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Biomechanics of elasmobranch locomotion Matt Gardner Laura Macesic Equilibrium • • • • Gravity Lift Drag Thrust Vectors that suck • Gravity • Drag 1. Skin friction • Depends on total exposed surface 2. Pressure drag • Depends on shape and Reynolds number Reynolds Number Ratio of inertial and viscous forces Re = Fi = ρlv Fv Bacteria swimming Re = 0.000001 Fruit fly flying Re = 100 Large whale swimming Re = 200 000 000 At low Re, streamlining does no good • decreases in pressure drag are offset by total exposed surface area At high Re, streamlining can be very effective • decreases drag by up to a full order of magnitude Vectors that are good: Lift Lower pressure, higher velocity above, Higher pressure, lower velocity below (Bernoulli Principle) - Caused by asymmetry, inclinations, or both - Force is created perpendicular to the direction of flow of the overall fluid Vectors that are good: Thrust lift resultant THRUST drag Angle of Attack How do fish make thrust? • Thrust is used to transfer momentum to liquid – Drag based • Pulling yourself through water – Lift based • Pushing water back Vortices • What is a vortex? – Translates about jet of fluid formed by airfoil • What do vortices mean? – Force imparted to fluid thrust or drag – Directionality Vortex shedding • Vortices formed at the trailing edge of the wing are shed as the shear forces become too great to maintain flow entrainment Swimming: 2 main ways • Drag based ‘paddlers’ – Usually paired-fin swimming – Better at acceleration • Lift based ‘flyers’ – – – – Rotating or folding wing/fin tail = hydrofoil Better at maintaining inertia Some paired-fin swimmers How it’s studied • Models • Experiments with fins removed How it’s studied • Videography 2 cam (3-D) High speed • Digital Particle Image Velocimetry (DPIV) • EMGs with sonomicrometry Sharks: function of the body Rising: 22° Holding: 4-11 ° Sinking: -11° Body orientation adjusted to induce appropriate lift Sharks: function of the caudal fin Generates both thrust and lift by moving water posteriorly and ventrally. Sharks: pectoral fins in horizontal swimming • Provide negligible lift • Pectoral fins held so that flow speed & pressure are equal on dorsal & ventral surfaces • Fins are not actively held in any particular position Sharks: pectoral fins in vertical maneuvering • Angle of P1 adjusted for (+) and (-) lift forces Biomechanics of benthic station-holding or…sitting Experience strong currents &/or heavy flow • Face current • Flat against substrate to reduce drag • (-) lift with P1 = increased friction with substrate All elasmobranchs are not created hydrodynamically equal Shark locomotion: Lateral undulations of axial skeleton Batoid locomotion Pectoral fins 1. Undulatory-drag based Pass waves down fins (ant to post) 2. Oscillatory- lift based Flap fins up and down 3. Axial-undulatory-lift based Undulate pec fins, but also pass waves down axial skeleton (ant to post) Batoid locomotion Pelvic fins – Punting - Skates QuickTime™ and a Sorenson Video decompressor are needed to see this picture. captive QuickTime™ and a Sorenson Video decompressor are needed to see this picture. field Holocephalan locomotion Pectoral fins - combination of: 1. Undulatory • Pass waves down fins (anterior to posterior) 2. Oscillatory • Flap fins up and down Body form & fin shape Sharks Type 1 Fast-swimming pelagics: Carcharodon, Isurus Externally symmetric Reduced for streamlining Conical head High heterocercal angle Narrow caudal peduncle Large pec fins Large, deep body Body form & fin shape Sharks Type 2 Generalized, continental swimmers Ex: Alopius, Carcharhinus, Negaprion, Sphyrna, Mustelus Moderately sized pelvic, 2nd dorsal, anal fins Flattened ventral head & body surface Less deep body Large pec fins Lower heterocercal tail angle Body form & fin shape Sharks Type 3 Slow swimming, epibenthic, benthic, & demersal sharks Ex: Ginglymostoma, Galeus, Hexanchiformes Large head More post. 1st dorsal fin Blunt snout Sm./no hypochordal & subterminal lobe Low HC tail angle More ant. Pelvic fins Body form & fin shape Sharks Type 4 Most are deepsea – Ex: Only squalean or dogfish sharks Many body shapes Large epicaudal lobe Lack anal fin Higher pec fin insertion Body form & fin shape Batoids Type 5 Benthic, but includes some pelagics Enlarged pec fins Dorsoventrally flattened body Reduced caudal half Body form & fin shape Holocephalans / chimeras Type 6 Leptocercal (long & tapering) to heterocercal tail Laterally compressed Conclusions • Current literature discusses only a small number of taxa • Studies carried out in controlled lab settings • Little information on biomechanics in natural conditions Pectoral Fin Morphology Limit to angle of attack Flow separates from object Boundary Layer Laminar Turbulent