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Performance of thunniform propulsion : a high bio-fidelity experimental study Delepine, Marc 2013

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 PERFORMANCE OF THUNNIFORM PROPULSION: A HIGH BIO-FIDELITY EXPERIMENTAL STUDY by Marc Delepine  B.S.Ag.&Env., McGill University, 2010   A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Zoology)   THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  October 2013  ? Marc Delepine, 2013 ii  Abstract Tunas, lamnid sharks and whales are some of the fastest sustained swimming animals. To propel themselves these animals use the thunniform propulsion mode, and are physically characterized by having streamlined bodies with narrow necking of the caudal peduncle and a high aspect ratio lunate tail generating lift-based thrust. For these reasons, thunniform propulsion has received considerable attention from biologists and bio-inspired engineers. Thunniform propulsion is assumed to have the highest propulsive performance of all swimming modes, meaning high propulsive efficiency at fast swimming speeds. However, there is no direct empirical evidence to support this common idea, due to the difficulty of obtaining force measurements for these animals. Therefore, indirect approaches are used, such as theoretical and experimental studies. But these experiments oversimplify the animal (motion, shape or material property) and/or the flow condition. Our goal was to assess the propulsive performance of the Atlantic bluefin tuna, Thunnus thynnus, which is our case study for thunniform propulsion, by an experimental approach of the highest bio-fidelity currently performed. A computed tomography scanner and a polyjetTM 3-Dimensional printer were used to make three tail models: two with materials of similar properties to the caudal fin, and one of uniform stiffness. Each model was actuated in a water tunnel by a computer controlled, motorized system to follow motion paths typical for a tuna. Propulsive efficiencies and thrust coefficients were calculated from force and torque measurements. Flow structures were visualized by means of particle image velocimetry (PIV). For the 30 motion regimes the mean thrust over a tail-beat was positive. About half of those generated sufficient thrust to counter the whole body drag estimates (CT ?0.19). Propulsive performance trends and values were similar for all our tail models and to previous experiments investigating a similar parametric space, where the peak propulsive performance was observed iii  for all tail models and hydrofoils at Sttip =0.35 and ???  =20?. The average peak propulsive performance for the tail models was ?p =0.43 and CT =0.3. As with recent studies, we conclude propulsive performance is more sensitive to kinematics rather than the shape and bending behavior of the caudal fin. iv  Preface This thesis is original, unpublished work by the author, M. Delepine.  The hardware design in Section 3.2 was done primarily by A. Richards, O. Barannyk and myself. The LabVIEW program in Section 3.2.2 was a modified version by A. Richards from original written by O. Barannyk. The PROG0 in Section 3.3.2 was written by A. Richards and myself. The data collection was primarily done by myself, except with the help of O. Barannyk for the initial quasi-static, A. Richards for the initial dynamic and both of them for the 2D-PIV experiments. The data analysis was my original work. v  Table of Contents Abstract	 ?..................................................................................................................................	 ?ii	 ?Preface	 ?..................................................................................................................................	 ?iv	 ?Table	 ?of	 ?Contents	 ?....................................................................................................................	 ?v	 ?List	 ?of	 ?Tables	 ?........................................................................................................................	 ?viii	 ?List	 ?of	 ?Figures	 ?.........................................................................................................................	 ?ix	 ?List	 ?of	 ?Symbols	 ?and	 ?Abbreviations	 ?.......................................................................................	 ?xiv	 ?Acknowledgements	 ?............................................................................................................	 ?xvii	 ?Dedication	 ?...........................................................................................................................	 ?xix	 ?1	 ?-??	 ?Introduction	 ?.......................................................................................................................	 ?1	 ?2	 ?-??	 ?Background	 ?......................................................................................................................	 ?10	 ?2.1	 ? The	 ?caudal	 ?fin	 ?.......................................................................................................................	 ?10	 ?2.2	 ? Swimming	 ?kinematics	 ?...........................................................................................................	 ?14	 ?2.2.1	 ? Force	 ?generation	 ?...................................................................................................................	 ?14	 ?2.2.2	 ? Literature	 ?requirements	 ?........................................................................................................	 ?18	 ?2.2.2.1	 ? Swimming	 ?parameters	 ?and	 ?realistic	 ?test	 ?range	 ?............................................................................	 ?18	 ?2.2.2.1.1	 ? Swimming	 ?speed	 ?...................................................................................................................	 ?18	 ?2.2.2.1.2	 ? Tail-??beat	 ?frequency	 ?...............................................................................................................	 ?20	 ?2.2.2.1.3	 ? Heave	 ?waveform	 ?and	 ?Strouhal	 ?number	 ?................................................................................	 ?21	 ?2.2.2.1.4	 ? Pitch	 ?waveform	 ?.....................................................................................................................	 ?24	 ?2.2.2.1.5	 ? Phase	 ?shift	 ?............................................................................................................................	 ?30	 ?vi  2.2.2.1.6	 ? Summary	 ?of	 ?motion	 ?regimes	 ?................................................................................................	 ?31	 ?2.2.3	 ? Required	 ?thrust	 ?level	 ?.............................................................................................................	 ?31	 ?3	 ?-??	 ?Methods	 ?..........................................................................................................................	 ?34	 ?3.1	 ? Design	 ?and	 ?construction	 ?of	 ?tail	 ?models	 ?.................................................................................	 ?34	 ?3.1.1	 ? Obtaining	 ?and	 ?describing	 ?a	 ?real	 ?tuna	 ?caudal	 ?fin	 ?....................................................................	 ?34	 ?3.1.2	 ? CT	 ?scan	 ?..................................................................................................................................	 ?37	 ?3.1.3	 ? Numerical	 ?3-??Dimensional	 ?model	 ?...........................................................................................	 ?37	 ?3.1.4	 ? Physical	 ?model	 ?......................................................................................................................	 ?40	 ?3.1.5	 ? Post	 ?3-??Dimensional	 ?printing	 ?modifications	 ?...........................................................................	 ?42	 ?3.1.6	 ? Model	 ?verification	 ?.................................................................................................................	 ?43	 ?3.2	 ? Experimental	 ?setup	 ?..............................................................................................................	 ?47	 ?3.2.1	 ? Motion	 ?system	 ?......................................................................................................................	 ?49	 ?3.2.2	 ? Force	 ?system	 ?.........................................................................................................................	 ?50	 ?3.3	 ? Collection	 ?and	 ?analysis	 ?of	 ?force	 ?and	 ?motion	 ?data	 ?..................................................................	 ?51	 ?3.3.1	 ? Quasi-??static	 ?testing	 ?...............................................................................................................	 ?52	 ?3.3.2	 ? Dynamic	 ?testing	 ?.....................................................................................................................	 ?55	 ?3.3.2.1	 ? Motion	 ?accuracy	 ?and	 ?repeatability	 ?...............................................................................................	 ?59	 ?3.4	 ? Flow	 ?visualization	 ?.................................................................................................................	 ?60	 ?4	 ?-??	 ?Results	 ?.............................................................................................................................	 ?62	 ?4.1	 ? Bending	 ?behavior	 ?of	 ?tail:	 ?......................................................................................................	 ?62	 ?4.2	 ? Motion	 ?system	 ?accuracy	 ?and	 ?isolation	 ?of	 ?tail	 ?force	 ?...............................................................	 ?67	 ?4.3	 ? Propulsive	 ?performance	 ?.......................................................................................................	 ?74	 ?4.4	 ? Flow	 ?structure	 ?visualization	 ?..................................................................................................	 ?82	 ?vii  5	 ?-??	 ?Discussion	 ?........................................................................................................................	 ?85	 ?5.1	 ? Tail	 ?model	 ?accuracy	 ?..............................................................................................................	 ?85	 ?5.2	 ? Tail	 ?forces	 ?isolation	 ?..............................................................................................................	 ?87	 ?5.3	 ? Propulsive	 ?performance	 ?.......................................................................................................	 ?90	 ?6	 ?-??	 ?Conclusion	 ?.....................................................................................................................	 ?101	 ?Bibliography	 ?.......................................................................................................................	 ?103	 ?Appendix	 ?A	 ?-??	 ?Summary	 ?data	 ?table	 ?.......................................................................................	 ?110	 ?Appendix	 ?B	 ?-??	 ?Masking	 ?and	 ?multi-??pass	 ?adaptive	 ?image	 ?interrogation	 ?algorithms	 ?..................	 ?112	 ? viii  List of Tables TABLE	 ?1	 ?-??	 ?TEST	 ?PARAMETER	 ?SPACE	 ?FOR	 ?THIS	 ?STUDY.	 ?COMBINATION	 ?OF	 ?THESE	 ?RESULTED	 ?IN	 ?30	 ?MOTION	 ?REGIMES.	 ?..............................	 ?31	 ?TABLE	 ?2	 ?-??	 ?ESTIMATED	 ?AND	 ?MEASURED	 ?MORPHOLOGICAL	 ?CHARACTERIZATION	 ?OF	 ?AN	 ?ATLANTIC	 ?BLUEFIN	 ?TUNA	 ?OF	 ?SAME	 ?CAUDAL	 ?FIN	 ?SIZE	 ?AS	 ?THE	 ?TAIL	 ?MODELS.	 ?..................................................................................................................................................	 ?36	 ? ix  List of Figures FIGURE	 ?1	 ?-??	 ?THUNNUS	 ?THYNNUS	 ?	 ??JON?S	 ?AMADEO	 ?LUCAS	 ?(HTTP://WWW.FLICKR.COM/PHOTOS/THEANIMALDAY/6996512012/).	 ?CC	 ?BY	 ?2.0	 ?...................................................................................................................................................................	 ?6	 ?FIGURE	 ?2	 ?-??	 ?FIN	 ?RAY	 ?DETAILS.	 ?(A)	 ?AREA	 ?DISSECTED	 ?ON	 ?CAUDAL	 ?FIN.	 ?SCALE	 ?BAR	 ?=	 ?10	 ?CM	 ?(B)	 ?COLLAGENOUS	 ?FILAMENTS	 ?SURROUNDING	 ?FIN	 ?RAYS.	 ?A	 ?SHEET	 ?OF	 ?THIS	 ?CLEAR	 ?RUBBERY	 ?MATERIAL	 ?IS	 ?PEELED	 ?AFTER	 ?REMOVING	 ?THE	 ?SKIN	 ?(IN	 ?BLACK).	 ?(C)	 ?THE	 ?FIFTH	 ?FIN	 ?RAY	 ?FROM	 ?THE	 ?LEADING	 ?EDGE	 ?IS	 ?ABOUT	 ?1.5	 ?CM	 ?WIDE	 ?(INDICATED	 ?BY	 ?TIPS	 ?OF	 ?THUMB	 ?FORCEPS)	 ?AND	 ?COMPOSED	 ?OF	 ?ABOUT	 ?14	 ?SMALL	 ?RECTANGULAR	 ?BEAMS.	 ?(D)	 ?SMALL	 ?RECTANGULAR	 ?BEAMS	 ?OF	 ?CROSS	 ?SECTION	 ?OF	 ?ABOUT	 ?1	 ?MM	 ?WIDE	 ?BY	 ?0.5	 ?MM	 ?THICK	 ?ARE	 ?FUSED	 ?TOGETHER	 ?TO	 ?FORM	 ?A	 ?FIN	 ?RAY.	 ?USING	 ?A	 ?SCALPEL,	 ?INDIVIDUAL	 ?BEAMS	 ?CAN	 ?BE	 ?SEPARATED.	 ?...................................................	 ?11	 ?FIGURE	 ?3	 ?-??	 ?HYDRODYNAMIC	 ?FORCE	 ?GENERATION	 ?AT	 ?THE	 ?PITCH	 ?AXIS	 ?ON	 ?A	 ?CROSS	 ?SECTION	 ?OF	 ?THE	 ?CAUDAL	 ?FIN	 ?FROM	 ?THE	 ?TOP	 ?VIEW.	 ?THE	 ?RESULTANT	 ?FLOW	 ?ENCOUNTERS	 ?THE	 ?TAIL	 ?AT	 ?A	 ?CERTAIN	 ?ANGLE	 ?OF	 ?ATTACK, ??,	 ?AND	 ?THEN	 ?CURVES	 ?AROUND	 ?THE	 ?TAIL,	 ?AS	 ?SEEN	 ?WITH	 ?THE	 ?BLUE	 ?STREAMLINES.	 ?A	 ?HYDRODYNAMIC	 ?FORCE	 ?IS	 ?GENERATED.	 ?THIS	 ?FORCE	 ?ALSO	 ?CALLED	 ?RESULTANT	 ?FORCE	 ?CAN	 ?BE	 ?RESOLVED	 ?IN	 ?A	 ?PAIR	 ?OF	 ?HYDRODYNAMIC	 ?FORCES.	 ?LIFT	 ?AND	 ?DRAG	 ?ARE	 ?RESPECTIVELY	 ?PERPENDICULAR	 ?AND	 ?PARALLEL	 ?TO	 ?THE	 ?DIRECTION	 ?OF	 ?THE	 ?RESULTANT	 ?FLOW.	 ?..................................................................................................................................................	 ?15	 ?FIGURE	 ?4	 ?-??	 ?HYDRODYNAMIC	 ?FORCE	 ?GENERATION	 ?AT	 ?THE	 ?PITCH	 ?AXIS	 ?ON	 ?A	 ?CROSS	 ?SECTION	 ?OF	 ?THE	 ?CAUDAL	 ?FIN	 ?FROM	 ?THE	 ?TOP	 ?VIEW.	 ?THE	 ?HYDRODYNAMIC	 ?FORCE	 ?OR	 ?RESULTANT	 ?FORCE	 ?CAN	 ?BE	 ?RESOLVED	 ?IN	 ?THREE	 ?PAIRS	 ?OF	 ?FORCES.	 ?THE	 ?HYDRODYNAMIC	 ?FORCES	 ?(LIFT	 ?AND	 ?DRAG	 ?IN	 ?PINK)	 ?ARE	 ?RESPECTIVELY	 ?PERPENDICULAR	 ?AND	 ?PARALLEL	 ?TO	 ?THE	 ?DIRECTION	 ?OF	 ?THE	 ?RESULTANT	 ?FLOW.	 ?THE	 ?LOAD	 ?CELL	 ?FORCES	 ?(FY	 ?AND	 ?FX	 ?IN	 ?ORANGE)	 ?ARE	 ?RESPECTIVELY	 ?PERPENDICULAR	 ?AND	 ?PARALLEL	 ?TO	 ?THE	 ?TAIL	 ?ORIENTATION	 ?AXIS.	 ?THE	 ?FORCES	 ?OF	 ?INTEREST	 ?(FLAT	 ?IN	 ?GREEN	 ?AND	 ?T	 ?IN	 ?BLUE)	 ?ARE	 ?RESPECTIVELY	 ?PERPENDICULAR	 ?AND	 ?PARALLEL	 ?TO	 ?THE	 ?FISH	 ?DIRECTION	 ?OF	 ?TRAVEL,	 ?THE	 ?THRUST	 ?AXIS.	 ?THE	 ?POSITIVE	 ?AND	 ?NEGATIVE	 ?SIGNS	 ?REFER	 ?TO	 ?THE	 ?DIRECTION	 ?OF	 ?THE	 ?SAME	 ?COORDINATE	 ?SYSTEM	 ?FOR	 ?BOTH	 ?FORCES	 ?AND	 ?MOTIONS.	 ?TORQUE	 ?AND	 ?PITCH	 ?FOLLOW	 ?THE	 ?SAME	 ?COORDINATE	 ?SYSTEM:	 ?POSITIVE	 ?IN	 ?THE	 ?CLOCKWISE	 ?DIRECTION.	 ?..............	 ?17	 ?FIGURE	 ?5	 ??	 ?CAUDAL	 ?FIN	 ?MOTION	 ?AND	 ?STROUHAL	 ?NUMBER.	 ?THE	 ?GRAY	 ?DASHED	 ?ARROW	 ?IS	 ?THE	 ?THRUST	 ?AXIS	 ?POINTING	 ?IN	 ?THE	 ?SWIMMING	 ?DIRECTION.	 ?THE	 ?CURVED	 ?BLACK	 ?SOLID	 ?LINE	 ?IS	 ?THE	 ?TAIL	 ?TIP	 ?WAVEFORM	 ?AND	 ?THE	 ?CURVED	 ?RED	 ?DASHED	 ?LINE	 ?IS	 ?THE	 ?PITCH	 ?AXIS	 ?WAVEFORM.	 ?RED	 ?DOT	 ?IS	 ?THE	 ?PITCH	 ?AXIS	 ?AND	 ?BLACK	 ?DOT	 ?IS	 ?THE	 ?TAIL	 ?TIP.	 ?WHEN	 ?THE	 ?PITCH	 ?AXIS	 ?IS	 ?AT	 ?THE	 ?MOST	 ?LATERAL	 ?POSITION,	 ?THE	 ?TAIL	 ?ORIENTATION	 ?IS	 ?PARALLEL	 ?TO	 ?THE	 ?THRUST	 ?AXIS.	 ?THE	 ?MEAN	 ?RELATIVE	 ?FLOW	 ?ANGLE	 ?DURING	 ?ONE	 ?STROKE	 ?(?)	 ?IS	 ?POSITIVELY	 ?x  CORRELATED	 ?WITH	 ?THE	 ?STROUHAL	 ?NUMBER.	 ?THE	 ?STRAIGHT	 ?BLUE	 ?ARROW	 ?IS	 ?THE	 ?MEAN	 ?WATER	 ?DIRECTION	 ?DURING	 ?A	 ?STROKE.	 ?IT	 ?IS	 ?DEPENDENT	 ?ON	 ?THE	 ?POSITION	 ?OF	 ?THE	 ?VORTICES	 ?(BLUE	 ?CIRCLES)	 ?AND	 ?THEREFORE	 ?DEPENDS	 ?ON	 ?THE	 ?STROUHAL	 ?NUMBER.	 ?............	 ?22	 ?FIGURE	 ?6	 ?-??	 ?PITCH	 ?WAVEFORMS	 ?TO	 ?GENERATE	 ?SINUSOIDAL	 ?ANGLES	 ?OF	 ?ATTACK.	 ?SOLID	 ?CURVES	 ?ARE	 ?MOTION	 ?REGIMES	 ?PITCH	 ?WAVEFORMS	 ?AND	 ?DASHED	 ?CURVES	 ?ARE	 ?SINUSOIDAL	 ?ANGLE	 ?WAVEFORMS	 ?OF	 ?THE	 ?SAME	 ?MAXIMAL	 ?ANGLE	 ?FOR	 ?COMPARISON.	 ?ONLY	 ?ONE	 ?STROKE	 ?OF	 ?THE	 ?TAIL-??BEAT	 ?IS	 ?SHOWN	 ?(50	 ?TO	 ?100%).	 ?(A)	 ?FOR	 ?MOTIONS	 ?WITH	 ?A	 ?MAXIMUM	 ?ANGLE	 ?OF	 ?ATTACK,	 ??MAX,	 ?OF	 ?30?,	 ?AT	 ?STTIP	 ?=35,	 ?30	 ?AND	 ?25	 ?RESPECTIVELY	 ?FROM	 ?TOP	 ?TO	 ?BOTTOM.	 ?(B)	 ?FOR	 ?MOTIONS	 ?WITH	 ?A	 ?STROUHAL	 ?NUMBER,	 ?STTIP,	 ?OF	 ?25,	 ?AT	 ??MAX=10,	 ?15,	 ?20,	 ?25	 ?AND	 ?30?	 ?RESPECTIVELY	 ?FROM	 ?TOP	 ?TO	 ?BOTTOM.	 ?................................................................................................	 ?27	 ?FIGURE	 ?7	 ?ANGLES	 ?WAVEFORM	 ?FOR	 ?MOTION	 ?30	 ?OF	 ?RELATIVE	 ?FLOW	 ?ANGLE,	 ??	 ?(DASH	 ?CURVE),	 ?AND	 ?PITCH	 ?ANGLE,	 ??	 ?(ORANGE	 ?CURVE),	 ?TO	 ?GENERATE	 ?A	 ?SINUSOIDAL	 ?ANGLE	 ?OF	 ?ATTACK,	 ??	 ?(SOLID	 ?CURVE).	 ?........................................................................................	 ?29	 ?FIGURE	 ?8	 ?-??	 ?CAUDAL	 ?FIN	 ?OF	 ?THUNNUS	 ?THYNNUS	 ?USED	 ?FOR	 ?CT	 ?SCANNING.	 ?THE	 ?TAIL	 ?WAS	 ?CT	 ?SCANNED	 ?VERTICALLY	 ?IN	 ?THIS	 ?POSITION.	 ?SCALE	 ?BAR	 ?=	 ?10CM.	 ?........................................................................................................................................................	 ?35	 ?FIGURE	 ?9	 ?-??	 ?NUMERICAL	 ?TAIL	 ?MODEL.	 ?(A)	 ?ABOVE	 ?IS	 ?A	 ?CT	 ?SLICE	 ?SHOWING	 ?TISSUE	 ?DENSITY	 ?VARIATION,	 ?WHERE	 ?WHITE	 ?IS	 ?FIN	 ?RAYS.	 ?BELOW	 ?IS	 ?SEGMENTED	 ?FIN	 ?RAYS	 ?AND	 ?SURROUNDING	 ?MATRIX.	 ?(B	 ?AND	 ?C)	 ?BONE	 ?STRUCTURE	 ?AROUND	 ?THE	 ?HYPURAL	 ?PLATE	 ?(HP)	 ?AND	 ?HYPURAPOPHYSIS	 ?(H).	 ?PITCH	 ?AXIS	 ?(YELLOW	 ?LINE)	 ?AND	 ?END	 ?OF	 ?ANTERIOR	 ?CAD	 ?REMODELING	 ?(RED	 ?LINE).	 ?(D)	 ?CHORDWISE	 ?CROSS	 ?SECTIONS	 ?OF	 ?MODIFIED	 ?TAIL	 ?MODEL	 ?ALONG	 ?THE	 ?DORSAL	 ?TAIL	 ?LOBE.	 ?(E)	 ?RAW	 ?NUMERICAL	 ?TAIL	 ?MODEL	 ?BEFORE	 ?MODIFICATIONS.	 ?SCALE	 ?BAR	 ?=	 ?2CM.	 ?.................................................................................................................................................	 ?39	 ?FIGURE	 ?10	 ?-??	 ?MODIFICATIONS	 ?TO	 ?NUMERICAL	 ?TAIL	 ?MODEL.	 ?(A)	 ?RAW	 ?(ORANGE)	 ?AND	 ?FINAL	 ?(YELLOW)	 ?TRANSPARENT	 ?BONE	 ?MODEL.	 ?(B)	 ?POSTERIOR	 ?VIEW	 ?OF	 ?THE	 ?HYPURAL	 ?PLATE	 ?(HP)	 ?AND	 ?FIN	 ?RAYS	 ?ON	 ?EITHER	 ?SIDE	 ?OF	 ?IT.	 ?FINAL	 ?TAIL	 ?MODEL	 ?SHOWING	 ?SPANWISE	 ?(C)	 ?AND	 ?CHORDWISE	 ?CROSS	 ?SECTIONS	 ?(D).	 ?.............................................................................................................................	 ?40	 ?FIGURE	 ?11	 ??	 ?THREE	 ?TAIL	 ?MODELS	 ?USED	 ?IN	 ?THIS	 ?STUDY.	 ?SCALE	 ?BAR	 ?=	 ?2CM	 ?..................................................................................	 ?42	 ?FIGURE	 ?12	 ?-??	 ?TEST	 ?LOCATION	 ?FOR	 ?FLEXURAL	 ?STIFFNESS	 ?CALCULATION	 ?SHOWING	 ?32	 ?TEST	 ?LOCATIONS	 ?FOR	 ?THE	 ?CAUDAL	 ?FIN.	 ?FOR	 ?THE	 ?TAIL	 ?MODELS	 ?ONLY	 ?THE	 ?VENTRAL	 ?LOBE	 ?WAS	 ?TESTED.	 ?BLUE	 ?IS	 ?LEADING	 ?EDGE,	 ?RED	 ?IS	 ?MIDLINE	 ?AND	 ?BLACK	 ?IS	 ?TRAILING	 ?EDGE.	 ?THE	 ?WHITE	 ?DOT	 ?IS	 ?THE	 ?LOCATION	 ?ON	 ?THE	 ?HYPURAPOPHYSIS,	 ?WHICH	 ?IS	 ?VERY	 ?CLOSE	 ?TO	 ?THE	 ?PITCH	 ?AXIS.	 ?SPAN	 ?IS	 ?20	 ?CM	 ?FOR	 ?TAIL	 ?MODELS	 ?AND	 ?54	 ?CM	 ?FOR	 ?THE	 ?CAUDAL	 ?FIN.	 ?.........................................................................................................................................	 ?44	 ?FIGURE	 ?13	 ??	 ?EXPERIMENTAL	 ?SETUP	 ?TO	 ?MEASURE	 ?THE	 ?FORCE	 ?AND	 ?DEFLECTION	 ?AT	 ?SEVERAL	 ?LOCATIONS	 ?ALONG	 ?THE	 ?REAL	 ?AND	 ?MODEL	 ?TAILS	 ?TO	 ?CALCULATE	 ?THE	 ?FLEXURAL	 ?STIFFNESS	 ?AND	 ?PROVIDE	 ?A	 ?CHARACTERIZATION	 ?OF	 ?THE	 ?RESISTANCE	 ?TO	 ?BENDING	 ?ALONG	 ?THE	 ?CAUDAL	 ?xi  FIN	 ?AND	 ?TAIL	 ?MODELS.	 ?WHITE	 ?ARROWS	 ?SYMBOLIZE	 ?THE	 ?DISPLACEMENT	 ?AXIS	 ?OF	 ?THE	 ?MTS	 ?ACTUATOR	 ?CONNECTED	 ?TO	 ?THE	 ?FORCE	 ?TRANSDUCER	 ?AND	 ?PROBE.	 ?........................................................................................................................................	 ?45	 ?FIGURE	 ?14	 ?-??	 ?DYNAMIC	 ?EXPERIMENTAL	 ?SETUP.	 ?THE	 ?HEAVE	 ?MOTOR	 ?AND	 ?LINEAR	 ?ACTUATOR	 ?TRANSLATE	 ?LATERALLY	 ?THE	 ?PITCH	 ?MOTOR,	 ?LOAD	 ?CELL,	 ?ROD	 ?AND	 ?TAIL	 ?MODEL.	 ?THE	 ?DASHED	 ?LINE	 ?IN	 ?THE	 ?OPPOSITE	 ?DIRECTION	 ?OF	 ?THE	 ?WATER	 ?VELOCITY	 ?(U)	 ?IS	 ?THE	 ?THRUST	 ?AXIS.	 ?ORTHOGONAL	 ?TO	 ?IT	 ?IS	 ?THE	 ?LATERAL	 ?AXIS.	 ?THE	 ?GREEN	 ?TRIANGLE	 ?IS	 ?THE	 ?ILLUMINATION	 ?PLANE	 ?OF	 ?THE	 ?LASER	 ?DURING	 ?PIV	 ?EXPERIMENTS.	 ?.......................................................................................................................................................	 ?48	 ?FIGURE	 ?15	 ?-??	 ?EXPERIMENTAL	 ?VERIFICATION	 ?OF	 ?FLEXURAL	 ?STIFFNESS	 ?SCALING.	 ?THE	 ?EI	 ?OF	 ?THE	 ?20	 ?CM	 ?TAIL	 ?SPAN	 ?ON	 ?THE	 ?Y-??AXIS	 ?AND	 ?THE	 ?EI	 ?OF	 ?THE	 ?10	 ?CM	 ?TAIL	 ?SPAN	 ?ON	 ?THE	 ?X-??AXIS.	 ?THE	 ?OBSERVED	 ?SLOPE	 ?OF	 ?THE	 ?BEST-??FIT	 ?LINEAR	 ?REGRESSION	 ?IS	 ?17.99	 ?(ILLUSTRATED	 ?BY	 ?THE	 ?DOTED	 ?LINE).	 ?THE	 ?THEORETICAL	 ?SLOPE	 ?IS	 ?16	 ?(SF4	 ?=	 ?24=16)	 ?(ILLUSTRATED	 ?BY	 ?THE	 ?THIN	 ?SOLID	 ?LINE)	 ?IS	 ?CONTAINED	 ?BETWEEN	 ?THE	 ?95%	 ?CONFIDENCE	 ?BANDS	 ?(ILLUSTRATED	 ?BY	 ?THE	 ?DASHED	 ?CURVES).	 ?...................................................................................	 ?63	 ?FIGURE	 ?16	 ?-??	 ?COMPARISON	 ?OF	 ?THE	 ?FLEXURAL	 ?STIFFNESS	 ?(EI),	 ?THAT	 ?IS	 ?THE	 ?RESISTANCE	 ?TO	 ?BENDING,	 ?OF	 ?THE	 ?TAIL	 ?MODELS	 ?(SB,	 ?FC	 ?AND	 ?FS)	 ?WITH	 ?THE	 ?REAL	 ?CAUDAL	 ?FIN	 ?(REAL).	 ?THE	 ?Y-??AXIS	 ?IS	 ?DIMENSIONLESS	 ?AS	 ?IT	 ?IS	 ?THE	 ?RATIO	 ?OF	 ?EI	 ?OF	 ?TAIL	 ?MODEL/EI	 ?OF	 ?CAUDAL	 ?FIN	 ?(SQUARE:	 ?SB/R,	 ?DIAMOND:	 ?FC/R,	 ?CIRCLE:	 ?FS/R).	 ?X-??AXIS	 ?REPRESENTS	 ?THE	 ?SPANWISE	 ?POSITION	 ?OF	 ?THE	 ?TEST	 ?LOCATION,	 ?WHERE	 ?0%	 ?IS	 ?THE	 ?SPANWISE	 ?MIDLINE	 ?OF	 ?THE	 ?TAIL	 ?PASSING	 ?THROUGH	 ?THE	 ?PITCH	 ?AXIS	 ?AND	 ?100%	 ?IS	 ?THE	 ?TAIL	 ?TIP	 ?(AS	 ?SHOWN	 ?WITH	 ?THE	 ?TAIL	 ?SCHEMATIC).	 ?IF	 ?THE	 ?FLEXURAL	 ?STIFFNESS	 ?RATIOS	 ?WERE	 ?ALL	 ?EQUAL	 ?TO	 ?ONE	 ?IT	 ?WOULD	 ?MEAN	 ?THE	 ?TAIL	 ?MODEL	 ?AND	 ?CAUDAL	 ?FIN	 ?WOULD	 ?DEFORM	 ?IN	 ?THE	 ?SAME	 ?FASHION.	 ?.....................................................................................................................	 ?64	 ?FIGURE	 ?17	 ?-??	 ?MOTORS	 ?ACCURACY	 ?I.	 ?THE	 ?COLORED	 ?LINES	 ?ARE	 ?13	 ?TAIL-??BEATS	 ?PLOTTED	 ?ON	 ?TOP	 ?OF	 ?EACH	 ?OTHER.	 ?TOP	 ?(POSITION)	 ?AND	 ?MIDDLE	 ?(ACCELERATION)	 ?PLOTS:	 ?OBSERVED	 ?PITCH	 ?(ORANGE)	 ?AND	 ?HEAVE	 ?(RED)	 ?TAIL+ROD	 ?MOTION	 ?COMPARISON	 ?WITH	 ?THE	 ?COMMANDED	 ?CAM	 ?TABLE	 ?MOTION	 ?(DASHED	 ?LINES)	 ?FOR	 ?THE	 ?HIGHEST	 ?HEAVE	 ?VELOCITY	 ?AND	 ?HIGHEST	 ?HEAVE	 ?AND	 ?PITCH	 ?ACCELERATION	 ?MOTION	 ?REGIME	 ?TESTED	 ?(MOTION	 ?REGIME	 ?30,	 ?SEE	 ?APPENDIX	 ?A).	 ?THE	 ?DIFFERENCE	 ?BETWEEN	 ?THE	 ?COLORED	 ?AND	 ?DASHED	 ?LINES	 ?REPRESENTS	 ?THE	 ?FOLLOWING	 ?ERROR.	 ?THE	 ?ROD-??ALONE	 ?HEAVE	 ?(GREEN)	 ?AND	 ?PITCH	 ?(BLUE)	 ?MOTION	 ?ARE	 ?BARELY	 ?VISIBLE,	 ?AS	 ?THEY	 ?ARE	 ?NEARLY	 ?IDENTICAL	 ?TO	 ?TAIL+ROD	 ?MOTIONS.	 ?BOTTOM	 ?PLOT:	 ?DIFFERENCES	 ?IN	 ?THE	 ?ACCELERATION	 ?OF	 ?HEAVE	 ?(RED)	 ?AND	 ?PITCH	 ?(ORANGE)	 ?MOTION	 ?UNDER	 ?DIFFERENT	 ?LOADS	 ?(WITH	 ?OR	 ?WITHOUT	 ?TAIL	 ?ATTACHED	 ?TO	 ?ROD).	 ?DIFFERENCES	 ?WERE	 ?CALCULATED	 ?BY	 ?SUBTRACTING	 ?THE	 ?ROD	 ?HEAVE	 ?AND	 ?PITCH	 ?ACCELERATIONS	 ?TO	 ?THE	 ?TAIL+ROD	 ?HEAVE	 ?AND	 ?PITCH	 ?ACCELERATIONS.	 ?.	 ?68	 ?xii  FIGURE	 ?18	 ?-??	 ?MOTORS	 ?ACCURACY	 ?II.	 ?SAME	 ?FIGURE	 ?CAPTION	 ?AS	 ?FIGURE.17	 ?EXCEPT	 ?FOR	 ?TOP	 ?(POSITION)	 ?AND	 ?MIDDLE	 ?(ACCELERATION)	 ?PLOTS:	 ?OBSERVED	 ?PITCH	 ?(ORANGE)	 ?AND	 ?HEAVE	 ?(RED)	 ?TAIL+ROD	 ?MOTION	 ?COMPARISON	 ?WITH	 ?THE	 ?COMMANDED	 ?CAM	 ?TABLE	 ?MOTION	 ?(DASHED	 ?LINES)	 ?FOR	 ?THE	 ?HIGHEST	 ?PITCH	 ?VELOCITY	 ?MOTION	 ?REGIME	 ?TESTED	 ?(MOTION	 ?REGIME	 ?26,	 ?SEE	 ?APPENDIX	 ?A).	 ?....	 ?69	 ?FIGURE	 ?19	 ?-??	 ?LEFT	 ?COLUMN	 ?IS	 ?MOTION	 ?26.	 ?RIGHT	 ?COLUMN	 ?IS	 ?MOTION	 ?30.	 ?BOTH	 ?MOTIONS	 ?ARE	 ?FOR	 ?THE	 ?SB	 ?TAIL	 ?MODEL.	 ?THE	 ?BLACK	 ?DASHED	 ?CURVES	 ?ARE	 ?THE	 ?TAIL+ROD	 ?DATA.	 ?THE	 ?BLACK	 ?SOLID	 ?CURVES	 ?ARE	 ?THE	 ?ROD-??ALONE	 ?DATA.	 ?THE	 ?COLORED	 ?CURVES	 ?ARE	 ?THE	 ?TAIL	 ?DATA.	 ?THE	 ?FIRST	 ?THREE	 ?ROWS	 ?ARE	 ?THE	 ?THRUST	 ?FORCE	 ?(N)	 ?(BLUE	 ?FOR	 ?TAIL	 ?ALONE),	 ?THE	 ?MIDDLE	 ?THREE	 ?ROWS	 ?ARE	 ?FOR	 ?THE	 ?LATERAL	 ?FORCE	 ?(N)	 ?(GREEN	 ?FOR	 ?TAIL	 ?ALONE)	 ?AND	 ?THE	 ?BOTTOM	 ?THREE	 ?ARE	 ?FOR	 ?THE	 ?TORQUE	 ?(NM)	 ?(PURPLE	 ?FOR	 ?TAIL	 ?ALONE).	 ?TWO	 ?TAIL-??BEATS	 ?AT	 ?2.54	 ?HZ.	 ?THE	 ?GREY	 ?SHADED	 ?AREAS	 ?ARE	 ?ONE	 ?STROKE,	 ?FOLLOWED	 ?BY	 ?THE	 ?RETURN	 ?STROKE	 ?REPRESENTED	 ?BY	 ?THE	 ?WHITE	 ?AREAS.	 ?.................................................................................................................................................................	 ?72	 ?FIGURE	 ?20	 ?-??	 ?LEFT	 ?COLUMN	 ?IS	 ?MOTION	 ?26	 ?FOR	 ?SB	 ?TAIL	 ?MODEL.	 ?RIGHT	 ?COLUMN	 ?IS	 ?MOTION	 ?26	 ?FOR	 ?FS	 ?TAIL	 ?MODEL.	 ?THE	 ?BLACK	 ?DASHED	 ?CURVES	 ?ARE	 ?THE	 ?TAIL+ROD	 ?DATA.	 ?THE	 ?BLACK	 ?SOLID	 ?CURVES	 ?ARE	 ?THE	 ?ROD-??ALONE	 ?DATA.	 ?THE	 ?COLORED	 ?CURVES	 ?ARE	 ?THE	 ?TAIL	 ?DATA.	 ?THE	 ?FIRST	 ?THREE	 ?ROWS	 ?ARE	 ?THE	 ?THRUST	 ?FORCE	 ?(N)	 ?(BLUE	 ?FOR	 ?TAIL	 ?ALONE),	 ?THE	 ?MIDDLE	 ?THREE	 ?ROWS	 ?ARE	 ?FOR	 ?THE	 ?LATERAL	 ?FORCE	 ?(N)	 ?(GREEN	 ?FOR	 ?TAIL	 ?ALONE)	 ?AND	 ?THE	 ?BOTTOM	 ?THREE	 ?ARE	 ?FOR	 ?THE	 ?TORQUE	 ?(NM)	 ?(PURPLE	 ?FOR	 ?TAIL	 ?ALONE).	 ?TWO	 ?TAIL-??BEATS	 ?AT	 ?2.54	 ?HZ.	 ?THE	 ?GREY	 ?SHADED	 ?AREAS	 ?ARE	 ?ONE	 ?STROKE,	 ?FOLLOWED	 ?BY	 ?THE	 ?RETURN	 ?STROKE	 ?REPRESENTED	 ?BY	 ?THE	 ?WHITE	 ?AREAS.	 ?....	 ?73	 ?FIGURE	 ?21	 ??	 ?MOTIONS	 ?AND	 ?FORCES	 ?PROFILES	 ?DURING	 ?MOTION	 ?REGIME	 ?27	 ?FOR	 ?FS	 ?TAIL	 ?MODEL.	 ?RED	 ?IS	 ?HEAVE	 ?AND	 ?ORANGE	 ?IS	 ?PITCH.	 ?THRUST	 ?IS	 ?LIGHT	 ?BLUE,	 ?LATERAL	 ?FORCE	 ?IS	 ?GREEN	 ?AND	 ?TORQUE	 ?IS	 ?PURPLE.	 ?ALL	 ?13	 ?TAIL-??BEAT	 ?CYCLES	 ?ARE	 ?PLOTTED	 ?AND	 ?THE	 ?BLACK	 ?CURVE	 ?IN	 ?THE	 ?MIDDLE	 ?OF	 ?THOSE	 ?CURVES	 ?IS	 ?THE	 ?MEAN.	 ?THE	 ?GREY	 ?SHADED	 ?AREA	 ?IS	 ?ONE	 ?STROKE.	 ?............................................	 ?74	 ?FIGURE	 ?22	 ??	 ?MOTIONS	 ?AND	 ?FORCES	 ?PROFILES	 ?DURING	 ?MOTION	 ?REGIME	 ?30	 ?FOR	 ?FS	 ?TAIL	 ?MODEL.	 ?RED	 ?IS	 ?HEAVE	 ?AND	 ?ORANGE	 ?IS	 ?PITCH.	 ?THRUST	 ?IS	 ?LIGHT	 ?BLUE,	 ?LATERAL	 ?FORCE	 ?IS	 ?GREEN	 ?AND	 ?TORQUE	 ?IS	 ?PURPLE.	 ?ALL	 ?13	 ?TAIL-??BEAT	 ?CYCLES	 ?ARE	 ?PLOTTED	 ?AND	 ?THE	 ?BLACK	 ?CURVE	 ?IN	 ?THE	 ?MIDDLE	 ?OF	 ?THOSE	 ?CURVES	 ?IS	 ?THE	 ?MEAN.	 ?THE	 ?GREY	 ?SHADED	 ?AREA	 ?IS	 ?ONE	 ?STROKE.	 ?............................................	 ?75	 ?FIGURE	 ?23	 ??	 ?COEFFICIENT	 ?OF	 ?THRUST	 ?(CT)	 ?AT:	 ?A)	 ?U	 ?=	 ?1	 ?BL/S	 ?AND	 ?B)	 ?U	 ?=	 ?1.5	 ?BL/S.	 ?MARKERS	 ?ARE	 ?THE	 ?MEAN	 ?OF	 ?CT ?OVER	 ?13	 ?TAIL-??BEATS.	 ?SMALL	 ?WIDTH	 ?ERROR	 ?BAR	 ?TICKS	 ?ARE	 ?THE	 ?MINIMUM	 ?AND	 ?MAXIMUM	 ?VALUES	 ?OF	 ?CT	 ?IN	 ?13	 ?TAIL-??BEATS.	 ?THE	 ?LARGE	 ?WIDTH	 ?ERROR	 ?BAR	 ?TICKS	 ?ARE	 ?THE	 ?STANDARD	 ?DEVIATION	 ?FROM	 ?THE	 ?MEAN	 ?CT.	 ?THE	 ?HORIZONTAL	 ?DASHED	 ?LINE	 ?IS	 ?CT ?	 ?=	 ?0.19.	 ?..............	 ?77	 ?FIGURE	 ?24	 ??	 ?PROPULSIVE	 ?EFFICIENCY	 ?(?P	 ?)	 ?AT:	 ?A)	 ?U	 ?=	 ?1	 ?BL/S	 ?AND	 ?B)	 ?U	 ?=	 ?1.5	 ?BL/S.	 ?MARKERS	 ?ARE	 ?THE	 ?MEAN	 ?OF	 ??P	 ?OVER	 ?13	 ?TAIL-??BEATS.	 ?SMALL	 ?WIDTH	 ?ERROR	 ?BAR	 ?TICKS	 ?ARE	 ?THE	 ?MINIMUM	 ?AND	 ?MAXIMUM	 ?VALUES	 ?OF	 ??P	 ?IN	 ?13	 ?TAIL-??BEATS.	 ?THE	 ?LARGE	 ?WIDTH	 ?ERROR	 ?BAR	 ?TICKS	 ?ARE	 ?THE	 ?STANDARD	 ?DEVIATION	 ?FROM	 ?THE	 ?MEAN	 ??P.	 ?..............................................................................................	 ?78	 ?xiii  FIGURE	 ?25	 ?-??	 ?COEFFICIENTS	 ?OF	 ?LIFT,	 ?DRAG	 ?AND	 ?TORQUE:	 ?COEFFICIENT	 ?OF	 ?LIFT	 ?(BLUE),	 ?DRAG	 ?(RED)	 ?AND	 ?TORQUE	 ?(BLACK)	 ?VALUES	 ?FOR	 ?THE	 ?TAIL	 ?MODELS	 ?AT	 ?VARYING	 ?ANGLES	 ?OF	 ?ATTACK.	 ?DATA	 ?WAS	 ?COLLECTED	 ?AT	 ?BOTH	 ?POSITIVE	 ?AND	 ?NEGATIVE	 ?ANGLES	 ?FOR	 ?TWO	 ?SPEEDS.	 ?THE	 ?ERROR	 ?BARS	 ?REPRESENT	 ?THE	 ?STANDARD	 ?DEVIATION	 ?BETWEEN	 ?THE	 ?MEANS	 ?CALCULATED	 ?AT	 ?1BL/S	 ?AND	 ?1.5	 ?BL/S.	 ?HOLLOW	 ?CIRCLES	 ?AND	 ?DASHED	 ?LINES	 ?ARE	 ?FOR	 ?SB	 ?TAIL.	 ?FULL	 ?CIRCLES	 ?AND	 ?SOLID	 ?LINES	 ?ARE	 ?FOR	 ?FC	 ?TAIL.	 ?..............................................	 ?80	 ?FIGURE	 ?26	 ?-??	 ?THEORETICAL	 ?VS.	 ?EXPERIMENT	 ?THRUST	 ?AND	 ?PROPULSIVE	 ?EFFICIENCY.	 ?A	 ?AND	 ?B	 ?ARE	 ?FOR	 ?SB	 ?TAIL	 ?MODEL.	 ?C	 ?AND	 ?D	 ?ARE	 ?FOR	 ?THE	 ?FC	 ?TAIL	 ?MODEL.	 ?SILVER	 ?EDGE	 ?MARKERS	 ?ARE	 ?FOR	 ?1	 ?BL/S	 ?AND	 ?BLACK	 ?EDGE	 ?MARKERS	 ?ARE	 ?FOR	 ?1.5	 ?BL/S	 ?MOTIONS.	 ?MARKER	 ?COLOR	 ?REPRESENTS	 ?THE	 ?STROUHAL	 ?NUMBER	 ?FOR	 ?TAIL	 ?TIP,	 ?WITH	 ?STTIP	 ?=	 ?0.25	 ?IN	 ?BLUE,	 ?STTIP	 ?=	 ?0.30	 ?IN	 ?YELLOW	 ?AND	 ?STTIP	 ?=	 ?0.35	 ?IN	 ?RED.	 ?MARKER	 ?STYLE	 ?CORRESPONDS	 ?TO	 ?THE	 ?MAXIMUM	 ?ANGLE	 ?OF	 ?ATTACK,	 ?WITH	 ??MAX	 ?=	 ?10?	 ?(LEFT	 ?POINTING	 ?TRIANGLE),	 ??MAX	 ?=	 ?20?	 ?(SQUARE),	 ??MAX	 ?=	 ?20?	 ?(DIAMOND),	 ??MAX	 ?=	 ?25?	 ?(CIRCLE)	 ?AND	 ??MAX	 ?=	 ?30?	 ?(RIGHT	 ?POINTING	 ?TRIANGLE).	 ?SOLID	 ?THIN	 ?BLACK	 ?LINE	 ?IS	 ?Y	 ?=	 ?X.	 ?DASHED	 ?THIN	 ?BLACK	 ?LINE	 ?IS	 ?THE	 ?LINEAR	 ?REGRESSION.	 ?.........................................................................................	 ?81	 ?FIGURE	 ?27	 ??	 ?FLOW	 ?STRUCTURE	 ?FOR	 ?MOTION	 ?15	 ?(COLUMN	 ?A)	 ?AND	 ?13	 ?(COLUMN	 ?B).	 ?ONE	 ?TAIL-??BEAT	 ?STROKE	 ?IS	 ?SHOWN	 ?FROM	 ?TOP	 ?IMAGE	 ?(MOST	 ?LATERAL	 ?HEAVE	 ?POSITION)	 ?TO	 ?BOTTOM	 ?IMAGE	 ?(START	 ?OF	 ?OPPOSITE	 ?STROKE).	 ?BLUE	 ?IS	 ?CLOCKWISE	 ?AND	 ?RED	 ?IS	 ?COUNTER	 ?CLOCKWISE	 ?VORTICES.	 ?YELLOW	 ?IS	 ?THE	 ?TAIL	 ?MODEL	 ?CROSS	 ?SECTION.	 ?WHITE	 ?AREAS	 ?ARE	 ?UNRESOLVED	 ?FLOW	 ?STRUCTURES	 ?(I.E.	 ?LASER	 ?SHADOW).	 ?THE	 ?FREE	 ?STREAM	 ?WATER	 ?VELOCITY	 ?IS	 ?0.7	 ?M/S	 ?AND	 ?THE	 ?TAIL-??BEAT	 ?FREQUENCY	 ?WAS	 ?AT	 ?1.95	 ?HZ.	 ?THEREFORE	 ?THE	 ?A	 ?AND	 ?B	 ?STROKES	 ?PRESENTED	 ?HERE	 ?OCCUR	 ?WITHIN	 ?0.25	 ?S.	 ?FOR	 ?THIS	 ?STOKE	 ?DIRECTION	 ?THE	 ?BLUE	 ?COLOR	 ?ALSO	 ?REPRESENTS	 ?THE	 ?FORMATION	 ?AND	 ?SHEDDING	 ?OF	 ?THE	 ?LEADING	 ?EDGE	 ?VORTEX	 ?(LEV)	 ?AND	 ?THE	 ?RED	 ?COLOR	 ?REPRESENTS	 ?THE	 ?TRAILING	 ?EDGE	 ?VORTICES.	 ?THE	 ?BLACK	 ?SCALE	 ?BAR	 ?AT	 ?THE	 ?BOTTOM	 ?IS	 ?10	 ?CM.	 ?.........................................................................................................	 ?84	 ?FIGURE	 ?28	 ??SIMPLIFIED	 ?FIN	 ?RAYS	 ?BENDING	 ?BEHAVIOR	 ?IN	 ?THE	 ?CAUDAL	 ?FIN.	 ?THE	 ?BOTTOM	 ?GRAY	 ?SCHEMATIC	 ?REPRESENTS	 ?FIN	 ?RAYS	 ?BEFORE	 ?LOADING.	 ?THE	 ?TOP	 ?BLACK	 ?SCHEMATIC	 ?REPRESENTS	 ?THE	 ?SIMPLIFIED	 ?FIN	 ?RAYS	 ?DEFORMATION	 ?WHILE	 ?UNDER	 ?LOADING	 ?AT	 ?THE	 ?MIDDLE	 ?OF	 ?THE	 ?FIN	 ?RAY	 ?(BLUE	 ?ARROW).	 ?THE	 ?RECTANGLE	 ?REPRESENTS	 ?THE	 ?HYPURAL	 ?PLATE.	 ?.............................................................	 ?85	 ? xiv  List of Symbols and Abbreviations A  = Instantaneous peak-to-peak tail tip heave amplitude (m) Achmax  = Maximum rod heave acceleration (m/s2) Ac? max  = Maximum pitch acceleration (rot/s2) ? ??  = Maximum peak-to-peak tail tip heave amplitude (m) ?? ? ???  = Coefficient of overall body drag (dimensionless) ?? = Coefficient of drag of tail (dimensionless) ?? = Coefficient of lift of tail (dimensionless) ?? = Coefficient of thrust of tail (dimensionless) ????  = Overall body drag (N) D ?p (FC) = Dynamic experimental propulsive efficiency for FC tail model (dimensionless) f  = Tail-beat frequency (Hz) FC = Flexible tail model with chordwise reinforcement FLat = Lateral force (N) FS = Flexible tail model with spanwise reinforcement Fx = Force measured by load cell parallel to the tail orientation axis (N) Fy = Force measured by load cell perpendicular to the tail orientation axis (N) ???  = Maximum half pitch axis heave amplitude (m) ? = Instantaneous half pitch axis heave amplitude (m) ?p = Propulsive efficiency of tail (dimensionless) l = Characteristic length (m) mcl =Mean chord length (m); 0.0328 for tail models xv  MR = motion regime number Q CT (SB) = Quasi-static theoretical coefficient of thrust for SB tail model (dimensionless) Re = Reynolds number (dimensionless) S  = Planform area of tail (m?); 0.007 m2 s  = Span length of tail (m); 0.54 for caudal fin, 0.2 for tail models. ??  = wetted surface of body (m?); SB = Stiff tail model in both spanwise and chordwise directions Strod = Strouhal number of pitch axis (dimensionless) Sttip = Strouhal number of tail tip (dimensionless) t  = Time (s) T = Thrust (N) U  = Free stream water velocity (m/s) ? = Kinematic viscosity (m?/2); 1.004?10?? for freshwater at 20? Vhmax = Maximum rod heave velocity (m/s) V?max = Maximum pitch velocity (rot/s)  ?  = Instantaneous angle of attack (deg in text and rad in calculations) ???  = Maximum angle of attack (deg in text and rad in calculations)  ? = Relative flow angle (deg in text and rad in calculations) ?  = Instantaneous pitching angle (deg in text and rad in calculations) ???  = Maximum pitching angle (deg in text and rad in calculations) ? = Density (kg/m?); 998.2 for freshwater at 20? xvi  ? = Phase shift by which pitch waveform leads heave waveform (deg in text and rad in calculations) ?  xvii  Acknowledgements I would like to specially thank my academic dad, Dr. Bob Shadwick, for having accepted me to become part of the Lab. This has allowed for many life-changing friendships and amazing experiences in beautiful British Columbia! Many times Bob surprised me with his kindness, trust and generosity. I am very grateful for this student-supervisor relationship he naturally invite to and the friendship that has developed. I?m so glad we met in Bamfield and thankful to the BMSC staff for creating these wonderful opportunities!  Thanks to Dr. John Gosline, Dr. Doug Altshuler and Dr. Peter Oshkai for taking the time to serve on my thesis committee. Thanks to Micha Ben-Zvi, who introduced me to this field of research. Thanks to John Gosline, Margo Lillie and Ken Savage for being available to lend me their ears when I came to their office with a question. Thanks to Trisha Clark and Benny Goller, my office mates, for their help and for enduring the random sounds and songs that come out of my mouth almost unconsciously when I?m happy. Thanks to James Whale for editing the thesis. Thanks to the past and present comparative physiology group and the zoology staff for the awesome West Coast warm work environment that I experienced.  I am grateful to Dr. Peter Oshkai, Oleksandr Barannyk and the rest of the lab who responded joyfully to the idea of me coming to work at their fluid mechanics laboratory and gave me a warm welcome (Department of Mechanical Engineering, UVIC). Oleksandr introduced me to the motion and force system he had developed for his MSc, helped to obtain the quasi-static data in September 2012 and provided LabVIEW programs he had written to record the force data. Later on I received help from Andrew Richards, who was doing similar research and also needed to upgrade the motion system to meet the faster motions and motion control needs. Andrew was an amazing help in designing, ordering, installing and testing the new motion xviii  system. I?m tremendously thankful we were together working long hours over the course of several trips made to UVIC between January to May 2013 to obtain an operational motion and force system. It made the time enjoyable and I could not have done it without him. PIV data collection would not have been possible without both of them. Thanks to both also for helping with engineering questions and for the many lunch breaks at Fujia, the official brain pause sponsor.  Thanks to Tony MacDonald for his generosity in providing the tuna caudal fins (Tony?s tuna fishing charter, PEI), Pierre-Yves Daoust and Darlene Weeks for carefully packing and shipping the frozen bluefin tuna caudal tails to UBC (Atlantic Veterinary College, PEI), Gabor Szathmary for making the CT scanning enjoyable (FPInnovations, BC), Rob Greer for providing excellent customer service with the 3D printing (Javelin Technologies Inc., Ontario), Bruce Gillespie for making the rods and welcoming me in my many visits with a smile (Zoology Mechanical Workshop, UBC) and Jim Wiley for the troubleshooting of the motion system (Parker Hannifin Corporation, CA). Finally to my parents who have shown me their love and trust since I can remember and wherever I am, I am eternally grateful. xix   Dedication To my friends and family whose presence reminds me of what truly makes me happy!  Vive la vie!  1  1 - Introduction Thunniform swimmers are marine animals, such as tunas, lamnid sharks and whales, which are grouped together as they share similar morphological characteristics and propulsion mode (thunniform propulsion) (Bernal et al., 2001; Donley et al., 2004). Interestingly, these animals with similar characteristics have evolved independently and are a classic case of convergent evolution, as the last common ancestor to today?s bony and cartilaginous marine animals lived in the Silurian Period some 410-438 million years ago (Bernal et al., 2001). As thunniform swimmers are some of the fastest sustained swimming animals, it is believed continuous fast swimming demands acted as the main selection pressure on the ancestors of todays thunniform swimmers, which resulted in adaptations to surpass previous hydrodynamic limitations (Borazjani and Sotiropoulos, 2010; Graham and Dickson, 2000). The mechanical design of thunniform swimmers stands out from other marine animals and includes several modifications for exceptional swimming performance (Bernal et al., 2001; Westneat and Wainwright, 2001). Some of the adaptations include a streamlined body with a narrow necking of the caudal peduncle, a high aspect ratio, stiff, lunate caudal fin, which generates lift-based thrust, and body undulations restricted to the posterior 1/3 portion of the body (Fig.1) (Bernal et al., 2001; Sfakiotakis et al., 1999). These characteristic features are believed to decrease the propulsive cost to oscillate the tail by shifting the muscle mass forward, which minimizes the inertia of the caudal peduncle and reduces the lateral momentum of water displaced by the caudal peduncle. In the overall mechanical cost to move the fish, it is thought that the inertial cost to move the tail (with fast reversals of the tail?s direction of motion), is higher than the drag cost (Webb, 1992). The body is relatively stiff due to the dense muscle mass and high blood pressure, which allows the body to remain streamlined at higher velocities 2  (Bushnell and Jones, 1994). In addition, it is believed that the function of the caudal keel is to provide a more hydrodynamic shape to the caudal peduncle (Westneat and Wainwright, 2001) and a vertical lift generating surface to counter the negative buoyancy (Magnuson, 1978). Also for tunas the first dorsal fin can totally retract in the body dorsal groove and the pectoral fins can flatten along the pelvic depression (Westneat and Wainwright, 2001).  It is clear thunniforms can generate high levels of positive thrust to power their fast swimming, but it is not clear at what cost. Hydrodynamic propulsive efficiency, or simply propulsive efficiency, is the ratio of the power to move the fish forward by the power expended to move the whole body in all directions. The power expended to oscillate the body does not include the digestive, muscle or other internal body efficiencies. It is simply the power to move the body through the water. High propulsive performance is defined here as the combination of high thrust generation and high hydrodynamic propulsive efficiency.  Biological studies have shown that tunas have a higher gross cost of transport, which is the energy or work (J) expended per mass (kg) per meter (m), than mackerels and bonitos (also members of the Scombridae family) of similar shape but of carangiform swimming mode (Sepulveda and Dickson, 2000). One reason for this is that tunas have a higher resting metabolic cost (2 to 3 times more). When looking at the net cost of transport, that is taking into account the resting metabolic rate, the tunas and the other non-thunniform scombrids had similar values (Korsmeyer and Dewar, 2001; Sepulveda et al., 2003). This suggests the thunniform propulsion mode does not increase the hydrodynamic propulsive efficiency, and might have evolved rather as a consequence of the red muscle arrangement in tunas to conserve metabolic heat (red muscle shifted closer to vertebral column) (Dowis et al., 2003). For the same cost of transport, one animal could be spending most of the energy on locomotion, whereas the other one could spend a fraction of the cost on 3  locomotion and the rest on growth and reproduction. Therefore it is not clear if thunniform aquatic animals have higher propulsive performance than other swimming animals. In the engineering community it is commonly assumed that thunniform propulsion exhibits the highest propulsive efficiency, due to the exceptional performance of thunniform swimmers (Sfakiotakis et al., 1999). This has led to many theoretical models (simple quasi-static models to complex CFD models) and experimental testing of thunniform ?robots? and other oscillating hydrofoil experiments (Rozhdestvensky and Ryzhov, 2003). Bio-inspired engineers have sought to mimic in their designs useful mechanisms present in living organisms that have been optimized by millions of years of evolution, as these can be successful or at least ?good enough? solutions to a certain problem that both living organism and engineering design have to deal with. Underwater robots for visual display, pollution and environmental monitoring, and defense and surveillance have been the main end goal of such research (e.g. ghostswimmer and BIOSwimmer, Boston Engineering Corporation's Advanced Systems Group (ASG); AquaRay, Festo Ltd.). Other interests in thunniform caudal fins have come from high performance bio-inspired snorkeling fin designers (e.g. Cetatek Product Inc. in Vancouver, BC) and animal prosthetics designers (Fuji dolphin (Japan) and Snowy dolphin (USA), which inspired the ?Dolphin Tale? movie). Some ?tuna-like? oscillating hydrofoils have received much attention as they were shown to compete or even outperform the conventional rotational propellers at lower speeds (Prempraneerach et al., 2003). One study on a rectangular rigid hydrofoil (60 cm span and 10 cm chord length) of NACA cross sectional shape reported propulsive efficiencies of 85% for a coefficient of thrust of 0.78 (Anderson et al., 1998). With the same setup others confirmed high propulsive efficiencies of 64% for a high coefficient of thrust of 0.62 (Hover et al., 2004). A 4  conventional propeller at that level of propulsive efficiency (85%) has a coefficient of thrust that is 4 times less than the one measured in Anderson?s study.  Although they are valuable for comparison, the goal for these studies was not to imitate the animal. The ?caudal fins? were rigid rectangular hydrofoils oscillating at frequencies and speeds far too low, given the size of the foil, in order to mimic biologically relevant tuna motions (hmax = 15 cm, U = 0.4 m/s and f = 1Hz (Anderson et al., 1998); hmax = 20 cm, U = 0.3 m/s and f = 0.5 Hz (Hover et al., 2004)). Most engineering studies investigating the propulsive performance of thunniform have oversimplified the experimental system (Lauder et al., 2011; Tangorra et al., 2011). Single components have been studied at a time (shape, chordwise or spanwise flexibility) rather than their interaction. In addition the majority of ?thunniform? motions performed were not biologically relevant (Shimizu et al., 2004). Many theoretical models are also questionable for diverse reasons, such as multiple assumptions (boundary layer state and separation) and simplifications (tail shape, deformation, motion and wake interaction)(Guglielmini and Blondeaux, 2004; Sfakiotakis et al., 1999). For example, Lighthill?s elongated-body theory is only valid for animals that have a small aspect ratio, a body cross section that does not change abruptly and is not too elongated (Lighthill 1971, Eloy 2012), and small amplitude tail-beats (Candelier et al 2001). Another way to estimate the propulsive performance other than mechanical and theoretical models is by quantifying the wake structures behind the swimming animal using planar or volumetric particle image velocimetry (2D PIV or 3D PIV). Unfortunately it is especially difficult on live thunniform swimmers and has not been performed. In this study the propulsive performance of thunniform swimmers was assessed by dynamic experiments on tail models mimicking, with high bio-fidelity, the caudal fin of the 5  Atlantic bluefin tuna, Thunnus thynnus, as a case study for thunniform propulsion. The Atlantic bluefin tuna is an exceptional fish and believed to be a top candidate within the thunniform swimmers for high propulsive performance due to the following characteristics. It undergoes long migrations across the Atlantic, from off the coast of North Carolina all the way to the Mediterranean Sea (about 8000 km) in as little as one month (Block and Stevens, 2001). In Greek the word ?Thynno? means ?to rush?, which further highlights this point. Being a pelagic fish where preys (fish, squid and crustaceans) can be spatially distant requires active and continuous swimming for feeding success (Dewar and Graham, 1994). In addition, having negative buoyancy and being obligate ram ventilators obliges tunas to swim continuously (Brill and Bushnell, 2001).  6   Figure 1 - Thunnus thynnus  ?Jon?s Amadeo Lucas (http://www.flickr.com/photos/theanimalday/6996512012/). CC BY 2.0 In addition to swimming at fast steady speeds, it seems tunas can accelerate to speeds relatively close to the physical limit imposed by fluid mechanics. Indeed, it is hypothesized that for lunate caudal fin animals, cavitation occurs above speeds of 10 to 15 m/s, which would damage the fin and cause loss of hydrodynamic force due to stall (boundary layer separation over the fin) (Iosilevskii and Weihs, 2008). Previous underwater observations of accelerating bluefin tuna swimming in sea pens support this hypothesis as clicking sounds matching the tail-beat frequency were heard, which might suggest cavitation (Pers. Com. Chris Harvey-Clark 2012). To power such swimming performance, tunas operate at high rates of standard and active metabolism, aerobic capacity, heart rate and gut clearance (Bernal et al., 2001; Graham and Dickson, 2004). They have a high metabolic cost to osmoregulate, due to their very large gills (7 7  to 9 times higher surface area relative to the gill size of trout) and thin blood-water barrier (Bushnell and Jones, 1994). These adaptations contribute to the fast life pace of tunas, which allows for fast growth that leads to early and high reproductive success (Brill, 1996; Pauly, 1989). It is interesting to note that tunas are also quite similar to whales in that regard, as both employ this life strategy where they will expend high metabolic energy to swim continuously for migrations that are favorable for feeding and reproductive success (Graham and Dickson, 2004). The hydrodynamic propulsive efficiency is probably one of the processes that is most plastic and can be most easily altered and optimized to improve the overall propulsive efficiency (conversion efficiency for food intake to movement). Therefore, as the gross cost of transport is already very high in tunas, selection for more efficient propulsion is probably stronger than other selective pressures. In this project only the caudal fin is modelled to investigate the propulsive performance of the Atlantic bluefin tuna. Not including the rest of the body certainly limits the accuracy of the biological significance of this study. Indeed, it was observed for different fish, such as trout, bluegill, eels and mackerel, that the water flow interacts with the body and appendages before interacting with the caudal fin (Fish and Lauder, 2006; Flammang et al., 2011; Liao, 2003; Liao, 2007; Nauen and Lauder, 2002; Tytell, 2006; von Ellenrieder et al., 2008). The water flow disturbance caused by the body preceding the caudal fin can enhance the propulsive performance of the fish, as the energy from the vortices shed from the body can constructively interact with the tail (Beal et al., 2006; Fish and Lauder, 2006; Flammang et al., 2011; Nauen and Lauder, 2001; Nauen and Lauder, 2002; Triantafyllou et al., 2000). In addition, in the case of the chub mackerel, Scomber japonicus, a scombrid fish with somewhat similar body shape as the tunas, the finlets positioned posteriorly to the second dorsal fin and ventral anal fin were shown to help 8  direct the flow to the caudal peduncle keel and over the tail (Nauen and Lauder, 2001; Nauen and Lauder, 2002).  Due to the extreme difficulty to reproduce such complex structures and deformation behaviours of the fish body, it is not evident that the physical model of the body in front of the tail would provide higher bio-fidelity. In addition, the caudal fin for tunas is the primary propulsive structure, generating more than 90% of the total thrust (Fierstine and Walters, 1968; Syme and Shadwick, 2002). Caudal amputation experiments have shown the thrust generation is not transferable to other parts of the body (Fierstine and Walters, 1968).   This study directly investigated the propulsive performance of the caudal fin of the Atlantic bluefin tuna, as an indicator of the whole animal propulsive performance. This study also tested tail models with different motion kinematics and passive deformation behaviors, in order to assess the relative contribution and sensitivity of these parameters on the propulsive performance. The caudal fins of swimming animals exhibit great variation in bending behavior, however, the propulsive benefit of having a flexible or stiff caudal fin is not well understood (Esposito et al., 2011; Lauder and Madden, 2007; Lauder et al., 2007; Prempraneerach et al., 2003). Previous theoretical and experimental investigations have reported that under proper motion and bending behaviour of the hydrofoil, an increase in propulsive efficiency with only a small decrease in thrust is achieved when using a flexible foil compared to a rigid one (Barannyk et al., 2012; Katz and Weihs, 1978; Liu and Bose, 1997; Prempraneerach et al., 2003; Takada et al., 2010). We hypothesized the flexible tail models would have higher propulsive performance compared to the stiff tail model. To explore these objectives, the structure and passive bending behavior of an Atlantic bluefin tuna caudal fin was first characterized in order to reproduce high bio-fidelity tail models. Three tail models were made using a computed tomography scanner and 9  a polyjetTM 3-Dimensional printer. Two of the tail models had materials of similar properties to the in vivo measurements, and the other was relatively stiff. Data from previous studies on the caudal fin kinematics of the Atlantic bluefin tuna during steady swimming were used to actuate the tail models. Each tail model was actuated in a water tunnel by a computer controlled, motorized system to follow 30 motion paths typical for a tuna. Propulsive efficiencies and thrust coefficients were calculated from the forces and torque measurement for each motion regime. Flow structures were visualized by means of particle image velocimetry (PIV). In this thesis we summarize this work and the main findings, then present the conclusions and recommendations for future research.  10  2 - Background 2.1 The caudal fin Structure of the tuna caudal fin Previous research has thoroughly described the mechanical design of swimming in tunas and other teleost fish (Westneat and Wainwright, 2001), with particular attention to the structure of the caudal fin (Becerra et al., 1983; Lauder, 1989; Morikawa et al., 2008). Similar observations were made for the Atlantic bluefin tuna caudal fin that was dissected and examined in this study. Below is a summary of the key observations. Tunas, being part of the superclass Osteichthyes (bony fish) and class Actinopterygii (ray-finned fish), have a caudal fin composed mostly of bone and collagen fibers. Fin rays are embedded in collagenous filaments forming sheets of clear rubbery material (see Fig.2 B). Together the fin rays, the hypural plate and the collagen fibers form a structure that is responsible for the majority of the resistance to bending in both spanwise and chordwise directions of the caudal fin. The muscles are reduced compared to other fish tails (Fierstine and Walters, 1968), and therefore any muscle asymmetry between the upper and lower lobe is minimized, which leads to the assumption that the dorsal and ventral lobes of the tail are internally and externally symmetrical. The great lateral tendons connect the axial muscles, located anterior to the caudal peduncle, to the caudal fin. As the cylindrical great lateral tendons reach the hypural plate, they form a flat sheet of collagen fibers, called an aponeurosis, which connects to each fin ray. Therefore the fin rays are not fused to the hypural plate; rather, collagen fibers link the two together. On either side of the hypural plate the fin rays extend all the way to the tail tips, where they fuse (Fig.10). Fin rays that are easily identified to the naked eye are actually composed of several smaller rectangular beams (with a cross section of about 1mm wide 11  by 0.5 mm thick) that are fused together (Fig.2 D). A 1.5 cm wide fin ray is composed of about 14 smaller beams (Fig.2 C). There are approximately 22 distinct fin rays and 3 caudal flaps on either side of the hypural plate. The caudal flaps are modified fin rays that are wide, short, triangular in shape, and located at the middle of the trailing edge (Fig.11 (FC), Fig.8 A). The exact number of fin rays is difficult to count, as the fin rays closest to the leading edge are either fused together or arranged in higher density.  Fused fin rays are probably the result of higher calcification in that area or higher density of interlepidotrichial ligaments (Becerra et al., 1983). For all the fin rays, the cross-sectional area is oval shaped near the hypural plate and becomes wider, thinner, and rectangular in shape towards the tail tips and trailing edge. The caudal peduncle keels are composed of a thick layer of collagen fibers, rending them quite stiff.   Figure 2 - Fin ray details. (A) Area dissected on caudal fin. Scale bar = 10 cm (B) Collagenous filaments surrounding fin rays. A sheet of this clear rubbery material is peeled after removing the skin (in black). (C) The fifth fin ray from the leading edge is about 1.5 cm wide (indicated by tips of thumb forceps) and composed of about 14 small rectangular beams. (D) Small rectangular beams of cross section of about 1 mm wide by 0.5 mm thick are fused together to form a fin ray. Using a scalpel, individual beams can be separated. 12  Deformation behavior of the tuna caudal fin Several observations on swimming tunas in water tunnels have shown the tail tips can form a cupping shape (tips towards the direction of tail side motion), which is opposite to what one would expect from the passive deformation of the tail due to water resistance (Bainbridge, 1963; Brill 2013 personal com.). Other studies have shown the tail tips to stay aligned in the same plane with the hypural plate or to be slightly deflected in the direction of the flow (Fierstine and Walters, 1968; Gibb et al., 1999). It has been hypothesized that the interradialis muscle, posterior to the hypural plate, might provide active control of the compression of the span of the tail (Gibb et al., 1999). Also it seems the span could be expanded by the carinalis muscles that are linked by tendons on the first fin rays of both lobes of the tail (Fierstine and Walters, 1968; Westneat and Wainwright, 2001). Previous research observed active span control in chub mackerel, Scomber japonicas, (Scombridae family), where span was longest at mid-amplitude and shortest at max-amplitude, in order to maximize thrust and minimize drag, respectively (Gibb et al., 1999). In addition, for Scomber japonicas, the dorsal tail tip undergoes greater lateral excursion than the ventral tail tip, resulting in its homocercal tail deforming asymmetrically. This asymmetry could potentially generate upward lift, as it is the case on some heterocercal tails (Wilga and Lauder, 2004). The hypochordal longitudinalis muscle might be responsible for the abduction the dorsal lobe (Gibb et al., 1999). This muscle is very reduced or even absent in Thunnus species, suggesting it is a vestigial trait and that tunas cannot actively deform their caudal fin asymmetrically (Fierstine and Walters, 1968; Westneat and Wainwright, 2001). An alternative hypothesis for the mechanism of the dorsal-ventral asymmetry is that anterior musculature contractions are transmitted to the tail through the caudal peduncle to control the caudal fin asymmetry (Gibb et al., 1999). In addition, the dorsal and ventral flexors 13  might control the camber of the tail by abducting the caudal flaps (similar to the flaps on a wing of a plane) (Westneat and Wainwright, 2001). More research is necessary to determine if the mackerels and tunas have similar tail deformation behaviours and muscle function. In order to reduce complexity, the caudal fin deformation behaviour of the Atlantic bluefin tuna was assumed to be passive, thus tail models were made with no active fine control of the tail shape.  Previous caudal fin models: The tail models in this study are different from previous inspired tuna tail models, as the approach here was to generate a high bio-fidelity tail model, rather than a simplified or optimized one. Previous tail models have excluded major biomechanical structures. The usual approach has been to investigate the effect of one or few components at a time, such as chordwise flexibility ((Park et al., 2012; Prempraneerach et al., 2003)) or spanwise flexibility (Liu and Bose, 1997) or shape (Low and Chong, 2010; Park et al., 2012). We believe the interaction of multiple components is what allows the complex deformation behaviour of the tail and therefore we attempted to accurately mimic the tuna caudal fin. Up until now, the tuna-inspired physical caudal fin model with the highest bio-fidelity seemed to be a lunate deformable wing made with a brass rod at the leading edge and covered with a rubber skin (Morikawa et al., 2001). The MIT ?Robot tuna? tail model had the correct shape but was totally rigid (and also actuated for a carangiform swimming mode)(Barrett et al., 1996). One study incorporated fin rays in a caudal fin model; however, it mimicked the caudal fin of the Bluegill sunfish, Lepomis macrochirus, which has a very different internal and external structure with more bending than the caudal fin of a tuna (Esposito et al., 2011). 14  The structure and deformation behavior of the caudal fin were replicated to our best attempt in the tail model. Of course due to the amazing morphological complexity of the caudal fin, it is impossible to replicate a tail model with every detail present; rather, key morphological features responsible for most of the deformation behavior of the tail were identified and mimicked in the tail model. These included the complex bone structure and surrounding fleshy matrix (mimicking the summed effects of collagen fibers, tendons and muscles). To our best knowledge this study is the first to include detailed internal structures, such as fin rays, which provide higher bio-fidelity in the shape and bending behaviour of the tail models.  2.2 Swimming kinematics Two of the defining characteristics for members of the thunniform propulsion group are a stiff high aspect ratio lunate caudal fin, which generates lift-based thrust, and body undulations restricted to the posterior 1/3 of the body (Donley et al., 2004; Sfakiotakis et al., 1999). The caudal fin undergoes heaving (lateral motion) and pitching (rotation along the dorsoventral axis) simultaneously. The kinematics of the caudal fin can be partitioned and described using five parameters: swimming speed, tail-beat frequency, heave waveform, pitch waveform, and phase shift between the heave and pitch motions.  Before defining these parameters and their relationships to each other, a brief explanation of how forces are generated by fluids in motion is presented.  2.2.1 Force generation To generate hydrodynamic forces, the fluid and tail need to be in motion relative to each other. For a fish swimming in a straight line, the local flow over the tail is the resultant of two 15  flow vectors. These are the flow of opposite and equal velocity to the fish forward motion and the lateral flow opposite and equal to the tail heaving motion (Fig.3).    Figure 3 - Hydrodynamic force generation at the pitch axis on a cross section of the caudal fin from the top view. The resultant flow encounters the tail at a certain angle of attack, ??, and then curves around the tail, as seen with the blue streamlines. A hydrodynamic force is generated. This force also called resultant force can be resolved in a pair of hydrodynamic forces. Lift and Drag are respectively perpendicular and parallel to the direction of the resultant flow.  There are two equally valid ways to understand how the hydrodynamic force is generated, otherwise stated as the resultant force (Fresultant) (Fig.3 and 4). The first one is based on pressure variation around the tail. As the resultant flow approaches the tail, the parallel ? "Flow opposite to heave Flow opposite to fish motion Lift FResultant Drag 16  streamlines representing the flow motion (in blue) are curved around the tail. When a fluid follows a curved path, it results in a pressure gradient perpendicular to the flow direction. The faster the flow over the curved surface, the lower the pressure, as stated by Bernoulli?s principle. If there is a pressure differential between both sides of the tail, it results in a force on the tail directed from the high pressure side to the low pressure side. That is the hydrodynamic force. The second way to understand the generation of this force is based on velocity variation. Newton?s 3rd law of motion states that for every force there is an equal and opposite reaction force. Consequently, as the water flow surrounding the tail is deflected by the action of the tail, then the surrounding flow exerts an equal and opposite force on the tail. That is the hydrodynamic force. The hydrodynamic force can be resolved into two perpendicular forces. Lift is the component of the hydrodynamic force that is perpendicular to the oncoming local flow direction of the fluid, otherwise stated as the hydrodynamic flow. The drag is the component of the hydrodynamic force that is parallel to the oncoming resultant flow. The angle of attack, ?, is the angle between the direction of resultant flow and the tail orientation. The magnitude and direction of the hydrodynamic force is dependent on the angle of attack, as well as the resultant flow velocity and the shape of the tail. The angle of attack, ??, can be defined by two other angles (Fig.4): ? ? = ? ? ? ??(?) Eq. 1 where the pitch angle, ?, ?is the angle between the thrust axis, which is the axis of the fish direction of travel, and the tail orientation. The pitch angle rotates about the vertical axis and is 0? when the leading edge is oriented into the thrust axis. The relative flow angle, ?, is the angle 17  between the thrust axis and the resultant flow direction. More will be said about these angles and forces in the following sections (Pitch waveform and Force system).   Figure 4 - Hydrodynamic force generation at the pitch axis on a cross section of the caudal fin from the top view. The hydrodynamic force or resultant force can be resolved in three pairs of forces. The hydrodynamic forces (Lift and Drag in pink) are respectively perpendicular and parallel to the direction of the resultant flow. The load cell forces (Fy and Fx in orange) are respectively perpendicular and parallel to the tail orientation axis. The forces of interest (FLat in green and T in blue) are respectively perpendicular and parallel to the fish direction of travel, the thrust axis. The positive and negative signs refer to the direction of the same coordinate system for both forces and motions. Torque and pitch follow the same coordinate system: positive in the clockwise direction. It should be noted that the hydrodynamic force is exerted from the center of pressure. This center of pressure changes position as the modification of the angle of attack causes the pressure distribution around the tail to change. Therefore when the center of pressure is not Thrust axis ? ()"? (+)"FResultant Lift Fy Torque +"+"#"#"FLat T Drag Fx Lateral axis ?!(+)!18  located at the pitch axis, which is most often the case, it results in a torque in addition to the forces measured at the pitch axis. In the same reference frame, compared to a force, a torque causes the tail to rotate around the reference center, here the pitch axis, as the torque is a force that is applied at a distance away from the pitch axis. The positive and negative signs refer to the direction of the same coordinate system for forces, torque and motions used throughout this study (Fig.4).  2.2.2 Literature requirements The literature on bluefin tuna and for other tunas was reviewed to retrieve kinematic and force data during steady swimming. The kinematic data was used to define and assign realistic values to the possible swimming motion parameters. The force data were used to estimate the required amount of thrust generated by the tail to balance or outweigh the total drag on the fish.   2.2.2.1 Swimming parameters and realistic test range As previously mentioned the kinematics of the caudal fin can be partitioned and described using five parameters: swimming speed, tail-beat frequency, heave waveform, pitch waveform, and phase shift between the heave and pitch motions.  The following sections define these parameters and their relationships to each other.  2.2.2.1.1 Swimming speed  It is commonly assumed migrating animals locomote at speeds (Uopt) corresponding to their minimum gross cost of transport (GCOT) (Videler and Wardle, 1991). That is the minimum energy or work (J) expended per mass (kg) per meter (m). GCOT is calculated by dividing the 19  metabolic rate (M?? ?estimated from oxygen consumption) by the swimming speed (U). The minimum GCOT (1.23 J/kg/m) for pacific bluefin tunas (n = 6, BL = 74? 3 ?cm) swimming in a swim tunnel occurs at speeds between 1.15 to 1.3 BL/s (Blank et al., 2007). The unit for speed is described body length per second, which scales swimming speeds for animals of different sizes. The body length measurement for swimming animals with crescent caudal fins, like tunas, is usually the fork length, which is the length from the snout to the middle of the trailing edge of the caudal fin. In the wild, migrating Pacific bluefin tuna of similar size (80 to 120 cm) have sustained mean speeds of 1 to 1.34 BL/s, accounting for both horizontal and vertical trajectories (Marcinek et al., 2001). For a 70 cm BL bluefin tuna that is equal to 2.5 to 3.4 km/h. These studies support the common assumption that migrating tunas swim close to their minimum GCOT speed.  Reynolds number, Re, is an important dimensionless parameter used to describe the flow condition (Vogel, 2013). The Re is a measure of the ratio of inertial forces to viscous forces: ?? = ???  Eq. 2 where l is the characteristic length of the object (m)(the tail?s mean chord length, mcl = 0.0328 m), U is the incoming water velocity (m/s) and ? is kinematic viscosity of the water (m2/s). Ranges of Re are related to certain types of flow condition. Reynolds numbers typically associated with turbulent flow are above 105. For this study, two speeds were chosen: 1 and 1.5 BL/s. The Reynolds number for the tail models was 22,900 when at 1 BL/s and 34,300 when at 1.5 BL/s. Since in all tests the flow was at Reynolds numbers below 105, the hydrodynamic force was assumed to change monotonically for the same motion regime between 1 and 1.5 BL/s. In 20  other words, as there should be no change in the flow condition within this range of flow speeds, an intermediary speed would be assumed to generate an intermediary hydrodynamic force. Therefore there was no need to test more swimming speeds in between these two outermost values of the biologically relevant sustained swimming speed range.   2.2.2.1.2 Tail-beat frequency Tail-beat frequency is strongly correlated with swimming speed (BL/s). There are several studies that provide linear equations relating swimming speed of thunniform swimmers to tail-beat frequency (Altringham and Shadwick, 2001; Blank et al., 2007; Dewar and Graham, 1994; Fish, 1998; Knower et al., 1999). The Atlantic bluefin tuna, Thunnus thynnus, is very similar to the Pacific bluefin tuna, Thunnus orientalis. These two species of bluefin tunas are so similar they used to be classified as the same species, then as subspecies, until they were recognized as separate species (Collette et al., 2001). In this study some morphological and kinematic data were only available for the Pacific bluefin tuna, and were therefore assumed to also be true for the Atlantic counterpart. The linear equation of Blank et al. (2007) was used in this study to provide tail-beat frequency given a swimming speed. It was originally calculated for Pacific bluefin tuna at speeds between 0.75 to 1.8 BL/s and for body lengths between 70 and 78 cm, which includes the body length and swimming speeds of this study.  TB ? =  ?1.178 ? ?x ? ?U ? +  ?0.768 ? Eq. 3  Where TB is tail-beat frequency (Hz) and U is swimming speed (BL/s), with R? = 0.87 and n = 34. The tail-beat frequency at 1 and 1.5 BL/s is respectively 1.95 and 2.54 Hz.   21   2.2.2.1.3 Heave waveform and Strouhal number In tuna and aquatic animals in general, the maximum caudal fin amplitude shows no correlation with speed or frequency (Altringham and Shadwick, 2001; Bainbridge, 1958; Wardle et al., 1989). Maximum amplitude (Amax) in biological swimming kinematics studies and in this thesis refers to tail tip amplitude, which is the maximum lateral displacement of the tip of the tail during each tail-beat. For fish in general during steady swimming, Amax is 13 to 21% of BL (Bainbridge, 1958; Webb et al., 1984). For Atlantic bluefin tunas swimming in a sea cage at speeds between 0.6 and 1.2 BL/s, the Amax varied from 7.7 to 23.5% of BL (Wardle et al., 1989).  For this study, we set Amax as 10 to 20% of the calculated body length. Another parameter, the Strouhal number (St), was used to set specific values of Amax for each motion regime. St is a dimensionless number describing oscillating flow mechanisms (Triantafyllou et al., 1991). ?? = ? ?? ??? = ? ?? ????? = ? ??  Eq. 4 Where A is the maximum amplitude (m), f is the tail-beat frequency (Hz), U is the swimming speed (m/s) and d is the distance the fish travels f number of times per second for a constant U (m). Technically the characteristic length used to calculate the Strouhal number is the width of the wake of the tail; the width of the wake is usually approximated by the maximum amplitude of the oscillation (A) (Triantafyllou et al., 1993). The maximum amplitude (A) in biological studies is usually the caudal fin maximum tip-to-tip displacement (Amax), as it is easier to measure than the maximum pitch axis heave amplitude (2?hmax) (Fig.5). On the contrary, in engineering studies it is easier to measure 2?hmax than Amax, as the motion system actuates the 22  foil at the pitch axis. Therefore Sttip (with A = Amax) is reported in the biological literature and Strod (with A = 2?hmax) in the engineering literature.    Figure 5 ? Caudal fin motion and Strouhal number. The gray dashed arrow is the thrust axis pointing in the swimming direction. The curved black solid line is the tail tip waveform and the curved red dashed line is the pitch axis waveform. Red dot is the pitch axis and black dot is the tail tip. When the pitch axis is at the most lateral position, the tail orientation is parallel to the thrust axis. The mean relative flow angle during one stroke (?) is positively correlated with the Strouhal number. The straight blue arrow is the mean water direction during a stroke. It is dependent on the position of the vortices (blue circles) and therefore depends on the Strouhal number. As we previously mentioned, the Strouhal number is a ratio of speeds or distances. There is another swimming parameter that is dependent on this same ratio; the mean relative flow angle during one stroke (?) is calculated as the inverse tangent of the time-averaged lateral flow at the pitch axis (2???? ??) divided by the incoming flow (U). That is the same ratio of speeds as used for the Strod calculation. Therefore ? is the inverse tangent of Strod, where low ? corresponds to low St and vice versa. Researchers have found there is a trade-off between propulsive efficiency and thrust generation, which can be explained by St (Triantafyllou et al., 1993). Low St and consequently low ? corresponds to high propulsive efficiency, as there is not much energy lost to the lateral flow, which does not contribute to forward movement. Indeed the lateral distance between vortices of alternating signs is relatively small compared to the distance along the thrust axis, resulting in a mean water jet direction that is oriented closer to the thrust axis than the lateral axis. (Fig.5). At high St and ? the efficiency drops, as more energy is lost to 23  lateral flow. On the other hand, the thrust is maximally extracted from the fluid. Indeed the lift vector, which is perpendicular to the resultant flow, is further oriented towards the thrust axis, and thereby has a larger thrust component. Interestingly the great majority of animals that flap their fins or wings do so at Sttip in the range of 0.2 ? 0.4, which suggests evolutionary pressures for efficient oscillating propulsion (Eloy, 2012; Taylor et al., 2003). Indeed this Strouhal range is optimal to reduce the inertial cost to move the tail (according the elongated body theory (Eloy, 2012)) and energy loss in the wake (Triantafyllou et al., 1993).  For tunas, Sttip is typically between 0.25 and 0.3 (Eloy, 2012). However these values have been mostly calculated for a fish swimming in water tunnels and tanks, where the fish might reduce its tail heave amplitude. Therefore in this study the Sttip values tested were 0.25, 0.3 and 0.35. Knowing Sttip, swimming speed and tail-beat frequency for each motion regime, specific values for maximum tail tip amplitude (Amax) could be calculated. The maximum tail tip amplitude (Amax) was converted to the maximum pitch axis half amplitude (hmax), as the motion system actuated the tail at the pitch axis. An iterative algorithm was written to find the hmax that, for specific parameters of the motion regime, would result in Amax.  In addition, maximum pitch axis heave amplitude (2???? ) ?was always more than 5 cm for all motion regimes, which is realistic and in agreement with a study on Yellowfin tuna (Thunnus albacares) where 2????  was 7-9% of BL at 1 BL/s (Dewar and Graham, 1994). In our study, the minimum ?2????  was 6.5 cm and the maximum was 12.8 cm. The maximum pitch axis heave amplitude (2???? ) ?was always less than the maximum tail tip amplitude (Amax). 24  The caudal fin heave motion undergoes symmetrical strokes, such that the waveform resembles a sinusoidal wave (Fierstine and Walters, 1968; Knower et al., 1999). Therefore the motion system actuated the tail at the pitch axis using the following formula: ? ? =  ????? sin(??) Eq. 5 where h(t) is the instantaneous location of the tail pitch axis, ?? ?  is the maximum half pitch axis heave amplitude, ? is the angular frequency and ? is time.  2.2.2.1.4 Pitch waveform Active control and waveform of the tail pitch angle or angle of attack during swimming has not been well documented in the fish literature. One study has looked at changes of the angle of attack of the caudal fin of the wavyback skipjack tuna (Euthynnus affinis)(Fierstine and Walters, 1968). This study by Fierstine and Walters in 1968 in its whole is excellent, but because of technical limitations, the accuracy of the angle of attack oscillation measured during a tail-beat is quite low. Additionally, and more importantly, these observations were for fast starts, where the kinematics is very different than during steady swimming. Hence, their data was not used in this study. Tunas have a double hinge mechanism in the caudal vertebrae, which allows control of the pitch angle of the tail (Fierstine and Walters, 1968; Westneat and Wainwright, 2001). The first pitch axis is anterior to the caudal peduncle and the second one is posterior to the caudal peduncle, between the last vertebra and the hypural plate (Dewar and Graham, 1994; Dowis et al., 2003; Fierstine and Walters, 1968). 25  Engineering studies have shown that sinusoidal pitch and heave motions, when at high St and high maximal angle of attack (??? ), can result in complex angle of attack waveform containing higher harmonics (Hover et al., 2004; Read et al., 2003). Angle of attack waveforms with higher harmonics are detrimental to the propulsive performance, as the number of peaks in the angle of attack profile for a tail-beat is related to the number of vortices shed in the wake (Guglielmini and Blondeaux, 2004; Hover et al., 2004). Too many shed vortices diminish or even prevent the occurrence of a reverse von k?rm?n vortex street wake (Hover et al., 2004). The reverse von k?rm?n vortex street wake is formed by constructive interaction between the leading and trailing edge vortex to form a propulsive jet and is characteristic of positive thrust generating foil kinematics (Guglielmini and Blondeaux, 2004; Triantafyllou et al., 1993). One study by Prempraneerach et al., 2003, compared the propulsive performance when performing the same motion kinematics, except for the pitch motion, where one motion regime was with a harmonic angle of attack waveform and the other was with a sinusoidal angle of attack waveform. For the same parameter range as the motion regimes tested in our study the sinusoidal angle of attack motion had a 20% increase of the coefficient of thrust and nearly no change in propulsive efficiency, for both flexible and rigid foils (see figures 12 and 13 of Prempraneerach et al., 2003, with Strod = 0.25 and ???  = 30). It seems reasonable to assume that fish control the caudal fin pitch waveform to result in a sinusoidal angle of attack waveform, as it results in higher propulsive performance than if the angle of attack waveform contained higher harmonics (Hover et al., 2004; Read et al., 2003). If we assume that fish can sense the propulsive force they generate, then they might be able to adjust their kinematics to generate the most thrust at a certain propulsive efficiency.  26  The sinusoidal oscillation of the angle of attack can be enforced by modifications of either or both pitch and heave motion (Hover et al., 2004). In this study, the pitch waveform was controlled to ensure a sinusoidal oscillation of the angle of attack for all motion regimes. For low Strouhal numbers (e.g. Sttip = 25) and high maximal angle of attack (e.g. ??? = 30?) the pitch waveform became increasingly bimodal with distinct peaks (Fig.6).  The 6 motion regimes with the highest angle of attack (???  = 30?) out of the 30 motion regimes had a bimodal pitch waveform for every stoke of the tail-beat. Other pitch waveforms were flattened compared to a sinusoidal pitch waveform of same maximal pitch angle. Contrary to Hover et al. 2004 and from an energy conservation point of view, it seems more probable that the fish adjust pitch rather than heave to make the angle of attack sinusoidal, as the power to reverse the movement of the posterior end of the body and surrounding fluid is surely greater than reversing the pitch angle. Precise adjustment of the tail pitch angle could be accomplished via the anterior musculature contractions transmitted to the tail through the caudal peduncle (Gibb et al., 1999; Westneat and Wainwright, 2001).   27   Figure 6 - Pitch waveforms to generate sinusoidal angles of attack. Solid curves are motion regimes pitch waveforms and dashed curves are sinusoidal angle waveforms of the same maximal angle for comparison. Only one stroke of the tail-beat is shown (50 to 100%). (A) For motions with a maximum angle of attack, ? ?? , of 30?, at Sttip =35, 30 and 25 respectively from top to bottom. (B) For motions with a Strouhal number, Sttip, of 25, at ? ?? =10, 15, 20, 25 and 30? respectively from top to bottom.  28  For all motion regimes, the pitch profile was calculated in such a way as to make the angle of attack sinusoidal (Fig.7):  ? ? = ? ? + ??(?) ? Eq. 6 with: ? ? =  ???? sin(?? ?  ??) Eq. 7 ? ? =  ? tan?? ??(?)?  ? Eq. 8 where: ?? ? = ??? ? ? = ??? (???? sin ?? ) = ??? ? cos(??) Eq. 9 ?? ?  is the instantaneous velocity of the tail pitch axis (m/s), ? ?  is the instantaneous location of the tail pitch axis (m), ???  is the maximum pitch axis heave amplitude (m).  From these equations one can understand that it is the relative flow angle waveform (?) that is responsible for the pitch waveform being composed of higher harmonics. Indeed if ? was sinusoidal, then the pitch waveform would also be, as the angle of attack waveform is sinusoidal and all these angle waveforms are phase locked. 29   Figure 7 Angles waveform for motion 30 of relative flow angle, ? (dash curve), and pitch angle, ? (orange curve), to generate a sinusoidal angle of attack, ? (solid curve).  As previously mentioned, the maximum angle of attack during steady swimming is not reported in the literature for tunas. It was assumed that the mean angle of attack during a tail-beat would be in-between the optimal angle of attack for the highest coefficient of lift (CL of 0.56 when angle of attack was 35?) and the highest coefficient of lift to drag ratio (CL/CD of 5 when angle of attack was 6?) of the investigated Atlantic bluefin tuna caudal fin. These values were determined from the quasi-static testing on the caudal fin, which is described later on. Mean angles of attack of approximately 7, 11, 14, 18 and 21? (above 20? the lift coefficient starts to plateau, while the drag coefficient keeps rising (Fig.25)) were converted to maximum angles of attack by dividing by 0.707 (as with sinusoidal waveforms), which corresponded to 10, 15, 20, 25 and 30?. Interestingly these values corresponded to the recommended test range from previous 30  engineering studies, where highest propulsive performance occurred (Anderson et al., 1998; Hover et al., 2004; Prempraneerach et al., 2003; Read et al., 2003).  2.2.2.1.5 Phase shift Phase shift refers to the offset between the heave and the angle of attack waveforms. For all the studies on tuna swimming kinematics the tail tips are shown to always lag behind the peduncle portion of tail, or in other words the pitch angle always leads the pitch axis heave amplitude (Fig.5) (Dewar and Graham, 1994; Fierstine and Walters, 1968; Knower et al., 1999). There are no studies that have quantified the phase shift in tunas; however, experimental studies suggest that 90? provides highest propulsive performance (Hover et al., 2004; Prempraneerach et al., 2003; Read et al., 2003; Schouveiler et al., 2005) and one study on dolphins reported a phase shift of 90? (Fish and Hui, 1991). With a phase shift of 90? the pitch axis of the tail is at its most lateral position (hmax) when the angle of attack and pitch waveforms are at zero, which corresponds to the tail axis being parallel to the thrust axis (e.g. Fig.4 and 5). A phase shift of 90? was applied for all motion regimes.  31   2.2.2.1.6 Summary of motion regimes For this study 30 motion regimes were assembled within the parameter space, with 3 tail tip Strouhal numbers (Sttip), 5 maximal angles of attack (??? ) and 2 swimming speeds (U). Table 1 - Test parameter space for this study. Combination of these resulted in 30 motion regimes. Parameters Test values Speed of fish, U (BL/s) 1/1.5 Frequency, f (Hz) 1.95/2.54 Strouhal number at tip, Sttip 0.25/0.3/0.35 Maximum tail tip Amplitude, Amax (cm) 9 to 14 Maximum Angle of Attack, ???  (?) 10/15/20/25/30 Phase Shift, ?  (?) 90  2.2.3 Required thrust level A steadily swimming self propelled fish generates as much positive lift-based thrust as it experiences drag over one tail-beat. Therefore only motion regimes with a thrust force value equal or above to the overall body drag were biologically relevant. There are a few overall body drag estimates in the literature; Magnuson (1978) is probably the first to estimate the overall drag exerted on a swimming tuna. He calculated for a 44 cm BL skipjack swimming at 66 cm/s a coefficient of overall body drag (?? ? ??? ) value of 0.01, and showed that it holds relatively constant over a variety of speeds. The Re for the average size and steady swimming Atlantic bluefin tuna is from 105 to 107 (Eloy, 2012; Marcinek et al., 2001). Magnuson?s ?? ? ???  was 32  obtained by theoretical calculations and assumed laminar conditions over all parts of the body. The fluid and body deformation and vortex interactions are not included, which tends to result in overestimation of the total drag (Barrett et al., 1996). Thus the overall drag is most likely less than reported.  More recently Tamura (2009) estimated the ?? ? ???  for the Pacific bluefin tuna, Thunnus orientalis, which is very similar in shape to the Atlantic bluefin tuna (Collette et al., 2001). Computational fluid dynamics (CFD) of water flow over an accurate computer model of a bluefin tuna in motion (generated using a 3-Dimensional laser profiler) estimated the ?? ? ???  to be 0.008 for a tuna of 0.7 m BL swimming at 1.5 BL/s. This is in good agreement with the study conducted by Magnuson. In our study the ?? ? ???  of 0.008 was used to calculate body drag at 1 and 1.5 BL/s. Also from Tamura (2009), it seems tunas might change morphology as they grow in order to produce enough thrust to compensate for their body drag, without having to change much of the swimming kinematics. Indeed, as a tuna grows bigger the coefficient of body drag decreases and the coefficient of lift generation at the caudal fin increases, as the sweepback angle decreases and aspect ratio increases (Magnuson, 1978). However thrust force is not only dependent on the coefficients, but also on the surface areas. The body surface area increases much more than the caudal fin surface area. Hence overall the ratio of caudal fin thrust generation to whole body drag might stay the same for an adult and juvenile tuna (Tamura and Takagi, 2009). Above a body length of 0.5 m, these coefficients and morphological variables start to plateau (Tamura and Takagi, 2009).    33   Knowing the body wetted surface, water density and the swimming speed, the overall body drag was calculated:  ???? = 12????? ?? ? ???  Eq. 10 where ? is density (kg/m?), ? is swimming velocity (m/s) and ??  is wetted surface of body (m2). Wetted surface was used rather than planform area of body, as the coefficient of overall body drag (?? ? ??? ) provided by Tamura was calculated using the wetted surface of body to normalize the drag. For a 70 cm bluefin tuna swimming at 1 BL/s we estimated the overall body drag as 0.45 N and at 1.5 BL/s as 1.01 N.  However, these overall body drag values include form, friction and induced drag generated by the caudal fin, which are already accounted for by default in the thrust values generated by the tail models.  Magnuson (1978) estimated the caudal fin drag contribution, relative to the overall body drag, to be approximately 27%. Knowing that the thrust must equal the difference between overall body drag and caudal fin drag, the corrected required thrust for a 70 cm bluefin tuna swimming at 1 BL/s is 0.33 N and at 1.5 BL/s it is 0.74 N. That is equivalent to a coefficient of thrust (CT) of 0.19, when using the planform area of the caudal fin to normalize the thrust, as that is the measure that most studies use to normalize the thrust. Only motions where the mean tail-beat thrust coefficient was equal or superior to a CT of 0.19 were considered biologically relevant.  34  3 - Methods In order to investigate the propulsive performance of the Atlantic bluefin tuna caudal fin and its sensitivity to the tail motion and bending behavior, several steps were required. This section summarizes all of the work that was conducted in this project in five subsections: Design and construction of tail models, design of experimental setup, data collection and analysis of the force and motion data, and flow visualization.  3.1 Design and construction of tail models To describe and replicate the internal and external features of a tuna caudal fin, Computed Tomography (CT) scanning, 3-Dimensional modeling, and printing were used, rather than conventional casting methods. This method provided a numerical model that could be remodeled and rescaled, before manufacturing several tail models with different bending behaviors.   3.1.1 Obtaining and describing a real tuna caudal fin After several unsuccessful attempts to obtain undamaged tuna caudal fins from fish suppliers, one fishing charter in PEI responded positively. Tony MacDonald had some fresh Atlantic bluefin tuna caudal fins in his freezer that he had caught by hook and line. The smallest of the three frozen tails shipped to UBC was in the best condition and was therefore selected for CT scanning. The fish had been 2 m FL, 125 kg and had a tail span of 54 cm. Atlantic bluefin tuna have a common size of 80 to 200 cm. The biggest ever-caught tuna was about 300 cm and 700kg (Block and Stevens, 2001). The study tail was sectioned at about the 3rd to last vertebra, leaving a good amount of the caudal peduncle. 35   Figure 8 - Caudal fin of Thunnus thynnus used for CT scanning. The tail was CT scanned vertically in this position. Scale bar = 10cm. In order for the tail models to fit inside the water tunnel they had to be scaled down versions of the caudal fin. A 20 cm tail span was chosen, as it was believed this size would provide a good force signal to noise ratio, while being small enough to minimize wall effects in the water tunnel during dynamic experiments. The imaginary tuna corresponding to that size of tail span had to be described in order to quantify its tail kinematics and body drag estimate. Using published scaling relationships for the Atlantic bluefin tuna as well as measurements on 36  the numerical tail model, morphological characteristics for a 70 cm BL Atlantic bluefin tuna were described (Table.2). Previous research has shown there is isometric scaling of the tuna caudal fin shape (AR, sweepback angle) with no significant changes in the coefficient of lift and drag within this size range (Fierstine and Walters, 1968; Tamura and Takagi, 2009; Westneat and Wainwright, 2001). The material properties of the caudal fin were assumed to be the same within this size range. Table 2 - Estimated and measured morphological characterization of an Atlantic bluefin tuna of same caudal fin size as the tail models. Parameters: Dimensions: References for scaling relationships: Tail span (cm) 20  Fork length (FL) (cm) 70 (Ti?ina et al., 2011) Body mass (kg) 7 (Alot et al., 2011; Ti?ina et al., 2011) Horizontal (chordwise) length from pitch axis to tail tip (cm) 8.5  Horizontal (chordwise) length from tip of rounded keel to pitch axis (cm) 3.5  Max chord length (cm) 7  Mean chord length (cm) 3.28  Aspect ratio (AR) 6  Planform area of tail (m2) 0.007  Wetted surface of body (m2) 0.23 (Tamura and Takagi, 2009)  37  3.1.2 CT scan One tail was CT scanned at FPInnovations, Vancouver, BC. The tail was kept frozen to prevent any shape relaxation during the scanning of 435 horizontal slices spaced 1mm apart. It was positioned with the tail tips pointing upwards. A 16 bit 2048 x 2048 pixel Tiff image was obtained for each slice. This provided high resolution CT scans with pixel resolution of 0.32 mm for the horizontal X and Y plane.  3.1.3 Numerical 3-Dimensional model ScanIP, an image processing software by Simpleware, with the CAD (computer-aided design) module was used to segment bone and surrounding matrix from volumetric CT data, and to assemble, remodel and export the 3-Dimensional model for rapid prototyping. First the Tiff images were imported twice into ScanIP to form two backgrounds, one for the bone segmentation and one for the whole tail segmentation. Bone refers to the vertebrae, hypural plate and fin rays. During that step a range within the full grey scale was selected for each background. Grey scale values outside the range became white if above and black if below. Narrowing the range allowed finer differentiation of densities. The smaller and lower density fin rays were harder to distinguish from the surrounding matrix compared to the vertebra.   To separate the pixels corresponding to the bone from the surrounding matrix and air, the threshold segmentation tool was applied to all slices. This highlighted the zones where grey scale values were within the density range. Then slice-by-slice the highlighted areas masking either the bone structures or the surrounding matrix were verified and, if needed, modified using the paint and flood fill segmentation tools to include missed area (e.g. small bone structure) or to remove falsely segmented areas (e.g. discrete noise connecting adjacent fin rays that are not fused in the 38  caudal fin). All these highlighted areas were assembled to form the bone and the surrounding matrix masks.  As the raw masks were somewhat jagged in the Z axis (vertical) due to the 1mm spacing of CT images, a ?binarise? pre-smoothing function was applied to the masks, followed by a ?discrete Gaussian filter? smoothing function with Gaussian sigma of 1.5 mm for the Z axis and 0.32 mm for the X and Y axes. Finally the masks were resampled cubically where the length of the voxel was doubled (0.64 mm). The masks were then saved as CAD models and modified to replace the caudal peduncle with a hydrodynamic conical shape with surrounding keel, which was assigned to the bone model to provide strong walls for the rod to insert and transmit the motion to the caudal fin (Fig.9 and 10). In the real tail, fin rays are present all the way to the tips of tail, yet in the raw numerical model the fin rays at the tips were not identifiable due to their decreasing size and CT settings (Fig.9, E). Therefore fin rays were extended to the tail tips. In addition, of the 11 distinct fin rays on either side of each tail lobe, the first three fin rays starting from the trailing edge (after the caudal flaps) were cleaned of residual noise connecting adjacent fin rays that are not fused in the caudal fin, to ensure these could deform somewhat independently, although still connected by the surrounding matrix (Fig.10, A). In preparation for the tail attachment to motion system, a space was designed at the pitch axis to receive the rod. The tail model pitch axis was positioned at the leading edge of the hypural plate, as in the caudal fin pitch axis in tunas (Dewar and Graham, 1994; Dowis et al., 2003; Fierstine and Walters, 1968). The CAD model was downscaled to a 20 cm tail span.  Finally the CAD model was exported as a STL file before being sent to a 3-Dimensional printing company.	 ?	 ?	 ?39   Figure 9 - Numerical tail model. (A) Above is a CT slice showing tissue density variation, where white is fin rays. Below is segmented fin rays and surrounding matrix. (B and C) Bone structure around the hypural plate (hp) and hypurapophysis (h). Pitch axis (yellow line) and end of anterior CAD remodeling (red line). (D) Chordwise cross sections of modified tail model along the dorsal tail lobe. (E) Raw numerical tail model before modifications. Scale bar = 2cm. 40   Figure 10 - Modifications to numerical tail model. (A) Raw (orange) and final (yellow) transparent bone model. (B) Posterior view of the hypural plate (hp) and fin rays on either side of it. Final tail model showing spanwise (C) and chordwise cross sections (D).  3.1.4 Physical model Tail models were manufactured using an Objet500 Connex 3-Dimensional printer at Javelin Technologies Inc. (Ontario, Canada). This system allowed us to print the complex geometrical tail models, layer by layer, in the vertical dimension, while using two materials simultaneously. Thus, bone structure and surrounding matrix were built together as one entity. 41  This ensured high accuracy and smooth surfaces with horizontal layers printed 30 micrometres thick. The choice of material was selected to match as closely as possible the properties of the bone and surrounding fleshy matrix in the tuna. One study measured the young's modulus in bending (MPa) of Pacific bluefin tuna fin rays to be about 4600 MPa (Morikawa et al., 2008). The young's modulus in bending for the combined tissues surrounding the bone was estimated to be 1 MPa. This fleshy matrix in vivo is composed of various soft tissues that we simulated by a single material. Three tails models were printed to investigate the effect of bending behavior of the tail on its propulsive performance. The first of these models was printed using two materials: RGD 8630-DM material was used for the bone (young's modulus in bending 1200 ? 1500 MPa) and FLX 930 material (Hardness Shore A 27 and measured young's modulus in bending of 1 MPa) for the surrounding matrix. This model was designated ?FS?, which stands for ?flexible and span reinforced tail model? (as explained in next section). The words flexible and stiff are subjective and are used here to differentiate the tail models among themselves. The next model, designated ?FC? for ?flexible and chordwise reinforced tail model?, was printed using two materials: RGD 525 material was used for the bone (young's modulus in bending 3100 ? 3500 MPa) and FLX 930 material for the surrounding matrix. RGD 525 and FLX 930 were respectively the highest and lowest young's modulus in bending material available at that time in 3-D printing systems. The third model, designated ?SB? for ?stiff and both span and chordwise reinforced tail model?, was printed using material RGD 525 only. 42  Two other tails were printed using the FLX 9595-DM material (Hardness Shore A 95 ? 96 and measured young's modulus in bending of 180 MPa). These were to test the scaling relationship of flexural stiffness.   Figure 11 ? Three tail models used in this study. Scale bar = 2cm   3.1.5 Post 3-Dimensional printing modifications Each tail model was glued using marine epoxy to a rod that would then attach to the load cell. A two-diameter rod was designed to minimize deflection at the end of the rod, while minimizing the diameter of the smaller diameter rod to minimize flow disturbance. Total length of the rod was 29.5 cm, with 15.5 cm of ? inch diameter rod and 14 cm of ? inch diameter rod. The tip of the rod, at the center of the tail, was deflected by a maximum of 0.8 mm from vertical 43  axis. This occurred when forces were at their highest, with 14 N of lateral force and 2 N of inflow force for tail+rod data during motion 30 (Appendix A). The FS tail model was made of less stiff fin rays in order to allow for more chordwise bending than the FC tail model (Fig.16). However FS tail model was too flexible at the tail tips. Fresh bluefin tuna caudal fins are described as being quite stiff all along the tail lobe, except very close to the trailing edge (Pers. Com. Robert Shadwick, Diego Bernal and Richard Brill 2013). Thus this tail model was reinforced with 5 flattened glass fibers (1 mm wide) positioned in the same arrangement on either side of both tail lobes along approximately the first centimeter of the leading edge (Fig.11). These were glued using cyanoacrylate glue while loaded in tension at 1 N. Then they were thinly coated with 24 h marine epoxy. This was followed by sanding the layer and reapplying a thin epoxy coat.  3.1.6 Model verification To compare the bending behavior between the real tuna caudal fin and the tail models, the passive flexural stiffness (EI) of the tails was calculated. Flexural stiffness is a measure of the resistance to bending. Specific values of EI are not very informative on their own, but calculating the ratio between the EI of different tails revealed how much more resistant to bending one tail was compared to the other for a specific location on the tail. E is the modulus of elasticity of the material and I is a shape factor called the second moment of area. Because calculating I for such a complex shape would be quite challenging, we measured flexural stiffness directly for the caudal fin and the tail models twice at 16 positions along the spanwise and chordwise direction of the ventral tail lobe (Fig.12). In addition, the dorsal tail lobe of the caudal fin was tested.  44   Figure 12 - Test location for flexural stiffness calculation showing 32 test locations for the caudal fin. For the tail models only the ventral lobe was tested. Blue is leading edge, red is midline and black is trailing edge. The white dot is the location on the hypurapophysis, which is very close to the pitch axis. Span is 20 cm for tail models and 54 cm for the caudal fin. Force and displacement measurements were made with a servo-hydraulic testing machine (MTS 858 Mini-Bionix?, MTS Systems Corp, Eden Prairie, MN, USA) instrumented with a 50 N force transducer (load cell) (SMT1-50N, Interface, Scottsdale, AZ, USA). Flexural stiffness was calculated with the formula: ?? =  ????3  Eq. 11 where k is the slope for the regression through the points defined by the load (N) on the y-axis and displacement (m) on the x-axis of the rise part of the stress-strain cycle, which corresponds to the spring constant. L is the distance (m) between the point where the tail is restrained from movement and the point where the tail is being loaded.  45   Figure 13 ? Experimental setup to measure the force and deflection at several locations along the real and model tails to calculate the flexural stiffness and provide a characterization of the resistance to bending along the caudal fin and tail models. White arrows symbolize the displacement axis of the MTS actuator connected to the force transducer and probe. The caudal fin and models were restrained from moving at the hypurapophysis located at the leading edge of the hypural plate (Fig.9 C and Fig.12). For the caudal fin this required us to cut small insertions through the flesh to the hypural plate. Hollow cylinders were positioned over the hypurapophysis on either side of the hypural plate. The tail was held firmly using a C-clamp, which pushed the hollow cylinders against the hypural plate. For the tail models, the rod attaching to the tail model was held at two locations along the rod (Fig.13). In addition the portion of the rod that was closest to the tail model was rested against a block of metal. In both cases the setup ensured the displacement and force measurements were representative of the area between the point where the tail was restrained and the point of loading, and prevented the whole 46  tail and support system from moving. The small probe deflections and associated high force for the three loading points closest to the pitch axis, along with the higher percentage error of uncertainty of the actual L when L is small, caused discrepancies in EI ratios between the caudal fin and tail models. Therefore these EI ratios were removed from analysis.  The tests were conducted twice on different days, and the average was used to calculate the flexural stiffness. The caudal fin was defrosted and hydrated in a saline solution for 3h. In addition flexural stiffness was calculated for the FC tail prior and after being submerged in water for 3h. The force and displacement data were sampled at 200 Hz, and the probe deflected the tail at 1.5 Hz for 65 cycles. The tail was preloaded with 0.7 N before being further deflected to a certain distance unique to each position, which generated an addition 1 N of reaction force. Several procedures were tested before this one, with different frequencies and displacements of the probe. The results were similar between procedures; however, for consistency, we used the described procedure for all tests.   A MATLAB (Mathworks Inc., Natick, MA, USA) code was created to analyse the data. Force and displacement data were filtered using a zero-phase low-pass Butterworth digital filter of 10th order and 20 Hz cut-off frequency (MATLAB function ?butter? and ?smooth?) and then smoothed using a moving average of window size representing 22% of the time steps in the stress-strain cycle (MATLAB function ?smooth?). The window size value provided good smoothing of the traces, while leaving the overall shape and orientation intact. The spring constants of cycle 10 to 60 were averaged and that mean was used in the EI calculation.   47  As the caudal fin is bigger than the tail models, the flexural stiffness (EI) had to be scaled in order to be compared. This was accomplished using the following equation:  ??????  ? ?? =  ??????  ? ???? ???? ? Eq. 12 where SF is the scaling factor and was equal to 2.7, as the caudal fin has a 54 cm span, which is 2.7 times longer than the 20 cm span of the tail models. This sort of scaling equation is usually used for uniform cross-sectional objects, such as beams and rods. As the tail models are complex in shape, scaling was verified experimentally. The flexural stiffness for the two tails of span 10 and 20 cm printed with FLX 9595-DM material were calculated and compared.  3.2 Experimental setup Quasi-static, dynamic and flow visualization experiments were conducted in the Fluid Mechanics Laboratory of the Department of Mechanical Engineering at the University of Victoria. The closed-circuit water tunnel, model 504 45 cm, made by Engineering Laboratory Design, Inc. had a test section of 250 ?? ?45 ?? ?45 ?cm in length, height and width and produced laminar flow for all water velocities in this experiment (0.7 and 1.05 m/s). Flow rates were controlled using the adjustable-speed drive of the pump.  Water was kept relatively constant at 23?C over the course of all experiments.   48   Figure 14 - Dynamic experimental setup. The heave motor and linear actuator translate laterally the pitch motor, load cell, rod and tail model. The dashed line in the opposite direction of the water velocity (U) is the thrust axis. Orthogonal to it is the lateral axis. The green triangle is the illumination plane of the laser during PIV experiments.  49  3.2.1 Motion system The 2-axis motion system generated simultaneously heaving and pitching motions of the tail model. To do so, a heave brushless rotary servomotor (M2 - MPP1003D1E-KPSN, Parker Hannifin Corp., Rohnert Park, CA) was mounted at the end of a belt-driven linear actuator (Parker?s OSPE32BHD). The pitch servomotor (Parker?s brushless rotary SM233AE-NPSN) was connected to a 10:1 gearhead (Parker?s RX60-010-S2, MU60-003) and mounted on the bottom side of the linear actuator. Servomotors, compared to stepper motors, allow for position output of both motors, control loop feedback (PID controller) and camming mode, which permits the use of CAM tables to define simple or complex (i.e. high order harmonic waveforms) motion profiles of heave and pitch. More on this will be said in the dynamic testing section. An ACR 9000 controller (Parker?s 9000P1U2B0) was used to command the motors. In between the controller and motors were two Aries AC servo drives (Parker?s AR-30AE for heave and AR-08AE for pitch), which powered and controlled the speed and torque of motors to match commanded signal from controller. Ethernet communication was used between the controller and a computer, to send the motion program (PROG0) and motions (CAM tables) to the controller and retrieve motion outputs from the controller to the computer. Before any of the dynamic experiments were conducted, the servo drives were tuned to minimize the following error (error between commanded and actual motions), by changing the gain parameters using some built-in wizards in ACR-View software (Version 6.2.2 10001, Parker Hannifin Corp., Rohnert Park, CA).  The motion system was positioned above the water tunnel in such a way that the tail model was centered at 22.5 cm from the bottom of the 45 cm deep water tunnel. A sturdy frame was made from 80/20?s aluminum T-Slotted beams and rectangular beams in order to ensure the 50  mechanical inertia of the motion system did not displace or bend the frame. Cables were attached to the frame with electrical tape to prevent them from moving and rubbing on surfaces. This motion system was stationary relative to the incoming flow, as opposed to being supported on friction-free linear air bearing. Therefore even if the thrust was non zero it would not move forward (accelerate) or backward (decelerate). There are limitations associated with this type of motion system to study steady swimming self-propelling bodies, as during a tail-beat the mean thrust is not necessarily equal to the mean drag (Lauder et al., 2007; Wen and Liang, 2010). However, most influential research groups in oscillating propulsion research used non-self propelling systems similar to the one in this study (Anderson et al., 1998; Hover et al., 2004; Read et al., 2003; Schouveiler et al., 2005; Triantafyllou et al., 1993).  3.2.2 Force system Instantaneous force and torque measurements were obtained using a 3-axial load cell (F233-Z3712, Novatech Measurements Ltd, St Leonards-on-Sea, GB-ESX), which rotated with the tail. It measured Fx, Fy and torque at the hypural plate where the rod inserts in the tail model. The load cell forces, Fy and Fx, were respectively perpendicular and parallel to the tail orientation axis. Load cell signals were amplified using Novatech?s SGA loadcell amplifiers, where ?10 V equaled ? 130 N for forces and ?10 V equaled ? 9 Nm for torque. Novatech Measurements Ltd performed a certified full recalibration and rescaling of the load cell and amplifiers a month before the tests. Forces and torque were recorded on a computer running LabVIEW, at 10,000 Hz to increase the synchronization accuracy of the force and motion measurements (LabVIEW Ver. 10.0.1, National Instruments Corp., Austin, TX, USA). The LabVIEW program, or Virtual 51  Instrument (VI), which recorded the forces and torque signals was a modified version of a previous VI (Barannyk et al., 2012). The hydrodynamic force, or resultant force, was decomposed into a third pair of orthogonal forces, in addition to lift/drag and Fx/Fy (Fig.4). That third pair is thrust (T) and lateral force (FLat), the forces of interest that are respectively parallel and perpendicular to the thrust axis (the fish?s direction of travel). T and FLat refer to the sum of the forces in the thrust axis and lateral axis respectively. Positive T is thrust and negative T is drag. For a self-propelled body, the time-averaged T is equal to zero. T and FLat were calculated using simple trigonometry on the load cell forces. These are the forces that were used to calculate the thrust coefficient and the propulsive efficiency. Details are provided in the analysis section.   3.3 Collection and analysis of force and motion data Both quasi-static and dynamic experiments were conducted for this project. The quasi-static data provided a lift and drag characterization of the FC and SB tail models for different angles of attack. From these results, the angle of attack test parameters were identified for the dynamic experiments and a quasi-static theoretical model was developed to estimate thrust and propulsive efficiency.  This study focuses on the propulsive performance of the main propulsive structure, the caudal fin, rather than the whole fish. To estimate the propulsive performance of the tail model alone, the hydrodynamic and inertial forces of the tail model had to be isolated from the forces generated by the rest of the motion system (inertial force of the motion system and rod, as well as the hydrodynamic force of the rod). The inertial force of the tail is the force that oscillates the tail, without the contribution of hydrodynamic force. We include in the calculation of the tail 52  model inertial force, the mass of the tail model and the added mass of water that is accelerated by the tail model. In aerodynamic studies the added mass of air surrounding the foil is usually considered negligible, however in water it probably contributed more to the inertial force than the actual mass of the tail (40g) (Dickinson and Gotz, 1993). Each motion regime was performed twice, once with the tail model attached at the end of the rod (abbr. tail+rod), and once with the rod alone (abbr. rod-alone). The rod-alone motion regimes were used to estimate and subtract the inertial forces of the motion system and rod, and the hydrodynamic force generated by the rod. Strengths and limitations of this approach are expressed in the discussions. The quasi-static theoretical thrust and lateral forces do not include the inertia force of the tail or any unsteady hydrodynamic effects, as the forces were measured at static heave and pitch positions. The measured dynamic thrust and lateral force included the hydrodynamic and inertial forces. The relative importance of the tail inertia and unsteady hydrodynamic effects could be estimated by comparing the theoretical and experimental results.  3.3.1 Quasi-static testing The quasi-static theoretical model is a rather simple model, which tends to underestimate the thrust and propulsive efficiencies; however it is useful to gauge which motions should have the highest propulsive performance in the dynamic experiments (Shadwick and Ben-Zvi, 2013). This quasi-static model required some experimental characterization of the tail?s capacity to generate lift and drag.  To do so, each rod of tail model, FC and SB, were screwed to the load cell and positioned in the center of the water tunnel at different angles of attack, and for two different speeds. The heave position and angle of attack were kept constant throughout experiment. The tail axis was 53  aligned with the load cell X-axis, which was aligned in the thrust axis. Water flow was turned on and once up to desired speed (1 or 1.5 BL /s), the Fy was ideally found to be close to 0 N, if the tail was perfectly symmetrical and well positioned relative to load cell X axis. If this was not the case, then the pitch was adjusted as needed (by up to 5 degrees) to bring the Fy to 0 N. This initial pitch angle adjustment, ??, was recorded. The tail was rotated to a certain desired pitch angle (?). The Fy, Fx and torque were measured for two minutes at 400Hz. The Fx and Fy forces were transformed to drag and lift, using the following equations: ???? t =  ??? cos(? + ??)+  ??? sin(? + ??) ???? t =  ??? cos(? + ??)?  ?F? sin(? + ??) Eq. 13 where ?? is the initial pitch angle (rad) and ? is the desired pitch angle (rad), which corresponds in this situation to the angle of attack. As the tail was stationary in the flow, that is without heave or pitch oscillation, the water flow was opposite to the direction of the fish motion, so pitch angle was equal to angle of attack. Therefore, in this simple case the drag was the same as negative T and lift was the same as Flat. The mean lift, drag, and torque were calculated and then subtracted by the corresponding mean forces and torque of the rod-alone. The mean lift, drag, and torque of the rod-alone for both test speeds were calculated using six repeated measurements obtained at different times of the week. As previously mentioned the rod-alone data subtraction to the tail+rod data was used to approximate the forces generated by the tail alone at both speeds.     54  The mean lift, drag and torque of the tail alone were then transformed to coefficients, to provide a dimensionless number of how much force or torque a foil generates at a particular angle of attack, normalized for fluid speed, density and foil size: ???? ? ????12 ????  ? ? ? ? ? ? ? ? ? ? ? ? ? ;  ? ? ? ? ? ? ? ? ? ? ? ????? ?????12 ????  ? ? ? ? ? ? ? ? ? ? ? ? ? ;  ? ? ? ? ? ? ? ? ? ? ? ??????? ???????12 ???? Eq. 14 where ????, ???? and ?????? are the mean forces (N) and torque (Nm), U is the water velocity, ? ?is water density and S is the planform area of the tail (m2). This whole procedure was repeated for angle of attack with 5? increments from -45 to 45? at 1BL/s water speeds, and from -65 to 65? at 1.5BL/s water speeds. As the tail models were symmetrical, the coefficients for the positive and negative angles of attack were averaged. Then for each positive angle of attack, the mean and standard deviation between the two coefficients at each speed were calculated (Fig.25). Using these results, it was possible to create a computer model to predict the thrust and drag production of each of the 30 motion regimes tested using a quasi-static analysis method. For each motion a standardized tail-beat of a thousand points was mathematically generated. At each point the instantaneous local resultant velocity and corresponding angle of attack were determined. With these two parameters and the coefficients of forces and torque presented in the quasi-static graph (Fig.25), the lift, drag and torque were obtained at each point. Lift and drag were transformed to T and Flat, using the following equations: ? t =  ????? cos(?)+  ????? sin(?) ??? t =  ????? cos(?)?  ?drag sin(?) Eq. 15 where ?, the relative flow angle (rad), is the angle between the thrust axis and the resultant flow direction (Fig.4). Finally the theoretical average thrust coefficient (CT) per tail-beat was 55  calculated as well as the propulsive efficiency (??). These calculations are explained in the following section.  3.3.2 Dynamic testing For the dynamic experiments, motions, forces and torque of the tail were recorded. There were two challenging requirements with these experiments. First, the pitch and heave motions had to be started in such a way to produce a phase shift of 90?. Second, the force recordings had to be synchronized with the motion data. After testing several hardware configurations and writing different programs, the requirements were finally satisfied. A program (PROG0) was written using the native programming language of ACR 9000 (AcroBasic), in ACR-View software. It contained information to receive and use CAM tables, control and record the motion of the tail and send an analogue trigger to the LabVIEW VI to start force recording at the same time as the motion recording.  A CAM table contains the motion profile information for one motor, defined by positions at regular time intervals for one cycle or tail-beat. A 100-point CAM table was used for pitch and heave, as it provided smooth camming motions as good as for CAM tables of 1000 points. The CAM tables for pitch and heave for each of the 30 motion regimes were prepared in Microsoft Excel. The CAM tables were downloaded to the controller using a Visual Basics program interface in Excel, courtesy of Jim Wiley at Parker Hannifin Corporation. That same interface was used to upload the actual heave and pitch positions during the recorded tail-beats to the computer once the motion came to a rest.  First the heave motion was started at 1/20th of its full amplitude. Then the pitch motion was also started at 1/20th of its full amplitude, when the heave position was at its midpoint (0 cm) 56  during its fourth tail-beat. Then the amplitude of the heave and pitch waveforms were ramped to full amplitude at the end of their tail-beat cycle over 20 tail-beats. The ramping minimized the motors following error by reducing the high torque and acceleration commands required if the motions started at full amplitudes. This was followed by 10 full amplitude tail-beats, before the analogue trigger was fired to record motion and force for 15 tail-beats. The ACR 9000 controller has an internal clock running at 2000 Hz. Therefore it obtained the position of both motors at best every 0.5 ms. If a trigger happened between two position points separated in time by 0.5 ms, then the first position was used to approximate the actual position. Motion was recorded at 500 Hz, that is one point every 2 ms. Forces were recorded at 10,000 Hz. Such a high force recording frequency (one point every 0.1 ms) was chosen to minimize the error between the actual and recorded force at any given time.  For each motion regime the following steps were performed. Water flow was set to desired velocity. The tail was commanded from the ACR-View terminal to move to its maximum negative value of both the heave and pitch waveform. A file was prepared to store the force data and the LabVIEW VI was started, so that it was ready to record force once it would receive the trigger. PROG0 was executed. It paused until the CAM tables were downloaded to the controller, after which the tail was set in motion. The heave and pitch actual position recordings were saved in Excel. Every five motion regimes the tail was commanded to move back to the middle of the water tunnel (i.e. heave amplitude of 0 cm) and face the incoming flow (i.e. pitch angle of 0?) to verify that the motion system had not accumulated some following errors and was still correctly positioned. No or very minor discrepancies were observed.   57  Analysis Analysis of the dynamic data was performed in MATLAB. The following explains in steps the analysis performed on the force and motion data of one motion regime. This was repeated for all other motion regimes. First, the force and torque data for the tail+rod and for the rod-alone were resampled to a lower frequency of 500 Hz (MATLAB function ?decimate?), to match the recorded frequency of the motion data. The Fx and Fy forces of the tail+rod and of the rod-alone data were each transformed to T and ??? , using the following equation:  ? t =  ??? cos(? + ??)+  ??? sin(? + ??) ??? t =  ??? cos(? + ??)?  ?F? sin(? + ??) Eq. 16 where ?? is the initial pitch angle (rad) and ? is the instantaneous pitch angle (rad). The pitch, heave, T, ???  ?and torque of the tail+rod and of the rod-alone data were each filtered using a zero-phase Butterworth digital filter of 12th order and 10.5 Hz cut off frequency (MATLAB functions ?butter? and ?filtfilt?). It was applied to all 15 cycles of force and motion data to reduce high frequency noise in the signal, while preserving the time synchronization between the force and motion signals. The cut-off frequency value was decided upon looking at the discrete Fourier transform (MATLAB functions ?fft?); furthermore, studies at similar oscillation frequencies have used similar cut-off frequencies (Rival et al., 2009; Shadwick and Ben-Zvi, 2013). The filtered T, ???  ?and torque of the rod-alone data were subtracted from the filtered T, ???  ?and torque of the tail+rod data. From now on T, ???  ?and torque will refer to the filtered T, ???  ?and torque of the tail alone data. The mean of T, ???  and torque of 13 cycles were calculated (first and last cycles were discarded).   58  The coefficient of thrust was calculated: ??? ?12 ???? Eq. 17 where ? is the mean thrust (N), ? is the planform area of the tail (m2), ? is the water density (kg/m3) and ? is the free stream water velocity (m/s).  Hydrodynamic propulsive efficiency was calculated using the standard engineering Froude efficiency. ?? =  ?????? ???????????? ?????? ?  Eq. 18 The power output is always inferior to the power input as described by the law of conservation of energy, due to friction and the nature of lift-based thrust, where energy is lost when displacing water laterally during a tail-beat. Power output is the time-averaged ?useful? power. That is, the power that moves the tail model forward: ?????? = ??? Eq. 19 where ? is the tail-beat averaged thrust (N) and U is the mean forward velocity of the fish (m/s). Positive power output signifies positive work is done in a certain amount of time to move the tail forward against the flow. Positive work is done on a system when the force doing the work acts in the direction of the motion of the object. Accordingly, positive work is when the thrust force and forward tail motion have the same direction. From the water flow reference frame the tail is moving forward even though it is connected to a structure that is screwed on top of the water tunnel.  59  Power input is the tail-beat averaged power expended to move the tail model laterally and angularly as defined by (Anderson et al., 1998): ????? = 1? ??? ? ???? ???? + ?????? ? ???? ????  Eq. 20 where P is the period of the tail-beat (s), FLat is the lateral force (N), ???  is the heave velocity (m/s), torque (Nm) and ? ?  is the angular pitch velocity (radians/s). Positive power input signifies positive work is done in a certain amount of time by the motion system to move the tail. It is equivalent in the fish to muscle contractions moving the tail. If the tail itself exerts on the motion system due to the hydrodynamic force a lateral force and torque respectively in the tail?s direction of heaving and pitching motions, then the power input is negative, as the force and torque exerted by the tail are actually helping the motion system to move the tail.   The coefficient of thrust (??) and propulsive efficiency (?p) of the 13 cycles of each of the 30 motion regimes performed for each tail models (SB, FC and FS) were calculated. For each motion regime the mean, minimum, maximum and standard deviation of the ?? and ?p of the 13 cycles were calculated.  3.3.2.1 Motion accuracy and repeatability The motion system accuracy was tested by looking at how the motors actually followed the commanded motion (following error) and under different loads. That allowed us to assess if the motors performed the same CAM motion for the tail+rod and rod-alone motions. In addition, the repeatability of the motion for a given load in 13 cycles was assessed. The motion regimes with most potential for motion inaccuracy were investigated: the fastest heave motion with the 60  highest pitch and heave accelerations (motion regime 30, see Appendix A) and the highest pitch velocity (motion regime 26, see Appendix A).   3.4 Flow visualization Flow structures were visualized by means of 2-Dimensional particle image velocimetry (PIV) for the FS and SB tail models at three different motion regimes (3, 13 and 15, see Appendix A for kinematic details). Two horizontal planes of the flow field were visualized, to attempt to assess the evolution of vortices generated by a flapping tail models. The first plane was located at the mid-span of the tail lobe (plane 1 = 50%, where 100% is the distance from the tail spanwise midline to the tail tip, see Fig.16), and the second plane was located near the tip (plane 2 = 95%). These two planes were therefore vertically separated by 4.5 cm. Due to the small cross sectional size of the tail model at plane 2 and the large field of view setting, we focus here on flow structure observed for plane 1. The experimental setup for the flow visualization is illustrated in figure 14. Small neutrally buoyant Mearlin Supersparkle particles were used as tracer particles and seeded in the water tunnel before experiments. A Photron FASTCAM APX-RS MONO camera with Nikon AF Nikkor lense 24mm 1:2.8 D (for large field of view) captured 400 double frame images at 200 Hz, where the paired frames were separated by 1 ms. This was synchronized with a 25 mJ Nd:YLF dual diode-pumped laser (Quantronix Darvin-Duo-527-40-M), which illuminated the particles in the flow with a double pulsed laser light sheet. The images were 1024 x 1024 pixels with a horizontal field of view around the tail model of 312 x 312 mm. Therefore the resolution was 0.3 mm/pixel. Instantaneous velocity fields and vorticity were calculated using LaVision DaVis 8.13 software (see Appendix B for details). As the final grid 61  size of the processed images was 16 x 16 pixels, the minimum size of flow structures presented here are 4.8 mm.  62  4 - Results Overall there are no major differences in the propulsive performance across the different tail models. As the motion and force traces for the different foils are qualitatively similar, we use a few motion regimes of the FS tail model as a case study to describe general observations of the effect of tail motion kinematics on propulsive performance.   4.1 Bending behavior of tail: Qualitative visual observations of the deformation and motion of the tail models as they were actuated in the water tunnel very closely resembled real tuna caudal fin kinematics. To quantify and compare the bending behavior of the caudal fin and tail models, the flexural stiffness was calculated for several locations as a measure of the resistance to bending. First the flexural stiffness (EI) scaling calculation (see eq. 12) was verified to be correct for the 10 and 20 cm span tail models, as the experimental best-fit linear regression was 17.99 ? ? 2.63 ?(95% ?CI), which contained the theoretical scaling slope (16) (SF4 = 24=16). This can be seen with the 95% confidence bands, which represent the area that has a 95% chance of containing the true best-fit linear regression line (Fig. 15). Therefore, the flexural stiffness scaling was applied to the tail models? flexural stiffness, to compare their resistance to bending against the caudal fin.  63   Figure 15 - Experimental verification of flexural stiffness scaling. The EI of the 20 cm tail span on the Y-axis and the EI of the 10 cm tail span on the X-axis. The observed slope of the best-fit linear regression is 17.99 (illustrated by the doted line). The theoretical slope is 16 (SF4 = 24=16) (illustrated by the thin solid line) is contained between the 95% confidence bands (illustrated by the dashed curves). The flexural stiffness (EI) was calculated twice for each test location. Repeatability is a measure of the consistency of repeated measurements. It was calculated by dividing the variation among test locations by the variation within location and among test locations. The repeatability for all repeated measures on the caudal fin and tail models (including FC model after 3h in water) was 98.4%. The ventral lobe of the Atlantic bluefin tuna appeared on average for all locations about 10% more resistant to bending than the dorsal lobe. However, as the measurements were only performed once on the ventral lobe, it would be best to repeat the 0.005 0.015 0.025 0.0350.010.030.050.07Y = 17.99 * X + 0.0008R 2 = 95.4 %EI span 10 cm  ( Nm2 )EI  span 20 cm  ( Nm2  )64  measurements in order to confirm this result. The comparison of the flexural stiffness (EI), that is the resistance to bending, of the tail models with the caudal fin is presented in figure 16. If the flexural stiffness ratio is equal to one it means the tail model and caudal fin resist bending in the same amount at that position.  Figure 16 - Comparison of the flexural stiffness (EI), that is the resistance to bending, of the tail models (SB, FC and FS) with the real caudal fin (Real). The Y-axis is dimensionless as it is the ratio of EI of tail model/EI of caudal fin (square: SB/R, diamond: FC/R, circle: FS/R). X-axis represents the spanwise position of the test location, where 0% is the spanwise midline of the tail passing through the pitch axis and 100% is the tail tip (as shown with the tail schematic). If the flexural stiffness ratios were all equal to one it would mean the tail model and caudal fin would deform in the same fashion. Comparison of the flexural stiffness (EI ratios) of the tail models with the caudal fin revealed interesting characteristics about the caudal fin and about the accuracy of the tail models. Before describing these results, a few points are reminded. Firstly, the experimental setup did not attempt to distinguish the chordwise from the spanwise bending resistance, but rather to measure 65  the combination of these effects. Secondly, the internal structure of the caudal fin and the tail model were quite different preceding the anterior ? of the hypural plate (equivalent to a horizontal red line (Fig.9 B)). Indeed this whole volume was made of the ?bone? material without any surrounding flexible matrix, to provide strong walls to attach the rod and transfer the motion from the rod to the tail (Fig.10 A). This anterior ?bone? volume was tapered as it approached the anterior ? of hypural plate to minimize the ?bone? reinforcement over the leading edge fin rays. The anterior ?bone? structure did not embed the caudal flaps and the first 5 fin rays starting from the trailing edge, which corresponds to the midline and trailing edge of the tail (Fig.10 A and B). Therefore this structural difference is probably responsible for only a small part of the higher resistance to bending of the tail models, as the leading edge fin rays are already fused to each other and well attached to the hypural plate in the caudal fin.  Most importantly this difference in structure between the tail models and the caudal fin causes an uncertainty of the actual L measurement to use in EI calculation for the caudal fin. If the structures were the same in the tail model and caudal fin, this issue would be non-existent, as the defined position from where the tail starts to bend would be the same, even though the actual position might be a bit off. Therefore, small magnitude changes of the EI ratio between the different test locations of the same tail model to caudal fin are possibly artifacts. That is why comparisons of EI ratios between the tail models and the caudal fin might be more informative than between positions on the same tail model or caudal fin.  Not surprisingly, the SB tail was always more resistant to bending than the caudal fin, FC and FS tail models at all test locations. The magnitude of the difference in bending behavior varied depending of the test location. Along the leading (blue dots) and midline (red dots) of the tail lobe the resistance to bending increased towards the tail tip, meaning the SB tail model did 66  not deflect as much as the caudal fin and other tail models towards the tail tips. Along the trailing edge (black dots) the opposite trend was noticed. Compared to the caudal fin, the overall resistance to bending of the SB tail model for all test locations was 12 times higher, specifically: for the trailing edge 8.5 times higher, for the midline 7.2 times higher and for the trailing edge 20.5 times higher. At the trailing edge the difference between the rigid and caudal fin was more pronounced, as the caudal fin had some chordwise flexibility, whereas the SB tail was very stiff. The flexible tail models are clear improvements in mimicking the caudal fin, as the EI ratios for all test locations are lower than the SB model. In addition the difference in bending behavior is relatively constant and somewhat linear for all test locations. Compared to the caudal fin, the overall resistance to bending of the FC tail model for all test locations was 2.2 times higher, specifically: for the trailing edge 2 times higher, for the midline 1.9 times higher and for the trailing edge 2.9 times higher. When at the highest resultant flow velocity, the tail tips for the FC model (the least resistant to spanwise bending) were not deflected by more than 1 cm or 5 degrees from the spanwise tail plane. Compared to the the caudal fin, the overall resistance to bending of the FS tail model for all test locations was 1.9 times higher, specifically: for the trailing edge 2.3 times higher, for the midline 1.4 times higher and for the trailing edge 2 times higher.  It seems the FS tail model better mimicked the caudal fin compared to the other tail models. The resistance to bending at the tail tip is 3 times greater for the FS model than in the caudal fin. However the ?extra? resistance to bending at the tail tip for FS model was found to be more realistic than the tail tip of the FC model, which was equal to the flexural stiffness of the caudal fin and yet considered too floppy by experts on the subject (Pers. Com. Robert Shadwick, Diego Bernal and Richard Brill 2013).  67  4.2 Motion system accuracy and isolation of tail force The motion system provided high accuracy motions, with minimal following error, as the observed motions were nearly identical to commanded motions (see Fig.17 and 18). In addition the motion was very repeatable between tail-beats, shown by the heave and pitch traces for all 13 tail-beats, which are all superimposed on top of each other (Fig.17, 18, 21 and 22). The motors were surprisingly well tuned for the range of loads exerted on the motors (presence or absence of the tail model), as maximum acceleration error in all trials between tail+rod and rod-alone motions was only 0.58 Rev/s2 (1.2 % error) for pitch and 0.27 m/s2 (0.8 % error) for heave (bottom graph of Fig.17 and 18). The percent maximum acceleration error was calculated by dividing the maximal acceleration error (bottom graph) by the total acceleration range (from min to max acceleration of the middle graph) (Fig.17 and 18).  We focus on two motion regimes: motion regime 30, with the fastest heave motion and the highest pitch and heave accelerations, and motion regime 26, with the highest pitch velocity (Appendix A). Any motion inaccuracy observed for these motion regimes would be less so for other motion regimes.  A minimal phase shift error was observed between the pitch and heave waveforms. Indeed the phase shift should have been 90?, where the pitch angle would be 0? when the heave amplitude would be at its maximum. However the pitch angle is a bit more than 0? when the heave amplitude is at its maximum (Fig.17, 18, 21 and 22). We believe it has insignificant effects, as the observed phase shift is now 92.34? (i.e. 1.3% phase shift error over a tail-beat) at 2.54 Hz and 91.8? (1%) at 1.95 Hz rather than 90?. The cause for this minimal phase shift error is probably due to technical limitations of the hardware (i.e. controller clock step and length of triggering cable).  68   Figure 17 - Motors accuracy I. The colored lines are 13 tail-beats plotted on top of each other. Top (position) and middle (acceleration) plots: Observed pitch (orange) and heave (red) tail+rod motion comparison with the commanded CAM table motion (dashed lines) for the highest heave velocity and highest heave and pitch acceleration motion regime tested (motion regime 30, see Appendix A). The difference between the colored and dashed lines represents the following error. The rod-alone heave (green) and pitch (blue) motion are barely visible, as they are nearly identical to tail+rod motions. Bottom plot: Differences in the acceleration of heave (red) and pitch (orange) motion under different loads (with or without tail attached to rod). Differences were calculated by subtracting the rod heave and pitch accelerations to the tail+rod heave and pitch accelerations.   69   Figure 18 - Motors accuracy II. Same figure caption as Figure.17 except for top (position) and middle (acceleration) plots: Observed pitch (orange) and heave (red) tail+rod motion comparison with the commanded CAM table motion (dashed lines) for the highest pitch velocity motion regime tested (motion regime 26, see Appendix A).     70  To estimate the propulsive performance of the tail model alone, the hydrodynamic and inertial forces of the tail and added mass of water had to be isolated from the forces generated by the rest of the motion system (inertial force of the motion system and rod, as well as the hydrodynamic force of the rod). The inertial force of the tail and added mass of water is proportional to the mass of the tail and mass of water displaced by the tail. To isolate the forces generated by the tail model, the rod-alone forces were subtracted to the tail+rod forces. Again we present motion regimes 26 and 30 as case studies, as these represent the most extreme cases with the highest hydrodynamic and inertial forces (Fig.19 and 20).  Hydrodynamic forces are expected to be highest when the resultant flow is highest, which occurs when the tail crosses the heave midline or, in other words, when the pitch angle is maximal (as the phase shift is 90?). Therefore the hydrodynamic thrust profile for example should have thrust peaks aligned with the pitch waveform peaks (Fig 21 and 22). This is what the theoretical quasi-static model showed. However, when you include the inertial forces, as in these dynamic experiments, a phase shift is observed between the motion and force profiles. We believe it is mostly the effect of the tail and added mass inertial forces.  Motions with higher pitch acceleration (i.e. motion regime 26, Fig.18 and 20) have larger shift between the motion and force profiles, compared to lower pitch acceleration motion regimes (i.e. motion regime 30, Fig.17,19 and 22). Inertial forces are proportional to mass and total acceleration (both heave and pitch). The heave acceleration is relatively similar between motion regimes at the same St and U (as motion regime 26 and 30), and therefore it is mainly the pitch acceleration that causes the observed difference in inertial force.  The harmonic ?noise? summed on top of the expected sinusoidal hydrodynamic force profiles has a harmonic frequency of 4 times the tail-beat frequency (most easily seen in the 71  torque trace of Fig.19 and 20). It seems to correspond with the peaks of the pitch acceleration profile, which also occur at a frequency of 4 times the tail-beat frequency (see Fig.17, 18 and 19). These observations support the idea that the phase shift observed between the motion and force profiles is mostly due to the inertial forces of the tail and added mass. Others, who have conducted experiments similar to the ones presented here, have published force traces similar to ours or even with higher asymmetry (See Fig.18 and 19, Prempraneerach et al., 2003; See Fig.7 Schouveiler et al., 2005).  72   Figure 19 - Left column is motion 26. Right column is motion 30. Both motions are for the SB tail model. The black dashed curves are the tail+rod data. The black solid curves are the rod-alone data. The colored curves are the tail data. The first three rows are the thrust force (N) (blue for tail alone), the middle three rows are for the lateral force (N) (green for tail alone) and the bottom three are for the torque (Nm) (purple for tail alone). Two tail-beats at 2.54 Hz. The grey shaded areas are one stroke, followed by the return stroke represented by the white areas. 73   Figure 20 - Left column is motion 26 for SB tail model. Right column is motion 26 for FS tail model. The black dashed curves are the tail+rod data. The black solid curves are the rod-alone data. The colored curves are the tail data. The first three rows are the thrust force (N) (blue for tail alone), the middle three rows are for the lateral force (N) (green for tail alone) and the bottom three are for the torque (Nm) (purple for tail alone). Two tail-beats at 2.54 Hz. The grey shaded areas are one stroke, followed by the return stroke represented by the white areas. 74  4.3 Propulsive performance All the motion regimes were designed to have a positive thrust component of the lift force throughout the tail-beat. This was achieved by generating sinusoidal angles of attack motions with 90? phase shift with sinusoidal heave motions, resulting in motions where the pitch angle and angle of attack were always of opposite sign (Fig. 7). If the motion regime had negative thrust (T) for part of the tail-beat, it meant the drag had a larger negative thrust component than the lift positive thrust component. Below are two typical force traces and associated kinematics, which represent one case for high propulsive efficiency while still generating enough thrust to counter body drag estimate (motion regime 27, Fig.21) and one case for high thrust generation but at lower propulsive efficiency (motion regime 30, Fig.22).   Figure 21 ? Motions and forces profiles during motion regime 27 for FS tail model. Red is heave and orange is pitch. Thrust is light blue, lateral force is green and torque is purple. All 13 tail-beat cycles are plotted and the black curve in the middle of those curves is the mean. The grey shaded area is one stroke. 25 75?0.0700.07Heave (m)?30030Pitch (Deg)0 25 50 75 100?12012Forces (N)Tailbeat (%)?0.400.4 Torque (Nm)75   Figure 22 ? Motions and forces profiles during motion regime 30 for FS tail model. Red is heave and orange is pitch. Thrust is light blue, lateral force is green and torque is purple. All 13 tail-beat cycles are plotted and the black curve in the middle of those curves is the mean. The grey shaded area is one stroke. The general shape of the force profile is similar for the different tail models at the same motion regime. For motion regimes at lower speed (motion regime 1 to 15) it seems only the magnitude of the force and motion profiles is reduced.  In the case for high propulsive efficiency (motion regime 27, Fig.21): ?p = 0.45 with a  CT = 0.23 (Sttip = 0.35, Strod = 0.27 and ???  ? ?= 15?). For the case for high thrust generation (motion regime 30, Fig.22): ?p = 0.34 with a CT = 0.31 (Sttip = 0.35, Strod = 0.31 and ???  ? ?= 30?). The increases by 13% of hmax (0.75 cm increase) and by 15? of ???  ?are responsible for the enhancement in thrust and decrease in propulsive efficiency. When visually comparing the force profiles for motion regime 27 and 30, the increase in thrust can be observed with the higher thrust peaks (blue curve) for motion regime 30 (Fig. 21 and 22). The propulsive efficiency 25 75?0.0700.07Heave (m)?30030Pitch (Deg)0 25 50 75 100?12012Forces (N)Tailbeat (%)?0.400.4 Torque (Nm)76  cannot directly be observed from these figures, but as the lateral and torque curves are further increased compared to the thrust curve (Fig.22), we can deduce a decrease in propulsive efficiency for motion regime 30.  The overall findings on the propulsive performance for the different tail models are illustrated in figure 23 and 24. The thrust coefficient (CT) and propulsive efficiency (?p) of each of the tail models are given as a function of the tail tip Strouhal number (Sttip) and maximal angle of attack (??? ). All of the 30 motion regimes for each tail model generated positive mean thrust over a tail-beat, and about half of these motion regime generated enough thrust to counter the whole body drag estimate (CT equal or above 0.19)(Fig. 23). For all tail models, motions with Sttip of 0.25, or ???  of 10? did not generate sufficient thrust. The maximum coefficient of thrust was about 0.35 and was observed for all tail models at Sttip of 0.35 and ???  of 30? (Fig. 23 and Appendix A). The general trend is that at high Sttip and ???  the thrust generation is increased. The maximum propulsive efficiency of 54% was observed for the SB tail model at Sttip of 0.25 and ???  of 10? (motion regime 16) (Fig. 24). For lower Sttip motion regimes the propulsive efficiencies were lower, though relatively similar for all of the Sttip range.   77   Figure 23 ? Coefficient of thrust (??) at: A) U = 1 BL/s and B) U = 1.5 BL/s. Markers are the mean of ??  ?over 13 tail-beats. Small width error bar ticks are the minimum and maximum values of ?? in 13 tail-beats. The large width error bar ticks are the standard deviation from the mean ??. The horizontal dashed line is ??  ? = 0.19. 78   Figure 24 ? Propulsive efficiency (?p ) at: A) U = 1 BL/s and B) U = 1.5 BL/s. Markers are the mean of ?p over 13 tail-beats. Small width error bar ticks are the minimum and maximum values of ?p in 13 tail-beats. The large width error bar ticks are the standard deviation from the mean ?p.  79  The thrust generation was qualitatively similar among the different tail models (Fig. 23). More variation was present for the propulsive efficiency between different tail models. The FS model, which mimicked the most accurately the deformation behavior of the real tuna caudal fin, had lower propulsive efficiency at all Sttip when at U = 1 BL/s, than the FC and SB tail models.  At U = 1.5 BL/s, the propulsive efficiency was comparable to the other tail models, except at a Sttip of 0.25. The larger spread between values of ??, and particularly of ?p at different Sttip values for the SB model at U = 1 BL/s is probably an artifact of the tail model being misaligned at the start of the experiment by a few degrees, which resulted in an asymmetrical tail model motion (potential minor misalignment of SB model for motion regimes 1 to 15). The spread of ?p at different Sttip is relatively constant between U = 1 and 1.5 BL/s for the FS and FC tail models. However the spread at U = 1.5 BL/s for the SB is tighter than at 1 BL/s. In addition the experimental ?p result for the SB tail at 1 BL/s are further away than the observed nearly identical slope of the regression lines between the quasi-static theoretical model and experimental results at U = 1 and 1.5 BL/s of the SB and FC tail models (Fig.26). Other studies have tested nonsymmetrical flapping, which is the same as an initial angle misalignment. They found that with a 5? misalignment the ?? is barely reduced, but the coefficient of lateral force, ??? , was increased, which leads to lower ?p (Schouveiler et al., 2005). The quasi-static coefficient of lift, drag and torque for tail model SB and FC at angles of attack 0? < ? < 55? are presented in Fig. 25. The highest coefficient of lift (CL) was 0.56 for an angle of attack of 35?. The highest ratio CL/CD was 5 when the angle of attack was 6?.    80   Figure 25 - Coefficients of Lift, Drag and Torque: Coefficient of lift (blue), drag (red) and torque (black) values for the tail models at varying angles of attack. Data was collected at both positive and negative angles for two speeds. The error bars represent the standard deviation between the means calculated at 1BL/s and 1.5 BL/s. Hollow circles and dashed lines are for SB tail. Full circles and solid lines are for FC tail. Using these results, the theoretical thrust and propulsive efficiency for each of the 30 motion regimes were calculated using a quasi-static analysis method for tail model SB and FC.  The quasi-static results are compared with the dynamic experimental results (Fig.26). 0 10 20 30 40 50 6000.10.20.30.40.50.6Coefficent Values Angle of Attack (?)  81   Figure 26 - Theoretical vs. experiment thrust and propulsive efficiency. A and B are for SB tail model. C and D are for the FC tail model. Silver edge markers are for 1 BL/s and black edge markers are for 1.5 BL/s motions. Marker color represents the Strouhal number for tail tip, with Sttip = 0.25 in blue, Sttip = 0.30 in yellow and Sttip = 0.35 in red. Marker style corresponds to the maximum angle of attack, with ? ??  = 10? (left pointing triangle), ? ??  = 20? (square), ? ??  = 20? (diamond), ? ??  = 25? (circle) and ? ??  = 30? (right pointing triangle). Solid thin black line is y = x. Dashed thin black line is the linear regression.  82  The thrust and propulsive efficiency from the quasi-static model calculations and from the experiments follow the same trend over the tested motion regimes. The dynamic experimental thrust is almost always higher than the thrust predicted by the quasi-static theoretical model (exception for SB motion regime 1, but as explained earlier on motion regimes 1 to 15 for SB model were probably asymmetrical by a few degrees and therefore should be considered with precaution. The silver edge markers in plots A and B represent these motion regimes). The dynamic experimental propulsive efficiency is almost always higher than the propulsive efficiency predicted by the quasi-static theoretical model, except at low ???  = 10 for Sttip = 0.3 and 0.35. Therefore the quasi-static theoretical model tends to under-predict the propulsive performance, as previously observed (Shadwick and Ben-Zvi, 2013). If one assumes the observed differences are mostly due to added inertial forces in the dynamic experiments, then it can be useful to estimate the inertial contribution for different motion regime. As expected the inertial force contribution is higher for high ???  and Sttip.   4.4 Flow structure visualization The flow structures observed in this study were qualitatively very similar between the investigated SB and FS tail models. The flow structures between the different motions (3, 13 and 15) were somewhat similar with variation mainly in the strength of the vorticity. The results for the FS tail model during motion 13 and 15 are presented in figure 27.  A masking algorithm identified the no flow structures present in the field of view (i.e. tail model (masked in yellow) and consequent laser shadow (masked in white)), in order to not attempt to resolve the flow structures in these areas. We can observe under both motion regimes what seems to be the formation, strengthening and shedding of a leading edge vortex (LEV) and 83  a nearly constant trail of small vortices being shed from the trailing edge. LEV is a flow structure caused by flow separation at the leading edge that reattaches before reaching the trailing edge (Borazjani and Daghooghi, 2013). Just as the stroke reverses direction at the maximal heave amplitude, a LEV is formed at the leading edge and curves back to the tail surface, which faces the opposite direction of the tail motion. The size or diameter of the LEV is proportional to the lateral velocity, which is maximal at the mid-stroke. As the heave motion starts to decelerate, the LEV is less well defined and starts to mix with the tailing edge vortices. As the stoke reverses direction, the LEV is shed and a trail of small vortices is formed from the trailing edge of that side of the tail model. The size of the LEV and trailing edge vortices (TEV) is bigger for motion regime 15, which has a higher maximal angle of attack (30? rather than 20? for motion 13). In addition the interaction between the LEV and trailing edge vortices appear more complex and turbulent for motion regime 15. 84   Figure 27 ? Flow structure for motion 15 (Column A) and 13 (Column B). One tail-beat stroke is shown from top image (most lateral heave position) to bottom image (start of opposite stroke). Blue is clockwise and red is counter clockwise vortices. Yellow is the tail model cross section. White areas are unresolved flow structures (i.e. laser shadow). The free stream water velocity is 0.7 m/s and the tail-beat frequency was at 1.95 Hz. Therefore the A and B strokes presented here occur within 0.25 s. For this stoke direction the blue color also represents the formation and shedding of the leading edge vortex (LEV) and the red color represents the trailing edge vortices. The black scale bar at the bottom is 10 cm.  85  5 - Discussion 5.1 Tail model accuracy The tail models designed for this study replicated with high bio-fidelity many of the physical characteristics and passive bending behavior of the caudal fin of the Atlantic bluefin tuna. An interesting passive deformation of the caudal fin was observed during the bending behavior testing of the caudal fin and tail models, which might contribute to the tail tip deformation behavior in the swimming tuna. As a probe deflected the middle of the leading edge of one tail lobe of the caudal fin, the tail tip did not move (Fig.28). For the tail models the tail tips were deflected in the same direction as the probe deflection. One might expect the caudal fin tail tips should have deflected to a greater extent than the point of loading if it behaved like a cantilever beam.   Figure 28 ?Simplified fin rays bending behavior in the caudal fin. The bottom gray schematic represents fin rays before loading. The top black schematic represents the simplified fin rays deformation while under loading at the middle of the fin ray (blue arrow). The rectangle represents the hypural plate. One explanation for this behavior involves understanding the structure of fin rays. Fin rays on either side of the hypural plate are not fused, except at the tail tips where the caudal fin narrows, as well as close to the leading edge along the caudal fin. In-between the fin rays are collagen fibers that allow shearing between the fin rays (Alben et al., 2007; Becerra et al., 1983). 86  As a force is applied in the middle of the leading edge of one tail lobe it deforms concavely, as the fin rays on the other side of the tail lobe prevent the tail tip from deflecting. The same deformation behaviour is expected with a uniform load distribution on the tail, which is what we would expect from the water flow over the tail. Similar observations were made on individual fin rays of the Bluegill sunfish (Alben et al., 2007). From there results we extrapolate that with increased tapering of the fin rays as they extend and fuse towards the fin tip, increased shear modulus, as well as increased spacing between fin rays on either side of the hypural plate, would result in decreased bending at the tail tip in the water flow or loading direction. Morphological studies could verify such predictions on a variety of caudal fins. As previously mentioned several observations of swimming tunas or other scombrids in water tunnels have shown the tail tips can form a cupping shape (tips towards the direction of tail side motion), which is opposite to what one would expect from the passive deformation of the tail due to water resistance (Bainbridge, 1963; Brill 2013 personal com.). Other studies showed the tail tips to either stay aligned in the same plane with the hypural plate or to be slightly deflected at the tail tips in the direction of the flow (Fierstine and Walters, 1968; Gibb et al.; 1999), as we observed in our passive tail models. This variability in observed bending behaviors suggests there might be active control of the caudal fin deformation. Whether passive, active control, or probably a combination of both, it was recently hypothesized that this type of tail lobe deformation could be related to the control of the formation and stabilization of the cylindrical spiral vorticity along the leading edge of the caudal fin, which is directly related to the propulsive performance (Borazjani 2013). More will be said about this in the propulsive performance section. 87  The caudal fin is by no doubt a much more complex structure than the tail models of this study. In the real tuna caudal fin the loose connective tissue (i.e. collagen fibers) between the fin rays, bones, and muscles allows shear strains between these materials. In this study the bone and surrounding matrix were formed in such a way that did not allow much shearing between these materials. Therefore the tail tips of the models deflected in the same direction as the probe deflection. It would be interesting to design a tail model with more shear possibility between the bone and surrounding matrix. Whether only passive or perhaps with some active control, it would probably generate interesting bending behaviors like those observed in the real tuna caudal fin.  As for the impact on the propulsive performance, such bending behavior would probably only slightly increase the propulsive performance relative to the effect of the oscillating kinematics. Indeed, though much effort was invested into making tail models with detailed and accurate bone structures, the observed variation in propulsive performance was minimal for the three different tail models and greatest for the oscillating kinematics. More will be said in the following section about the importance of the foil shape versus motion on propulsive performance, as recently investigated by a number of researchers (Borazjani and Sotiropoulos, 2010; Tytell, 2007; Tytell et al., 2010).  5.2 Tail forces isolation To estimate the propulsive performance of the tail model alone, the hydrodynamic and inertial forces of the tail had to be isolated from the forces generated by the rest of the motion system (inertial force of the motion system and rod, as well as the hydrodynamic force of the 88  rod). To do so the rod-alone forces were subtracted from the tail+rod forces. There are strengths and limitations with this approach.  The main strength of this approach is that by directly subtracting the tail+rod by the rod-alone forces, the electrical and mechanical noises present in both sets of forces and specific for each motion regime are directly removed in the tail force data. In addition, the experimental setup using such an approach to isolate the tail model or hydrofoil forces is relatively less complex to build than a self-propelled untethered system. On that note most studies on oscillating foils have hydrofoils that are tethered (not self-propelled) (Anderson et al., 1998; Hover et al., 2004; Read et al., 2003; Schouveiler et al., 2005; Triantafyllou et al., 1993). This certainly is a notable difference with certain numerical simulations and experiments with frictionless air bearings, as the incoming flow within a tail-beat for these studies is varying with the generation of hydrodynamic force and body inertia (Lauder et al., 2007). Minor variation of the free stream flow would modify the strength and direction of the resultant flow and thereby the stability of the leading edge vortex and the hydrodynamic force (Borazjani and Daghooghi, 2013). It would be best to quantify the differences in flow structure and propulsive performance when commanding the same motion to a tethered system and to a self-propeller body. One possible limitation with this approach is that the heave and pitch motions for one motion regime could potentially differ between the tail+rod and rod-alone experiments, as the absence of the tail mass and added mass of displaced water changes the load on the heave and pitch motors. In our experiments the tail mass was 40 g and we did not estimate the added mass of displaced water. Estimating the added mass of water around the tail would be very challenging to separate from the hydrodynamic force, as both vary with the angle of attack and resultant flow acceleration (Dickinson and Gotz, 1993).  However, as the acceleration profiles of heave and 89  pitch motions did not differ between the tail+rod and rod-alone tests by more than 0.58 Rev/s2 (1.2 % error) for pitch and 0.27 m/s2 (0.8 % error) for heave, we assume the stainless steel rod (385g) contributed to most of the load on the motors and that these were properly tuned for the tested load range (Fig. 17 and 18). Another possible limitation is that the rod modified the flow velocity profile encountering the leading edge of the dorsal lobe of the tail, which would affect the pressure gradients and therefore the hydrodynamic force. The velocity profile around the rod connected to the tail was possibly also affected by the presence of the tail model behind it. We did not verify this experimentally, as it was too challenging with the setup of the PIV and motion system. However here we present the case that the rod only had minimum interaction with the bottom 1/3rd of the caudal tail dorsal lobe. Only twice in a tail-beat were the rod and tail orientation axis aligned in series (i.e. tandem arrangement) with the flow. This occurred when the tail was at its most lateral heave position, where ? = 0?. For the rest of the tail-beat the rod and tail model leading edge are in a staggered configuration. There are multiple studies that have looked at flow interaction between two static circular cylinders in tandem and staggered configurations (Sumner, 2010). These provide an estimation of the flow interaction between the rod and leading edge of the dorsal lobe of the tail model. The Reynolds numbers at the rod for all motion regimes were between 4400 and 9200 (with ? = 6.35 ???, ? =  ?1.004 ??10??, ??? = 0.7 ??/? (slowest free stream water velocity) and ??? = 1.45 ??/? (maximum resultant flow for fastest motion regime)). When at Re between 50 ?and ?10? circular cylinders continuously shed small vortices that form a von K?rm?n vortex street, which is a wake where vortices are shed alternatively on either side of the cylinder with opposite vorticity sign and interact to form drag jets of flow (Vogel, 2013). 90  Previous researchers have studied the wake interaction between static staggered circular cylinders at different angles of attack (defined in the same way as in our study), relative distances (distance between center of cylinders divided by cylinder diameter) and Reynolds numbers similar to the arrangement and kinematics of the rod and tail of our study (Hu and Zhou, 2008). From these studies we estimate the interactions between the von K?rm?n vortex streets shed from the rod and flow structure at the leading edge of the tail models. When the rod and tail leading edge are less than 1.5 cm apart or when the angle of attack is less than 20? with a distance of less than 2.5 cm apart, the wake shed from the rod and the flow structure around the leading edge interact. It is unknown if the interaction would enhance or diminish the propulsive performance. If the angle of attack is between 20 and 30? with a rod to tail distance greater than 1.5 cm or for higher relative distance and lower angle of attacks, we hypothesis the wake of the rod and flow structure at the tail leading edge stay separate and distinct from each other. In addition Hu and Zhou?s experimental study was for static cylinders. We believe the rod wake and tail leading edge flow structure would be further spatially separated than reported in their study, as while the rod wake trail would travel down flow, the leading edge would already have moved away laterally. We assume therefore that the presence of the rod had minimal flow impact over the upper 2/3rd section of tail model dorsal lobe.  5.3 Propulsive performance First of all we showed that about 15 of the 30 motion regimes for each of the tail model generated enough thrust to counter the whole body drag estimate (CT equal or above 0.19) (Fig.23). These ?successful? 15 motion regimes were mostly at high Sttip and ???  values of the tested parameter range. All motion regimes that did not generate enough thrust to counter the 91  body drag were at Strod below 0.25 (Appendix A). This suggests tunas probably operate at Sttip equal or above 0.3 or that other mechanisms increase the thrust production in real tunas, which were reported to swim at Sttip between 0.2 and 0.3 (Eloy, 2012). One of the possible thrust increasing mechanisms that was not included in this study is simply the presence of the body preceding the caudal fin. The body can enhance the propulsive performance of the aquatic animal, as the energy from the vortices shed from the body structures can constructively interact with the tail (Beal et al., 2006; Fish and Lauder, 2006; Flammang et al., 2011; Nauen and Lauder, 2001; Nauen and Lauder, 2002; Triantafyllou et al., 2000).  The maximum propulsive efficiency for a CT equal or above 0.19 was between 45 and 50% depending on the tail model and was observed when at Sttip of 0.35 and ???  of 15?. The peak propulsive performance, which is the combination of a high coefficient of thrust and a high propulsive efficiency, was observed for all tail models at Sttip of 0.35 and ???  of 20?, where ?p = 0.43 and CT = 0.3 for the average values of all three tail models (Fig. 23, 24 and Appendix A). Within the biologically relevant motion regimes tested, we found a peak propulsive performance supporting the common assumption that migrating tunas swim close to their minimum gross cost of transport speed. The three tail models in our study had, to our initial surprise, similar propulsive performance. The shape of the tails was identical, but the bending behavior varied between the tail models in both the chordwise or spanwise direction. In general and for large variations in the flexural behavior of the hydrofoil, there exists a compromise between high propulsive efficiency and high thrust generation, as improving the thrust coefficient usually requires increased stiffness and improving the propulsive efficiency usually requires increased flexibility (Shimizu et al., 2004). However previous theoretical and experimental investigations have reported that under 92  proper motion and bending behaviour of the hydrofoil, an increase in propulsive efficiency with only a small decrease in thrust is achieved when using a flexible foil compared to a rigid one (Barannyk et al., 2012; Katz and Weihs, 1978; Liu and Bose, 1997; Prempraneerach et al., 2003; Takada et al., 2010). For a similar kinematic parameter range as the motion regimes tested in our study the propulsive efficiency was increased by 36% with nearly no change for the coefficient of thrust for a rectangular foil with chordwise flexibility compared to a rigid one. (Prempraneerach et al., 2003). Our results failed to support the hypothesis that the flexible tail models would have enhanced propulsive performance compared to the stiff tail model. However, the flexible foil used in that study was made of a material with a young?s modulus in bending (E) of 2 orders of magnitude less than the bone material used in our study. In comparison the bending behaviors of the ?flexible? tail models (FC and FS) were only about 5 times less resistant to bending than the stiff SB model. This certainly could be reason why we did not observe major changes in the propulsive performance between the different tail models of this study.  In contrast, we observed greater variation in propulsive performance between the different motion regimes. For all tail models, motions with low ???  had high propulsive efficiency and low coefficient of thrust. At high ???  the coefficient of thrust was high and the propulsive efficiency was low. High Sttip increased the coefficient of thrust and also slightly increased the propulsive efficiency. It seems the tail kinematics had a greater impact on the propulsive performance of the tail models compared to the different bending behaviors tested in this study. These findings of our study are in agreement with the current scientific understanding of key parameters for high propulsive performance. Indeed numerous recent studies have shown 93  that shape and bending behavior of the hydrofoil to have less impact on the propulsive performance than the hydrofoil kinematics (Borazjani and Daghooghi, 2013; Borazjani and Sotiropoulos, 2010; Hartloper, 2013; Rival et al., 2009; Tytell et al., 2010; von Ellenrieder et al., 2008). A recent numerical simulation suggests the shape affects the smoothness and complexity of the vortex loops, while the kinematics affect the formation and strength of the vortex loops (Borazjani and Sotiropoulos, 2010). Even a rectangular plate oscillating with the right kinematics can generate a stable leading edge vortex (LEV) (Borazjani and Daghooghi, 2013). The LEV causes a lower pressure region by the leading edge of the tail, which changes the pressure distribution along the caudal fin and therefore is related to the generation of the hydrodynamic force. A strong LEV is associated with a high thrust coefficient (Anderson et al., 1998). The leading edge geometry of rectangular foils was shown to affect the onset of the LEV growth, but the overall trend for the LEV growth and shedding is the same for different leading edge geometries (Rival et al., 2013).  The flow structures observed in this study were qualitatively very similar between the investigated SB and FS tail models (Fig.27). This is in agreement with the dynamic force data, where the coefficients of thrust were nearly identical and the propulsive efficiencies for the FS tail model followed the same trend as SB tail model, but at slightly lower values, when comparing tail models for a same motion regime (Fig.23 and 24). The flow structures between the different motions (3, 13 and 15) were somewhat similar with mainly the strength of the vorticity varying. Motion regime 15 had a higher maximum angle of attack (??? = 30?) and slightly higher ???  (by 10%), which is probably why the LEV was larger in diameter than for the similar motion regime 13 (except with ??? = 20?). Though the force measurements were not performed at the same time as the flow visualization, we can assume these sets of force and 94  flow structure data acquired for the same motion regime were synchronized in order to discuss general trends. The higher vorticity size and the higher number of vortices shed in the wake (due to the interaction of the LEV with the trailing edge vortices) for motion regime 15 is in agreement with the higher CT = 0.34 and lower ?p = 0.31 calculated from the force experiments, compared to motion regime 13 with CT = 0.27 and ?p = 0.4. Recently a study has shown with numerical simulations that when a homocercal tail, such as a mackerel caudal fin, oscillates at Strod = 0.25 (as well as with other biologically relevant kinematics) that a stable LEV remains attached near the leading edge over the duration of the tail-beat (Borazjani and Daghooghi, 2013).  Much research considering 2-Dimensional flow, where flow is constricted in the chordwise direction (e.g. using circular endplates at each end of the foil), have found that for thrust generating hydrofoils undergoing a sinusoidal angle of attack waveform, there is one relatively large-scale well defined vortex that is shed from the tail at each stroke. Other smaller drag contributing vortices are present if the angle of attack waveform is composed of higher harmonics (Anderson et al., 1998; Hover et al., 2004; Read et al., 2003; Schouveiler et al., 2005; Triantafyllou et al., 1993). Vortices are shed around the instant of maximum rate of change of the angle of attack (Anderson et al., 1998; Hover et al., 2004). For the large-scale vortices this occurs when the tail pitch axis is at the most lateral heave position (with phase shift being 90?) (Hover et al., 2004). Maximum propulsive performance is obtained when the two large-scale vortices shed within a tail-beat are spatio-temporally arranged in such a way that they positively interact to form a reverse von k?rm?n vortex street, where propulsive jets are formed. This usually occurs at a Strod within 0.25 to 0.35 (Anderson et al., 1998; Eloy, 2012; Triantafyllou et al., 1993; von Ellenrieder et al., 2008).  95  When considering 3-Dimensional flow experiments, it is still true that the maximum propulsive performance occurs within the same kinematic parameter range, however the shape of the wake structure is quite different (von Ellenrieder et al., 2008). Recently researchers provided an explanation for this difference: it is mainly caused by the spanwise flow from the mid-anterior portion of the caudal fin to the tail tips (Borazjani and Daghooghi, 2013; von Ellenrieder et al., 2008). As we previously mentioned, in 2-Dimensional studies the flow over the tail model or foil is only in the chordwise direction. However with 3-Dimensional flows the interaction between the spanwise flow and the LEV forms a cylindrical spiral along the leading edge, where vorticity convects along the leading edge and joins with at the tail tip vortex, where it then forms a vortex loop. This prevents the LEV from growing or ?rolling? to the point of becoming unstable, being shed and causing the foil to stall during the tail-beat stroke. The sweepback angle of the caudal fin was shown to increase the spanwise flow and therefore helps to stabilize the LEV. Similar conclusions have been made from 3-Dimensional Particle Tracking Velocimetry (3D-PTV) experiments (Hartloper, 2013). These recent studies support the hypothesis that the sweepback shaped lunate caudal fin of tunas evolved to satisfy the needs for faster and sustained swimming of these pelagic fish during the expansion of oceans (Graham and Dickson, 2000; van Dam, 1987). Our study provides an estimate of the propulsive performance of the caudal fin of the Atlantic bluefin tuna that can be used as an indicator of the propulsive performance of the whole animal. However it is uncertain how the propulsive performance would be affected when accounting for the whole body. The thrust generation would probably increase due to the constructive interaction of the vortices shed from the body with the caudal fin, as previously shown for a number of fish (Beal et al., 2006; Fish and Lauder, 2006; Flammang et al., 2011; 96  Nauen and Lauder, 2001; Nauen and Lauder, 2002; Triantafyllou et al., 2000). The propulsive efficiency would only increase if the extra thrust generation due to body vorticity interaction with the caudal fin were higher than the increase in power to oscillate the body (recall eq.18).  There are a few considerations that need to be expressed before comparing our propulsive performance results with previous studies. First of all, comparisons should be made for similar sized animals and swimming speeds. Fish and marine animals usually have the highest propulsive efficiency when swimming at their natural most common swimming speeds (Tytell et al., 2010). A thunniform animal has a higher propulsive efficiency at high speeds and an anguilliform animal is more efficient at lower speeds. Anguilliforms (e.g. eels and lampreys) generate drag-based thrust by pushing fluid in the opposite direction of travel with their body, whereas thunniform swimmers generate lift-based thrust (Sfakiotakis et al., 1999; Tytell, 2007). The power requirements from an anguilliform swimmer to move at similar speeds to a tuna would be much higher (Videler and Wardle, 1991; Wardle and Videler, 1980). This also emphasizes the need to report in studies the amount of thrust generation for a given propulsive efficiency rather than only one or the other, which is much less informative. In addition there are many kinematic parameters that together form a biologically relevant motion. Most of the oscillating foil experiments from the MIT group have been conducted at constant heave amplitudes and by modifying the oscillating frequency to generate motions with similar Strod (0.25 to 0.35) to those in our experiments (Anderson et al., 1998; Hover et al., 2004; Prempraneerach et al., 2003; Read et al., 2003; Schouveiler et al., 2005; Triantafyllou et al., 1991; Triantafyllou et al., 1993). As our goal was to mimic tuna propulsion, the frequency was kept constant for a given swimming speed (flow rate), as it is observed to be the case in tunas. Therefore, though our study was at similar Strod numbers as most oscillating 97  foil studies interested in high propulsive performance, the oscillating frequencies (f), Reynolds numbers (Re) and free stream water velocities (U) were much higher than most of these studies. In addition the maximum half pitch axis heave to chord ratio (hmax/mcl) was 0.75 or 1 for most of their experiments, whereas in our study the hmax/mcl was between 0.95 and 1.88. These kinematic differences could considerably alter foil deformation, added mass effects and wake structure.  Secondly there are a number of differences between our study and previous ones. Most experiments investigated foils with constant cross sectional shape and chord length. In the literature the suggested key kinematic parameter space for certain flow structure categories and resulting propulsive performances are for the most part normalized by the chord length of the foil. Reynolds number (Re), reduced frequency (k), heave amplitude to chord length (hamp/c) are parameters that require a characteristic chord length measurement in their calculation. For our tail models there is no constant chord length, so the mean chord length was used in the calculations. The planform area is also used to normalize the coefficient of force. However the planform area of the tail models includes the planform area of the anterior conical shaped volume preceding the pitch axis of the tail model, which probably is not a positive thrust-generating surface. As previously mentioned the tail tip Strouhal (Sttip) is reported in the biological literature and the pitch axis Strouhal (Strod) in the engineering literature. Therefore values of propulsive performance should not be directly compared, as these cannot be easily normalized to account for differences in shape and other experimental design differences; rather, trends in propulsive performance for varying kinematic and shape parameters should be compared between studies. Thought most previous studies actuated hydrofoils at speeds and frequencies far too slow for the size of the foil in order to mimic biologically relevant tuna motions, there are some 98  common trends (e.g. hmax = 15 cm, U = 0.4 m/s and f = 1Hz, (Anderson et al., 1998); hmax = 20 cm, U = 0.3 m/s and f = 0.5 Hz, (Hover et al. 2004); hmax = 7.5 cm, U = 0.4 m/s and f = 0.5 to 1 Hz (Prempraneerach et al., 2003; Read et al., 2003; Schouveiler et al., 2005)). Interestingly the studies with the most similar kinematics as ours have also found a peak propulsive performance to occur at ??? = 20 and Strod = 0.35 (Hover et al., 2004; Prempraneerach et al., 2003; Read et al., 2003). The effect of Strouhal number (St) on propulsive performance follows the same trend as what we observed in this study. Strouhal number (St) is recognized as the most crucial parameter for the formation of certain wake structures corresponding to high propulsive performance (Anderson et al., 1998; Borazjani and Sotiropoulos, 2010; Prempraneerach et al., 2003; Triantafyllou et al., 1993). The difference in shape between the tail model and the rectangular hydrofoils used in these studies is striking however the peak propulsive performance was described for the same motion kinematics. This strengthens the argument that kinematics have a stronger effect on the propulsive performance than the shape of the foil. In addition the flow structures observed in our study are similar to those reported for rectangular hydrofoils oscillating with the similar kinematics (Fenercioglu and Cetiner, 2012; Rival et al., 2009; Rival et al., 2013). The flow category D described by Fenercioglu and Cetiner 2012 for a rectangular foil is somewhat similar to the one observed in this study with the exception that the LEV is stronger in our study. The lower strength of wake structure is probably due to the lower oscillating frequency (theirs was 0.1 < f  < 0.6 and ours 1.95 and 2.54 Hz), heave amplitude to chord length ratio (theirs was 0.25 < hamp/c < 1 and ours 1 < hamp/c < 2) and Reynolds numbers (theirs was 825 < Re < 13 700 and ours 22,900 and 34,300) (Fenercioglu and Cetiner, 2012). This category of flow structure was shown to be typical of motions with Strod between 0.2 and 0.4. The spanwise flow was certainly reduced for these rectangular shaped foil experiments 99  compared to the tail models, and as we previously mentioned such reduction of spanwise flow could decrease the stability of the LEV. However Rival (2009) suggests careful tuning of the foil kinematics can stabilize the LEV without the presence of spanwise flow, which might explain why the 2-Dimensional wake structure visualizations were similar.  The flow visualization in our study is incomplete and indicates, along with recent studies, the importance and need of investigating 3-Dimensional flow for accurate understanding of flow structures in most biological situations (Borazjani and Daghooghi, 2013; Borazjani and Sotiropoulos, 2010; Flammang et al., 2011; Nauen and Lauder, 2002; Wilga and Lauder, 2004). A numerical simulation observed a vortex-within-a-vortex structure for a large-aspect ratio homocercal tail (Borazjani and Sotiropoulos, 2010), similar to 2D-PIV flow visualization for the heterocercal tail of the spiny dogfish shark,	 ?Squalus acanthias (Wilga and Lauder, 2004) where the cylindrical spiral at the leading edge creates the outer vortex loop while the trailing edge creates the inner vortex loop. Other 2D-PIV flow visualization of the wake of chub mackerel, Scomber japonicas, (Scombridae family) for swimming speeds of 1.2 to 2.2 FL/s revealed single vortex loop formation per stroke. These single or double vortex loops are linked in series and form a reverse von K?rm?n wake, where the vortex loops interact to produce propulsive jets (Nauen and Lauder 2002). Characterizing the smoothness and complexity of the vortex loops shed from tail model with different shapes but actuated with identical motion regimes would be useful to understand the mechanism involved in generating enhanced propulsive performance. Also, as PIV systems and high-speed cameras are becoming more portable and submersible (Flammang et al., 2011; Tritico et al., 2007), it soon might be feasible to describe the 3-Dimensional kinematics and hydrodynamics around different freely swimming aquatic animals, 100  which could reveal associations between fine-tuning of the caudal fin and body deformation with increased propulsive performance. As an alternative to experimental work with live fish or complex actively deformable tail models, numerical simulation (such as by Borazjani and Daghooghi, 2013) could investigate the effects of active control of the caudal fin deformation kinematics on the wake structure. In addition, it would be interesting to continue numerical simulations, such as those performed by Borazjani and Daghooghi (2010) to see if the biological variation of high aspect ratio and sweepback angle in thunniform caudal fins might be tuned to caudal fin kinematics of the animal in such a way that the spanwise flow is of the right magnitude to stabilize the LEV during each tail-beat, which would increase the propulsive performance.   101  6 - Conclusion In this study tuna tail models replicated, with a high level of bio-fidelity, the motion kinematics, structure and bending behavior of the caudal fin of the Atlantic bluefin tuna. For all of the motion regimes the mean thrust over a tail-beat was positive and about half of those generated sufficient thrust to counter the whole body drag estimates (CT equal or above 0.19). The three tail models in our study had similar propulsive performance trends and values, even though the overall bending behaviors of the ?flexible? tail models (FC and FS) were about 5 times less resistant to bending than the stiff SB model. Propulsive performance trends and values were similar to previous experiments investigating a similar parametric space, where the peak propulsive performance, which is the combination of a high coefficient of thrust and a high propulsive efficiency, was observed for all tail models and hydrofoils at Sttip of 0.35 and ???  of 20?. The average peak propulsive performance for the three tail models was ?p = 0.43 and CT = 0.3. As with recent studies, we conclude that propulsive performance is more sensitive to kinematics rather than the shape and bending behavior of the caudal fin or hydrofoil. Future work should directly compare, within the same experimental system, the propulsive performance for different tail models in shape, bending behavior and motion kinematics of aquatic animals of different swimming modes of propulsion. These direct comparisons between swimming modes would be very helpful to characterize and quantify the relative propulsive performance enhancements of one swimming mode over another. Within the thunniform swimmers, members exhibit vast morphological differences in their caudal fin. For example whales have thicker cross sectional shaped caudal fins and do not have fin rays, but the complex arrangement of ligamentous layers and dense connective tissues gives stiffness to the caudal fin (Sun et al., 2010). It would be interesting to compare the effect of bending behaviour kinematics of these 102  caudal fins on their propulsive performance. These direct comparisons would shed light on the interplay between natural selection and evolutionary constraints. 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Hydrodynamic Experimental Investigation on Efficient Swimming of Robotic Fish Using Self-propelled Method. Int. J. Offshore Polar Eng. 20, 167?174. Westneat, M. W. and Wainwright, S. A. (2001). Mechanical design for swimming: muscle, tendon, and bone. In Fish Physiology (ed. Barbara Block and E. Stevens), pp. 271?311. Academic Press. Wilga, C. D. and Lauder, G. V. (2004). Biomechanics: Hydrodynamic function of the shark?s tail. Nature 430, 850?850.   110  Appendix A - Summary data table MR	 ?	 ? Sttip	 ? Amax	 ? ?max	 ? Strod	 ? hmax	 ? ?max	 ? V?max	 ? Ac?max	 ? Vhmax	 ? Achmax	 ? Q	 ?CT	 ?(SB)	 ? D	 ?CT	 ?(SB)	 ? Q	 ??p	 ?(SB)	 ? D	 ??p	 ?(SB)	 ? Q	 ?CT	 ?(FC)	 ? D	 ?CT	 ?(FC)	 ? Q	 ??p	 ?(FC)	 ? D	 ??p	 ?(FC)	 ? D	 ?CT	 ?(FS)	 ? D	 ??p	 ?(FS)	 ?1	 ? 0.25	 ? 0.09	 ? 10	 ? 0.18	 ? 0.0325	 ? 19.63	 ? 0.77	 ? 7.63	 ? 0.40	 ? 4.88	 ? 0.06	 ? 0.05	 ? 0.42	 ? 0.20	 ? 0.07	 ? 0.09	 ? 0.41	 ? 0.43	 ? 0.04	 ? 0.21	 ?2	 ? 0.25	 ? 0.09	 ? 15	 ? 0.20	 ? 0.0350	 ? 16.49	 ? 0.68	 ? 7.24	 ? 0.43	 ? 5.25	 ? 0.07	 ? 0.08	 ? 0.33	 ? 0.26	 ? 0.07	 ? 0.13	 ? 0.33	 ? 0.42	 ? 0.09	 ? 0.29	 ?3	 ? 0.25	 ? 0.09	 ? 20	 ? 0.21	 ? 0.0375	 ? 13.28	 ? 0.60	 ? 7.08	 ? 0.46	 ? 5.63	 ? 0.06	 ? 0.11	 ? 0.23	 ? 0.27	 ? 0.06	 ? 0.16	 ? 0.23	 ? 0.39	 ? 0.12	 ? 0.28	 ?4	 ? 0.25	 ? 0.09	 ? 25	 ? 0.22	 ? 0.0400	 ? 10.00	 ? 0.51	 ? 7.09	 ? 0.49	 ? 6.00	 ? 0.04	 ? 0.13	 ? 0.14	 ? 0.24	 ? 0.05	 ? 0.17	 ? 0.13	 ? 0.32	 ? 0.11	 ? 0.21	 ?5	 ? 0.25	 ? 0.09	 ? 30	 ? 0.23	 ? 0.0420	 ? 6.50	 ? 0.41	 ? 7.02	 ? 0.51	 ? 6.30	 ? 0.02	 ? 0.14	 ? 0.06	 ? 0.20	 ? 0.02	 ? 0.15	 ? 0.05	 ? 0.22	 ? 0.10	 ? 0.15	 ?6	 ? 0.3	 ? 0.11	 ? 10	 ? 0.21	 ? 0.0380	 ? 23.63	 ? 0.96	 ? 9.74	 ? 0.47	 ? 5.70	 ? 0.09	 ? 0.09	 ? 0.48	 ? 0.32	 ? 0.10	 ? 0.13	 ? 0.47	 ? 0.45	 ? 0.07	 ? 0.27	 ?7	 ? 0.3	 ? 0.11	 ? 15	 ? 0.23	 ? 0.0410	 ? 20.66	 ? 0.89	 ? 9.76	 ? 0.50	 ? 6.15	 ? 0.10	 ? 0.15	 ? 0.40	 ? 0.39	 ? 0.11	 ? 0.19	 ? 0.40	 ? 0.50	 ? 0.13	 ? 0.34	 ?8	 ? 0.3	 ? 0.11	 ? 20	 ? 0.24	 ? 0.0435	 ? 17.29	 ? 0.80	 ? 9.79	 ? 0.53	 ? 6.53	 ? 0.10	 ? 0.22	 ? 0.30	 ? 0.41	 ? 0.11	 ? 0.23	 ? 0.30	 ? 0.44	 ? 0.17	 ? 0.32	 ?9	 ? 0.3	 ? 0.11	 ? 25	 ? 0.26	 ? 0.0460	 ? 13.84	 ? 0.72	 ? 9.98	 ? 0.56	 ? 6.90	 ? 0.08	 ? 0.24	 ? 0.21	 ? 0.35	 ? 0.09	 ? 0.25	 ? 0.21	 ? 0.38	 ? 0.19	 ? 0.28	 ?10	 ? 0.3	 ? 0.11	 ? 30	 ? 0.27	 ? 0.0480	 ? 10.10	 ? 0.62	 ? 10.00	 ? 0.59	 ? 7.20	 ? 0.06	 ? 0.24	 ? 0.14	 ? 0.30	 ? 0.06	 ? 0.25	 ? 0.13	 ? 0.31	 ? 0.19	 ? 0.22	 ?11	 ? 0.35	 ? 0.13	 ? 10	 ? 0.25	 ? 0.0440	 ? 27.60	 ? 1.16	 ? 12.29	 ? 0.54	 ? 6.60	 ? 0.12	 ? 0.16	 ? 0.53	 ? 0.44	 ? 0.13	 ? 0.17	 ? 0.52	 ? 0.48	 ? 0.12	 ? 0.31	 ?12	 ? 0.35	 ? 0.13	 ? 15	 ? 0.26	 ? 0.0470	 ? 24.44	 ? 1.09	 ? 12.57	 ? 0.58	 ? 7.05	 ? 0.14	 ? 0.26	 ? 0.45	 ? 0.50	 ? 0.15	 ? 0.25	 ? 0.45	 ? 0.49	 ? 0.20	 ? 0.39	 ?13	 ? 0.35	 ? 0.13	 ? 20	 ? 0.28	 ? 0.0495	 ? 20.91	 ? 1.01	 ? 12.79	 ? 0.61	 ? 7.43	 ? 0.14	 ? 0.31	 ? 0.35	 ? 0.47	 ? 0.15	 ? 0.31	 ? 0.35	 ? 0.46	 ? 0.27	 ? 0.40	 ?14	 ? 0.35	 ? 0.13	 ? 25	 ? 0.29	 ? 0.0520	 ? 17.31	 ? 0.92	 ? 13.11	 ? 0.64	 ? 7.80	 ? 0.13	 ? 0.36	 ? 0.27	 ? 0.42	 ? 0.14	 ? 0.36	 ? 0.26	 ? 0.41	 ? 0.31	 ? 0.36	 ?15	 ? 0.35	 ? 0.13	 ? 30	 ? 0.30	 ? 0.0545	 ? 13.68	 ? 0.84	 ? 13.62	 ? 0.67	 ? 8.18	 ? 0.11	 ? 0.38	 ? 0.20	 ? 0.36	 ? 0.12	 ? 0.37	 ? 0.19	 ? 0.34	 ? 0.34	 ? 0.31	 ?Min	 ? 0.25	 ? 0.09	 ? 10.00	 ? 0.18	 ? 0.0325	 ? 6.50	 ? 0.41	 ? 7.02	 ? 0.40	 ? 4.88	 ? 0.02	 ? 0.05	 ? 0.06	 ? 0.20	 ? 0.02	 ? 0.09	 ? 0.05	 ? 0.22	 ? 0.04	 ? 0.15	 ?Max	 ? 0.35	 ? 0.13	 ? 30.00	 ? 0.30	 ? 0.0545	 ? 27.60	 ? 1.16	 ? 13.62	 ? 0.67	 ? 8.18	 ? 0.14	 ? 0.38	 ? 0.53	 ? 0.50	 ? 0.15	 ? 0.37	 ? 0.52	 ? 0.50	 ? 0.34	 ? 0.40	 ?Motion regime 1 to 15: U = 0.7 m/s, f = 1.95 Hz, ? = 90?, Re = 22900. See list of Abbreviations and Symbols. CT above 0.19 in red. 111   MR	 ?	 ? Sttip	 ? Amax	 ? ?max	 ? Strod	 ? hmax	 ? ?max	 ? V?max	 ? Ac?max	 ? Vhmax	 ? Achmax	 ? Q	 ?CT	 ?(SB)	 ? D	 ?CT	 ?(SB)	 ? Q	 ??p	 ?(SB)	 ? D	 ??p	 ?(SB)	 ? Q	 ?CT	 ?(FC)	 ? D	 ?CT	 ?(FC)	 ? Q	 ??p	 ?(FC)	 ? D	 ??p	 ?(FC)	 ? D	 ?CT	 ?(FS)	 ? D	 ??p	 ?(FS)	 ?16	 ? 0.25	 ? 0.10	 ? 10	 ? 0.19	 ? 0.0395	 ? 20.98	 ? 1.08	 ? 14.07	 ? 0.63	 ? 10.05	 ? 0.07	 ? 0.12	 ? 0.44	 ? 0.53	 ? 0.08	 ? 0.10	 ? 0.43	 ? 0.44	 ? 0.07	 ? 0.31	 ?17	 ? 0.25	 ? 0.10	 ? 15	 ? 0.20	 ? 0.0420	 ? 17.55	 ? 0.95	 ? 13.31	 ? 0.67	 ? 10.69	 ? 0.08	 ? 0.14	 ? 0.35	 ? 0.45	 ? 0.08	 ? 0.12	 ? 0.35	 ? 0.41	 ? 0.11	 ? 0.35	 ?18	 ? 0.25	 ? 0.10	 ? 20	 ? 0.22	 ? 0.0445	 ? 14.07	 ? 0.83	 ? 12.87	 ? 0.71	 ? 11.33	 ? 0.07	 ? 0.15	 ? 0.25	 ? 0.35	 ? 0.07	 ? 0.15	 ? 0.24	 ? 0.37	 ? 0.14	 ? 0.32	 ?19	 ? 0.25	 ? 0.10	 ? 25	 ? 0.23	 ? 0.0470	 ? 10.54	 ? 0.70	 ? 12.66	 ? 0.75	 ? 11.96	 ? 0.05	 ? 0.16	 ? 0.15	 ? 0.28	 ? 0.05	 ? 0.17	 ? 0.15	 ? 0.30	 ? 0.15	 ? 0.27	 ?20	 ? 0.25	 ? 0.10	 ? 30	 ? 0.23	 ? 0.0485	 ? 6.57	 ? 0.54	 ? 12.00	 ? 0.77	 ? 12.34	 ? 0.02	 ? 0.14	 ? 0.06	 ? 0.20	 ? 0.02	 ? 0.15	 ? 0.05	 ? 0.22	 ? 0.13	 ? 0.19	 ?21	 ? 0.3	 ? 0.12	 ? 10	 ? 0.22	 ? 0.0465	 ? 25.25	 ? 1.35	 ? 18.19	 ? 0.74	 ? 11.84	 ? 0.10	 ? 0.12	 ? 0.50	 ? 0.43	 ? 0.11	 ? 0.13	 ? 0.50	 ? 0.47	 ? 0.12	 ? 0.42	 ?22	 ? 0.3	 ? 0.12	 ? 15	 ? 0.24	 ? 0.0495	 ? 21.96	 ? 1.24	 ? 18.10	 ? 0.79	 ? 12.60	 ? 0.12	 ? 0.19	 ? 0.42	 ? 0.46	 ? 0.13	 ? 0.18	 ? 0.42	 ? 0.45	 ? 0.18	 ? 0.45	 ?23	 ? 0.3	 ? 0.12	 ? 20	 ? 0.25	 ? 0.0520	 ? 18.32	 ? 1.12	 ? 17.94	 ? 0.83	 ? 13.24	 ? 0.11	 ? 0.23	 ? 0.32	 ? 0.40	 ? 0.12	 ? 0.21	 ? 0.32	 ? 0.39	 ? 0.22	 ? 0.40	 ?24	 ? 0.3	 ? 0.12	 ? 25	 ? 0.26	 ? 0.0545	 ? 14.64	 ? 0.99	 ? 18.08	 ? 0.87	 ? 13.87	 ? 0.09	 ? 0.26	 ? 0.23	 ? 0.35	 ? 0.10	 ? 0.25	 ? 0.22	 ? 0.36	 ? 0.26	 ? 0.36	 ?25	 ? 0.3	 ? 0.12	 ? 30	 ? 0.27	 ? 0.0565	 ? 10.71	 ? 0.85	 ? 17.91	 ? 0.90	 ? 14.38	 ? 0.07	 ? 0.25	 ? 0.15	 ? 0.28	 ? 0.07	 ? 0.24	 ? 0.14	 ? 0.28	 ? 0.25	 ? 0.29	 ?26	 ? 0.35	 ? 0.14	 ? 10	 ? 0.26	 ? 0.0540	 ? 29.38	 ? 1.64	 ? 23.13	 ? 0.86	 ? 13.74	 ? 0.14	 ? 0.17	 ? 0.55	 ? 0.44	 ? 0.15	 ? 0.16	 ? 0.54	 ? 0.45	 ? 0.16	 ? 0.46	 ?27	 ? 0.35	 ? 0.14	 ? 15	 ? 0.27	 ? 0.0565	 ? 25.65	 ? 1.51	 ? 23.03	 ? 0.90	 ? 14.38	 ? 0.16	 ? 0.25	 ? 0.46	 ? 0.47	 ? 0.17	 ? 0.24	 ? 0.46	 ? 0.48	 ? 0.23	 ? 0.45	 ?28	 ? 0.35	 ? 0.14	 ? 20	 ? 0.29	 ? 0.0595	 ? 22.12	 ? 1.41	 ? 23.64	 ? 0.95	 ? 15.14	 ? 0.16	 ? 0.31	 ? 0.37	 ? 0.43	 ? 0.17	 ? 0.29	 ? 0.37	 ? 0.42	 ? 0.28	 ? 0.41	 ?29	 ? 0.35	 ? 0.14	 ? 25	 ? 0.30	 ? 0.0620	 ? 18.30	 ? 1.28	 ? 23.96	 ? 0.99	 ? 15.78	 ? 0.14	 ? 0.35	 ? 0.28	 ? 0.38	 ? 0.15	 ? 0.36	 ? 0.28	 ? 0.41	 ? 0.33	 ? 0.37	 ?30	 ? 0.35	 ? 0.14	 ? 30	 ? 0.31	 ? 0.0640	 ? 14.24	 ? 1.14	 ? 24.17	 ? 1.02	 ? 16.29	 ? 0.12	 ? 0.36	 ? 0.21	 ? 0.31	 ? 0.12	 ? 0.35	 ? 0.20	 ? 0.32	 ? 0.34	 ? 0.31	 ?Min	 ? 0.25	 ? 0.10	 ? 10.00	 ? 0.19	 ? 0.0395	 ? 6.57	 ? 0.54	 ? 12.00	 ? 0.63	 ? 10.05	 ? 0.02	 ? 0.12	 ? 0.06	 ? 0.20	 ? 0.02	 ? 0.10	 ? 0.05	 ? 0.22	 ? 0.07	 ? 0.19	 ?Max	 ? 0.35	 ? 0.14	 ? 30.00	 ? 0.31	 ? 0.0640	 ? 29.38	 ? 1.64	 ? 24.17	 ? 1.02	 ? 16.29	 ? 0.16	 ? 0.36	 ? 0.55	 ? 0.53	 ? 0.17	 ? 0.36	 ? 0.54	 ? 0.48	 ? 0.34	 ? 0.46	 ?Motion regime 16 to 30: U = 1.05 m/s, f = 2.54 Hz, ? = 90?, Re = 34300. See list of Abbreviations and Symbols. CT above 0.19 in red. 112  Appendix B - Masking and multi-pass adaptive image interrogation algorithms Performed operation list as shown in DaVis 8.13: 1) Particle Image Velocimetry (PIV): Vector calculation ? double frames a. Image preprocessing i. Sliding background subtracted using scale length of 10 pixel ii. Particle intensity normalization using scale length of 10 pixel b. Mask Definition i. A geometric mask was applied to all frames to remove velocity calculation around the border of the frames, where particle intensity was low. ii. An algorithmic mask (set value): 1. Invert image (0) 2. Erosion (3) 3. Above threshold (750) 4. Binarize image (2) 5. Dilate(3) 6. Smoothing (3) 7. Dilate (1) 8. Erosion (1) c. Vector calculation parameters i. Old mask is deleted and new algorithmic and geometric masks are added.  ii. Cross-correlation.  iii. Multi-pass (decreasing size)  1. First-pass is 64 x 64 window size, weight is 1:1, overlap is 50 and 2 passes 2. Second-pass is 16 x 16 window size, weight is 1:1, overlap is 50 and 2 passes 3. Option applied: Image correction and High ?accuracy mode for final passes (Lanczos reconstruction 10)  iv. GPU (NVIDIA graphics processing unit) was used for image preprocessing, vector calculation and vector post-processing. Maximum shift settings: 1. Pass 1 of window size 64 x 64, overlap 50%, maximum shift is 10 pixel 2. Pass 2 of window size 64 x 64, overlap 50%, maximum change in shift is 4 pixel 3. Pass 3 of window size 32 x 32, overlap 50%, maximum change in shift is 2 pixel and same for all further passes. v. Multi-pass options 1. Initial window shift for image reconstruction is constant with default values dx and dy at 0 pixel/s. 113  2. Deformed interrogation windows have symmetric shift for both frames. vi. Multi-pass post processing 1. A median filter was applied 3 times to remove vectors in difference to average was superior to 1.5 x RMS of neighbours. 2. Empty spaces adjacent to at least two neighbors were filled up using interpolation. 3. A smooting filter was applied 3 times to the final vector field using a 3 x 3 window.  2) Second operation is vector post processing a. Vectors were deleted if their peak ratio Q were smaller than 1.5 b. A median filter was applied 3 times to strongly remove vectors if their difference to average was superior to 1.2 x RMS of neighbors and (re)insert vectors if difference to average was inferior to 2.2 x RMS of neighbors. c. Groups inferior to 10 vectors were removed d. Empty spaces adjacent to at least two neighbors were filled up using interpolation. e. A smoothing filter was applied 3 times to the final vector field using a 3 x 3 window. 3) Operation 3 is to extract the two-dimensional vorticity, rotation-Z, in the XY plane (Eyx ? Exy) from the vector field.  

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