Module 5: Locomotion – Land vs. Water
Pinnipeds are an extraordinary evolutionary compromise: a mammal that retains the ability to haul out on land or ice to breed, moult, and rest, yet spends 80–95% of its life submerged in water. The morphological solutions adopted by phocids and otariids diverge so strongly that the two groups have been described as separate locomotor experiments. True seals (phocids) abandoned terrestrial walking almost entirely and propel themselves ashore by abdominal undulation; eared seals (otariids) retained quadrupedal walking by rotating the hindlimbs under the body. This module derives the hydrodynamics of seal swimming, contrasts the gait patterns of phocid and otariid locomotion, and quantifies the cost of transport (COT) for both.
1. Two Locomotor Lineages
The Carnivoran order Pinnipedia comprises three living families. The Phocidae(true or earless seals: harbor, grey, ringed, harp, Weddell, elephant, monk, leopard, etc.) diverged from their musteloid ancestors about 30 Ma ago and evolved hindlimb-dominant swimming with pelvic undulation. Their pelvis rotated posteriorly so that the hindlimbs point backward and cannot be brought forward under the body; on land they perform a “caterpillar crawl” combining abdominal undulation with forelimb drag.
The Otariidae (eared seals: sea lions, fur seals) diverged from a separate ursid-like ancestor about 25 Ma ago and evolved forelimb-dominant swimming using flapping-wing thrust. They retained a pelvis capable of rotation and therefore a quadrupedal terrestrial gait: on land they walk, run, and even gallop with recognisable mammalian kinematics.
The Odobenidae (walrus, Odobenus rosmarus) is intermediate. Walruses use both hindlimb undulation and forelimb wing-like strokes in water, and on land they rotate the hindlimbs forward for a slow quadrupedal shuffle. Fossil evidence places odobenids phylogenetically closer to otariids than to phocids.
2. Swim Hydrodynamics
An adult pinniped typically swims at Reynolds number\(\mathrm{Re} = U L / \nu \sim 10^5 - 10^6\). In this regime flow around the streamlined body is fully turbulent but the boundary layer stays attached over most of the surface, giving a drag coefficient \(C_d \approx 0.05 - 0.12\) based on wetted area. Fish (1996) compiled the classical comparative data and showed that pinnipeds achieve some of the lowest \(C_d\) values of any mammal, comparable to dolphins.
\[F_{\text{drag}} = \tfrac{1}{2}\rho_w C_d S\, U^2,\qquad P_{\text{mech}} = F_{\text{drag}}\, U \propto U^3\]
Power dissipated to drag scales as the cube of speed; therefore the locomotor metabolic cost rises steeply above the optimal cruise speed.
Phocid Pelvic Undulation
A phocid seal generates thrust by lateral oscillation of the hindlimb flipper at frequencies of 1–2 Hz and amplitudes of 0.15–0.20 body lengths. The hindlimbs are splayed outward and the digits webbed, forming a single paddle; the tail is short and vestigial. Thrust is generated by the lift-based action of the hindlimb in a mode similar to a thunniform fish tail (Williams & Kooyman 1985), with Strouhal number\(\mathrm{St} = fA/U \approx 0.25\text{-}0.35\), in the classic propulsive-efficiency optimum range for oscillating foils.
Otariid Forelimb Flapping
Sea lions and fur seals propel themselves by synchronous or alternating strokes of the enlarged fore-flippers, generating thrust on both the downstroke and the upstroke (Feldkamp 1987). The motion resembles the flight of a bird or sea turtle and the fore-flippers are literally hydrofoils—cross-section is a low-drag airfoil profile. Because thrust is bird-like, otariids accelerate rapidly to high sprint speeds (to 8 m/s) but have slightly higher swim COT than phocids due to the non-axisymmetric propulsion cycle.
Propulsive Efficiency
Propulsive efficiency \(\eta_{\text{prop}}\) is the ratio of useful thrust power to mechanical power delivered to the water. Phocid \(\eta_{\text{prop}}\)reaches ~0.85 at cruise speed (Fish 1992); otariid values are somewhat lower at 0.70–0.80 but compensated by faster acceleration. Williams (1999) summarised all available data in her review of marine mammal locomotion energetics.
3. Muscle Anatomy and Propulsive Mass
In a phocid seal approximately one-third of locomotor muscle mass is concentrated in the axial body wall (epaxial and hypaxial musculature) and the pelvic-girdle muscles that drive hindlimb oscillation. The caudal body is therefore heavily muscled; the fore-body carries the large blubber depot and the organ mass. Pabst (1996) and Fish (1993) used MRI and dissection to map the swimming mass budget and confirmed that phocid swim kinematics are dominated by a large-amplitude caudal oscillation driven by big axial muscles.
In an otariid, by contrast, the biggest locomotor muscles are the pectoralis and latissimus dorsi complex that drives fore-flipper flapping. The fore-flipper itself is long, bony, and muscular—its distal segments have ossified insertions for tendons that impose a stiff flapping action. Terrestrially the forelimb doubles as a walking limb.
Williams 2015: Muscle Efficiency
Williams et al. (2015) used biologging to quantify locomotor efficiency during naturally occurring dive-exercise bouts. They found that phocid hindlimb muscle efficiency (mechanical/metabolic) approaches 0.27 at cruise and drops to 0.18 at sprint. Otariid forelimb muscle efficiency is similarly 0.20–0.25 at cruise. These values are modestly above those of terrestrial carnivores and consistent with the slow-twitch-dominant composition of pinniped swim muscle.
4. Terrestrial Locomotion
Phocid Caterpillar Crawl
A phocid cannot bring its hindlimbs forward under the body, so terrestrial progression is achieved by a peristaltic sequence of axial undulation. The animal lifts its trunk off the substrate by arching the back, then translates the arch from shoulder to pelvis, drawing the body forward a stride length of ~40–50 cm per cycle. The forelimbs plant and brace through the arch-propagation; hindlimbs trail and provide only occasional push. On soft sand or wet clay the motion is efficient; on ice it is awkward but still serviceable.
Terrestrial COT for phocids is 30–50 J/(kg·m)—15–30× the swimming value. A 200 kg harp seal covering 100 m on ice burns roughly 200–400 kJ (~50–100 kcal), comparable to 10 min of sustained cruising in water. Phocids therefore spend the minimum possible time on land—only for breeding, pupping, moulting, and emergency haul-out.
Otariid Quadrupedal Walk
Otariids rotate the hindlimbs forward so that the digits face anteriorly, supporting a conventional lateral-sequence walk (left-hind, left-fore, right-hind, right-fore). Stride lengths of 60–80 cm and cycle periods of ~0.8 s yield walking speeds of 0.7–1.0 m/s. On bare rock, sand, or even short grass, otariids can maintain brisk travel over hundreds of meters without overheating.
Terrestrial COT for otariids is 8–12 J/(kg·m), 4–6× their swim COT. The penalty is noticeable but not prohibitive, which is why sea lions and fur seals use rocky outcrops, beaches, and cliff faces—and not just water edges—as breeding haul-outs.
Ice-Hole Emergence
Weddell seals and harbor seals in ice-covered waters must emerge through a breathing hole that the animal itself enlarges by tooth-grinding. Emergence kinematics combine an abdominal contraction that propels the body upward through the hole and a forelimb grip on the ice edge. Force-plate measurements by Williams et al. (2004) show peak emergence forces of 2–3× body weight, consistent with ballistic ejection against gravity plus buoyancy.
5. Gait Comparison
Phocid vs. Otariid: land gait silhouettes
6. Cost of Transport: Theory
The cost of transport (COT) is the metabolic energy required to move one unit body mass one unit distance, usually expressed in J/(kg·m). For a swimmer obeying Pennycuick’s flight-power analog:
\[P_{\text{met}}(U) = \text{BMR} + \frac{\tfrac{1}{2}\rho_w C_d S U^3}{\eta_{\text{prop}}\eta_{\text{musc}}},\qquad \text{COT}(U) = \frac{P_{\text{met}}(U)}{m U}\]
Basal rate dominates at low speed (COT falls as 1/U), drag dominates at high speed (COT rises as U2). The minimum of the resulting U-shaped curve defines the energetically optimal cruise speed.
For an 85 kg harbor seal with \(C_d = 0.07\), \(S = 0.095\) m2, BMR = 230 W, and overall mechano-metabolic efficiency of 20%, the predicted optimum is near 1.5 m/s, exactly the observed cruise speed during telemetered foraging trips. Phocid COTmin of 1.5–1.8 J/(kg·m) is among the lowest of any mammal, close to cetaceans and below most fish.
Sprint Performance
Short-duration anaerobic sprints reach 25 km/h (6.9 m/s) in leopard seals and ~30 km/h (8.3 m/s) in California sea lions. At such speeds drag power exceeds 3 kW, unsustainable beyond a few seconds, and drawn from muscle ATP and creatine phosphate stores rather than aerobic oxidation.
Porpoising
Above a critical speed \(U^* = 0.425\sqrt{gL}\) (for a 1.7-m phocid,\(U^* \approx 1.74\) m/s) surface wave drag rises sharply. Porpoising—a ballistic leap between surface breaths—becomes energetically cheaper than continued surface swimming. Sea lions and dolphins porpoise routinely; phocids porpoise occasionally when travelling long distances at the surface.
Simulation 1: Swim Power & Cost of Transport
Build a Pennycuick-style power curve for an 85-kg harbor seal. Drag follows \(F = \tfrac{1}{2}\rho C_d S U^2\), metabolic power adds BMR and divides by overall efficiency, and COT is the result divided by \(m U\). The simulation sweeps speed 0.05–4 m/s, locates the optimal cruise speed, computes Reynolds and Froude numbers, and compares COT across seven marine and human swimmers. A sprint case is computed for the 6.9 m/s leopard-seal record.
Click Run to execute the Python code
Code will be executed with Python 3 on the server
7. Boundary Layer, Skin, and Drag
At cruise Reynolds numbers of ~106 a seal’s skin is immersed in a turbulent boundary layer approximately 1 cm thick along most of the body. Skin drag dominates over pressure drag on streamlined bodies, so reducing skin friction is the key to low\(C_d\). The blubber layer underneath the dermis contributes to passive shape control: a slight undulation of the skin surface in response to pressure fluctuations, known as compliant-wall damping, has been proposed as a drag-reducing mechanism in cetaceans and seals (Bushnell & Moore 1991), although quantitative support is mixed.
Fur seals carry a double-layered pelt with a dense underfur that traps an air layer underwater (Scholander 1950). In still water this air gives superb insulation, but at swim speeds the boundary-layer shear washes the air out, leaving only a very thin layer of trapped water. The effective drag coefficient at cruise is therefore similar to the naked phocid skin, but insulation drops.
Thrust-Drag Decomposition
During each undulation cycle thrust peaks in the middle of the stroke and drag dominates at the extremes. Time-resolved PIV studies (Fish 2003) show that instantaneous propulsive efficiency can dip as low as 0.6 at stroke extremes yet averages ~0.85 over the cycle. The cyclic modulation argues against simple steady-state drag models; a full unsteady hydrodynamic treatment captures the subtleties.
8. Metabolic Scaling and Foraging Economics
Basal metabolic rate scales with body mass as BMR = a m0.75 (Kleiber 1947), although pinniped species lie 2–3× above the eutherian baseline due to thermal and diving demands (Williams 1999). A 200 kg harp seal has BMR ∼ 500 W vs. predicted 250 W for a generic mammal of that mass.
Foraging economics link BMR, locomotor cost, and food energy content. A seal’s net daily energy gain is given by
\[E_{\text{net}} = n_{\text{prey}} \epsilon_{\text{fish}} - \left(T_{\text{locomotion}} P_{\text{swim}} + T_{\text{rest}}\,\text{BMR}\right)\]
A phocid catching 8 herring per day (1 MJ each) and foraging for 8 h at 1.5 m/s has a net surplus of 4–5 MJ/day, supporting maintenance and blubber deposition.
Sexual Dimorphism and Locomotor Cost
In elephant seals and grey seals adult males reach 3–4× female mass. Because both sexes swim in the same fluid environment, COT scales approximately with L−1and male COT is therefore lower than female COT in absolute J/(kg·m). Males can afford longer foraging trips, compatible with the polygynous territorial strategies reviewed in Module 6.
9. Stride Cycle and Footfall Diagrams
Gait analysis uses the footfall diagram (Hildebrand 1966): a plot of limb contact vs. time with a shaded bar for each support phase and a gap for each swing phase. The duty factor is the fraction of the stride spent in contact; phase offsets between limbs determine the gait class (walk, trot, pace, gallop).
A phocid caterpillar crawl has forelimb duty factor ∼0.78 (almost always in contact) and hindlimb duty factor ∼0.55 (hindlimbs are dragged but not bearing full weight). Interlimb phase places both forelimbs nearly in phase, as the caterpillar arch propagates axially rather than laterally.
An otariid lateral-sequence walk has balanced duty factors near 0.62 and interlimb phase offsets of 0.25 cycles between adjacent footfalls—the classic mammalian walking pattern of a dog or cat. At higher speeds an otariid can transition to a rotary gallop with in-air phases and asymmetric footfall.
Simulation 2: Phocid vs. Otariid Gait Analysis
Generate footfall diagrams for phocid caterpillar crawl and otariid lateral-sequence walk. Compute stride periods, stride lengths, duty factors, and interlimb phase offsets. Track the CoM trajectory of both gaits and contrast the heave-dominated phocid motion with the level otariid walk. Finally plot terrestrial COT for both morphotypes across 0.05–2.5 m/s and compare with the swim COT values from Simulation 1, exposing the 20× penalty phocids pay for terrestrial travel.
Click Run to execute the Python code
Code will be executed with Python 3 on the server
10. Aquatic-Terrestrial Trade-Offs
The divergence between phocid and otariid locomotion reflects two extremes on a broader continuum of aquatic adaptation. Phocids have gone farther into the aquatic realm—they are near-obligate swimmers with a vestigial terrestrial gait. Otariids kept one foot on land, so to speak, and their body plan is a compromise that performs moderately well in both environments.
The trade-off expresses itself in breeding ecology. Otariids breed on steep rocky coasts inaccessible to phocids and use terrestrial mobility for male territory defence; lactational foraging trips are long because the mother must return to a fixed breeding rookery. Phocids breed on ice floes or open beaches accessible from the water and use short, explosive lactation periods that minimise time on land (Module 6). Walruses, as intermediate, use both strategies depending on sea-ice conditions.
Evolutionary Origins
Molecular phylogenies (Higdon 2007, Berta 2018) confirm that pinnipeds are monophyletic and descended from a terrestrial musteloid ancestor. The split between phocid and otariid locomotor modes appears to have occurred early in pinniped evolution: by 25 Ma ago the two lineages already had distinct body plans, and convergence on any single aquatic mode appears not to have occurred since.
Key References
• Fish, F. E. (1996). “Transitions from drag-based to lift-based propulsion in mammalian swimming.” Am. Zool., 36, 628–641.
• Fish, F. E. (1993). “Influence of hydrodynamic design and propulsive mode on mammalian swimming energetics.” Aust. J. Zool., 42, 79–101.
• Fish, F. E. (2003). “Maneuverability by the sea lion Zalophus californianus.” J. Exp. Biol., 206, 667–674.
• Williams, T. M. & Kooyman, G. L. (1985). “Swimming performance and hydrodynamic characteristics of harbor seals.” Physiol. Zool., 58, 576–589.
• Williams, T. M. (1999). “The evolution of cost efficient swimming in marine mammals.” Phil. Trans. R. Soc. B, 354, 193–201.
• Williams, T. M. et al. (2015). “Exercise at depth alters bradycardia and incidence of cardiac anomalies in deep-diving marine mammals.” Nature Comms, 6, 6055.
• Feldkamp, S. D. (1987). “Swimming in the California sea lion.” J. Exp. Biol., 131, 117–135.
• Pabst, D. A. (1996). “Morphology of the subdermal connective tissue sheath of dolphins.” J. Zool., 238, 35–52.
• Hildebrand, M. (1966). “Analysis of the symmetrical gaits of tetrapods.” Folia Biotheor., 6, 9–22.
• Tarasoff, F. J., Bisaillon, A., Pierard, J. & Whitt, A. P. (1972). “Locomotory patterns and external morphology of the river otter, sea otter, and harp seal.” Can. J. Zool., 50, 915–929.
• Pennycuick, C. J. (1989). Bird Flight Performance: A Practical Calculation Manual. Oxford UP.
• Kleiber, M. (1947). “Body size and metabolic rate.” Physiol. Rev., 27, 511–541.
• Bushnell, D. M. & Moore, K. J. (1991). “Drag reduction in nature.” Annu. Rev. Fluid Mech., 23, 65–79.
• Higdon, J. W. et al. (2007). “Phylogeny and divergence of the pinnipeds.” BMC Evol. Biol., 7, 216.
• Berta, A. (2018). Return to the Sea: The Life and Evolutionary Times of Marine Mammals. University of California Press.
• Scholander, P. F. (1950). “Physiological adaptation to diving in animals and man.” Harvey Lect., 57, 93–110.
• Williams, T. M., Davis, R. W. et al. (2004). “The cost of foraging by a marine predator, the Weddell seal.” J. Exp. Biol., 207, 973–982.
Appendix: Worked Example — Foraging Trip Budget
Consider an 85 kg harbor seal on a typical 8-hour foraging trip. Cruise speed 1.5 m/s, swim drag coefficient \(C_d = 0.07\) applied to reference area\(S = 0.095\) m2. Drag power:
\[P_{\text{mech}} = \tfrac{1}{2}\rho C_d S U^3 = \tfrac{1}{2}(1025)(0.07)(0.095)(1.5)^3 \approx 11.5\,\text{W}\]
Divided by efficiency \(\eta = 0.2\), the locomotor metabolic requirement is ~58 W. Adding BMR of 230 W gives total metabolic power of ~290 W, or 8.3 MJ over an 8-hour trip. This is roughly 40% of the seal’s daily energy budget, consistent with field measurements using accelerometer-derived ODBA (Overall Dynamic Body Acceleration) calibrated to metabolic rate (Halsey et al. 2011).
Distance covered: 43 km. Average energy per km: 190 kJ, or 2.3 J/(kg·m). The agreement between this trip-level calculation and the point-wise COT curve from Simulation 1 confirms the energy-accounting logic used in pinniped foraging ecology.