M6 Aquatic Locomotion

Topic

Aquatic mammals propel themselves through the water in two distinct ways: via limb-based propulsion, as seen in otters and beavers, or via whole-body undulatory propulsion, as seen in cetaceans and seals.

In both modes of propulsion, the hydrodynamic drag exerted by the water against the body scales with the square of the swimming speed; this drag is the dominant factor in the energetic cost of swimming—far more so than any other variable.

To reduce this hydrodynamic drag, cetaceans have evolved toward fusiform shapes—elongated bodies tapered at both ends—which minimize water resistance. Thanks to this fusiform shape, a cetacean's drag coefficient drops to very low values ​​comparable to those of fish—among the lowest drag coefficients found in bodies moving through water.

In addition to scaling with the square of the speed, hydrodynamic drag causes the swimming power required to overcome it to increase with the cube of the swimming speed: the faster the animal swims, the more rapidly the power demand rises. This steep relationship means that the optimal swimming speed ends up being much lower than the maximum speed the animal could achieve during a short burst of effort.

In mammals that propel themselves through body undulation—such as cetaceans and seals—forward thrust is primarily generated by the oscillation of the caudal fin. This movement is described by the same oscillating-wing theory that explains how a moving wing generates propulsive force rather than just lift. The efficiency with which the oscillation of the caudal fin converts muscular power into thrust is governed by the Strouhal number—the same dimensionless parameter that compares the frequency and amplitude of each oscillation cycle to the animal's forward speed. When the Strouhal number falls within the 0.2 to 0.4 range, the propulsive Froude efficiency reaches its peak values—between 0.85 and 0.95—coming very close to the theoretical maximum.

Deep diving presents these aquatic mammals with an additional physiological challenge distinct from hydrodynamic drag: as the animal descends, increasing water pressure compresses its lungs in accordance with Boyle's Law—the same law describing how gas volume decreases as surrounding pressure rises. To sustain the effort of diving despite this lung compression, the animal relies on oxygen stored prior to submersion—held in blood hemoglobin and muscle myoglobin—rather than on breathing while submerged.

Returning to the energetic cost of swimming, the optimal swimming speed is the one that minimizes the "cost of transport"—the energy the animal expends per unit of distance traveled. This optimal speed arises from a balance between two costs moving in opposite directions: at low speeds, the basal metabolic cost dominates the cost of transport, as the animal expends roughly the same basal energy regardless of how slowly it swims; at high speeds, conversely, hydrodynamic drag—which increases with the cube of the speed—becomes the dominant factor. The cost of transport reaches its minimum precisely at the point where hydrodynamic drag equals one-third of the total swimming cost. This optimal swimming speed—determined by the balance between basal metabolic cost and hydrodynamic drag that increases with the cube of the speed—is the one an aquatic mammal effectively adopts during long-distance travel, whether propelled by limbs (like otters and beavers) or by undulation of the body and caudal fin (like cetaceans and seals); it is also the speed the animal must temporarily abandon when deep diving requires it to manage pulmonary compression and oxygen reserves in hemoglobin and myoglobin, rather than the cost of transport associated with horizontal movement.

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