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Hydrodynamics of Balistiform swimming in the Picasso Triggerfish, Rhinecanthus aculeatus Loofbourrow, Hale 2009

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HYDRODYNAMICS OF BALISTIFORM SWIMMING IN THE PICASSO TRIGGERFISH, RHINECANTHUS ACULEATUS by HALE LOOFBOURROW BSc. University of British Columbia, 2006  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Zoology)  THE UNIVERSITY OF BRITISH COLUMBIA (VANCOUVER) January 2009  © Hale Loofbourrow, 2009  ii  Abstract Aquatic propulsion by means of undulatory movements of the median (dorsal and anal) fins is the primary mode of transport for the Picasso triggerfish (Rhinecanthus aculeatus). Known as balistiform locomotion, this form of propulsion is an adaptation for highly efficient movement within complex environments such as coral reefs. A principle component of balistiform locomotion has been the development of momentum enhancement, a fin-force multiplier that increases swimming efficiency. This study examines the kinematics and energetics of balistiform locomotion employing theoretical models of thrust, power, and efficiency. Thrust and power were calculated and compared with theoretical values modeled by Lighthill and Blake (1990). This model has heretofore not been thoroughly vetted and was tested for accuracy and applicability. Thrust force was estimated from resistance (drag) using a vertical dead drop to determine terminal velocity; power was calculated from oxygen consumption measurements at different speeds. The Lighthill and Blake (1990) model requires median fin kinematics (frequency, wavelength, amplitude, wave angle), which were measured from high-speed videography and followed statistically predicted trends with frequency being the dominant variable, and the others changing little or not at all with speed. Momentum enhancement was found to be 3.6, close to Lighthill and Blake’s (1990) theoretically predicted value of 2.5. Momentum enhancement is experimentally proven here for the first time. Theoretical and empirical thrust force values are closely matched; theoretical thrust is greater at lower speeds and lower at higher speeds. The ratio of theoretical thrust to drag-estimated thrust averages 1.08. Theoretical values for power are greater than those measured by a factor of about 3.6 and cannot be explained by measurement error.  iii  Table of Contents  Abstract ...................................................................................................................................... ii Table of Contents ...................................................................................................................... iii List of Tables .............................................................................................................................. v List of Figures ............................................................................................................................vi List of Abbreviations .............................................................................................................. viii Acknowledgements .................................................................................................................. xii  Introduction ................................................................................................................................. 1 Materials and Methods .............................................................................................................. 12 Animals ........................................................................................................................................ 12 Morphology ................................................................................................................................. 12 Kinematics ................................................................................................................................... 13 Drag ............................................................................................................................................. 17 Oxygen Consumption .................................................................................................................. 18 Microscopy .................................................................................................................................. 21 Statistics ....................................................................................................................................... 22  Results ....................................................................................................................................... 23 Morphology and Drag.................................................................................................................. 23 Kinematics ................................................................................................................................... 23 Oxygen Consumption .................................................................................................................. 25 Musculature ................................................................................................................................. 26  Discussion ................................................................................................................................. 27  iv  Morphology ................................................................................................................................. 27 Kinematics ................................................................................................................................... 28 Balistiform Model........................................................................................................................ 33 Drag ............................................................................................................................................. 34 Oxygen Consumption .................................................................................................................. 36 Muscle ......................................................................................................................................... 37 Future Research Directions.......................................................................................................... 38  Conclusions ............................................................................................................................... 40 Tables And Figures ................................................................................................................... 41 Reference List ........................................................................................................................... 61  v  List of Tables  Table 1  Morphometric measurements of Rhinecanthus aculeatus ..................................... 41  Table 2  Individual high speed kinematic measurements of Rhinecanthus aculeatus ......... 42  Table 3  Individual calculations of kinematic-dependent parameters .................................. 43  vi  List of Figures  Figure 1  Schematic of Brett-type swimming flume ........................................................ 44  Figure 2  Schematic of Blazka-type swimming flume ..................................................... 45  Figure 3  Representative outline of R. aculeatus .............................................................. 46  Figure 4  Drag versus fish velocity ................................................................................... 47  Figure 5  Fin wave speed versus fish velocity .................................................................. 48  Figure 6  Fin angular velocity versus fish velocity........................................................... 49  Figure 7  Fin amplitude versus fish velocity .................................................................... 50  Figure 8  Fin wave angle versus fish velocity .................................................................. 51  Figure 9  Momentum enhancement versus fish velocity .................................................. 52  Figure 10  Mechanical efficiency versus fish velocity ....................................................... 53  Figure 11  Oxygen consumption rate versus fish velocity ................................................. 54  Figure 12  Total cost of transport versus fish velocity ....................................................... 55  Figure 13  Net cost of transport versus fish velocity .......................................................... 56  Figure 14  Fin power versus fish velocity .......................................................................... 57  Figure 15  TEM sections..................................................................................................... 58  vii  Figure 16  Strouhal number versus fish velocity ................................................................ 59  Figure 17  Thrust versus fish velocity ................................................................................ 60  viii  List of Abbreviations  TL  Total length  SL  Standard length  BL  Body length (total length)  d  Depth of body  Lf  Median fin length  l  One-half fin plus body depth  s  One-half body depth  b  Tail depth  l-s  Fin depth  FR  Fineness ratio  AR  Aspect ratio  ARt  Aspect ratio of the tail  SAt  Total surface area  SAd  Surface area of the dorsal median fin  SAa  Surface area of the anal median fin  ix  SAc  Surface area of the caudal fin  m  Mass of median fin musculature  ppt  Parts per thousand  ρ  Water density  Vt  Terminal velocity  U  Water or fish velocity  θ  Fin excursion angle   av  Average undulation angle (the angle of the fin as viewed from above)  f  Fin beat frequency  λ  Fin beat wavelength  υ  Fin wavespeed  ω  Fin beat angular velocity  A  Fin beat amplitude  β  Momentum enhancement  ζ  Pressure component  M  Momentum per unit length  Mo  Momentum produced by fins ‘on their own’  x  P  Pressure force  Po  Pressure produced by the fins ‘on their own’  Cd  Drag coefficient  D  Drag force  F  Fin force on the water  FD  Measured drag force  FT  Theoretical thrust force  UF  Corrected flow speed  UT  Speed in the flume without a fish in the swimming section  εS  Fractional error due to solid blocking  λo  Shape factor for the object swimming in the flume  τ  Dimensionless factor for swimming flume  A0  Maximal cross sectional area of the fish  AT  Cross sectional area of swimming section  ṀO2  Oxygen consumption rate by mass  PO2  Partial pressure of oxygen  SMR  Standard metabolic rate  xi  TCOT  Total cost of transport  NCOT  Net cost of transport  AMR  Active metabolic rate  ψ  Oxycalorific coefficient  Pmuscle  Measured muscle power input  Ptheoretical  Theoretical power output  Re  Reynolds number  TEM  Transmission electron microscopy  St  Strouhal number  PIV  Particle image velocimetry  BCF  Body caudal fin  MPF  Median paired fin  ATP  Adenosine triphosphate  xii  Acknowledgements  This thesis would not have been possible without the generous support of many people within the Department of Zoology. First, I would like to thank my supervisor, Dr. Robert Blake, for his help with the experimental and written processes. Bob initially introduced me to zoological science as an undergraduate in 2003. I have been working with him ever since and it has been a wonderful experience. His patience and understanding have been enormously helpful and have made this work possible. I would like to thank the members of my committee: Dr. Colin Brauner, Dr. John Gosline, and Dr. Robert Shadwick for their assistance over the last two years. I would also like to thank Derrick Horne for help with microscopy. Jeff Richards for advice on respirometry, and Pat Tamke for suggestions regarding fish maintenance. Carla Corbett, Dan Baker, Jodie Rummer, Anne Dalziel, Cosima Cihuandu, Graham Scott and others have all helped with various procedural and technical challenges.  1  Introduction  Aquatic propulsion has played a significant role in evolution for nearly one billion years and in fishes for the last several hundred million years (Lighthill and Blake, 1990). Over time, genetic variations have produced an array of traits enabling fish to branch out to different ecosystems and compete for resources within these settings (Webb, 1984). Adaptations to aquatic environments include the maximization of efficiency for foraging, mating, and predator/prey relations. Speed and acceleration are paramount in predators/prey interactions (Webb, 1994; Videler, 1993). Prey strike a balance between defensive armour, camouflage, escape responses and manoeuvrability to find food and escape predator attacks (Brainerd and Patek, 1998). The actinopterygian fishes have produced a great diversity of forms that differ in their propulsive mechanisms using the body, caudal fin, pectoral fins, and median (dorsal and anal) fins (Breder, 1926; Drucker and Lauder, 2001), which has facilitated an extensive adaptive radiation. Adaptations include greater ossification of the axial skeleton, fewer vertebrae, homocercal tails, and deep-bodied specialists using non-caudal propulsion, among others (Webb, 1982; Greenwood et al., Gosline, 1980). Deep-bodied specialization is considered a secondary development within actinopterygians and is seen only among higher teleosts (Webb, 1982). This adaptation may benefit in a number of ways: manoeuvrability in complex environments and at higher speeds, and specialization in acceleration to escape from predators (Blake, 1983). Coral reefs are an environment where defensive armour (e.g. thick impenetrable skin, poisonous barbs, and inflatable pincushions) has developed at the expense of speed in a number of orders of fishes, including Tetraodontiformes, Syngnathiformes and Zeiformes (Lighthill and Blake, 1990). Cruising within the complex habitat of coral reefs requires exact manoeuvring  2  around and within the coral reef structure. Large predators (e.g. shark and tuna) lack the fine control to navigate within these environments (Blake, 2004). Coral reef fish must be able to situate their bodies in any number of directions with minimum expenditure of energy (Gerstner, 1999). This includes the ability to swim backwards effectively and to turn in a circle of small radius (Blake, 1978, 1983, 2004; Webb, 1994). Body undulations are inefficient at swimming backwards and turning, so modes of locomotion that enable these difficult movements will be strongly selected. For example, to turn in a tight circle, “body undulators” may be required to swim in a circle rather than simply rotate (Blake, 1976, 2004; Gerstner, 1999). However, such adaptations usually come at the expense of speed; many fish that are highly adapted to living within coral reefs are unsuited to other levels of the water column where they would be required to swim at higher velocities for prolonged periods of time (Wainwright, 2002; Ohlberger et al., 2006). To fill the niche of fast but manoeuvrable forms, the family Balistidae (Tetraodontiformes) have a rough, thick skin (Lighthill and Blake, 1990; Brainerd and Patek, 1998) and have developed a swimming style that enables steady swimming at relatively high speeds termed balistiform locomotion (Blake, 1978). Historically, research on aquatic locomotion has primarily focused on steady swimming in the body and caudal fin (BCF) mode of locomotion (Blake, 1983; Webb 1975, 1984, 1998). This ranges from snakes and eels using a whole-body undulatory mechanism of propulsion (anguilliform locomotion) to sharks and tuna using only their caudal fin and caudal peduncle in an oscillatory manner (thunniform locomotion; Breder, 1926; Lindsey, 1978; Blake, 2004). A characteristic of the BCF mode of locomotion is an undulatory wave that passes down the whole or part of the body with increasing amplitude (Blake, 2004; Lighthill, 1970; Sfakiotakis et. al, 1999; Wright, 2000). Despite the number of species employing this method of locomotion, body forms are constrained to be of a streamlined form and tend to converge on a single fusiform  3  design (Howell, 1930; Blake, 2004) that is not well suited for manoeuvrability and is associated with adaptation to open, simple environments where speed and power are required (Blake, 2004; Webb, 2004). While BCF is the primary mode of aquatic propulsion of many forms, there are a significant number of other ways with which to move a body through the water. Median paired fin (MPF) locomotion describes fish locomotion using either paired fins (pectorals) and/or median fins (Blake 1983, 2004; Webb, 1984). Approximately one third of all fish species use MPF locomotion (Breder, 1926; Lindsey, 1978; Webb, 1994; Plaut and Chen, 2003). Types of MPF locomotion include: using the pectoral fins for propulsion in a rowing and lift-based manner (labriform), using the caudal fin in a rotary manner about the base of the caudal peduncle (ostraciiform), using the anal fin in an undulatory manner (gymnotiform), and using both median fins in an undulatory or oscillatory manner (balistiform), among others (Lighthill and Blake, 1990; Blake, 2004). MPF swimmers are known for their manoeuvrability rather than their speed and are often found within coral reefs (Sfakiotakis, 1999; Webb, 1984). Arguably, MPF swimmers are released from the constraints of body streamlining, enabling them to adapt to a wide range of environments. Triggerfish have evolved a deep body with elongate median fins that are used as their primary means of locomotion for both finely controlled movements and steady swimming (Breder, 1926; Blake, 1978; Webb et al., 1996; Korsemeyer et al., 2002). Triggerfish are the sole species of the family Balistidae and are the “type form” for balistiform locomotion (Breder, 1926; Blake, 1978). Lighthill and Blake (1990) describe balistiform locomotion as propulsion by undulations or oscillations propagated simultaneously down a posterior pair of highly flexible dorsal and anal fins that do not change in amplitude. Triggerfish use their dorsal and anal fins as their sole method of propulsion at speeds up to half of their maximum swimming velocity (Korsemeyer et al., 2001). In order to swim backwards,  4  triggerfish reverse the wave on their median fins (waves move posterior to anterior; Blake, 1978; Lighthill and Blake, 1990), providing a very efficient method of swimming backwards. When performing turning manoeuvres, triggerfish use a combination of median and paired fins resulting in little to no vertical or lateral translation of the body (Blake, 1978). Within the Balistidae, body form does not differ greatly. Most triggerfish are laterally compressed, deep bodied and somewhat “diamond shaped” (Plaut and Chen, 2003; Gordon et al., 2000). They have a thick, rough skin and a dorsal trigger adapted to hold themselves in the coral against wave action and predators (Breder, 1926; Hertel, 1966). Morphological differences primarily arise in the form and size of their dorsal and anal fins (Wright, 2000). Median fins range from elongate (rectangular shaped with the long side along the axis of the body, also known as low aspect ratio) to flag shaped (triangular, high aspect ratio), with species covering nearly every point between the two (Wright, 2000). Fish possessing fins of high aspect ratio (defined as the ratio of span to chord of the fin) have stiffer fin rays to counteract water forces as the fin oscillates. Fish with low aspect ratio are limited by the total amount of force that can be produced by their fins. Triggerfish have two sets of fins rays: spines and soft rays. The soft rays of triggerfish are used as their primary means of locomotion. The coordinated movement of these soft rays was originally modeled as three pairs of oxidative muscles inserted at the base of each ray: the erectors, depressors, and inclinators (Arita, 1971). The inclinator muscles are responsible for the longitudinal (front to back) movement, whereby the fin is raised and lowered (Arita, 1971). The erector and depressor muscles work to displace the rays laterally and together produce an undulatory motion (Marshall, 1965; Winterbottom, 1974). Sorrenson (2008) has recently suggested five pairs of muscles are attached to each fin ray, two depressors lying laterally, and two erectors lying medially along the saggital plane between pterygiophores and the inclinator  5  under the pterygiophores. Opposite erector and depressor muscles work with each other to pull fin rays laterally and collectively produce undulatory motions (Arita, 1971; Sorrenson, 2008). The inclinators may also work with the erectors and depressors to produce a curvature of the median fin (Jayne et al., 1996; Arita, 1971). Triggerfish are separated into two groups on the basis of fin morphology. Those that possess stiff high aspect ratio fins (e.g. Ocean Triggerfish, Canthidermis sufflamen, Bluelined Triggerfish, Pseudobalistes fuscus and Grey Triggerfish, Balistes capriscus) use an oscillatory, large wavelength form of balistiform locomotion (Lighthill and Blake, 1990; Wright, 2000). Secondly, forms possessing low aspect ratio median fins (e.g. Gilded Triggerfish, Xanthichthys auromarginatus, Clown Triggerfish, Balistoides conspicillum and Picasso Triggerfish Rhinecanthus aculeatus; Lighthill and Blake, 1990; Wright, 2000) use an undulatory, small wavelength mode of balistiform locomotion. There are more than 40 known species of triggerfish (fishbase.org, 2008), and many lie between the two morphological continua. In addition to triggerfish, fin undulations and oscillations are a common method of propulsion for many other MPF fish species. Filefishes (superfamily Balistoidea) and skates and rays (order Rajiformes) employ oscillatory balistiform locomotion as their primary mode of locomotion (Rosenberger and Westneat, 1999). Some fish, such as the Order Zeiformes (John Dories and boarfish), have adopted a truly undulatory mode of locomotion, creating multiple wavelengths along the length of their median fins (Lighthill and Blake, 1990). Flatfish (family Pleuronectidae) and tube-mouthed fishes (order Syngnathiformes) use an undulatory mode of balistiform locomotion at very low velocities when efficiency is more important than thrust (Lighthill and Blake, 1990). Triggerfish, however, appear to be the only fish to use their median fins in an undulatory fashion to cruise at relatively high speeds (Blake, 1978).  6  A series of papers written by Sir James Lighthill between 1960 and 1990 have been highly influential in modelling fish propulsion. Lighthill‟s first paper on fish locomotion (Lighthill, 1960 was inspired by earlier work of classical slender-body theory: the body of a fish or other high-Reynolds swimmers is elongate and smooth, with minimal variation in depth or width along the body axis (Katz and Plotkin, 1991; Sparenberg, 2002). Flow of each cross-sectional slice of the body is considered independent, and forces on the body are only dependent on those measured at the posterior edge of the body (Lighthill, 1975; Webb, 1978; Lighthill and Blake, 1990). Thrust depends only on the acceleration of fluid along each body slice. A primary conclusion from this work is that the backward velocity of the propulsive wave on the fin must be greater than the forward velocity of the animal (Lighthill, 1960). The theory predicts that frequency, amplitude and wave speed all increase with thrust (Lighthill, 1960; Wright, 2000). The opposite is true of efficiency: wave speed increases with thrust but ultimately reduces efficiency (Lighthill, 1960). However, slender body theory is considered „linear‟ and fails to account for inertial effects; conversely, elongated body theory is „nonlinear‟ and largely dominated by inertial effects (Wright, 2000). Indeed, Lighthill and Blake (1990) propose in their balistiform locomotion model that inertial effects will dominate triggerfish thrust capacity. Lighthill introduced his elongated body theory in 1971 to explain the propulsive thrust and efficiencies of fish of elongated bodies (Lighthill, 1971; Lighthill and Blake, 1990). This is most applicable to anguilliform and carangiform locomotion, where fish use undulatory and oscillatory body waves, respectively. Anguilliform locomotion is most commonly used to describe the swimming of eels and snakes, where a large propulsive wave is propagated down the length of the body with increasing amplitude (Sparenberg, 2002); an undulatory motion is said to be one in which a wavelength, or a large part of one, is clearly visible on the propulsive segment of the body. Efficiency of anguilliform locomotion is thought to be relatively low due to  7  large side forces generated by the body that are wasted while swimming (Blake, 1980). Carangiform locomotion is most commonly used to describe the swimming of trout and salmon, whereby the propulsive segment is limited to the posterior section of the animal in a transitory undulatory-oscillatory fashion. Efficiency of carangiform locomotion is somewhat higher than anguilliform due to a more derived (and efficient) caudal fin and a deeper body section which further reduces side forces (Blake, 2004). Elongated body theory is thus ideally suited to be extended to analyze the motion of triggerfish median fins, where both oscillatory and undulatory motions are used (Lighthill and Blake, 1990). The models of elongated body swimming by Lighthill (1960, 1970, 1971) proved exceptionally useful as the basis of further research into balistiform locomotion. Lighthill and Blake (1990; Lighthill 1990a-c) developed a model for fish with elongate median fins as their primary propulsors. This model assumes elongate fins of uniform depth, attached to a rigid body (i.e. no BCF propulsion) and a body section attached to the median fins that is relatively deep compared with the depth of the fin (Lighthill and Blake, 1990; Wright, 2000). Altogether, the model summarizes the thrust generated by triggerfish when swimming steadily with given fin morphology and kinematic variables. As with Lighthill‟s earlier work, the theory describes thrust as being generated primarily from added mass forces and fluid being accelerated normal to each segment of the undulating fin (Daniel, 1984; Sparenberg, 2002). How is it that triggerfish are able to move up to four body lengths per second using such modest means of propulsion? Lighthill and Blake (1990) propose that when median fins are attached to a deep rigid body the momentum of water shedding off the posterior edge of the fin is increased beyond that which would be expected by the fins „on their own‟ by a momentum enhancement factor (β) of three or more. Such an increase in momentum is achieved without increasing wasted wake energy; thus efficiency is also improved (Lighthill and Blake, 1990).  8  Additionally, sideforces are significantly reduced with the presence of nearly one complete wave on the fin when compared with oscillatory propulsion where lateral displacement of each fin causes greater sideforces (Lighthill and Blake, 1990). Body drag is further reduced with respect to the drag associated with undulatory propulsion of the body (Webb, 1992). The mean drag on a rigid body moving through the water may be three to five times less than one that is continuously undulating (Alexander, 1967; Webb and Blake, 1985; Lighthill and Blake, 1990; Webb, 1992). With both momentum enhancement and the reduced drag effects are considered, the triggerfish‟s high velocities through the water can be understood. However, the model assumes a uniform deep and rigid body of negligible width. When the effects of body width are accounted for we find similar results albeit with a reduction of momentum enhancement to between two and three (Lighthill, 1990b). In this study, triggerfish were used in a series of performance and kinematic tests in which they were placed in a swimming flume and subjected to increasing water velocities. Speed was increased in slow steps in order to acclimate the fish to the specific water velocity and to allow time to decrease any “stressors” that might arise with the fish being subjected to such an unfamiliar environment. Experiments were always terminated at their gait transition speed defined as the speed at which they were unable to maintain steady balistiform locomotion without a strong dependence on pectoral fins or use of their caudal fin (Cannas et al., 2006; Drucker, 1996). Gait transition speed was effectively the maximum speed at which balistiform locomotion is sufficient to maintain its current velocity in the water (Korsemeyer et al., 2001). Rhinecanthus aculeatus, the Picasso triggerfish, was selected for this study based on the morphology and kinematics of its median fins and its availability from aquarium stores. Reasonable availability was required to ensure that fish of appropriate size could be found. R. aculeatus is found in the tropical Pacific Ocean near reefs in its juvenile stages and progressively  9  further away from the reefs as it matures (Stobutzki, 1994; Leis, 1991). It has thick rough skin, laterally compressed and deep body, and relatively small, elongate dorsal and anal fins. The median fins are short in height and longer in length along the body (low aspect ratio). The low profile of the median fins assured a proper fit to the Lighthill and Blake (1990) model. The fish propel themselves by producing waves moving down the length of the dorsal and anal fins in an undulatory motion through the water at slow and moderate speeds (up to 2.5 body lengths/s) using balistiform locomotion before switching to body undulations and employing the caudal fin at higher speeds. Several models describing the undulatory propulsion of steady-swimming fish have set clear guidelines to maximize propulsive thrust and efficiency (Lighthill and Blake, 1990; Lighthill, 1960, 1970, 1971). From these models the following predictions are made: Frequency will increase with increasing fish velocity. Wavelength will increase marginally but not largely affect overall performance. Wave speed will increase strongly with increasing velocity and always exceed swimming velocity. Neither amplitude nor stroke angle will be affected by swimming speed and the amplitude will remain constant down the length of the fin. These kinematics should result in a momentum enhancement value of about 2.5. At water speeds up to the gait transition speed, oxygen consumption was measured as a means of testing muscle performance. Oxygen consumption was used to determine the power used while swimming at different velocities (Cannas, 2006). Kinematic measurements were taken by means of a high-speed camera recording dorsal fin strokes. Frequency, wavelength, undulation angle and amplitude were measured and entered into the balistiform locomotion model proposed by Lighthill and Blake (1990; Lighthill, 1990a-c) in order to test the efficacy of the model. By comparing direct measurements of triggerfish drag and power and comparing it to  10  the theoretical model, it was possible to test momentum enhancement, force production and efficiency. Blake (2004) proposes that the primary advantage of balistiform locomotion is its energetic efficiency. Generally, MPF swimming is thought to require less energy than BCF swimming at equivalent length specific speeds (Blake, 2004, Korsemeyer et al., 2002). Efficiency is measured in a number of ways: Locomotor efficiency is the total power input divided by the useful power output (Lighthill, 1960, 1970; Webb and Blake, 1985; Wright, 2000; Sfakiotakis, 1999; Ohlberger, 2006). This describes the fundamental conversion of muscle energy to energy used to propel the fish forward. Power output is calculated in this study by measuring the oxygen consumption for an individual fish indirectly indicating the amount of ATP that is consumed per unit distance swum. Mechanical efficiency is the measure of the efficiency of the propulsive system. For example, triggerfish median fins will move at a speed relative to the fish‟s forward speed in the water. Measuring the ratio of forward speed to wave speed describes how much of the force of the fins is being translated into forward thrust of the animal. Ideally, mechanical efficiency will be one (wave speed equals forward speed), although this is never the case. Triggerfish are able to modulate a number of parameters in their median fins including: frequency, undulation angle, stroke angle, wavelength and angular velocity among others. Each of these kinematic variables is used to optimize thrust and efficiency (Bose, 1995). Additionally, morphological parameters have been selected to improve mechanical efficiency. The deep body of triggerfish and passive chordwise flexibility of the fin is expected to result in increased efficiency (Lighthill and Blake, 1990; Wright, 2000). The goals of this thesis are: 1. To record and analyze fish morphology, performance, and fin kinematics of the Picasso triggerfish (Rhinecanthus aculeatus). 2. To examine the hydrodynamic equivalents of the recorded morphological and kinematic variables with respect to the  11  hydrodynamic theory put forth by Lighthill and Blake (1990; Lighthill, 1990a-c). 3. To assess the validity of this model with comparisons of thrust, power and efficiency calculated by other means. 4. Determine the extent to which momentum enhancement affects balistiform propulsion.  12  Materials And Methods Animals Eleven adult triggerfish (Rhinecanthus aculeatus; mass 18.4g-27.0g, total length 9.4cm10.3cm) were obtained from Clark‟s Feed and Seed, a commercial dealer in Bellingham, Washington. All fish were kept in a 500L holding tank with dechlorinated and aerated water. A 15% water change was done once per week to prevent build up of toxic substances. The temperature of the tank was kept at 26°C ± 1° and salinity at 33.0 ppt ± 1.0 ppt. Each fish was fed a maintenance ration of 5g store bought bloodworms twice per day. A 12 hour light:dark schedule was kept throughout the experiment. The holding tank was kept clean by a 3-step filter, a protein skimmer, and a mechanical filter. 10kg of live rock and 3kg of live sand were used to filter the water as well. 10kg of dead coral was used as natural protection for the triggerfish. Fish were kept in this environment for two weeks before experiments were initiated to give sufficient time for acclimation. At the end of experiments fish were euthanized with an overdose of MS222 (200 mg/L). Morphology Fish were euthanized (overdose of MS-222), and their weight and submerged weight with a suspension apparatus were taken (Mettler PK300 scale, ±0.001g,; Columbus, Ohio, USA). Pictures of the fish were taken with a Nikon Coolpix digital camera (Nikon Canada Inc; Missisauga OT). Total Length (TL, tip of rostrum to the trailing edge of the caudal fin), standard length (SL, tip of rostrum to posterior section of the caudal peduncle), depth (d, deepest vertical section of the body), fin length (Lf, length of median fin base), fin-body depth (l, average distance between the midline and the top of the fin), half body depth (s, average distance from the midline to the base of the fin), fin angle (θ, angle between the bases of the dorsal and anal  13  fins), tail depth (b, maximum tail depth), total surface area (SAt), dorsal fin surface area (SAd), anal fin surface area (SAa) and caudal fin surface area (SAc) were measured from the digital image using ImageJ (National Institutes of Health; http://rsb.info.nih.gov/ij/; Table 1). Surface area was taken to be 7% greater than that captured by a digital camera due to rounded edges and bumps that do not project on a 2-dimensional image (Wright, 2000). The representative outline of Rhinecanthus aculeatus is shown in Fig. 3 with the body measurements also shown. The fineness ratio (FR, depth divided by the total length), fin depth (l-s), aspect ratio (AR, total length squared divided by the total surface area) and the tail aspect ratio (ARt, surface area divided by depth squared) were calculated (Table 1). The mass of propulsive musculature was measured by dissecting out the inclinator and declinator muscles and their respective bone attachments and recording their wet mass. The muscle was subsequently boiled off the bone, and the difference of the muscle and bone yielded an approximate mass of the muscle. Kinematics All kinematic experiments were performed in a transparent Plexiglas Brett-type 12L recirculating swim flume (Loligo Systems, swim 10, Tjele, Denmark; Fig.1) with flow generated by a propeller and calibrated to the voltage output of the motor. The swimming section of the flume measures 10cm x 10cm x 50cm. The cross-sectional area of the fish versus that of the flume ranged from 5.3%-6.6% and was assumed not to appreciably affect flow (Korsemeyer, 2002). Laminar flow was promoted by a honeycomb flow-straightener immediately upstream of the swimming section. The water within the swim tunnel and external tank was mixed thoroughly with a submersible pump (Eheim-1046, 5L/min) and kept at 33ppt and 26°C. The swimming flume and outer tank were sterilized every day with bleach to minimize subsequent microbial respiration after experiments were performed and then emptied and dried overnight.  14  Continuous steady swimming was recorded with a high-speed camera (125 Hz; 640x480 resolution; Troubleshooter high-speed camera, Model TS500MS, Fastec Imaging, San Diego, CA; Cosmicar tv zoom lens 8-48mm 1:1.2 lens) during kinematic measurements (~3sec per swimming velocity; n=10 per fish). A 2cm x 2cm grid was drawn on the top of the swimming section to calibrate kinematic measurements. At the water surface, a flat Plexiglas sheet was used to eliminate ripples in the water. A mirror above the swimming section was angled at 45° and the camera was positioned horizontally 1.3m away to eliminate stereoscopic effects, giving a clear undistorted view of the dorsal fin against the grid. One 300W tungsten bulb was used to illuminate the fish. Video segments were selected for analysis only when the fish swam steadily with no perceptible accelerations or decelerations, was vertical, and did not use its pectoral or caudal fins for locomotion. Every triggerfish was uniquely labelled with fluorescent elastomere on both sides after the filming was completed in order to distinguish each fish in later kinematic and drag experiments. Fish velocity (measured as velocity of the water when the fish was stationary), fin beat frequency (time of excursion of the median fin from one side of the body to the other and back again), amplitude (distance between the two lateral-most positions of the tip of the fin during one complete fin beat cycle), wavelength (distance between two crests of a fin wave) and undulation angle (angle of the fin relative to the saggital plane of the body, Fig. 3b) were measured using still frames uploaded to ImageJ (Table 2). Wave speed (the speed of the crest of a wave as it moves posteriorily), stroke angle (angle of fin relative to the vertical axis of the body, Fig. 3a) and angular velocity (speed at which the stroke angle changes) were calculated from previously mentioned measurements (Table 2). Fish swimming speed was recorded as the velocity of the water given digitally by the Loligo Systems computer. Water velocity was voltage-calibrated using a flow probe (Hontzch flow meter; Tjele, Denmark). Frequency was taken as the average  15  of five cycles of the dorsal fin divided by the duration. Measurements were made graphically using ImageJ (National Institutes of Health; http://rsb.info.nih.gov/ij/) with the following guidelines: Amplitude is the average of five measurements of one half of a wave. Wavelength is the average, crest to crest, of one wave travelling down the dorsal fin. Undulation angle is the angle of the fin as it twists caudally along the spine of the fish (Fig. 3); a perfectly erect and normal fin would have a undulation angle of 0°, and one that is erect but displaced laterally would have an angle of 90°.Undulation angle was averaged for each fish. Wave speed is the product of frequency and wavelength. Stroke angle is calculated as θ = sin-1(amplitude/fin depth; Fig. 3). Angular velocity is frequency multiplied stroke angle (in radians). Mechanical efficiency was calculated from kinematic and morphometric measurements as the ratio of fish velocity to fin wave speed (U/υ). It indicates the amount of energy transferred from the undulatory motion of the fin to the forward motion of the fish. The undulatory motion of the median fins produces a thrust force. The force of the undulating median fins acting on the surrounding water is the sum of the momentum and the pressure components generated by the fin as follows:  F  UM a 0  P  (1)  where F is the mean fin force on water, U is the mean forward velocity of the fish, M is the mean momentum per unit length and P is the mean pressure force (Lighthill and Blake 1990; Lighthill 1990a-c). The momentum component is expanded to represent the various kinematic variables and efficiencies of the fin acting on the water to produce a momentum: 1  UM a 0  UM 0 (1   1U ) sin  av 2  (2)  16  where  is the momentum enhancement (a morphological constant), Mo is the momentum created by fins „on their own‟, υ is the wave velocity and  is the undulation angle (the angle of the fin relative to the midline as viewed from above; Fig. 3b). From the mathematics produced by Lighthill and Blake (1990) it is seen that momentum will be increased above that which is produced by the fins alone by a certain factor β (momentum enhancement). The fins produce a given momentum:  M0   1  (l  s) 3 4  (3)  where  is the fluid (water) density and l-s is the fin depth (Fig. 3c). Momentum enhancement is represented as follows:     M M0  (4)  M is the total momentum of the fin-fish system and is represented by a complex integral  equation. Here, β is found using its graphical representation in Lighthill (1990b, Fig. 7). The pressure component of equation (1) is found from:  1 U P   (1  ) 2 P0 cos 3  av 2 f  (5)  where f is the fin beat frequency,  is wavelength and: 𝑃0 = 𝜌𝜔2 ((𝑙 − 𝑠)2 )4  (6)  where ζ is a complex integral. This constant is found using its graphical representation in Lighthill (1990a, Fig. 1b). The full right-hand side of equation 7 calculates the pressure distribution between the fin and the body it is attached to (Lighthill, 1990a). This is thought to be only a small part of the full thrust (Lighthill and Blake, 1990) and has not been pursued in this dissertation.  17  Combining equations (1) through (5) above, we achieve a final thrust force equation: 1 1 U 1 U F  U (  (l  s) 3 )(1  ) sin  av   (1  )(  2 (l  s) 4 ) cos 3  av 2 4 f 2 f  (7)  This theoretical thrust may be verified by comparing it with the thrust measured by our drag determination (FT/FD). In theory, theoretical thrust should be equal to the drag force, thus supporting or rejecting that value of β. Drag Dead drag (D) was determined according to Gal and Blake (1987). Terminal velocity (Vt) measurements were obtained by dropping a euthanized fish down a water filled Plexiglas column (50cm x 50cm x 200cm). The fish were stabilized by a dart that ran through the length of the fish, stiffening the body and caudal fin. The fins of the dart were triangular, 2cm on edge, and attached to the end of a 1.5mm diameter steel wire. The pectoral, dorsal and anal fins were removed to eliminate fin flutter (Webb, 1975; Blake, 1983). Two optical sensors near the bottom measured time to pass between the two. The distance between the two sensors divided by the time to cross gave the terminal velocity of the fish. Terminal velocity was assured by measuring the velocity at two different depths with the heaviest (and thus fastest) fish; if the velocities were equal, Vt was assumed. A terminal velocity range was attained by changing the buoyancy of the fish by placing lead split-shot into their mouth. Terminal velocity was always achieved, and only fish that fell straight were analyzed. Fish drag at Vt was calculated by subtracting the drag of the stabilizer from that of the stabilizer-fish drag. At terminal velocity, drag is equal to the submerged weight (Ws):  𝐷 = 𝑊𝑠 = 1 2 𝜌(𝑆𝐴𝑡 )𝐶𝑑 𝑉𝑡  (8)  18  where 𝐶𝑑  =  0.072 𝑅𝑒 1/5  (9)  ρ is the water density (1000 kg/m3), Cd is the drag coefficient (assuming a turbulent boundary layer) and Re is the Reynolds number (the ratio of inertial forces to viscous forces; Gal and Blake, 1987). For steady swimming drag is equal to thrust, therefore an empirical thrust force can be calculated. Because the drag was calculated at velocities greater than those at which the triggerfish swim in balistiform mode, drag was extrapolated back to velocities at which the triggerfish swam steadily. Because the drag of the fish was calculated after the median fins were removed, the drag of the fins must be added as well. Fin drag was calculated as follows: 𝐷 = 𝜌(𝑆𝐴𝑓 )𝐶𝑑 𝑈 2 × 0.072 × 𝑅𝑒 −1/5 Oxygen Consumption Oxygen consumption was measured in a modified Blazka-type respirometer (Fig. 2). A different tunnel was used for respirometry because this had a smaller volume (3.5L), causing oxygen partial pressure (PO2) levels to decline faster and thus giving a more accurate measurement of oxygen consumption rate. The swimming section approximated an ellipse and was made of two semi-circles with dimensions of 4cm x 7cm x 30cm. This ellipse within a circle produced a water current difference of less than 10% between the centre and bottom. The front of the swimming section was wrapped externally by black plastic to simulate a dark hiding place that triggerfish prefer. This minimized stress and variability in oxygen consumption rate (ṀO2). Water was mixed thoroughly and kept at 1022 kg/m3 and 26°C. The swimming tunnel and outer tank were sterilized every day after experiments were performed and dried over night. The electrode was zeroed following addition of sodium sulphite to sea water and set to 100% following exposure to aerated water.  19  Oxygen consumption rate was measured as the amount of oxygen used per unit mass of the fish per unit time (mgO2/kg/hr) using a Loligo Systems Clark-type submersible oxygen electrode. The respirometer was programmed to follow a 9:7:2 protocol for measuring, flushing, and mixing times respectively constituting one 18 minute respirometry cycle. This allowed adequate time for oxygen levels to decline by up to 15% (Korsemeyer et al., 2002), and time to resaturate the flume with oxygen. Oxygen measurements were taken once every second, the slope of the decline in PO2 was taken as the ṀO2 of that cycle. Water velocities did not exceed the speed at which gait change began (~2 BL/s). Beyond this water speed, oxygen measurements became highly variable and inconsistent. These data values were excluded Triggerfish were placed in the swim tunnel at a speed of 7.4 cm/s for 144 minutes (8 cycles) prior to the first increase in water velocity. Fish swam at water velocities increased every 54-90 minutes (increase by ~3 cm/s). If the least square regression of the Po2 decline was less than 0.80 the water velocity remained unchanged for two extra cycles. This was not expected to alter ṀO2 values because the triggerfish was still swimming well below its fatigue speed. Following each experiment, oxygen measurements were taken for two cycles to account for bacterial respiration (Steffensen, 1989), again following a 9:7:2 protocol. This was subsequently subtracted from the ṀO2 values. Bacterial respiration did not exceed 10% of the total oxygen consumption. Because the cross section of the swimming section is small, flow velocities were higher around the fish, causing a difference in the actual water speed felt by the fish. The cross-sectional area of the fish ranged between 15% and 19% of the cross section of the swimming flume. Calculation of the water velocity around the triggerfish was corrected according to Bell and Terhune (1970): 𝑈𝐹 = 𝑈𝑇 (1 + 𝜀𝑆 )  (10)  20  where UF is the corrected flow speed, UT is the speed in the flume without a fish in the swimming section, and εS is the fractional error due to solid blocking: εS = τλo (  A0  AT )  3  2  (11)  where τ is a dimensionless factor, λo is the shape factor for the object, A0 is the maximal cross sectional area of the fish, and AT is the cross sectional area of swimming section. Water speeds were found to increase by an average of 6% around the fish. Oxygen consumption rate (ṀO2), standard metabolic rate (SMR), active metabolic rate (AMR), total cost of transport (TCOT) and net cost of transport (NCOT) were calculated as follows. ṀO2 is the oxygen consumption rate and is described above. SMR is the oxygen consumption rate of all energy expenditures unassociated with activity such as ingestion, digestion, absorption, metabolic processing and growth (Alsop and Wood, 1997) and was approximated as the y-intercept of the ṀO2 versus Velocity curve. The SMR is assumed to be constant at all velocities. AMR is ṀO2 minus SMR representing the increase in oxygen consumption when active and mobile. TCOT is measured as the amount of oxygen used per unit mass per unit distance (mgO2/kg/m); this is a simple conversion following calculation of ṀO2. 𝑀𝑂  2 𝑇𝐶𝑂𝑇 = 𝑈×3600  (12)  NCOT is a measure of the oxygen used for activity requiring a subtraction of the SMR from ṀO2. 𝑁𝐶𝑂𝑇 =  (𝑀𝑂2 −𝑆𝑀𝑅) 𝑈×3600  (13)  Because oxygen consumption is the result of muscles doing work on a system, it can be converted from an oxygen consumption rate (mgO2/kg/hr) to power (Watts) assuming certain inefficiencies throughout the system using the following model.  21  𝑃𝑚𝑢𝑠𝑐𝑙𝑒 = 𝑚 × 𝐴𝑀𝑅 × 𝜓  (14)  Where ψ is the oxycalorific value. (14.1 J/mgO2; Videler 1993) and m is the mass of the median fin propulsive musculature. Velocity independent muscle efficiency will be assumed for this thesis. If this power result is divided by the power theoretically produced by the muscles (thrust force times velocity), we are given an estimate of the accuracy of equation (7). Locomotor efficiency is calculated as the ratio of Pmuscle to power calculated by the Lighthill and Blake (1990) model, Ptheoretical. This gives the total efficiency of biochemical and mechanical systems, from muscle efficiency to forward thrust. Microscopy The red, oxidative dorsal fin musculature was dissected out of two triggerfish for examination by transmission electron microscopy. Fish were euthanized with an overdose of MS-222 then decapitated and the skin was deflected to expose the muscle. The fish were stored in 0.1 M sodium cacodylate-buffered 4% formaldehyde/2% glutaraldehyde (pH 7.4) overnight at 4°C. The muscle was then dissected out and samples fixed at 28oC, pH 7.4, 0.1M, 4/2.5% formaldehyde/glutaraldehyde in laboratory microwave (Pelco, Redding California USA) under vacuum for two cycles (2 min each, 100W/off/100W) without changing fixative. After three changes of buffer, muscle samples were washed 3 times with 0.1M sodium cacodylate (pH 7.4) and either post-fixed or stored in buffer at 4°C. Buffered samples were post-fixed with buffered 1% OsO4, the same as the primary fixation. Samples were washed 3 times with ddH2O, and then microwave dehydrated at 28oC through a graded ethanol series (30, 40, 50, 60, 70, 80, 90, 95, 3x 100%) at atmospheric pressure for 40s, 270W each step. Propylene oxide was used as a transition medium for infiltration. Samples were taken stepwise through 1:3, 1:1, 3:1 % resin:PO and 3x 100% Spurr/Epon before embedding and sectioning (Reichert Ultracut E) with a glass or  22  diamond (Drukker) knife. Images were acquired on a Hitachi (H7600 Tokyo, Japan) TEM (procedure organized and performed by Derrick Horne of the UBC microscopy lab). Mitochondrial density was determined using the point-count method (Mathieu et al., 1981; Watson et al., 2007). Twenty TEM cross sections of the muscle bundle at 10,000x were selected at random, and a 1μm square grid was placed over the TEM picture using Adobe Illustrator CS3. Intersections landing on sub-sarcolemmal mitochondria were divided by those that did not. The ratio gave relative mitochondrial densities that were compared with other triggerfish or other segments within that triggerfish. Statistics Morphometrics, kinematics, and mitochondrial density were each separately analyzed using 1-way ANOVA (Sigmastat 3.5 for Windows). The locations of any significant differences were obtained (Tukey-HSD test). Slopes and intercepts for drag, swimming kinematics (frequency, wavelength, amplitude, undulation angle, stroke angle), and oxygen consumption rates were calculated using Sigmaplot 10. The null hypothesis was rejected at P < 0.05 in all cases.  23  Results Morphology And Drag Morphometric measurements are given in Table 1. The size and body measurements between the fish in this study were statistically indistinguishable; all triggerfish were of the same approximate size. No triggerfish was considered an outlier, and averages are considered good representations of the data. Drag force (D), calculated indirectly by dropping fish in a water column, increased with the square of water velocity (U; r2 = 0.94; P < 0.0001; Fig. 4). Extrapolation of drag values to speeds swum by triggerfish (5.9 – 20.6 cm/s; ~0.5-2.0 BL/s) ranged from 0.0013 N to 0.0091 N. Cd decreased with the inverse square of velocity and Reynolds number; however, because they are directly dependent on velocity alone, a true U versus Cd correlation could not be determined. Kinematics All triggerfish swam in a steady balistiform mode (Breder, 1926) at water velocities up to 2 body lengths per second. Beyond this speed, fish were much more prone to erratic behaviour that prohibited filming (the triggerfish could not sustain a steady, vertical and unaccelerating swim). Of the eleven fish that were filmed, seven were steady enough at low speeds to record accurate measurements. Two results from individual 5 were eliminated as extreme outliers because wave speed was greater than forward speed, giving negative thrust values. Frequency, wavelength, amplitude and efficiency increased with respect to water velocity; no correlation was seen for stroke angle or angular velocity (Table 2, Figs. 5-8). Fin beat frequency (f) increased linearly with fish velocity for all individuals (r2 = 0.46, P < 0.0001). Wavelength (λ) also increased linearly with fish velocity for all but one individual, however the correlation was still strong (r2 = 0.20, P = 0.0020). Wave speed (υ), the product of  24  frequency and wavelength, showed a significant positive linear relationship with fish velocity in all individuals (Fig. 5, n = 35, r2 = 0.58, P < 0.0001), ranging from 0.11 to 0.27 m/s, with each fish normally doubling its wave speed through the experiment. Angular velocity (ω) showed a significant correlation with fish velocity (Fig. 6, n = 35, r2 = 0.46, P < 0.0001). Angular velocities ranged from about 37-65 rad/s and increased on average by 70% from lowest to highest recorded velocities. Fin amplitude (A) was used to calculate the stroke angle (stroke angle = sin-1 (amplitude / fin length) and showed a significant correlation with fish swimming velocity (Fig. 7, n = 35; r2 = 0.17; P = 0.0154). Amplitude increased linearly with velocity in all fish, and most variations were between fish, rather than differences in trends for individuals. Undulation angle (α) did not show a significant correlation with fish swimming velocity (Fig. 8, n = 35, r2 = 0.00 P = 0.98). The average wave angle was 0.81 radians, with fish-specific averages ranging from 0.67-0.95 radians. As per the Lighthill and Blake (1990) model, the average undulation angle (αav) for each fish was used rather than speed-specific values. Substituting the theoretical thrust force with the equivalent thrust force calculated from the drop tank experiment, it was possible to estimate the value for momentum enhancement (β). Momentum enhancement significantly increased with fish velocity (Fig. 9, n = 41, r2 = 0.28, P = 0.0019). Momentum enhancement normally doubled over the range of speeds tested and averaged 3.59 ± 2.11. As a measure of accuracy of the Lighthill and Blake (1990) model, the theoretical thrust force was divided by the thrust force predicted by the drop tank experiment (Table 3, column Ft/Fd). In all but one fish, the theoretical force was greater at low speeds and drop tank force was greater at higher speeds. The FT/FD ratio averaged 1.08 ± 0.34 indicating good accuracy of the Lighthill and Blake (1990) model and clear evidence of momentum enhancement. Theoretical  25  force and drag force are compared (Fig. 17) and it can be seen that the values for both theoretical force and drag force are similar. It was predicted that the pressure component of the thrust force would account for 10-15% of the total force (Lighthill and Blake, 1990). By dividing the Pressure component by the Force, pressure as a percentage of the total force was calculated (Table 3, listed as %P). It was found to average 24% ± 8% and decrease slightly with velocity in all fish. This is larger than predicted, but comparable to the model. Mechanical efficiency, the ratio of fish velocity to wave speed (U/υ), increased from about 0.5 at the lowest velocities, and plateaued around 0.8 at 1.9 BL/s (Fig. 10, n = 45, r2 = 0.49, P < 0.0001). It is evident that fin efficiency increases with the velocity. Oxygen Consumption When first placed in the small Blazka-type respirometer, triggerfish oxygen consumption rate (ṀO2) was typically elevated for at least one hour. When oxygen consumption plateaued at some level lower than where it started, usually around 2.5 hours, the triggerfish was assumed to be at resting ṀO2 and trials began. ṀO2 increased significantly with swimming speed (Fig. 11, n = 7, r2 = 0.79, P < 0.0001) from a minimum average of 136 mgO2/kg/hr to a maximum average of 235 mgO2/kg/hr. Average SMR was 82.2 mgO2/kg/hr ± 32 mgO2/kg/hr. This supports the findings of Korsemeyer et al., (2002) who calculated a mean SMR of 74.7 mgO2/kg/hr for R. aculeatus. Total cost of transport (TCOT) was calculated from the ṀO2 values (Fig 12, n = 7, r2 = 0.98, P = 0.002). TCOT is normally U-shaped with the minimum defined as the optimal swimming speed (Korsemeyer et al., 2002). The lack of a positive slope at higher fish velocities with R. aculeatus is supported by Korsemeyer et al., (2002) where TCOT was found to decrease until body undulations were used. This may be the result of efficiencies not possessed by other swimming styles (i.e. momentum enhancement). TCOT values ranged from 0.45 mgO2/kg/m at  26  the lowest speeds to 0.30 mgO2/kg/m at the highest. Net cost of transport (NCOT) shows the expected increase in oxygen consumption use per meter when travelling faster (Fig. 13, n = 7, r2 = 0.88, P = 0.0422). Power (P) was calculated both from the oxygen consumption (AMR) values (muscle power) and from the theoretical values (theoretical power), calculated from the model of Lighthill and Blake (1990). Muscle power is shown to increase with velocity by a factor of five. Theoretical power (thrust x velocity) increased by a factor of seven, had a higher starting value, and was consistently greater than muscle power (Fig. 14). The ratio of theoretical power to muscle power (Locomotor efficiency) depends on the muscle and mechanical efficiencies. Empirical power, calculated assuming perfect efficiency, gave a locomotor efficiency of 0.03 ± 0.003. When the mechanical efficiency (U/υ) is factored in, locomotor efficiency increases to 0.05 ± 0.004. Finally, when 20% muscle efficiency is factored in, locomotor efficiency averages 3.56 (assuming 20% muscle efficiency). Exact triggerfish muscle efficiency is not known. Musculature One triggerfish was dissected and its propulsive musculature weighed. Of the 27.5g weight of the fish, 0.81g of red oxidative muscle, or 2.94%, was median fin propulsive musculature. Electron microscopy found evidence of a difference between two sizes of R. aculeatus. Using the standard point-counting method, large fish (26g, n=12) were found to have 30% fewer mitochondria in their median fin musculature than small fish (14g, n=10). The large fish had a mitochondrial density of 5400 ± 1440 mitochondria/mm2 and small fish had a density of 7910 ± 970 mitochondria/mm2 (P < 0.05). There was no difference in anterior/posterior oxidative muscle sections within specific fish. The reasons for this are unclear and have been previously undocumented.  27  Discussion  The theoretical model of balistiform locomotion of Lighthill and Blake (1990; Lighthill, 1990ac) is supported; drag measurements strongly support the model, although power measurements are somewhat misaligned. Empirical evidence of momentum enhancement is proven for the first time. Morphological measurements showed very little deviation from the average and kinematic analysis showed statistical significance with fish velocity, indicating that the models may suffer inconsistency, rather than experimental measurements. Reasons for this discrepancy are further explained below to shed light on the assumptions made in the model as well as those made while testing it. Morphology Generally, theoretical models (Lighthill and Blake, 1990) have proposed that a triggerfish moving steadily through the water in balistiform fashion should be deep to resist large recoil forces, streamlined to minimize parasite drag, and rigid to minimize profile drag. This ideal body is thought to be responsible for „momentum enhancement‟, a means of increasing the fin‟s thrust force beyond that which would be possible by the fin „on its own‟. The six Rhinecanthus aculeatus measured had a mean fineness ratio (depth divided by length) of 0.41, much larger than that found on more elongate BCF swimmers whose optimum fineness ratio averages between 0.15 and 0.25 (Blake, 2004). The optimum fineness ratio is important for fast steady swimming (greater than two body lengths per second) in order to minimize both parasite and profile drag. The fins of a balistiform swimmer vary from elongate (low aspect ratio) to flag-like (high aspect ratio). R. aculeatus was selected, among other things, for its fit to the Lighthill and Blake  28  (1990) model as a low-AR swimmer. Lighthill and Blake (1990) propose that the smaller the ratio of fin depth to body depth (actually written as the ratio of half body depth „s‟ to half body+fin depth „l‟, s/l) the more efficient a balistiform swimmer is. Triggerfish in this study had fins with depth and length averaging 0.91cm and 2.1cm, respectively and a mean s/l of 0.66 ± 0.11. Together, the deep body and shallow depth of the fins applies well to the model and suggests an efficient swimming style. Despite both theoretical and hydrodynamic evidence that a high fin aspect ratio translates to a higher thrust, it remains to be seen whether this would be a prime selection factor for triggerfish (Wright, 2000). Due to the diversity of fin shapes, it is evident that one set of morphological characteristics may not confer a significant advantage over another. It is also possible, although undocumented, that these fins may function as a means of display or for use in pairing and mating (Bischoff et al., 1985). Despite the fact that high aspect ratio aquatic propulsion has been documented empirically and theoretically as providing more thrust and being more efficient, it is unclear why some triggerfish have high aspect ratio median fins while others have a low aspect ratio fins. Kinematics According to theory (Lighthill and Blake, 1990; Lighthill 1990a-b; equation 7), balistiform propulsion is entirely based on three kinematic variables: fin wave speed (υ), undulation angle (α), and angular velocity (ω). Triggerfish alter these kinematic variables in countless ways and are continually doing so in order to optimize thrust and efficiency. Incremental modifications in kinematics may equate to large changes in the cost of locomotion. Thrust and efficiency, however, are found at two ends on a cost-benefit continuum, increasing the absolute value of one is often done to the detriment of the other (Daniel, 1988). This section compares previous  29  theoretical kinematic predictions with empirical triggerfish measurements to explain how this specific biological system has approached the thrust-efficiency duality. Amplitude (Fig. 7), and by extension, stroke angle and angular velocity, is expected to remain constant or increase slightly with swimming speed in various species (Blake, 1978, 1983, 2004; Lighthill and Blake, 1990). This is common to most undulating swimmers (both BCF and MPF) where undulation amplitude will increase to a maximum long before the frequency maximum is reached (Blake, 2004). Velocity-independent amplitude was documented in gymnotiform swimmers (elongate, low aspect ratio fin; Blake 1983) and stingrays (high aspect ratio fin; Rosenberger and Westneat, 1999). Simulations by Wright (2000) have shown that changes in amplitude are unimportant to a balistiform swimmers as long as the forward velocity is balanced by changes in frequency. Both high-amplitude, low-frequency and low-amplitude, high-frequency can theoretically generate equivalent thrust (Wright, 2000). However, a highamplitude fin would increase drag due to an increase in profile drag, perhaps causing fin frequency to over-compensate for undue drag (Daniel, 1988; Webb, 1992). Additionally, amplitude has an upper limit based on muscle shortening and the physical extremes to which a fin can move laterally before it is impeded by the body. Indeed, R. aculeatus shows a stronger increase in frequency (65%) than for amplitude (20%) over the range of speeds tested. Without exception, all fish showed the same trend with respect to water velocity. Frequency correlations for individuals were of much higher significance than those for amplitude, suggesting amplitude was adjusted secondarily to frequency. Frequency modulation is the primary kinematic variable change in all undulatory swimmers (e.g. Rosenberger and Westneat, 1999; Hove et al., 2001). However, because of physical limitations such as drag and muscle contraction velocity, frequency is complemented by other kinematic factors. Wavelength most often follows trends in frequency. In general, frequency  30  should increase strongly and wavelength should increase slightly with fish velocity (Lighthill and Blake, 1990; Blake, 1983). The end result is a slight decrease in the number of waves on the fins and a strong increase in the wave speed (Fig. 6). Undulation angle (twist of the fin relative to the long axis of the body) should not change with speed, and is taken as the average over the range of speeds in the Lighthill and Blake (1990) model. These predicted trends were followed closely by R. aculeatus; amplitude, wave speed and angular velocity all increased with swimming speed (Figs. 5-7). Undulation angle showed no correlation with swimming speed (Fig. 8). Small differences between fish resulted in low least squares regressions, however even with the few fish (n=7) that completed the trials, significant relationships were observed for all kinematic variables (P < 0.05). Wave speed shared the strongest correlation with swimming speed and was expected to be the primary influence on thrust production. These trends, first recorded in triggerfish by Blake (1978), have been seen throughout the aquatic animals. Aquatic flappers such as sea turtles and penguins or fish using their pectoral or median fins all show a correlation between swimming speed and propulsor frequency (e.g. Webb, 1973; Clark and Bemis, 1979; Davenport, 1987; Archer and Johnston, 1989; Gibb et al., 1994; Drucker and Jensen, 1996; Gordon et al., 1996; Walker and Westneat, 1997; Wright, 2000; Blake, 2004; Korsemeyer et al., 2002). Fish velocity is affected by many external factors that alter swimming costs while inside the flume. Both swimming flumes used in this study, Blazka-type and Brett-type, are based on the principle that a fish swimming at a given speed is the same as a fish swimming against a current of the same speed. While this may be true in an open system, the artificial surroundings used only roughly approximate the actual costs of swimming in an open environment. Wall effects are a thinning of the boundary layer near the wall of a swimming flume, where the water velocity is less than the average velocity of the flume (Webb, 1993) and are thought to decrease the effort of  31  a swim. They may be exceptionally important for triggerfish because their propulsive fins extend normal from their body possibly interacting with the floor and ceiling of the swimming section. However, the swimming flumes selected were large enough that R. aculeatus spent most of its time in the middle of the flume, unaffected by wall effects. Additionally, both the Brett- and Blazka-type flumes use straws directly upstream of the swimming section as a means of straightening the flow and decreasing turbulence. Boisclair and Tang (1993) found that this produces microturbulence which elevates the cost of swimming relative to that of pure laminar flow. These adverse effects are have been assumed to be negligible in this paper, and it is unclear to what degree these external factors affect actual swimming costs. Mechanical efficiency, U/υ, is used to measure the efficiency of an undulatory locomotor apparatus (Lighthill, 1960). Lighthill (1960) was the first to expound on the importance of this ratio, high U/υ ratios indicate less wasted energy or „slip‟ of the propulsion mechanism and low values indicate an inefficient propulsor. Mechanical efficiency in BCF swimmers is never higher than 0.7-0.8 (Webb, et al., 1984, Gillis, 1997). However, as U/υ approaches 1, frequency increases to biologically unrealistic values. R. aculeatus swam at speeds ranging from 5.9cm/s to 20.6cm/s and maintained an average mechanical efficiency of 0.68 ± 0.15 (Fig. 9). This is in agreement with the mechanical efficiency of 0.70 measured by Wright (2000). Mechanical efficiency did increase with swimming velocity from about 0.5 to a plateau of about 0.8 at 1.9BL/s after which it drops slightly before the fish fatigues. This increase in mechanical efficiency has been seen in other fishes such as the gymnotiform swimmer X. nigri (Blake, 1983), the stingray T. lymma (Rosenberger and Westneat, 1999), and some BCF swimmers (Web et al., 1984; Wassersug and Hoff, 1985; Gillis, 1997). However, triggerfish most often present a slope of zero (Wright, 2000)  32  This plateau is most likely the result of a trade-off between efficiency and thrust. As speed increases, the fish is able to optimize its swimming performance by varying fin kinematics, but beyond a certain point it becomes necessary to maximize thrust at the expense of efficiency. The increase in mechanical efficiency (U/υ) with speed reflects a more rapid increase in fish velocity than wave speed, which may be partly explained by increases in amplitude. Because amplitude is not accounted for, real (total) efficiency of the fin cannot be concluded. Amplitude clearly plays a significant role in the dynamics of the fin and is expected to have a role in buffering frequency changes. Therefore mechanical efficiency is only a rough guide to total propulsor efficiency. Such high values of mechanical efficiency cannot be explained by the classical theories of aquatic undulatory propulsion. These theories depend on undulatory movements in a single plane such as in classical BCF locomotion, whereas triggerfish flap their median fins on an axis thereby producing unique motions in another plane that may contribute to additional thrust (Wright, 2000). It is possible that triggerfish modulate their frequency and amplitude in order to optimize the structure of their trailing vortex wake. The lateral motions of undulatory propulsors create trailing edge vortex wakes that either contribute to the thrust or create negative pressure that negates it (Sfakiotakis, 1999). The Strouhal number is used to describe such vortex wake and depends on fish velocity, frequency, and amplitude: 𝑆𝑡 =  𝑓𝐴 𝑈  (15)  (Sfakiotakis et al., 1999). Both theoretical and experimental studies have shown an optimal Strouhal number to be between 0.25 and 0.4 (Triantafyllou et al., 1993; Anderson et al., 1998; Barrett et al., 1999). This range is considered optimal because it is the point at which the counter-rotating vortices of water expelled at the trailing edge of the caudal fin interact in a positive manner (Sfakiotakis et al., 1999). These numbers have been documented in a range of cetaceans and fishes at or near their maximum steady swimming speed (Triantafyllou, 1993)  33  R. aculeatus has a Strouhal number well above the theoretical optimal range (Table 1, Fig. 15). With values averaging 0.65 ± 0.12, it would seem that there is a large negative contribution to thrust. Strouhal values above 0.4 indicate adverse reactions between the trailing vortex wakes produced by the propulsor (Triantafyllou et al., 1993; Anderson et al., 1998; Sfakiotakis et al., 1999). However, most studies have examined BCF propulsion where the body and tail are responsible for the thrust, essentially acting as a single propulsor (Sfakiotakis, 1999; Blake, 2004; Sparenberg, 2002). In contrast, triggerfish use both median fins, and the nature of dual propulsion wake forms has not been studied. Triggerfish stagger their median fin waves by onehalf wavelength, presumably so that identical vortices do not appear at the same time and eliminate one another (Blake, 1978). The decrement in Strouhal number as fish velocity increases is explained by increases in fish velocity that outpace increases in fin beat frequency. The median fin kinematics were recorded for the dorsal fin and the anal fin was assumed to produce an equivalent thrust force. Both fins were similar in size and shape but average surface area of the dorsal fins was 30% larger than anal fins (Table. 1). It is not known whether R. aculeatus compensated for this difference with changes in frequency or amplitude although total thrust is almost certainly less than calculated. Blake (1978) has shown that the median fins move with approximately equal fin kinematics over the length and depth of the fins. Lighthill and Blake (1990) did not account for this difference when modelling balistiform locomotion. Balistiform Model Momentum enhancement, β, is hydrodynamic phenomenon postulated by Lighthill and Blake (1990). While the momentum enhancement value is not directly calculated in this paper (giving only what is already given in a figure in Lighthill and Blake, 1990), it is valuable to calculate the increase in thrust needed to fit empirical thrust values. Momentum enhancement  34  reacts strongly to changes in wave speed; when wave speed is greater than forward speed, β will have a very large increasingly negative value. Momentum enhancement (Fig. 9) showed an increase with fish velocity (P < 0.002). Because β is only dependent on morphological characteristics rather than kinematics, it is not expected to show any change with fish velocity. Lighthill and Blake (1990; Lighthill 1990a-c) proposed a single value for momentum enhancement throughout the range of speeds a triggerfish would swim in balistiform mode. Momentum enhancement is calculated here by solving equation 7 for β over the range of speeds tested. The measured mean momentum enhancement value of 3.6 is very close to the value predicted by Lighthill and Blake (1990) of 2.5. Deviation from the expected value of suggests either the values for β are inadequate in the model or that increases in swimming speed come at a higher cost than predicted. The exponential increase may be due to increased effort by unexplained resistance to swimming. If R. aculeatus were to sacrifice optimal swimming kinematics for increased thrust, this would result in an increase in momentum enhancement above that which would be expected normally. When calculating thrust, the momentum enhancement and pressure components were taken from those predicted by Lighthill and Blake (1990) at 2.5 and 0.31, respectively. Mean theoretical thrust was comparable in slope and magnitude to the thrust values calculated from drag measurements Drag A rigid body when swimming steadily is a defining aspect of balistiform locomotion. Dead drag measurements do not reflect the drag of a swimming fish performing undulatory motions (body-caudal fin locomotion), where drag is augmented due to boundary layer thinning (Bone in Lighthill, 1971). However, rigid body values are useful for assessing steady swimming drag on triggerfish and other rigid body swimmers (Blake, 1983). The undulatory motions of their  35  median fins produce a small amount of additional drag similar to that of BCF undulations, but to a significantly smaller degree (Gal and Blake, 1987; Li, 2007). Dropping a fish down a vertical column of water can estimate drag at terminal velocity (e.g. Gal and Blake, 1987). Drag is equal to thrust when swimming steadily through a viscous medium; therefore thrust force can be estimated at equivalent speeds by extrapolating backwards on the drag curve. A simple way of testing the validity of the Lighthill and Blake (1990) model is to compare the theoretical thrust force with the thrust force predicted by measuring the drag. The ratio of theoretical thrust to drop tank thrust (FT/FD) varied by about 50% for each fish but averages 1.08 ± 0.34 for all fish at all speeds (Fig. 17; Table 2). This suggests that the model is generally accurate at predicting the required thrust force, but slightly overestimates thrust at high speeds and underestimates it at low speeds. Mechanical efficiency may explain the discrepancy, Lighthill and Blake (1990) assumed U/υ is roughly constant. An increase in efficiency at higher swimming speeds would result in a decreased thrust requirement and a decrease in efficiency results in an increase in thrust output. A laminar boundary layer was assumed in Lighthill‟s early work on slender body theory and carried through to his subsequent papers on fish locomotion (Lighthill, 1960, 1970; Lighthill and Blake, 1990). The difference between laminar and turbulent boundary layers is significant and considered a primary drag-reducing mechanism (Gray, 1936; Lighthill, 1971; Barret et al., 1999). Triggerfish swimming at steady cruising speeds must optimize speeds so as to promote a laminar boundary layer. Failure to do so may promote a turbulent boundary layer which significantly increases drag (Blake, 1983). Oxygen Consumption The metabolic requirements of a reef fish rarely necessitate high-powered swimming for long periods of time. R. aculeatus, although physically able to swim steadily at moderate speeds  36  without fatigue (Korsemeyer, 2002), it seems to be adapted to swimming at low speeds for most of the time. However, they do demonstrate the ability to cruise at higher speeds when necessary. As predicted by Korsemeyer et al., (2002), use of median fins alone was common among all fish at low speeds but was unsustainable at higher speeds and gait transitions began to occur. MPF swimming was only used at speeds up to 2.5 BL/s, beyond which intermittent or full BCF swimming occurred and experiments were terminated. ṀO2 displays the characteristic exponential increase that implies more work as a fish travels faster (Trudel et al., 2004). At speeds less than ~0.7 BL/s triggerfish demonstrated erratic behaviour that prevented the direct measurement of the standard metabolic rate (SMR). Instead, SMR was taken as the y-intercept of the ṀO2 curve (82 mgO2/kg/hr) and this is considered more accurate than zero-velocity measurements (Li, 2007). Cost of transport curves were drawn using equations 12 and 13. Total cost of transport (TCOT; Fig. 12) represents the total cost per meter of swimming at different speeds (Korsemeyer, 2002; Ohlberger, 2006) and net cost of transport (NCOT; Fig. 13) represents the cost per meter of swimming above SMR (Korsemeyer, 2002; Ohlberger, 2006). The shape of the TCOT curve typically takes a „U‟ shape (Ohlberger, 2006), the low point indicating the optimal swimming speed at which a certain species should cruise. The optimal swimming speed for fish of this size that swims in BCF mode (~10cm) is thought to be between 1 and 2 BL/s (Videler, 1993; Weihs, 1973). Korsemeyer et al., (2002) have calculated an optimal swimming speed of 2.3 BL/s for R. aculeatus suggesting an adaptation to high cruising speeds. In contrast, the TCOT curve (Fig. 12) shows no statistical difference in cost of transport between swimming at 1.2BL/s and 2.3BL/s. This plateau of the TCOT curve for R. aculeatus indicates there is no optimal swimming speed, rather a range of speeds at which R. aculeatus might swim with equal cost. The NCOT curve (Fig. 13), however, shows that swimming faster does require  37  an increase in energy input (also seen in the ṀO2 graph, Fig. 11). The discrepancy is a result of the efficiency of travelling each unit of distance; while increasing energy input, R. aculeatus is travelling sufficiently faster so as to maintain its cost per meter. This may be either the cause or a result of the mechanical efficiency seen previously. Beyond the gait transition speed, Korsemeyer et al. (2002) have shown a doubling of oxygen consumption rate increase due to use of BCF locomotion. This would inevitably give the TCOT curve a final „U‟ shape. Fin power (Fig. 14) was calculated as a means of testing empirical swimming results with the Lighthill and Blake (1990) theoretical model. As it stands in equation 14, theoretical power is much higher than muscle power because it assumes perfect efficiencies throughout the system. The muscle power does not factor in muscle or propulsive efficiency. Propulsive efficiency is taken as the mechanical efficiency calculated above. Muscle efficiency is generally assumed to be ~20% (Moon, 1991). However, when such efficiencies are implied, theoretical power output is still calculated to be larger than muscle power (locomotor efficiency) by a factor of nearly 3.6. Only by increasing muscle efficiencies to an unrealistic 40% do the two power equations approximate each other. However, at lower swimming velocities, locomotor efficiency is much closer and only expands significantly at higher velocities. Due to unavoidable stress of the fish within the flume, AMR, and thus muscle power is probably slightly elevated and may increase the gap between the muscle and theoretical power. This has been assumed not to be the case in the calculations of power because the amount to which power has been overestimated is unknown and probably small. What is the reason for the discrepancy between theoretical and muscle power? Firstly, the theoretical model may have overestimated the full cost of swimming. Secondly, simply multiplying thrust force by fish velocity may be an oversimplification of theoretical power. However, with regards to the balistiform model, measurements are considered statistically very  38  accurate and thus the error may lie in the calculation of muscle power. Because the mass of propulsive musculature was only taken on a single fish, the average mass may be greater than assumed. Additionally, it may be the case where a small amount of axial musculature is used while swimming in balistiform mode, thus increasing the propulsive muscle mass. Finally, due to intrinsic inaccuracies within the oxygen measurement system, the difference between the calculated muscle power and the real muscle power may be quite large and thus more closely approximate theoretical power. Muscle The steady swimming (red, oxidative) musculature of BCF swimmers is located along the longitudinal midline of the body (Shadwick and Lauder, 2006). Triggerfish have diverged from this classical body structure; the primary location of their oxidative muscle fibers is under their median fins (Sorrenson, 2008). Body undulators partition 50% or more of their body mass to propulsive musculature, whereas MPF swimmers use less than 20% (Webb and Blake, 1985). Although BCF swimmers only allocate 1.5% of their body mass for red, oxidative muscle, when swimming steadily they commonly use a much greater amount (Randall and Daxboeck, 1982; Webb, 1975). Triggerfish allocate nearly 3% of their body mass to balistiform propulsive musculature. This suggests triggerfish are able to use their steady swimming musculature very effectively. Mitochondrial density data was analyzed via TEM for distinguishing characteristics, and none were found within fish or between fish of similar size. However the younger fish showed an unexplained, statistically significant, elevated mitochondrial density implying a decrease in mitochondrial density with age. One would normally expect an increase with age as triggerfish venture further from the reef and depend more on their steady-swimming abilities.  39  Future Research Directions Wake flow visualization by means of particle image velocimetry (PIV) would advance the understanding of balistiform locomotion enormously. It is unclear how Strouhal numbers of 0.68 do not seriously impede aquatic propulsion; dual propulsion is surely the key, yet this has been heretofore previously unexplored. Wake diameter is a direct result of the kinetic energy transferred to the surrounding water (Lighthill and Blake, 1990). PIV would allow measurements of wake diameter giving another, more direct, means of calculating propulsive thrust (Drucker and Lauder, 2001, 2002, 2005; Lauder et al., 2002; Standen and Lauder, 2005). Additionally, the wake structures of both median fins and how they interact may be of importance to submersible vehicles that often use more than one propulsor. The study of various species employing balistiform types of locomotion would enhance understanding of low cost aquatic locomotion by expanding our knowledge base of similar types of locomotion. Many species from a variety of orders use some type of undulatory mechanism to propel themselves at low speeds for low cost. The benefits of single undulatory propulsion as in Gymnotidae, versus those that use two fins or more as in Balistidae may shed light on undulatory fin wake dynamics. Additionally, the cost and timing of gait transition speeds between Balistidae and Pleuronectidae (flatfishes) may shed light on the limits of balistiform propulsion.  40  Conclusions The theoretical model of balistiform locomotion presented by Lighthill and Blake (1990) accurately describes the kinematics to overcome the influence of drag but may not fully account for the total cost of propulsion. Kinematic experiments have shown clear trends in the undulatory movements of the median fins; insertion into the model results in thrust forces similar to those empirically tested. Evidence from kinematic analysis is a clear demonstration of momentum enhancement, a multiplication of thrust efficiency. Power, as measured by oxygen consumption rate, is considerably greater than that predicted by the current model. Particle image velocimetry may resolve this discrepancy by providing insight into the wake forms initiated at the trailing edges of the median fins.  41  Table 1. Morphometric characteristics of Rhinecanthus aculeatus. See figure 1 for definitions of the measurements of the defined parameters.AR = aspect ratio. SA = surface area. Fish #1 Fish #2 Fish #3 Fish #4 Fish #5 Fish #6 TL (c m) SL (c m) depth (c m) FR ( d/l ) fin length (c m) l (avg) s (avg) l-s (avg) s/l avg fin angle (θ) b (tail depth) b^2 AR tail (SA / b^2) AR (length/area) Volume (ml) SA total (c m^2) SA dorsal fin (c m^2) SA anal fin (c m^2) SA fins total (c m^2) SA tail (c m^2)  9.93 8.47 3.89 0.39 2.00 1.71 0.97 0.99 0.57 53.97 1.63 2.66 1.41 1.89 18.4 52.14 2.82 2.07 4.89 3.75  9.89 8.63 3.85 0.39 2.04 1.77 1.10 0.98 0.62 54.10 1.43 2.04 1.66 1.92 20.30 51.05 3.04 1.84 4.89 3.39  9.41 8.27 4.01 0.43 2.16 1.50 0.97 0.92 0.64 69.15 1.62 2.62 1.44 1.73 20.30 51.06 2.13 2.01 4.14 3.79  9.42 8.05 4.25 0.45 1.85 1.48 1.05 0.70 0.71 64.62 1.28 1.64 1.82 1.79 17.80 49.58 1.90 1.82 3.73 2.98  9.81 8.48 3.80 0.39 2.08 2.02 1.72 1.00 0.85 59.66 1.45 2.10 1.83 1.86 18.10 51.68 3.04 2.71 5.75 3.85  10.27 8.76 4.48 0.44 2.46 1.79 1.01 0.95 0.56 65.92 1.44 2.07 1.84 1.80 24.30 58.66 3.54 2.69 6.23 3.81  avg 9.79 8.44 4.05 0.41 2.10 1.71 1.14 0.92 0.66 61.24 1.48 2.19 1.67 1.83 19.87 52.36 2.75 2.19 4.94 3.59  SEM 0.15 0.11 0.12 0.01 0.09 0.09 0.13 0.05 0.05 2.84 0.06 0.17 0.09 0.03 1.09 1.43 0.28 0.18 0.42 0.15  42  Table 2. Kinematic measurements of R. aculeatus measured from the high-speed camera film. Indiv.  1 1 1 1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 5 5 5 5 5 5 6 6 6 6 7 7 7 7 7 7  U (m/s) fish velo.  0.059 0.072 0.087 0.115 0.141 0.101 0.142 0.150 0.206 0.085 0.094 0.124 0.131 0.159 0.178 0.101 0.125 0.132 0.152 0.067 0.095 0.113 0.135 0.144 0.169 0.068 0.099 0.122 0.152 0.089 0.099 0.117 0.121 0.134 0.142 0.118 0.04  BL/s fish velo.  0.60 0.73 0.89 1.17 1.44 1.03 1.45 1.53 2.10 0.89 0.98 1.29 1.36 1.66 1.85 1.02 1.26 1.33 1.54 0.69 0.98 1.16 1.39 1.48 1.74 0.69 1.00 1.23 1.54 0.94 1.04 1.23 1.27 1.41 1.49 1.217 0.38  ω (rad/sec) angular velo.  41.34 43.63 37.40 49.09 52.36 49.09 56.10 60.42 56.10 39.27 46.20 43.63 52.36 56.10 60.42 52.36 65.12 65.12 56.10 35.70 39.27 39.27 37.40 41.34 49.92 35.70 39.27 43.63 49.09 43.63 46.20 46.20 52.36 46.20 52.36 48.439 8.33  f (Hz) frequency  6.58 6.94 5.95 7.81 8.33 7.81 8.93 9.62 8.93 6.25 7.35 6.94 8.33 8.93 9.62 8.33 10.36 10.36 8.93 5.68 6.25 6.25 5.95 6.58 7.94 5.68 6.25 6.94 7.81 6.94 7.35 7.35 8.33 7.35 8.33 7.709 1.33  λ (m) wavelength  0.022 0.022 0.026 0.026 0.028 0.022 0.022 0.025 0.027 0.023 0.023 0.026 0.025 0.028 0.028 0.018 0.023 0.021 0.022 0.021 0.018 0.021 0.025 0.022 0.021 0.022 0.020 0.023 0.026 0.020 0.022 0.021 0.019 0.021 0.020 0.023 0.00  A (m) amplitude  0.0098 0.0086 0.0105 0.0098 0.0119 0.0079 0.0077 0.0090 0.0100 0.0081 0.0086 0.0118 0.0093 0.0103 0.0117 0.0094 0.0080 0.0094 0.0098 0.0091 0.0084 0.0108 0.0099 0.0127 0.0116 0.0096 0.0100 0.0115 0.0108 0.0094 0.0100 0.0106 0.0088 0.0110 0.0100 0.010 0.00  α (rad) wave angle  0.70 0.75 0.61 0.65 0.75 0.80 0.73 0.70 0.72 0.58 0.73 0.77 0.63 0.68 0.65 0.99 0.80 0.73 0.89 0.79 0.96 0.93 0.89 0.94 0.94 0.96 0.75 0.87 0.87 0.94 0.89 0.94 0.93 0.96 1.06 0.810 0.12  v (m/sec) wave speed  0.14 0.16 0.15 0.20 0.24 0.17 0.20 0.24 0.24 0.14 0.17 0.18 0.21 0.25 0.27 0.15 0.24 0.22 0.20 0.12 0.11 0.13 0.15 0.14 0.17 0.13 0.13 0.16 0.20 0.14 0.16 0.16 0.16 0.16 0.17 0.17 0.04  43  Table 3. Results of the kinematic measurements as predicted by theoretical models.  Indiv. 1 1 1 1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 7 7 avg. stdev.  Mechanical Eff. Strouhal # l-s Fd (N) U/v fin depth drop tank 0.41 1.09 0.0088 1.09E-03 0.46 0.83 0.0088 1.11E-03 0.57 0.72 0.0088 1.13E-03 0.57 0.67 0.0088 1.17E-03 0.60 0.70 0.0088 1.22E-03 0.60 0.61 0.0090 1.15E-03 0.72 0.48 0.0090 1.22E-03 0.63 0.58 0.0090 1.23E-03 0.85 0.43 0.0090 1.33E-03 0.60 0.60 0.0087 1.13E-03 0.55 0.67 0.0087 1.14E-03 0.69 0.66 0.0087 1.19E-03 0.64 0.59 0.0087 1.20E-03 0.64 0.58 0.0087 1.25E-03 0.66 0.63 0.0087 1.28E-03 0.69 0.78 0.0086 1.15E-03 0.52 0.66 0.0086 1.19E-03 0.60 0.74 0.0086 1.20E-03 0.78 0.58 0.0086 1.24E-03 0.55 0.77 0.0110 1.10E-03 0.83 0.55 0.0110 1.14E-03 0.88 0.60 0.0110 1.17E-03 0.89 0.44 0.0110 1.21E-03 0.54 0.80 0.0102 1.10E-03 0.78 0.63 0.0102 1.15E-03 0.78 0.65 0.0102 1.19E-03 0.74 0.56 0.0102 1.24E-03 0.63 0.73 0.0100 1.13E-03 0.61 0.74 0.0100 1.15E-03 0.74 0.67 0.0100 1.18E-03 0.77 0.61 0.0100 1.18E-03 0.86 0.60 0.0100 1.21E-03 0.85 0.59 0.0100 1.22E-03 0.67 0.65 0.009 1.18E-03 0.13 0.12 0.00 0.00  P (N) LB90 4.41E-04 4.46E-04 2.64E-04 4.56E-04 4.83E-04 4.05E-04 3.65E-04 5.59E-04 2.04E-04 2.70E-04 4.23E-04 2.58E-04 4.36E-04 4.91E-04 5.41E-04 2.05E-04 4.85E-04 4.13E-04 1.69E-04 3.05E-04 1.40E-04 1.01E-04 8.03E-05 2.81E-04 1.64E-04 1.99E-04 2.95E-04 2.17E-04 2.56E-04 1.71E-04 1.95E-04 9.34E-05 1.27E-04 0.0003 0.0001  Ft (N) Ft/Fd LB90 1.07E-03 0.98 1.18E-03 1.07 8.78E-04 0.78 1.52E-03 1.30 1.78E-03 1.46 1.39E-03 1.20 1.45E-03 1.19 2.19E-03 1.78 1.09E-03 0.81 8.19E-04 0.73 1.23E-03 1.08 9.48E-04 0.80 1.46E-03 1.21 1.80E-03 1.44 2.04E-03 1.59 1.00E-03 0.87 2.36E-03 1.98 2.10E-03 1.74 1.09E-03 0.88 1.43E-03 1.30 8.06E-04 0.71 6.73E-04 0.57 6.50E-04 0.54 1.19E-03 1.08 8.65E-04 0.75 1.14E-03 0.96 1.85E-03 1.49 1.38E-03 1.21 1.69E-03 1.47 1.30E-03 1.11 1.37E-03 1.16 8.03E-04 0.67 1.02E-03 0.84 1.32E-03 1.11 4.52E-04 0.36  %P  β  41.2 37.8 30.1 29.9 27.1 29.2 25.1 25.5 18.8 33.0 34.4 27.3 29.9 27.3 26.6 20.5 20.6 19.7 15.5 21.3 17.4 15.0 12.3 23.7 19.0 17.4 16.0 15.8 15.1 13.1 14.2 11.6 12.3 22.5 7.8  0.90 1.32 3.12 2.27 2.57 2.21 3.57 2.27 8.11 3.26 2.12 4.59 2.92 3.01 3.06 3.81 1.73 2.24 5.90 1.28 4.66 7.01 8.94 1.64 4.38 4.20 3.25 2.32 2.09 3.62 3.58 7.27 6.07 3.61 2.01  44  Figure 1. Loligo Systems swim 10 swimming flume used for kinematic experiments. The top view shows all the working components of the flume. 1) Water exit port. 2) Oxygen electrode port. 3) Submersible injection pump. 4) Water rectifying grid. 5) Water rectifying plane. 6) Viewing section. 7) Submersible water heater. 8) Submersible mixing pump. 9) Air stone. 10) Motor.  45  Figure 2. Custom Blazka-type swimming flume used for respiration experiments. The top view (a) shows all the components of a working swimming flume. The front view (b) shows the crosssection of the swimming section that triggerfish preferred. 1) Submersible water heater. 2) Submersible injection pump. 3) Submersible mixing pump. 4) Air stone. 5) Submersible pump. 6) oxygen electrode. 7) External water flow. 8) Swimming section.  46  Figure 3. Individual morphometric and kinematic measurements of R. aculeatus. a) Crosssectional view of the triggerfish median fins showing the stroke angle, θ. b) Top view showing the dorsal median fin and the undulation angle, α. c) In the following list, measurement abbreviations from table 1 are given in parentheses when necessary. AH, total length; AG, standard length; BM, body depth; DF, one-half body depth (s); CF, one-half fin-body depth (l); CD, fin depth (l-s); EI, tail depth; LK, fin length; J, one-half fin angle.  b)  c)  47  Figure 4. Drag force (D) as a function of fish swimming velocity (U, median fins removed) of R. aculeatus. The curve of best fit is given by D = 0.0102U + 0.019U2, y-intercept is set through zero (n = 30; r2 = 0.94; P < 0.0001). Six fish were dropped each at five different weights.  48  Figure 5. Wave speed (υ) as a function of fish swimming velocity (U) of R. aculeatus. Seven fish were filmed each at different velocities. The large solid line represents the average trend of all fish. The mean curve of best fit is given by υ = 0.0748 + 0.0820U, (n = 35; r2 = 0.58; P < 0.0001). 0.30  0.25  Wave Speed (cm/s)  0.20  0.15  0.10  0.05  0.00 0.00  0.50  1.00  1.50  Velocity (BL/s)  2.00  2.50  49  Figure 6. Fin angular velocity (ω) as a function of fish swimming velocity (U) of R. aculeatus. Seven fish were filmed each at different velocities. The large solid line represents the average trend of all fish. The mean curve of best fit is given by ω = 0.1708 - 0.0325U, (n = 35; r2 = 0.46; P < 0.0001). 70 65 60  Angular velocity (rad/sec)  55 50 45 40 35 30 25 20 0.00  0.50  1.00  1.50  Velocity (BL/s)  2.00  2.50  50  Figure 7. Fin amplitude (A) as a function of fish swimming velocity (U) of R. aculeatus. Seven fish were filmed each at different velocities. The large solid line represents the average trend of all fish. The mean curve of best fit is given by A = 0.8049 + 0.1475U, (n = 35; r2 = 0.17; P = 0.0154). 1.30  1.20  Amplitude (cm)  1.10  1.00  0.90  0.80  0.70  0.60 0.00  0.50  1.00  1.50  Velocity (BL/s)  2.00  2.50  51  Figure 8. Undulation angle (α) as a function of fish swimming velocity (U) of R. aculeatus. Seven fish were filmed each at different velocities. The large solid line represents the average trend of all fish. The curve of best fit is given by α = 0.1708 - 0.0325U, (n = 35; r2 = 0.00; P = 0.98). 1.10  1.00  Undulation Angle (degrees)  0.90  0.80  0.70  0.60  0.50  0.40 0.00  0.50  1.00  1.50  Velocity (BL/s)  2.00  2.50  52  Figure 9. Momentum enhancement (β) as a function of fish swimming velocity (U) of R. aculeatus. The curve of best fit is given by β = -0.4471U2 + 4.5140U – 1.1155, (n = 41, r2 = 0.38, P < 0.0001). Seven fish were filmed each at different velocities.  53  Figure 10. Mechanical efficiency (Em) as a function of fish swimming velocity (U) of R. aculeatus. The curve of best fit is given by Em = -0.1917U2 + 0.7389U + 0.0902, (n = 45; r2 = 0.49; P < 0.0001). Seven fish were filmed each at different velocities.  54  Figure 11. Oxygen consumption rate (ṀO2) as a function of fish swimming velocity of R. aculeatus. Small dots represent MO2 of individual fish (n = 32). Large dots represent velocitygrouped averages of MO2. Error bars represent standard error. The curve of best fit is given by ṀO2 = 92.24 + 25.24(exp(0.76U-1)/0.76), (n = 7; r2 = 0.79; P < 0.0001). Seven fish were swum until gait transition occurred.  55  Figure 12. Total Cost of Transport (TCOT) as a function of fish swimming velocity of R. aculeatus. Small dots represent TCOT of individual fish (n = 32). Large dots represent velocitygrouped averages of TCOT. Error bars represent standard error. The curve of best fit is given by TCOT = 0.29exp(0.066/(U-0.65)), (n = 7; r2 = 0.98; P = 0.002). Seven fish were swum until gait transition occurred.  56  Figure 13. Net Cost of Transport (NCOT) as a function of fish swimming velocity of R. aculeatus. Small dots represent NCOT of individual fish (n = 32). Large dots represent velocitygrouped averages of NCOT. Error bars represent standard error. The curve of best fit is given by NCOT = 0.13 - 0.0421U + 0.033U2, (n = 7; r2 = 0.88; P = 0.0422). Seven fish were swum until gait transition occurred.  57  Figure 14. Power (P) as a function of Fish swimming velocity (U). Squares represent muscle propulsive power produced by the fish calculated from its oxygen consumption. The curve of best fit is given by P = 0.001e11.846U, (n = 32; r2 = 0.79; P < 0.0001). Triangles represent theoretical power given by Lighthill and Blake (1990). The curve of best fit is given by P = 3E05e13.361U, (n = 35; r2 = 0.44; P = 0.0001). 5.0E-04  4.5E-04  4.0E-04  3.5E-04  Power (W)  3.0E-04  Muscle Power Theoretical Power  2.5E-04  2.0E-04  1.5E-04  1.0E-04  5.0E-05  0.0E+00 0.00  0.05  0.10  0.15  Fish Velocity (m/s)  0.20  0.25  58  Figure 15. Transmission electron micrographs of propulsive red musculature. TEMs a), b), and c) show location of the mitochondria within triggerfish red muscle. TEMs d) and e) show the orientation of mitochondria within the red muscle. TEM f) shows the tubular cristae of triggerfish mitochondria.  a)  b)  c)  d)  e)  f)  59  Figure 16. Strouhal number (St) as a function of fish swimming velocity (U) of R. aculeatus. The curve of best fit is given by St = 0.1907U2 – 0.7374U + 1.2469, (n = 35; r2 = 0.55; P < 0.0001). Seven fish were filmed each at different velocities.  60  Figure 17. Thrust as a function of fish swimming velocity (U) of R. aculeatus. 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