Biomechanics of elasmobranch

locomotion

Matt Gardner

Laura Macesic

Equilibrium

• Gravity

• Lift

• Drag

• Thrust

Vectors that suck

• Gravity

• Drag1. Skin friction• Depends on total exposed surface

2. Pressure drag• Depends on shape and Reynolds number

Ratio of inertial and viscous forcesRe = Fi = ρlv

Fv Bacteria swimming Re = 0.000001Fruit fly flying Re = 100Large 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

Reynolds Number

Vectors that are good: LiftLower 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

Angle of Attack

lift resultant

THRUST

drag

• Thrust is used to transfer momentum to liquid– Drag based

• Pulling yourself through water

– Lift based• Pushing water back

How do fish make thrust?

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

• Videography2 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 finGenerates both thrust and lift by moving water

posteriorly and ventrally.

• 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

• Angle of P1

adjusted for (+)

and (-) lift forces

Sharks: pectoral fins in vertical maneuvering

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 locomotionPectoral fins

1. Undulatory-drag basedPass waves down fins (ant to post)

2. Oscillatory- lift basedFlap fins up and down

3. Axial-undulatory-lift based

Undulate pec fins, but also pass waves down axial skeleton (ant to post)

Batoid locomotionPelvic fins – Punting

- Skates

QuickTime™ and aSorenson Video decompressorare needed to see this picture.

QuickTime™ and aSorenson Video decompressorare needed to see this picture.

fieldcaptive

Holocephalan locomotion

Pectoral fins - combination of:1. Undulatory

• Pass waves down fins (anterior to posterior)

2. Oscillatory• Flap fins up and down

Narrow caudal peduncle

Body form & fin shapeSharks Type 1 Fast-swimming pelagics: Carcharodon, Isurus

Conical head

Large pec fins Large, deep body

Reduced for streamlining

Highheterocercal angle

Externally symmetric

Body form & fin shapeSharks 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, 2nd dorsal, anal fins

Lower heterocercaltail angle

Body form & fin shapeSharks Type 3 Slow swimming, epibenthic, benthic, &

demersal sharks Ex: Ginglymostoma, Galeus, Hexanchiformes

Blunt snout

Large head More post. 1st dorsal fin

Sm./no hypochordal& subterminal lobe

More ant. Pelvic fins

Low HC tail angle

Body form & fin shapeSharks Type 4 Most are deepsea

– Ex: Only squalean or dogfish sharks

Many body shapes

Higher pec fin insertionLack anal fin

Large epicaudal lobe

Body form & fin shape

Batoids Type 5 Benthic, but includes some pelagics

Dorsoventrallyflattened body

Enlarged pec fins

Reduced caudal half

Body form & fin shape

Holocephalans / chimeras Type 6

Laterally compressed

Leptocercal (long & tapering)to heterocercal tail

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 attackFlow separates from object

Laminar Turbulent

Boundary Layer