1. Biomechanics of elasmobranch locomotion Matt Gardner Laura Macesic

2. Equilibrium Gravity Lift Drag Thrust

3. Vectors that suck Gravity Drag 1.Skin friction Depends on total exposed surface 2. Pressure drag Depends on shape and Reynolds number

4. Ratio of inertial and viscous forces Re = Fi = ρlv Fv  Bacteria swimming Re = 0.000001 Fruit fly flyingRe = 100 Large whale swimmingRe = 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 Reynolds Number

5. 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

6. Vectors that are good: Thrust Angle of Attack lift resultant THRUST  drag

7. Thrust is used to transfer momentum to liquid –Drag based Pulling yourself through water –Lift based Pushing water back How do fish make thrust?

8. 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

9. Vortex shedding Vortices formed at the trailing edge of the wing are shed as the shear forces become too great to maintain flow entrainment

10. 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

11. How it’s studied Models Experiments with fins removed

12. How it’s studied Videography 2 cam (3-D) High speed Digital Particle Image Velocimetry (DPIV) EMGs with sonomicrometry

13. Sharks: function of the body Rising: 22° Holding: 4-11 ° Sinking: -11° Body orientation adjusted to induce appropriate lift

14. Sharks: function of the caudal fin Generates both thrust and lift by moving water posteriorly and ventrally.

15. 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 horizontal swimming

16. Angle of P1 adjusted for (+) and (-) lift forces Sharks: pectoral fins in vertical maneuvering

17. 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

18. All elasmobranchs are not created hydrodynamically equal

19. Shark locomotion: Lateral undulations of axial skeleton

20. 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)

21. Batoid locomotion Pelvic fins – Punting - Skates fieldcaptive

22. Holocephalan locomotion Pectoral fins - combination of: 1.Undulatory Pass waves down fins (anterior to posterior) 2.Oscillatory Flap fins up and down

23. Narrow caudal peduncle Body form & fin shape Sharks Type 1 Fast-swimming pelagics: Carcharodon, Isurus Conical head Large pec fins Large, deep body Reduced for streamlining High heterocercal angle Externally symmetric

24. Body form & fin shape Sharks Type 2 Generalized, continental swimmers Ex: Alopius, Carcharhinus, Negaprion, Sphyrna, Mustelus Less deep body Flattened ventral head & body surface Large pec fins Moderately sized pelvic, 2 nd dorsal, anal fins Lower heterocercal tail angle

25. Body form & fin shape Sharks Type 3 Slow swimming, epibenthic, benthic, & demersal sharks Ex: Ginglymostoma, Galeus, Hexanchiformes Blunt snout Large headMore post. 1 st dorsal fin Sm./no hypochordal & subterminal lobe More ant. Pelvic fins Low HC tail angle

26. Body form & fin shape Sharks Type 4 Most are deepsea –Ex: Only squalean or dogfish sharks Many body shapes Higher pec fin insertion Lack anal fin Large epicaudal lobe

27. Body form & fin shape Batoids Type 5 Benthic, but includes some pelagics Dorsoventrally flattened body Enlarged pec fins Reduced caudal half

28. Body form & fin shape Holocephalans / chimeras Type 6 Laterally compressed Leptocercal (long & tapering) to heterocercal tail

29. Conclusions Current literature discusses only a small number of taxa Studies carried out in controlled lab settings Little information on biomechanics in natural conditions

30. Pectoral Fin Morphology

35. Limit to angle of attack Flow separates from object Laminar Turbulent Boundary Layer