Observations of rolled swimming

We tagged two wild great hammerhead sharks with accelerometer loggers that allow the estimation of body pitch and roll angles as they swim freely in their environment (see Methods, Supplementary Fig. 1 and Supplementary Notes 1 and 2); one at the Great Barrier Reef, Australia, and another off the Mesoamerican Reef, Belize. Unexpectedly, the shark tagged at the Great Barrier Reef spent ∼90% of the 18 h deployment period (which was from early evening till late morning) swimming on its side at absolute roll angles between 50° and 75° (Fig. 1a,b and Supplementary Fig. 2). The shark exhibited this rolling behaviour whether it was ascending, descending or swimming at constant depth, and alternated between rolling to the left and right sides approximately every 5–10 min. An onboard video camera visually confirmed the observations (Supplementary Movie 1). The shark tagged off Belize exhibited a very similar pattern; it was monitored for almost 3 days, and spent the majority of night-time hours swimming at roll angles between 30° and 80°, and tended to swim more upright during daylight hours (Supplementary Fig. 3 and Supplementary Note 2). It is unlikely that this behaviour is a response to the capture, handling and tagging procedure because a further three sharks fitted with onboard video cameras via SCUBA (that is, cameras were fitted to the shark’s dorsal fins underwater without being captured or handled) in the Bahamas also exhibited frequent rolled swimming throughout the 2–3 h of each daytime video deployment (Fig. 1e,f and Supplementary Movie 2), and untagged specimens of this species in public aquaria invariably spend a large proportion of time swimming at the same roll angles seen in our wild, tagged animals (Supplementary Movie 3). Ostensibly, this seems a bizarre and unexpected mode of swimming, and has no precedent in the literature. What possible advantage could be obtained by swimming rolled in this way? Doing so would presumably inhibit use of their cephalofoil for detecting electrical signals from benthic prey; therefore, rather than representing a foraging strategy, our hypothesis was that the rolled swimming confers hydrodynamic advantages.

Figure 1: Rolled swimming in great hammerhead sharks Sphyrna mokarran. For a to d, roll and pitch angles were measured by an electronic tag attached to a 295 cm shark’s dorsal fin, and monitored as it swam freely at the Great Barrier Reef, northern Australia. (a,c) A typical hour-long time series for that animal. (b,d) Probability distributions of roll and pitch angles based on the last 15 h of the monitoring period for the Great Barrier Reef shark. Images in e,f were taken with a fin-mounted video camera attached to another wild S. mokarran (∼350 cm) as it swam rolled to the left and right (respectively) at South Bimini Island, the Bahamas, at absolute roll angles of ∼60° (see Supplementary Movie 2 for examples of this and other wild S. mokarran swimming rolled). Full size image

Hydrodynamics of a swimming shark

Hydrodynamic forces acting on a swimming shark can be conveniently divided into lift L, drag D, thrust T and buoyancy B. For simplicity, we will assume that the thrust is generated mainly by the caudal, anal and the second dorsal fins, and is directed along the swimming path, whereas lift and drag are generated by all other fins and by the body of the shark; they are directed perpendicular and parallel to the swimming path, respectively. When swimming at constant speed along a straight horizontal path, all forces cancel out with gravity, G:

Lift and drag are commonly expressed in terms of the respective coefficients C L and C D with

in which ρ is the density of water, v is swimming speed and S is an arbitrary reference area, chosen here as the maximal cross-section area of the body. The lift coefficient depends mainly on the angle between the surface that generates the lift (as a fin) and the swimming direction; the drag coefficient depends mainly on the lift coefficient:

C D0 is the parasite (zero lift) drag coefficient associated with friction between the body and water; KC L 2 is the induced drag coefficient—the cost of lift generation. At a given speed, the combination of (1a) and (2a) determines the lift coefficient needed to counteract gravity (and hence the set angle of the lift-generating surfaces); the combination of equations (3), (2b) and (1b) determines the thrust needed to maintain that speed.

The induced drag depends on the horizontal span of the lift-generating surfaces, b, and on the distribution of lift along these surfaces, reflected in the numerical coefficient k K :

k K varies between 1.1 and 1.3 for a planar surface8. Rolling on its side, a shark gradually transfers some of the lift from its pectoral fins to the dorsal fin (Fig. 2), changing both the horizontal span and the distribution of lift.

Figure 2: Reconfiguration of lifting surfaces in great hammerhead sharks S. mokarran. By swimming rolled, a shark changes the surfaces that generate lift, L, from the pair of pectoral fins at zero roll angle (left) to the combination of the pectoral and dorsal fins at greater roll angles (right). For the great hammerhead, doing so increases the effective span of the lifting surfaces, b. The model to the right is rolled 65°. Full size image

Intriguingly, the dorsal fin of a great hammerhead is longer than its pectoral fins; the opposite is true for all other sharks for which we have data (the closely related9 scalloped hammerhead S. lewini approaches the unique morphology of the great; Supplementary Table 1 and Supplementary Fig. 4). Rolling to its side, a great hammerhead therefore increases the horizontal span of its lift-generating surfaces. Because an increase in horizontal span of lifting surfaces potentially makes the generation of lift more efficient, it is conceivable that great hammerheads induce less drag when they roll to their side than when they swim upright.

To examine this possibility, we built a morphologically accurate model of a great hammerhead (see Supplementary Figs 5–7), and conducted a series of experiments in a wind tunnel, keeping the Reynolds number similar to that of a free-swimming shark. In each experiment, the model was set at a constant roll angle (from 0° to 90°, every 10°), and its orientation relative to the flow (equivalent to the pitch angle of a shark swimming at constant depth) was manipulated (between −15° and 15°) while lift and drag were measured with a string balance (see Supplementary Note 3). Remarkably, the minimal drag coefficients occurred at roll angles between 50° and 70° (Fig. 3b), which closely matches the range of roll angles at which our tagged sharks swam in the wild (Fig. 1 and Supplementary Figs 2 and 3). At the relevant range of lift coefficients, the reduction in drag is more than 10% (Fig. 3b). The corresponding energy saving is estimated below.

Figure 3: Hydrodynamics of rolled swimming in great hammerhead sharks S. mokarran. (a) Contours of constant lift C L and (b) drag coefficients C D for a range of pitch and roll angles, measured through wind tunnel experiments with a physical S. mokarran model. (c) Contours of constant COT for a 2.95 m shark for a range of roll angle and either pitch angles or (d) swimming speeds. COT was estimated from wind tunnel data summarized in b, and by assuming values for standard metabolic rate and both chemomechanical and propulsive efficiencies (see Supplementary Notes 4). In a, the difference between adjacent contours is 0.2, and in b–d, the difference is 0.02. Full size image

Energy savings

Energy expenditure per distance swam (commonly termed the ‘cost of transport’, COT) is defined as: