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BIOMECHANICS of SWIMMING in the FROG, by JULIANNA MARY

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BIOMECHANICS of SWIMMING in the FROG, by JULIANNA MARY BIOMECHANICS OF SWIMMING IN THE FROG, HYMENOCHIRUS BOETTGERI By JULIANNA MARY GAL B.Sc. The University of British Columbia, 1984. A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Zoology) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA JUNE 1987 © Julianna Mary Gal, 1987. In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date DE-6(3/81) ii ABSTRACT Although frogs are recognized as accomplished swimmers, no detailed biomechanical study has been done. The hydrodynamics and mechanics of swimming, in the frog, Hymenochiius boettgezi, are investigated in this thesis. Hydrodynamic drag, of the body and splayed hind limbs of preserved H. boettgeri, was assessed by drop-tank experiments. Drag tests were also performed with the semi-terrestrial Rana pipiens. A comparison of their drag coefficients (Cn) under dynamically similar conditions, suggests that jumping performance may not compromise the swimming ability of R. pipiens. Drag of the expanded foot of H. boettgeri, and acetate models thereof, was investigated by free fall drop-tank experiments, and a subtraction technique. The results of these methods and flow visualization experiments support the assumption that animal paddles can be treated as three dimensional flat plates, oriented normal to the direction of flow. Cine films were used to study swimming during the near-vertical breathing excursions of H. boettgeri. The acceleration of frogs throughout hind limb extension (power stroke), is distinct from other drag-based paddlers (eg. angelfish and water boatman), which accelerate and decelerate within the power stroke phase. The propulsive force generated during the power stroke of a single sequence (sequence 1) is calculated from quasi-steady drag (static-body drag measurements, see Chapter I) and inertial considerations. Additional components of the force iii balance, including the net effect of gravity and buoyancy, and the longitudinal added mass forces associated with the frog's body, are integrated to establish upper and lower bounds of the propulsive force. The propulsive force remains positive throughout extension. The validity of using static drag estimates to describe dynamic resistance is explored. Results from Chapter II suggest that simple drag-based models may not be sufficient to explain the swimming patterns observed. The right hind limb of the sequence 1 animal was modelled as a series of linked circular cylinders (the femur, tibiofibula, and metatarsal-phalangeal segments) and a flat plate (the foot). A blade-element approach was used to calculate the instantaneous drag-based and accelerative force components (parallel to the direction of motion) generated by hind limb flexion and extension. The negative thrust, generated by hind limb flexion, is probably responsible for the observed deceleration of the sequence 1 animal. Positive thrust is generated only during the initial stages of extension, almost exclusively by the feet. The impulse of the accelerative-based thrust far exceedes the impulse of the drag-based thrust. Negative thrust is initiated midway, and continues thoughout extension, despite the acceleration of the animal. Hind limb interaction, is thought to provide propulsive thrust for the latter half of the extension phase. A jet and/or ground effect may be involved. It is suggested that a combination of reactive, resistive and interactive forces are required to explain propulsion in H. boettgeri, and probably other anurans. iv TABLE OF CONTENTS Abstract ii Table of Contents iv List of Tables vi List of Figures vii List of Symbols x Acknowledgements xiii General Introduction 1 Chapter One: Hydrodynamic Drag of Hymenochirus boettgezi and Rana pipiens Abstract 3 Introduction 4 Materials and Methods 6 Results 10 Discussion 22 Chapter Two: Whole Body Kinematics: Motion Analysis and Estimation of the Propulsive Force Generated by the Frog, Hymenochirus boettgeri Abstract 26 Introduction 28 Materials and Methods 31 Results 40 Discussion 47 Chapter Three: Hind Limb Kinematics: A Blade-Element Approach to Calculating the Forces Generated in Flexion and Extension of the Hind Limbs of Hymenochirus boettgeri V Abstract 57 Introduction 59 Analyses 62 Results 74 Discussion 83 Concluding Remarks 92 Literature Cited 95 LIST OF TABLES Table 3.1 Hind Limb Element Morphometries of H. boettgezi vii LIST OF FIGURES Figure 1.1: Drag force on the body and hind limbs (feet removed) 11 of H. boettgezi, plotted against velocity in free fall. Figure 1.2: Drag force on the body and hind limbs (feet removed) 12 of Rana pipiens, plotted against velocity in free fall. Figure 1.3: Drag coefficients of the body and hind limbs (feet 13 removed) of H. boettgeri and R. pipiens, plotted against Reynolds number. Figure 1.4: Drag force on the foot of H. boettgeri (oriented 14 normal to the flow), plotted against velocity in free fall. Figure 1.5: Drag coefficients of the real and model foot of H 15 boettgeri, plotted against Reynolds number. Figure 1.6: Calculating the drag force on the feet of 16 H. boettgeri by a subtraction method. Figure 1.7: Comparing the drag coefficients of the foot of 17 H. boettgeri, calculated by free fall drop-tank experiments and a subtraction method. Figure 1.8: Calculating the drag force on model feet of H 18 boettgeri, by a subtraction method. Figure 1.9: Comparing the experimental drag coefficients for the 19 real and model foot of H. boettgeri, with literature values for technical equivalents. viii Figure 1.10: The flow characteristics of the body and hind limbs 21 (feet removed) of ff. boettgeri, in free fall. Figure 2.1: The Locam camera speed curve 32 Figure 2.2: The camera and tank set-up for filming the breathing 33 excursions of H. boettgeri. Figure 2.3: Scaling the total wetted surface area with snout-vent 37 length in H. boettgeri. Figure 2.4: Scaling the total body mass with snout-vent length in 38 H. boettgezl. Figure 2.5: Smooth and experimental whole body kinematics (vent 41 displacement, velocity, acceleration, and snout-vent length) of H. boettgeri, sequence 1. Figure 2.6: Smooth vent velocity of H. boettqeiif sequences 43 1-4. Figure 2.7: Smooth vent acceleration of H. boettgeri, sequences 44 1-4. Figure 2.8: Comparing the drag coefficients of the static body 46 and hind limbs (Chapter I), with the drag coefficients calculated from the force corresponding to the deceleration of H. boettgeri during hind limb flexion (sequence 1). Figure 2.9: Comparing the body velocity patterns of frogs with 48 other paddling animals. Figure 2.10: Estimating the upper and lower bounds of the 50 propulsive thrust of H. boettgeri, from the force balance of sequence 1. ix Figure 3.1: Whole body tracing of H. boettgeri, illustrating the 63 estimation of the central long axes of the torso and hind limb segments. Figure 3.2: Diagrammatic representation of the positional angle 64 of the hind limb segments, and the numbering of the hind limb elements of H. boettgeri. Figure 3.3: Calculating the drag-based thrust of an element of 66 the right hind limb of H. boettgeri. Figure 3.4: Calculating the accelerative force of an element of 71 the right foot of H. boettgeri. Figure 3.5: A symmetric composite stick diagram of H. boettgeri, 75 illustrating hind limb flexion and extension. Figure 3.6: Experimental and smooth positional angles of the 76 right hind limb segments of H. boettgeri (sequence 1). Figure 3.7: Smooth angular velocities of the right hind limb 78 segments of H. boettgeri (sequence 1). Figure 3.8: Smooth angular accelerations of the right hind limb 79 segments of H. boettgeri (sequence 1). Figure 3.9: The relative velocity of the right hind limb elements 80 of H. boettgeri (sequence 1). Figure 3.10: The total calculated force (drag-based and 81 accelerative), generated throughout hind limb flexion and extension of H. boettgeri (sequence 1). Figure 3.11: Comparing the total calculated force (drag-based and 88 accelerative), with the inertial force of the body, and the propulsive estimate from the force balance, of H. boettgeri (Chapter II, sequence 1). X LIST OF SYMBOLS LENGTH r distance from segment pivot point to element midpoint X snout-vent length of frog AREA Sw total wetted surface area; planform area (foot only) TIME t duration of the power stroke (hind limb extension) VELOCITY (angular) w angular velocity of a segment VELOCITY (linear) U terminal velocity of a body v relative velocity of an element to the fluid VR normal component of the relative velocity of an element v spanwise component of the relative velocity of an element Vg velocity of the frog's body V £ relative velocity of the pivot point of a segment ACCELERATION (angular) a angular acceleration of a segment ACCELERATION (linear) a acceleration of the frog's body A add component of AR parallel to the direction of motion 2 A centrepetal acceleration of an element. (ru>) /r cen Anej. relative acceleration of the pivot point of a segment A acceleration component of A , normal to the element n rei A , vector addition/subtraction of A . and A rei net res xi resultant acceleration of A and A.
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