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September 2001
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The Emergence of Whales, Chp. 10

Synopsis of Chapter 10: Biomechanical Perspective on the Origin of Cetacean Flukes

by Frank E. Fish Department of Biology, West Chester University West Chester, PA 19383

[I’m hoping that this chapter will be fun, accessible, and interesting. Let’s see.]

1. Introduction

A remarkable opening sentence:

“The evolution of aquatic forms from terrestrial ancestors has been a reoccuring (!!) event in the history of the vertebrates.”

(Presumably he means that the evolution of the Pinnipeds is distinct from cetaceans.)

As one might guess, swimming is the sole mode of locomotion for cetaceans. Horizontal tail flukes are a hydrofoil, allowing propulsion via vertical oscillations, producing hydrodynamic thrust against the considerable drag of the media. Thrust is due to force generated by the hydrofoil. Dolphins can hit speeds of 10 m/s (putting that into perspective, my best speed in the water is about 1.7 m/s). Whales can get nearly airborne.

Chapter focus: how thrust is generated by varied morphology of whale tail flukes, via biomechanical analysis of extant cetaceans, allowing perspective on the fossils of primitive cetaceans.

2. Morphology Design and Construction of Flukes

2.1 Structure

Flukes are lateral extensions of the tail, composed of the same layers (cutaneous, subcutaneous blubber, ligamentous, and dense fibrous tissue) as covers the rest of the animals.

The bulk of the fluke is a core of fibrous tissue, collagen fibers attached to the short caudal vertebrae. The pattern of fiber bundles is oriented for incurring high tensile stresses.

The ligamentous layer is arranged to resist tension of the flukes, particularly at the trailing edge and tips. Bending capability is variable between species. Vertebrae end at the fluke notch; vertebrae anterior to the fluke are laterally compressed, in the fluke are dorsoventrally compressed. The intervertebral joint at the base of the flukes functions mechanically as a low- resistance hinge, with some rotation via “ball” vertebrae.

Wow, these things are certainly well-desi… scratch that. They certainly are amazingly well-suited for the propulsion function (a lesser-known disco hit that followed “Do the Locomotion”).

Because the flukes are soft tissue, fossil preservation has not occurred. BUT (lest ye creationists take heart) modern cetaceans have associated features that can be compared to fossils “to indicate the course of fluke evolution”.

2.2 Design and Physics of Flukes

(Figure 1 shows fluke silhouettes for 20 different species. Prettiest is the narwhal (looks like a handlebar moustache; beluga is the broadest and flattest across the base; narrowest looks like Heaviside’s dolphin or the false killer whale. From a uninformed viewpoint, smaller species appear to have flukes with a larger relative surface area.

Flukes act like a pair of wings, but oscillation of the flukes creates life-derived thrust. Shape (see above) influences energy requirements of swimming.

Figure 2 shows a diagram of relevant parameters to be measured on the fluke. Figure 3 relates fluke span _S_ (distance from tip to tip) and area A to body length. Both show a very compact, linear distribution in log-log plots.

Aspect ratio (this is cool): AR = S^2/A. High AR is long, narrow flukes; low AR is broad, with short span. High AR is for relatively fast swimmmers.

Natural selection devotees, take note. Lowest AR (2.0) is for the Amazon river dolphin. (Based on the silhouettes, the beluga, gray, and northern right whale dolphin also appear to be low AR. Highest AR (6.1-6.2) is for the fin whale and false killer whale (I judged that right). The false killer whale can hit 7.5 m/s, schooling speed at 3 m/s. Fin whales can hit 10 m/s. Apparent maximum speed for the river dolphin is about 4 m/s (but with a current assist from the river it can go much faster).

High-performance flukes maximize the lift to drag ratio. AR above 8-10 does not provide further advantage and may be structurally limited.

Drag is inversely dependent on AR. A discussion of how drag is produced due to formation of tip vortices [an aside — I’ve read recent articles about how insects fly that discuss how the energy in the vortices is utilized – very interesting stuff!] Drag is also limited by the sweep angle of the flukes. The sweep angle (it helps to see the diagram, but it’s defined as the angle from a perpendicular to the root chord and the one-quarter chord position) is inversely related to the AR. Low-sweep angle, high AR allows for high-efficiency rapid swimming. Sweep angle greated than 30 deg leads to a reduction in efficiency; the sweep angle – AR relationship indicates a structural limitation on fluke strength and stiffness.

Flukes have some flexibility; without going into detail, the right kind of flexibility can increase efficiency by 20% with only a moderate decrease in overall thrust.

Fluke sections show a conventional streamlined foil profile. Think “airplane wing”. The shape does not produce extremes in pressure that could lead to cavitation (bubble) damage at routine swimming speeds.

SO: flukes are a hydrofoil that provides lift. Their morphology creates high lift with low drag performance. To make it work, though, they have to be moved correctly. See below.

(I hope everyone reading will appreciate how great this is; optimization of the shape for propulsion. Gotta love it.)

3. Kinematics and Hydrodynamic Performance

3.1 Propulsive movement

Thrust is generated exclusively through caudal movement, with the tail flukes oscillating dorsoventrally. The flukes are pitched through a joint at the base of the fluke, aided by a double hinge mechanism in the caudal vertebrae. Heave and pitch motions of the fluke results in a varying pitch angle between the flukes and the horizontal plane. All of this (and more) results in control of the angle of attack, where maintenance of a positive angle of attack allows thrust generation through the majority of the stroke cycle. Magnitude of the attack angle affects propulsive efficiency. Increasing angle of attack for a hydrofoil increases both lift and drag; lift increases faster up to a critical point. Beyond that, increased drag results in stall.

The angle of attack in the tail downstroke and upstroke increases rapidly, maximizing in the first third of the stroke. Maximum observed angles for Tursiops are 12-21 degrees, and for Lagenorhynchus (Pacific white-sided dolphin) up to 24 degrees. Stall occurs at about 30 degrees.

Maximum heave amplitude (which I think is body curvature) is about 20% of body length.

Stroke frequency varies with swimming speed in a positive linear relationship (different from semiaquatic paddlers).

3.2 Thrust Production and Efficiency

The author describes analysis of thrust production, noting that the way in which the flukes function is essentially separated from the body. Some of this is a little redundant; most of it would be greatly appreciated by aerodynamicists and boat designers. Notable points:

– Lift depends on the frequency of oscillation of the flukes; thrust increases with frequency, and efficiency decreases.

– Momentum imparted to the fluid is concentrated in a jet of fluid directed on average opposite to the swimming direction. The jet induces a vortex wake in the surrounding resting water. The wake is necessary to produce thrust. Visualized as alternating clockwise and anticlockwise vortex rings.

– Leading edge suction also contributes to thrust.

– Efficiency = ratio of mean thrust power required to overcome drag divided by the mean rate of work against the surrounding water. 3-D models of lunate tail swimming predict efficiencies below 0.99 but above 0.7. Few engineered propellers achieve effiencies greater than 0.7. The keys: fluke, ahem, design enhances high thrust with reduced drag and fluke oscillation allows continuous thrust production.

4. Evolution

Pay attention now. Because “the ancestors of cetaceans were terrestrial”, they didn’t have flukes before adopting a semi-aquatic or mostly aquatic existence. 2 questions: how did the flukes evolve, and what were the transitional stages and levels of performance.

Guess what? There isn’t much information to go with regard to archaeocete flukes (or even the caudal ends of the spine). But skeletons and fin impressions of mosasaurs, particularly a lower Triassic ichthyosaur Chensaurus chaoxianensis (my guess is that this was found in China) allowed investigators to look at the skeletal transformation accompanying changing swimming styles. I’ll give the reference for this one:

Motani, R., You, H., and McGowan, C., 1996. Eel-like swimming in the earliest ichthyosaurs. Nature, 382, 347-348. I invite a reader to go look this one up and comment on it.

So what is Fish to do? A. Examine ontogenetic information, and B. use model specimens. Similarities between ontogenetic and phylogenetic sequences reflect a possible developmental pathway. It’s been done before for the mammalian middle ear and neocortex. (Rowe, T., 1996, Science, 273, 651-654).

Models of swimming performance in modern species can be used as analogues of primitive intermediate (!!) forms, allowing examination of performance characteristics, leading to a mechanically plausible evolution scenario. The key is the mechanics of swimming, not the actual organisms examined. Also already done before (Lauder, G.V., “On the Inference of Function from Structure, pp. 1-18 in “Functional Morphology in Vertebrate Paleontology” edited by J.J. Thomason, Cambridge University Press).

4.1 Ontogeny

Studied over 100 years ago. Ryder supported the idea that the flukes were “integumentary limb-folds” that had migrated caudally, rather than a secondarily acquired structure. Ryder assumed a seal-like ancestor that used hind limbs for propulsion, where the limbs would have fused and the feet would form rudimentary flukes.

Well, that was wrong. Now we know that the whales gradually lost hindlimbs and relied more and more on the tail for propulsion. So we look at whale embryos. The flukes initially appear as a diamond/spade shape with rounded edges on either side of the tail. The extend to each side, becoming more pointed, adding the final details (tip flaring) at the end of the process. While based on examination of one species, other whales exhibit a similar pattern. So this is how it *might* have happened.

(I have this strange image of some kind of organism with a diamond-shaped “fluke” on the end of its tail. Does anyone know if there is a real creature like this?)

4.2 Functional Model

Before the flukes appeared, modern cetacean ancestors needed to modify their morphology AND their primary mode of propulsion in water. There are several stages. This is the reference for a detailed discussion of the model.

Fish, F.E. 1996: Transitions from drag-based to lift-based propulsion in mammalian swimming. Am. Zool. 36: 628-641.

The model assumes that neuromotor patterns for locomotion are conservative. So large-scale changes in kinematics and performance should be accomplished with only minor modification of the terrestrial gait neuromotor pattern.

I.e.: walking and trotting are the basis of paddling-style swimming: lift-based swimming is based on “asymmetrical” gaits, like galloping or bounding.

The assumption is that the (1) fully terrestrial ancestor of cetaceans was a paddler, swimming much like a dog in the water. Moving to a (2) semiaquatic existence, only the hind limbs are utilized. (No modern analog for this stage is given.) Enlarged hind feet and digital webbing would be expected as morphological modifications.

(3) To aid diving, development of simultaneous hind limb stroking, which occurs with flexion of the spine, undulating the tail. Prime example: otters. Using the tail for thrust increases speed, aiding prey acquisition. Morphologically speaking, broadening and flattening the tail is a good idea. Prime example: giant river otter (and it seems to me the beaver might be a good candidate, too).

(4) Switch from limb paddling to primarily axial undulation. Requires a long tail. Without going into detail, another reason for the long tail might be thermoregulation. Cetaceans originated in tropical/sub- tropical climes where a long tail would be useful for thermoregulation. Morphology: reduced hindlimbs for reduced drag and faster swimming.

(5) Caudal undulation exclusively. Morphologically: flukes increase the performance of this mode and the addition of a hinge joint to control pitch.

OK, so let’s look at the fossils. Pakicetus (based on the _initiation_ of changes in the ear and dentition) was still primarily terrestrial and probably a paddler (but that is not based on any postcranial elements, of course).

Ambulocetus natans: Well-developed limbs and prominent tail. Fish expects that Ambulocetus used pelvic paddling and caudal undulation. (Otter-like, stage 3.) Hind feet had elongate bones, increasing surface area. Tail length and limited spinal modifications indicate that Ambulocetus probably didn’t have tail flukes.

Rodhocetus probably had flukes, due to the presence of “spinal characteristics associated with generating large forces from the dorsoventral movement of the tail, including robust vertebrae with high neural spines and unfused sacral vertebrae”. (I know at least one t.o. reader that’s heard that before.) Also, Rodhocetus had reduced hindlimbs. (Stage 4). Oxygen isotopes (reference given; also a later chapter in the book) indicate that Rodhocetus/Indocetus ingested seawater and inhabited a neritic (shallow sea) environment. So swimming fast (with flukes) would be a necessity to get around and find prey.

After that, swimming was exclusively with flukes/tail, with hindlimbs “inconsequential or absent”.

The larger the body (take a look at 70-foot long Basilosaurus), the greater the necessity for tail flukes to get the big bodies around.

5. Summary and Conclusions

Basically a reiteration of the points made in the chapter. Probably the “big point” is that the ancestral cetaceans likely had long tails that helped them early in the aquatic adaptation process. So anybody thinking that whales evolved from something like a bear isn’t paying attention: the difference in morphology between whales and pinnipeds shows that their ancestry was different. Pinnipeds evolved from an animal like a bear: whales evolved from a long-tailed ungulate.

A fun chapter to read: hope you liked the synopsis. Next up, Chapter 11, “Implications of Vertebral Morphology for Locomotor Evolution in Early Cetacea”.

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This page was last updated September 1, 2001.
It was reformatted and moved August 6, 2007
Copyright © 2001 by James Acker

table of contents
September 2001