximum thickness on otariids coincides with the location of their shoulders and foreflippers. This location may be constrained by their evolutionary history (Lauder, 1982), and may also be associated with the demands of terrestrial locomotion which relies on the foreflippers for quadrupedal movement. From the drag data I have concluded that Steller sea lions swim with a largely turbulent boundary layer at their preferred speeds, and although it may remain partially 46 laminar at lower Reynolds numbers, this region of laminar flow would be smaller than on other marine mammals whose location of maximum thickness is farther back. Otariids rely on their foreflippers for propulsion, and their swimming mode allows thrust production throughout the entire stroke cycle. The flippers act as hydrofoils during the power and recovery phases of the three part stroke cycle (English, 1976; Feldkamp, 1987a; Godfrey, 1985). They have a crescent, winglike design to maximize lift and thrust (Van Dam, 1987). Greater lift production is also associated with foreflippers of high aspect ratio, which additionally lowers the induced drag from tip vortices (Vogel, 1981). The average aspect ratio of the Steller sea lions' flippers was 3.37, which is much lower than the average of 7.85 measured for California sea lions (Feldkamp, 1987b). The Steller sea lions' aspect ratio is also low in comparison to bird and insect wings (Vogel, 1981). The foreflippers of Steller sea lions are large and long like an ideal hydrofoil, but they are also rather wide, which reduces the aspect ratio. Otariids also use their flippers as paddles in the final stroke phase. Feldkamp (1987a) showed that during the paddle phase the velocity of the flipper is relatively slow, which should increase efficiency. To be most efficient, paddles should have an unstreamlined shape and a large surface area for creating drag and therefore thrust (Blake, 1981). The large surface area of the Steller sea lions' foreflippers constitute about 16.5% of their total wetted body surface area, a proportion almost identical to that of California sea lion foreflippers (Feldkamp, 1987b). This is a large propulsive area compared to animals which have a greater reliance on paddling, such as otters and muskrats whose paw area is only about 5% of their total surface area (Williams, 1989). The sea lion's flippers make effective paddles since thrust is produced most efficiently by moving a large volume of water at a slow speed (English, 1976). Although the low aspect ratio of the Steller sea lions' foreflippers may reduce their ability to generate lift during the power and 47 recovery phase of their propulsive movements, they are well designed paddles, and it is this final phase that is likely to generate the majority of forward thrust, similarly to California sea lions (Feldkamp, 1987a). Conclusions Steller sea lions utilize the same propulsion mode as other otariids, but their performance differs from California sea lions due to their larger size. They swam at higher velocities as predicted, and these higher speeds along with their greater body length result in higher Reynolds numbers. Gliding occurred at Reynolds numbers beyond the transition zone; therefore it is not surprising that the drag data indicated that the Steller sea lions were swimming with a largely turbulent boundary layer. This is not necessarily a disadvantage though because the turbulence in the flow delays separation of the boundary layer, resulting in a lower overall drag. Their well streamlined bodies also help to delay separation, and their flippers are designed to produce thrust throughout the stroke cycle, especially during the paddle phase. The results from this study agree with other research on marine mammal swimming (Lang and Pryor, 1966; Fish et al., 1988; Fish, 1993b) that show no unusual ability to maintain laminar flow as suggested by Gray (1936). 48 CHAPTER 3: ERROR ANALYSIS AND COMPARISON OF METHODS INTRODUCTION Swimming is likely to be a major energetic cost for an aquatic mammal. Measurements of the encountered drag provide information regarding power requirements, along with the characteristics of flow in the boundary layer. These drag values can be used to predict the costs associated with swimming over a range of speeds; the information can then be applied to energy budget models. The method used to determine the coefficient of drag will affect the accuracy of the values. As discussed in Chapter 2, measurements of drag from decelerating glides provides the most accurate estimates of passive drag. Although the active drag on a swimming animal is predicted to exceed these values by 2-7 times (Blake, 1983), passive drag can be used to determine the minimum costs of swimming. The "deceleration during glide" approach relies on the idea that passive glides are resisted only by the drag force of the water. The rate of deceleration can then be used to calculate the drag, based on the principle that force equals mass times acceleration. The animal should theoretically decelerate at a constant rate, but in practice there may be small variances. Slight movements of the animal's body configuration and changes in the water current can temporarily affect the deceleration. The rate of deceleration can be determined from velocity measurements made twice, or more, over the course of the glide. Traditionally, studies have used the "two-point" method. The velocity of an animal is measured as it passes two markers separated by a small distance. This method ignores changes in velocity that occur as the animal is gliding past the marker, and any changes in velocity between the measurement points. Some studies (e.g. Clark and Bemis, 1979, on penguins; Videler and Kainermans, 1985, on dolphins) 49 have simply stated that an average rate of deceleration was used in calculating the coefficient of drag (Cd), without specifying the number of velocity measurements made. An alternative method was proposed by Bilo and Nachtigall (1980), it will be referred to here as the "instantaneous rates" method. Velocity is measured frequently over the course of the glide, essentially determining the instantaneous velocity. Regression of the inverse velocity against time provides an average rate of deceleration over the entire glide, and the slope of this line is used to calculate the coefficient of drag. This method includes all changes in velocity and smoothes small fluctuations in the rate of deceleration (Williams, 1987). It also provides an assessment of whether the glide is undisturbed, and compensates for errors in measuring and plotting during the digitizing process (Bilo and Nachtigall, 1980). In this study the "instantaneous rates" method was utilized in an attempt to minimize all possible errors. There are additional experimental errors involved in the measurement of the other parameters necessary to calculate the coefficient of drag. These errors were assessed by comparing multiple measurements of the same parameter. The two principal methods ("instantaneous rates" and "two-point") for determining the coefficient of drag were also compared, and their respective benefits and drawbacks are discussed. Drag measurements provide important information for determining the energetic requirements of a biological organism moving in a fluid. This information can be applied to models of energy budgets which may be used in management decisions, as in the case of the endangered Steller sea lions. Therefore, it is essential that the estimates be as accurate as possible, and any associated experimental error be assessed. 50 METHODS AND RESULTS Comparison of Approaches To compare the two "deceleration during glide" methods, each was used in the analysis of identical glide sequences. For the "two-point" method (following Williams, 1987), the initial velocity (Ui) was determined by measuring the time required for the animal's body total body length to completely pass one window divider. The final velocity (Uz) was determined in the same manner at the next window divider. With the known body length of the sea lion, the velocity past each point was calculated, along with the geometric mean of the two velocities (Ua). Time (t) to travel the distance (approximately \.5 m) between the two dividers was also measured. The average deceleration (A) was then calculated from: A = U i = U 2 (1) t Based on the principle that the only force acting on a gliding body is the drag, the total mass (M) of the animal, including its added mass, and the average deceleration were used to calculate drag: Drag = M A (2) The coefficient of drag can then be calculated: Cd = Drag (3) Vi p Ua 2 S This coefficient of drag was compared to values obtained by the "instantaneous rates" method as described in Chapter 2. Glides were only selected for comparison if the entire glide past each divider was relatively straight. A total of 13 glides were compared, and there was no significant difference (t-test; t=-0.585, df=24, p=0.5641, power=0.05 with an alpha=0.05) between the average coefficients of 51 drag determined from each method. The values estimated with the "two-point" method were an average of 14% greater than the values from the "instantaneous rates" method. Based on the absolute value of the differences, there was an average difference of 38% between the two methods. The coefficient of variation was 37% for the "two-point" method, and 33% for the "instantaneous rates" method. Experimental Error Three reference areas were used in this study: total wetted surface area, frontal area, and volume273. The error in the body measurements used to calculate these areas was estimated. The surface area of the flippers was determined from video images with a software program (SigmaScan/Image, version 2.01, Jandel Scientific). A reference grid (2.5 cm squares) was used for a 3 point calibration. The accuracy of this calibration was verified by comparing measurements of the maximum lengths of the flippers from the video images with the values measured directly by the trainers. Surface area of each flipper was measured a minimum of two times (calibration was repeated each time) to estimate the experimental error. These values were compared to determine the average percent difference in the surface area measurements. The average difference (using absolute values) between measurements of surface areas for both the fore- and hindflippers was 7.0%. This causes the total wetted surface area of the sea lion to differ by an average of 1.9% and the total body volume by 0.46%. Measurements of body girths and lengths taken by the trainers were assumed to be accurate to ± 1 cm for each value. To estimate the maximum error, 1 cm was added to each girth and length measurement. This resulted in a difference of 3.1% for the total wetted surface area, 5.6% for the volume, and 1.3% for frontal surface area. Combining the maximum possible 52 errors in the surface area measurements of the flippers with the errors in girth and distance measurements, the total error was 5.0% for the body wetted surface area and 6.1% for the body volume. The precision of the digitizing method was also investigated. Thirteen of the glides were digitized two separate times. The glide sequences were very similar between each digitizing attempt. Slight differences, in start and end time of the analyzed glide or in the stationary reference point, were ignored because the coefficient of drag should be a true value for the glide. In this study the drag coefficients did not change with Reynolds numbers, therefore they should not vary with glide duration or choice of reference point. The values calculated for the coefficients of drag, glide velocity, and Reynolds number were compared from the separate analyses of each glide. The coefficients of drag varied by an average (absolute difference) of 17%> (range 4-44%), and the average velocity and thus Reynolds number characterizing the glide had an average difference of less than 1.0%. DISCUSSION "Deceleration during glide" measurements provide the most accurate estimates of the passive drag acting on a gliding animal. This approach allows the animals to swim unrestrained, with very little interference from the experimenters. Natural glides between swim stokes or from coasting to a stop can be used to measure drag. Also, normal body configurations and any skin distortions are included in the estimated values. Although active swimming should increase the drag, these passive drag measurements provide baseline values to estimate the power requirements. The experimental method used to determine the coefficient of drag will affect the 53 accuracy of the values and thus the confidence with which they can be applied to energetics models. Essentially two methods have been discussed in the literature for determining the coefficient of drag based on the deceleration principle. The "two-point" method is more commonly used (e.g. Williams and Kooyman, 1985; Feldkamp, 1987b), while the "instantaneous rates" method has rarely been applied (e.g. Nachtigall and Bilo, 1980). Presumably, this is because it is a more time consuming process, yet it is also inherently more accurate. Both methods require that the animal maintain its body in a gliding position throughout the analyzed sequence, but small fluctuations in deceleration can be smoothed by using the "instantaneous rates" method (Williams, 1987). The analyzed glide sequences should be brief with small changes in velocity because the drag equations are technically correct only for instantaneous measurements of velocity (Williams, 1987). This is the major drawback of the "two-point" method; the velocity is measured as the time for the animal's entire body to pass a reference point, assuming that the velocity does not change over this relatively long time period. Yet, the approach relies on the idea that the animal is decelerating, and this very change in velocity is being ignored. Any velocity changes that occur between the two points are also excluded with the "two-point" method. The rate of deceleration is not actually a constant, and with only two velocity measurements, the calculated rate may be based on extreme values. The "instantaneous rates" method includes the contributions of all velocity changes during the glide, which are used to determine the rate of deceleration. The deceleration approach assumes that the drag coefficients are constant over the range of velocities and Reynolds numbers encountered during the glide (Bilo and Nachtigall, 1980), which is a very reasonable assumption for both methods if brief glide sequences are used at these relatively high Reynolds numbers. 54 The analysis of video or film records has its own associated measurement errors, but there is the benefit that the glides can be analyzed repeatedly. The total change in velocity over the glide must necessarily be small, so that the drag equations are applicable. Therefore, both the length measurements of the animal and the video images must be accurate (Williams, 1987). Any errors of this type would affect both methods similarly. Body lengths can be measured to reasonable accuracy with trained animals, and these lengths are then used to calibrate the true distances on the video image. When using a single camera, parallax distortion may result in the miscalculation of glide velocity (Van Sciver, 1972). In this study, the extent of distortion was evaluated and determined to be a problem only at the extreme ends of the field of view, these areas were not included in the analyzed glides (see Chapter 2). The major experimental error is in the digitizing process, because it can be difficult to mark the reference points consistently. The digitizing error is more of a concern with the "instantaneous rates" method applied in this study, due to the frequency of measuring the animal's position over the course of the glide. By redigitizing thirteen of the glides and comparing the results between each attempt, the digitizing error in this study was estimated to be 17%. There may be an additional unknown error associated with the application of a running average to the position measurements from the digitizing. Yet, the running average is actually likely to decrease measurement errors by reducing scatter and de-emphasizing the farthest ends of the glide, which are the only areas where parallax distortion is a possibility. During some of the glides vertical movements occurred. If the change was steady and not extreme, these glides were still included for analysis. These movements should have little effect on the position values because a vector distance was used for the measurements. Glides which angled away or towards the window were not included 55 in the analysis. Any such movement not obvious on the video record would be a small enough distance that the associated error is negligible. The coefficient of drag equation (3) requires values for the body mass, added mass, water density, and average velocity. The mass can be measured on a platform scale, in this study the scale was accurate to ± 0.05 kg, and since the mass of the animals ranged from 104 to 185 kg, the error was considered negligible. The added mass values were determined from coefficients (a) provided by Landweber (1961) for particular fineness ratios. Although the difference in the a values for the range of fineness ratios in this study was small (example: a = 0.0514 for an FR of 5.5 and a = 0.0591 for an FR of 5.0), a values not given were extrapolated from the bordering values, assuming that the rate of change was constant. Thus the coefficient of added mass appropriate for the exact fineness ratio of an individual was used in each Cd calculation. The values for the density of sea water at specific temperatures were obtained from the CRC handbook. Density values for temperatures between 5° to 10°C, and 10° to 15°C were extrapolated in the same manner as the added mass coefficients. The temperature of the water in the glide tank was measured by aquarium staff daily; the density associated with the temperature on the day of the glide was used in each Cd calculation. The maximum error in the measurement of average glide velocity was only 1.0% as determined from an assessment of the digitizing error. It appears that the error is negligible in the all of the above glide parameters. Another parameter in the drag coefficient equation is the reference area. This can be the total wetted surface area, frontal surface area, or volume273. There was an estimated error of 5.0% for total wetted surface area measurements. If this error is combined with the digitizing error of 17%, the coefficient of drag (CdA) can vary from 10% to 26%. The measurement error associated with the frontal surface area is approximately 1.3%, combining this with the digitizing 56 error, the CdF values varied from 13% to 22%. The body volume error was determined to be 6.1%), causing the Cdv to vary by 11-25%. Thus it appears that the total error associated with the drag coefficient values has a maximum of 26% and are ori average closer to 18%. There is no clear consensus in the literature regarding which reference area is most appropriate for calculating the drag of a marine mammal. The frontal surface area is the easiest to measure and consistently increased as expected with the growth of the animals in this study (see Chapter 2), yet it provides the least information concerning the body shape and surface encountered by flow of water. The total wetted surface area and volume are more difficult to measure, because the body forms are not exact geometric shapes. Sea lions are generally torpedo shaped but with less predictable changes in their circumference or girth. Considering the body to be a series of truncated cones provides a reasonable estimate of their body shape. In this study, seven cones were used to approximate the shape, and girth measurements were made at locations on the body where the shape changed (e.g. hips, shoulders). Both total wetted surface area and volume changed unpredictably in this study as the animal's grew. In one case it appeared that the total wetted surface area decreased as the animal grew, which is not possible. The change was only 0.4%, which is smaller than the estimated error of 5%, and is likely due to inaccuracies in the girth and distance measurements. Volume also appeared to decrease for two animals, again the change of 3.3% is within the error of 6.1%. Although the measurements of total wetted surface area and volume were not always accurate, they probably reflect true changes in the body shape with age and season better than the frontal surface area, which is based on only one girth measurement. Thus, as reference areas they provide a better indication of the animal's overall hydrodynamic shape. 57 Vogel (1981) considers body volume to be the most biologically relevant reference area because it is important for animals to both maximize volume and minimize drag. From the hydrodynamic point of view, total wetted surface area is the most meaningful reference area for a streamlined body. It represents the actual surface encountered by the flow, and at high Reynolds numbers friction drag is responsible for the majority of total drag. An interesting point is that the total wetted surface may actually change slightly during swimming. If the flippers are held firmly against the body, then an amount equivalent to the surface area of the foreflippers would not be encountered by the flow, thus increasing the calculated coefficient of drag. In this study it appeared that the flippers were usually held at least 2 cm from the body, which is a distance greater than the boundary layer thickness, and the total area of the flippers would therefore be in contact with the flow. Studies often report drag coefficients referenced to only one area, but for comparison purposes it is helpful to calculate the values for all three reference areas. If only one is provided, the total wetted surface area is the most appropriate choice, and is also the most commonly reported in the biological literature. Conclusions The methods used to determine drag coefficients from decelerating glides have some similar sources of error. In this study, the errors associated with measurement of the reference areas were relatively small, 6% for volume, 5% for total wetted surface area, and 1.3% for frontal surface area. The error involved in the digitizing process appears to be the main contributor to the total experimental error of approximately 18%. The "two-point" method would involve the same errors in reference area, but the digitizing process would likely yield 58 more precise values because of the limited measurements. This does not imply accuracy though. Some of the necessary assumptions are not met with the "two-point" method (i.e. the velocity at each point is not a constant), and large parts of the glide are excluded which are likely to affect the drag. The coefficients of drag measured with the "two-point" method differed from the values determined by the "instantaneous rate" method by an absolute average of 38%. Although the mean values were not significantly different, the coefficient of variation was higher for the "two-point" method (37% compared to 33%). The difference between drag coefficients obtained by the two methods for individual glides was large and often greater than the estimated experimental error. In this study, such a difference would not affect the conclusions regarding the turbulent boundary layer. Yet, if the measured values were closer to the theoretical values, it would be possible to form incorrect conclusions based on results from the "two-point" method. In hydrodynamic literature a single drag coefficient is reported for a particular shape. This custom has continued in biological research, but a single value can not truly represent the drag of a living organism. Slight changes in the body configuration of swimming animals can affect their drag, as demonstrated in the range of results from this study. The coefficient of drag values did not vary with Reynolds number and appear to be unaffected by depth, yet the values ranged from 0.0025 to 0.0098. A single value for the coefficient of drag may allow more straightforward comparisons between species, but it is important also to include the range of values. To form conclusions regarding the hydrodynamic properties of flow, it is important to keep in mind the range of values due to biological variability, natural movements, experimental error, and experimental method. When applying these values to models for predicting energetic costs, a range of values will provide more accurate estimates. 59 C H A P T E R 4: EFFICIENCIES A N D M E T A B O L I C R E Q U I R E M E N T S OF S W I M M I N G Steller Sea Lion Decline In May of 1997, a population of Steller sea lions was placed on the U.S. Endangered Species List by the National Marine Fisheries Service. These animals in the Gulf of Alaska and the Aleutian Islands decreased by more than 100,000 from 1960 to 1990 (NMFS, 1992), and the population is continuing to decline. Steller sea lion numbers appear to have stabilized in the region from southeast Alaska through Oregon (NMFS, 1992), and this population is listed as threatened. The cause of the decline has not been determined, but much of the research is examining the hypothesis that the animals are nutritionally stressed. The North Pacific Universities Marine Mammal Research Consortium was formed to undertake long term studies on the relation between fisheries and marine mammals, with a focus on addressing the cause of the Steller sea lion decline. Research projects are generating data to be used in a model which relies on energy budgets to predict the Steller sea lions' food requirements. Studies of wild animals are providing information on their activity budgets, while captive studies allow determination of the energetic costs of these various activities. Pinnipeds rely on swimming and diving to forage, and for travel between rookeries and haul-out sites to feeding grounds. Steller sea lions often spend extended time at sea and may travel great distances, thus swimming costs may constitute a large portion of their total energy budget. Individual metabolic needs and the availability of prey should determine the amount of time an individual will spend capturing prey (Stephens and Krebs, 1986). The duration and distance of feeding trips, along with dive frequency and total home range are expected to respond 60 to spatio-temporal changes in prey density (Merrick and Loughlin, in press). Otariids spend little time resting when at sea (Feldkamp et al., 1989), therefore the energetic costs of swimming may limit their potential to respond to changes in prey availability. Investigation of this issue requires data on the energetic costs associated with swimming over a range of velocities. Measurement of Swimming Costs Researchers are currently working on determining the field metabolic rate of Steller sea lions, using the doubly-labeled water technique. These measurements provide data on total energetic costs, but also include the time spent on land. Therefore it is not possible to separate the metabolic requirements of their different behaviors: nursing and resting on land, swimming, diving, and resting at sea. Yet, knowledge of how metabolic costs change with swimming velocities is necessary to estimate the energetic requirements of Steller sea lions in different situations. Metabolic rates during swimming can be investigated with two approaches: measurement of oxygen consumption in a swim flume (or free swimming in a testing tank), and determination of drag forces to calculate power requirements. In the swim flume the animal swims against set water currents, and the effects of swimming speeds on oxygen consumption can be determined. As this method directly measures energy expenditure, it does not require any assumptions regarding efficiencies of swimming. Yet, when working with large animals, such as Steller sea lions, the enclosure may restrict their forefiipper movement, so that they are not able to swim naturally. Also, it is difficult to generate high enough water velocities to represent their higher swimming speeds, and wave formation may become a problem as the current is increased. Some studies have attempted to simulate swimming at higher speeds in a flume by attaching a cup on the animal to increase their drag (e.g. Feldkamp, 1987b; Williams et al., 1991). This 61 technique may not provide accurate results though, because increasing the drag will not affect the boundary layer flow in the same manner as would actual increases in the speed of movement. Measurements of glide drag provide an estimate of the minimum power requirements, and when combined with information on swimming efficiencies, the metabolic costs of swimming can be calculated. Advantages to this approach are that the animal is not required to learn new behaviors, they are in a familiar and low stress situation, and the swim area is less restricted. Therefore, their swimming behavior should be more natural. The animals also choose the speed at which they swim, so the data is for swimming speeds within their normal range, and often includes the higher velocities. Coefficient of drag values can also be used to calculate the metabolic costs of swimming at speeds other than those observed. This approach should provide very accurate results at Reynolds number beyond the transition point, since coefficients no longer vary with speed. The primary drawback to this approach is that the calculations require assumptions about swimming efficiencies and active drag, but estimates based on research into these parameters for other marine mammals can provide reasonable values. In addition, drag coefficients can be difficult to determine accurately; careful methodology and measurements will reduce these errors. The main advantage to measuring drag rather than oxygen consumption, is that the equipment is more readily available and mobile, so that a variety of species can be investigated with this approach. Ideally, using both methods provides the most accurate data, and comparisons at similar swimming speeds allows confirmation of the values. The swim flume provides measures of the metabolic rate at slow swimming speeds, while the drag values can be used to calculate the costs associated with swimming at higher velocities. In this chapter, metabolic rate determinations from both approaches are compared and evaluated. 62 Swimming Efficiencies Metabolic rates were provided by D. Rosen (unpublished data). Resting metabolic rates (RMR) were measured in a dry chamber using open circuit (gas) respirometry as described in Rosen and Trites (in press). The metabolic rates during swimming (SMR) were measured in a swim flume covered with a plexiglass dome for gas collection. Calibration for measurements over a water surface were made using a nitrogen dilution technique. Water current was generated in the flume with dual turbines, and swimming metabolic rates were measured for two Steller sea lions. Tag and Sugar, at velocities ranging from 0.13 to 1.4 m/s. Metabolic rates increased with velocity and were described by an exponential regression. This equation was used to predict the power input (i.e. metabolic rate) for velocities up to 3.6 m/s (the maximum speed at which drag was determined). Aerobic efficiencies (r\a) of swimming were calculated as the power output (drag x velocity) divided by the total power input (SMR converted to watts by assuming a caloric equivalent of 20.1 Joules/ ml O2), such that: r|a = power output (1) power input Propulsive efficiencies (r\p) were calculated in the same manner with the exception that the power input value was corrected to account only for the energy that actually reaches the foreflippers, or propulsive appendages. The regression of the net metabolic rate (SMR-RMR) versus swimming velocity was used, and the values multiplied by a muscular efficiency of 25% (Cavagna et al., 1964) to determine the available power input. rip = power output (2) net power input x muscular efficiency Since the C d A was not significantly different between individuals and did not vary with Reynolds number, the overall average C d A of 0.0056 was used in the drag calculations for both individuals. 63 Total wetted surface area of the individual tested, along with the appropriate water density, were used in the calculations of expected drag. Calculated efficiencies increased curvilinearly with swimming velocity. This trend has been shown in sea lions and minks (Williams, 1983; Feldkamp, 1987b), while studies on dolphins and seals (Fish et al, 1988; Fish, 1993b) showed no change in efficiency with velocity. In this study, maximum aerobic efficiencies (na) were 13% for Tag and 17% for Sugar (Tables 4.1 and 4.2). These maximums occurred at the highest swimming speed for which efficiencies were calculated. These values appear reasonable, as maximum aerobic efficiencies of 15-30% have been reported in the literature for other otariids (Feldkamp, 1987b; Williams et al., 1991). Maximum propulsive efficiencies for both animals occurred at the highest speeds of 3.6 m/s, where np reached 59% for Tag and 159% for Sugar. Propulsive efficiency has been reported to plateau between 80% and 90% in trout, sea lions, and seals (Webb, 1971; Feldkamp, 1987b; Fish et al., 1988). Thus, the values calculated here for propulsive efficiency seem unreasonable; the maximum for Tag may be a slight underestimate and the maximum for Sugar is not possible since efficiencies can not exceed 100%. Aerobic efficiencies calculated in this study are similar to values measured for other marine mammals, but the propulsive efficiencies are obviously inaccurate. The lack of data on metabolic rates and drag over the same range of swimming velocities makes it difficult to form definite conclusions regarding the efficiencies of Steller sea lion swimming. Metabolic measurements were not made at high swimming speeds and are limited at the lower velocities, thus the relationship between swimming metabolic rates and velocity had a relatively low R (0.4782 for Tag and 0.4877 for Sugar). There was a very poor relationship of net metabolic rate to swimming velocities (R 2 of 0.3443 for Tag and 0.1247 for Sugar). Extrapolating these 64 Table 4.1: Comparison of metabolic rates and efficiency values for Tag. The left columns report metabolic rates calculated from drag data using efficiencies based on values from other pinniped research. The right columns report metabolic rates extrapolated from measurements made in the swim mill, the efficiencies were calculated from these rates and measured drag, rja-aerobic efficiency, rip-propulsive efficiency, and Pin-power input (i.e. swimming metabolic rate). Velocity rja : based on r)p : based on Pin: calculated T|a : calculated r|p: calculated Pin: predicted from (m/s) literature values literature values from drag metabolic rates (ml 02/min kg) (ml 02/min kg) 2.0 4.0% 30% 32 3.4% 22% 37 2.5 7.3% 50% 34 5.9% 34% 43 3.0 11% 65% 40 9.0% 46% 49 3.5 14% 73% 49 13% 57% 57 Table 4 .2 : Comparison of metabolic rates and efficiency values for Sugar. The left columns report metabolic rates calculated from drag data using efficiencies based on values from other pinniped research. The right columns report metabolic rates extrapolated from measurements made in the swim mill, the efficiencies were calculated from these rates and measured drag, na-aerobic efficiency, np-propulsive efficiency, and Pin-power input (i.e. swimming metabolic rate). Velocity (m/s) T|a : based on literature values Tip : based on literature values Pin: calculated from drag (ml 02/min kg) na : calculated r ip: calculated Pin: predicted from metabolic rates (ml 02/min kg) 2.0 4.7% 35% 28 4.4% 46% 30 2.5 8.0% 51% 32 7.5% 77% 33 3.0 12% 69% 37 • 12% 110% 38 3.5 15% 79% 46 17% 150% 44 relationships past the maximum speed tested of 1.4 m/s to 3.6 m/s may lead to inaccuracies. Metabolic rates were collected over a two month time period, and there were seasonal changes in the resting rates, which has a greater effect on swimming metabolic rates at the slow velocities. Other possible sources of error in the calculated efficiencies are the power output values (i.e. drag), which was estimated to be 18% (see Chapter 3). This is not a large enough value though to explain the highest propulsive efficiency of 159%. Muscular efficiency values could also affect the calculated propulsive efficiencies, but the value used (25%) is considered to be the maximum for mammalian muscular systems, and lower values would increase the apparent propulsive efficiencies. The metabolic data at swimming speeds below 1.4 m/s is reliable, and the calculated efficiencies are very low (rja < 2% and r)p < 20%). The power output was calculated based on a completely turbulent boundary layer, if it is assumed that at lower Reynolds numbers the flow would be partially laminar and the drag values are reduced, this only lowers the efficiencies further. These results tend to confirm that swimming at slow speeds is relatively inefficient for Steller sea lions. Metabolic rates increased with velocity at a slower rate than the hydrodynamic drag forces in this study; a commonly observed trend (Hind and Gurney, 1997). At slow swimming speeds, the majority of the power input is used to meet basal metabolic needs and for thermoregulation. At higher speeds, the waste heat generated from swimming can be used to warm the body, Hind and Gurney (1997) show that if this is taken into account the metabolic rate of marine mammals responds as would be predicted based on drag. 67 Predicted metabolic rates Another approach to understanding the swimming energetics of Steller sea lions is to calculate the predicted metabolic rates based on drag data and assumed efficiencies. Values of drag encountered by a swimming animal indicate the power needed to overcome resistive forces. The total metabolic rate during swimming must provide for basal metabolic needs, the muscles to power the movement, and losses due to inefficiencies. To estimate the metabolic costs of swimming for Steller sea lions over a range of speeds, the drag coefficients measured in this study were used. Studies on pinnipeds have shown efficiency values increasing with speed, reaching a plateau near the higher swimming speeds. The highest efficiencies calculated in this study are unlikely to reflect true maximums since no plateau was seen, and a velocity of 3.6 m/s is probably not near their upper limit. Other research on sea lions indicates maximum propulsive efficiencies (np) of 90% (Feldkamp, 1987b), and aerobic efficiencies (na) between 15% (Feldkamp, 1987b) and 30% (Williams et ai, 1991); a maximum r\a of 20% was used here. Efficiency values used to predict metabolic rates were based on values reported by Feldkamp (1987b) for California sea lions at the same length specific swimming speeds. Muscle efficiency (rim) was assumed to be 25% (Cavagna et al., 1964). The metabolic costs of swimming were calculated for a range of velocities and drag coefficients; the following sample demonstrates the approach. For Tag to swim at 3.15 m/s (1.4 L/s), the na «10% and r\p « 60%, and the average C d A = 0.0056. The power input (Pin = metabolic rate) should equal the power output (Pout = Drag x velocity), including the losses due to inefficiencies. Total Pin = Drag x velocity na 68 Pin (net) = Drag x velocity rip x r)m RMR = Total Pin - Pin (net) It was assumed that the metabolism necessary to meet basal requirements (i.e. resting metabolic rates in this study) does not change with activity. Total metabolic rates determined in this manner were only considered reasonable if the calculated resting rates were close to measured resting rates (D. Rosen, unpublished data). The metabolic requirements were calculated for both Tag and Sugar at swimming velocities equivalent to 1.4 L/s and 2.0 L/s. The lower value represents the speed for which the cost of transport was a minimum for California sea lions (Feldkamp, 1987b), and is close to the average glide speed of the Steller sea lions in this study (range 1.23 - 1.46 L/s). The efficiencies of the California sea lions reached a plateau at speeds of approximately 2.0 L/s (Feldkamp, 1987b); maximum efficiency values were used to calculate metabolic rates of the Steller sea lions at this speed. Assuming maximum efficiencies and maximum metabolic scope, the highest possible swimming speed was also calculated for each drag coefficient. Metabolic rates were calculated using the average, minimum, and maximum drag coefficients measured in this study (Tables 4.3, 4.4, and 4.5). Calculated metabolic rates can be assessed based on reasonable estimates of metabolic scope, resting rates, and efficiency. A range of maximum metabolic scopes for California sea lions have been reported from 5 times resting rates (Williams et al., 1991) to 9 times resting rates during maximai exercise (Ponganis et al., 1991). Harbor seals were also reported to have a maximum aerobic scope of 9 times resting rates (Williams et al. 1991), which tends to support acceptance of this value for sea lions. Metabolic rates calculated here from the minimum, average, and maximum drag coefficients are 69 Table 4.3: Metabolic requirements to swim at speeds of 1.4 L/s, 2.0 L/s, and the maximum possible speed, based on the average drag coefficient (CdA^O.0056). The associated efficiencies are also reported (based on literature values), with maximums (aerobic efficiency = 20% and propulsive efficiency = 90%) used to calculate the highest speeds. Sea Lion Velocity (m/s) Velocity (L/s) Aerobic efficiency Propulsive efficiency Total Power input (ml Ch/kg min) Total Power input (watts) Tag 3:15 1.40 10% 60% 50.5 2360 Tag 4.50 2.00 20% 90% 73.6 3450 Tag 5.40 2.40 20% 90% 127 5960 Sugar 3.01 1.40 10% 60% 44.4 1630 Sugar 4.30 2.00 18% 90% 71.9 2630 Sugar 5.40 2.51 20% 90% 128 4700 T a b l e 4 .4 The metabolic requirements to swim at speeds of 1.4 L/s, 2.0 L/s, and the maximum possible speeds, based on the minimum drag coefficient (CdA~0.0025). The associated efficiencies (based on literature values) are also reported, with maximums (aerobic efficiency = 20% and propulsive efficiency = 90%) used to calculate the highest speeds. Sea Lion Velocity (m/s) Velocity (L/s) Aerobic efficiency Propulsive efficiency Total Power input (ml 0 2/kg min) Total Power input (watts) Tag 3.15 1.40 8% 60% 28.3 1320 Tag 4.50 2.00 15% 90% 43.9 2060 Tag 7.00 3.11 20% 90% 124 5810 Sugar . 3.01 1.40 7% 60% 28.4 1040 Sugar 4.30 2.00 14% 90% 41.4 1520 Sugar 70 3.26 20% 90% 125 4580 Table 4.5: The metabolic requirements to swim at speeds of 1.4 L/s, 2.0 L/s, and the maximum possible speeds, based on the maximum drag coefficient (CdA=0.0098). The associated efficiencies are also reported (based on literature values), with maximums (aerobic efficiency = 20% and propulsive efficiency = 90%) used to calculate the highest speeds. [Note: only two sets of values are reported for Tag, because the maximum speed was 2.0 L/s] Sea Lion Velocity (m/s) Velocity (L/s) Aerobic efficiency Propulsive efficiency Total Power input (ml 02/kg min) Total Power input (watts) Tag 3.15 1.40 12% 60% 73.8 3460 Tag 4.50 2.00 20% 90% 129 6050 Sugar 3.01 1.40 12% 60% 65.0 2380 Sugar 4.30 2.00 20% 90%' 114 4160 Sugar 4.50 2.09 20% 90% 130 4770 reasonable, with total metabolic scopes ranging from 2 to 9 times resting. Metabolic rates calculated from drag data and those predicted from rates measured in the swim flume are compared in Tables 4.1 and 4.2. The metabolic rates and aerobic efficiencies are very similar for both approaches, but propulsive efficiencies are only similar at the lowest speed of 2.0 m/s. At higher speeds, the metabolic rates calculated from drag data should provide reasonable estimates, especially at speeds of 4.5 m/s and above since the efficiencies are well established for maximum speeds (Table 4.6). The similarity of the values for aerobic efficiency and metabolic rates calculated from flume measurements to those calculated from drag data supports the validity of this approach of estimating metabolic rates from hydrodynamic studies. To confirm the validity of the efficiency estimates used in these calculations, further comparisons were made using directly measured metabolic rates. Metabolic rates were determined in the flume at speeds of 0.8 m/s and 1.3 m/s. Values for efficiency were adjusted until a similar metabolic rate could be calculated from drag data, with appropriate resting metabolic rates. These efficiencies were very low (r|a= 0.4-1.4%, r|p= 4.0-13%), but almost exactly the same as measured by Feldkamp (1987b) at the same specific speeds (referenced to body length). If efficiencies corresponding to the same absolute speeds (measured in m/s) from Feldkamp's (1987b) study were substituted, the calculated metabolic rates were unreasonably low (lower than resting rates). This supports the use of efficiencies based on Feldkamp's (1987b) results for the same specific speeds, to estimate metabolic rates of swimming for Steller sea lions at velocities of 2 m/s to 5.5 m/s (Tables 4.1, 4.2 and 4.6). Webb (1975) discusses the idea that specific speeds provide a better means of comparison than absolute speeds. Larger animals tend to swim at faster absolute speeds, yet the specific speeds do not increase at the same rate (Webb, 1975). This trend was also observed in 73 Table 4.6: Metabolic rates calculated from drag with efficiencies based on other pinniped research. Near maximum efficiency values are used at these higher swimming speeds, 5.5 m/s is considered the maximum velocity for a Steller sea lion. r)a-aerobic efficiency, rjp-propulsive efficiency, and Pin-power input (i.e. swimming metabolic rate). Sea Lion Velocity (m/s) r)a : based on literature values rjp : based on literature values Pin: calculated from drag (ml 02/min kg) Tag 4.0 17% 83% 60 Tag 4.5 19% 90% 76 Tag 5.0 20% 90% 101 Tag 5.5 20% 90% 134 Sugar 4.0 1-8% 86% 58 Sugar 4.5 20% 90% 74 Sugar 5.0 20% 90% 102 Sugar 5.5 20% 90% 135 this study; there was no consistent relationship between the average velocity of the glides, measured in m/s, and body length. Yet, when the average specific speeds of individuals were compared, it was noted that the smaller sea lions (Kiska and Sade) had the highest speeds (1.5 L/s) and the larger sea lions (Adak, Tag, and Woody) displayed the lower speeds (1.2-1.3 L/s) (Figure 2.1). Efficiency values which allowed accurate prediction of metabolic rates from drag data were based on Feldkamp's (1987b) results at the same specific speeds. Therefore, although there is no set relationship between body size and swimming speeds, the results presented here support the use of length specific speeds, especially for comparison between species. Assessment of Drag Values The extent of active drag is unknown but can be approximated from metabolic rate measurements of swimming in a flume by calculating the drag associated with a defined aerobic efficiency. Swimming at slow speeds is associated with low efficiencies. At a velocity of 1.3 m/s the r\& was calculated to be approximately 1% for the Steller sea lions, which is the similar to the value determined by Feldkamp (1987b) for California sea lions at the same length specific speed. These efficiencies were calculated based on passive drag and thus are likely to be underestimates. This does provide an indication of the efficiency of swimming at slow speeds however, and can be used to estimate the true increases in drag due to active swimming. If r|a is actually 2%, the active drag would be 1.69 x the average C d A for Tag, and 1.35 x C d A for Sugar. If the efficiencies are higher, the drag increases to approximately 3.38 x Cd^ ; for Tag this occurs with an rja of 4%, and for Sugar with an r\a of 5%. The maximum swimming speed possible with this range of active drag values is shown in Table 4.7. 75 Table 4.7: Maximum velocities possible, based on a range of active drag values expressed as a multiples of the drag coefficient. At maximum speeds the metabolic scope was assumed to be approximately nine times resting rates, and the efficiencies were at maximum values. Sea Lion Multiple ofCd Maximum Velocity (m/s) Maximum Velocity (L/s) Aerobic efficiency Propulsive efficiency Total Power input (ml CVkg min) Total Power input (watts) Tag 3.4 x Cd (avg) 3.60 L60 20% 90% 128 5980 Tag 1.7 x Cd (avg) 4.50 2.00 20% 90% 124 5830 Tag 2.0 x Cd (min) 5.60 2.49 20% 90% 127 5950 Sugar 3.4x Cd (avg) 3.60 1.67 20% 90% 128 4700 Sugar 1.4 x Cd (avg) 4.90 2.28 20% 90% 129 4740 Sugar 2.0 x Cd (min) 5.60 2.60 20% 90% 128 4690 To determine which drag values are most accurate, the calculated maximum speeds can be compared to measured swimming velocities of otariids in the wild. Kooyman (1989) reports a maximum speed of 5.5 m/s or 3.3 L/s for California sea lions, and Ponganis et al. (1990) reports a similar maximum diving velocity of 5.3 m/s for Galapagos sea lions (Zalophus californianus wollebaeki). Preliminary data for Steller sea lions swimming in the wild indicates a maximum speed of approximately-5.0 m/s, « 2 L/s (R. Andrews, unpublished data). The maximum speed measured in this study on captive Steller sea lions was 3.6 m/s (1.6 L/s) for passive glides. It is unlikely that the maximum speed attainable by Steller sea lions is slower than for other otariids. These values do provide an indication of their upper range of swimming speeds, and it will be assumed for this analysis that the maximum specific speed possible is at least 2.0 L/s and is unlikely to exceed 3.3 L/s. The minimum, average, and maximum drag coefficients measured in this study would limit the Steller sea lions' maximum speeds to approximately 3.3, 2.5, and 2.1 L/s, respectively (Tables 4.3, 4.4, and 4.5). These values all fall within the range defined above. Drag was measured for gliding animals and is, expected to increase with active swimming; higher values for drag would decrease the maximum speed possible. Active drag was estimated above; if the increased drag is 3.4 times the average drag, the maximum possible speed would be only 1.6 L/s and 1.7 L/s (Table 4.7). This is very unlikely since glides in this study reached similar speeds, and they are also below the maximum speeds observed in the wild. Active drag could be increased by a lower augmentation factor, or the passive drag coefficient value may be lower than the reported average. If the active drag is greater by a factor of 1.7 times the average for Tag, and 1.4 times for Sugar, their maximum possible swimming speeds are 2.0 and 2.3 L/s, respectively (Table 4.7). These values are similar to maximum speeds recorded for Steller sea 77 lions, although lower than maximums observed for California sea lions. Active drag has been estimated to increase the passive drag values by 2 to 7 times in other marine mammals (Fish et al, 1988; Fish, 1993b). The active drag of animals that are propelled by pectoral fins, such as sea lions, rather than body oscillations should be well approximated by glide drag (Blake, 1983). Therefore, an increase of only 2 x Cd A is a reasonable approximation of the drag acting on a swimming Steller sea lion. If the minimum drag coefficient measured in this study is assumed to represent the true passive drag, then an active drag of 2 times this coefficient results in a maximum velocity of 5.5 m/s (2.5-2.6 L/s) for both sea lions. This is similar to maximum velocities observed for other otariid species. Active drag for an animal swimming in the wild is likely to vary slightly with changes in swimming patterns, therefore an absolute value for the drag coefficient can not be determined. From the results discussed above though, it appears that the active drag coefficient lies somewhere between the range of passive drag values calculated in this study. The average Cd A value of 0.0056 gives a reasonable maximum velocity of 5.4 m/s, therefore, this value was an appropriate choice for the metabolic rate predictions. Conclusions To investigate the cause of the Steller sea lion decline and make informed management decisions, it is important to understand the ability of the animals to alter their foraging behavior with changes in the density and location of fish stocks. Information on the energetic requirements of swimming over a range of normal velocities can be used for this purpose. In this chapter it was demonstrated that drag data can be used to estimate the metabolic costs of swimming for otariids over a range of velocities, ideally supplemented with metabolic measurements in a flume. This information can be used to determine the maximum travel 78 duration or distance to foraging grounds, assuming knowledge of average swimming velocities and available energy. 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