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Hydrodynamics of Balistiform Swimming in the Picasso

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Hydrodynamics of Balistiform Swimming in the Picasso 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
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