How seabirds plunge-dive without injuries
- aDepartment of Biomedical Engineering and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061;
- bNational Museum of Natural History, Smithsonian Institution, Washington, DC 20560;
- cSetor de Ornitologia, Museu Nacional, Universidade Federal do Rio de Janeiro, São Cristóvão, Rio de Janeiro RJ 20940-040, Brazil;
- dNorth Carolina Museum of Natural Sciences, Raleigh, NC 27601
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Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved August 30, 2016 (received for review May 27, 2016)

Significance
Plunge-diving is a very unique foraging method in the animal kingdom. A limited set of water birds exhibit this behavior, and only one family of seabirds (Sulidae) exhibit this behavior at high speeds. We studied the stability of the bird’s slender and seemingly fragile neck during a plunge-dive by conducting simple experiments that mimic this behavior. An elegant analysis of the interaction among hydrodynamic forces, neck elasticity, and muscle contraction reveals that seabirds dive at appropriate speeds to avoid injury. Considering the popular recreational sport of diving, we also find a diving speed limit for humans to avoid injury.
Abstract
In nature, several seabirds (e.g., gannets and boobies) dive into water at up to 24 m/s as a hunting mechanism; furthermore, gannets and boobies have a slender neck, which is potentially the weakest part of the body under compression during high-speed impact. In this work, we investigate the stability of the bird’s neck during plunge-diving by understanding the interaction between the fluid forces acting on the head and the flexibility of the neck. First, we use a salvaged bird to identify plunge-diving phases. Anatomical features of the skull and neck were acquired to quantify the effect of beak geometry and neck musculature on the stability during a plunge-dive. Second, physical experiments using an elastic beam as a model for the neck attached to a skull-like cone revealed the limits for the stability of the neck during the bird’s dive as a function of impact velocity and geometric factors. We find that the neck length, neck muscles, and diving speed of the bird predominantly reduce the likelihood of injury during the plunge-dive. Finally, we use our results to discuss maximum diving speeds for humans to avoid injury.
Nature contains several species of creatures that interact with the air–water interface (1). A number of bird species are able to dive into water from the air as a hunting mechanism (e.g., kingfishers, terns, and gannets), a behavior known as plunge-diving (2, 3). Some seabirds, like the northern gannet, are highly specialized plunge-divers, making 20–100 dives per foraging trip, diving from heights of 5–45 m, and attaining speeds of more than 20 m/s (4⇓⇓–7). Thus, the bird’s structure and behavior have presumably evolved to withstand a variety of high dynamic stresses, because no injuries have been reported in plunge-diving seabirds. Biologists have previously focused on the diving behavior in terms of ecological factors, such as diving depths, prey species, and hunting success rate (8⇓–10), and physiological features, such as the role of vision while crossing the air–water interface (11, 12). Unique kinematic and morphological features during the dive have also been observed, such as having a sharp, arrow-like body posture and a straight, long, and slender neck (13, 14). However, a mechanical understanding of plunge-diving birds is not well-established.
To study such a phenomenon, Morus bassanus (hereafter gannets) and Sula leucogaster (hereafter boobies), from the Sulidae family, are used as a model species due to their highly specialized diving characteristics (5, 13). First, they plunge-dive at very high speeds, using that momentum to carry them to some depth. Then, they use their webbed feet and/or wings to propel themselves further underwater, like penguins and cormorants (15, 16). Although plunge-diving at high speeds allows the bird to dive deeper, it induces much larger stresses on the seabird’s body than pursuit diving alone (13). The two main forms of plunge-diving observed are known as the V-shaped dive and the U-shaped dive (5). During V-shaped dives, the seabird impacts the surface at an angle, whereas during U-shaped dives the impact trajectory is more perpendicular to the surface (14, 17). Although the mechanical forces may differ between the two dives, both U-shaped and V-shaped dives experience an axial force significantly larger than a transverse force. Therefore, this present study focuses on the U-shaped dive, which is a model for understanding the effect of an axial force on the risk of a buckling neck.
From a mechanics standpoint, an axial force acting on a slender body may lead to mechanical failure on the body, otherwise known as buckling. Therefore, under compressive loads, the neck is potentially the weakest part of the northern gannet due to its long and slender geometry. Still, northern gannets impact the water at up to 24 m/s without injuries (18) (see SI Appendix, Table S1 for estimated speeds). The only reported injuries from plunge-diving occur from bird-on-bird collisions (19). However, for humans, diving into water at speeds greater than 26 m/s risks severe fractures in the cervical or thoracic vertebrae and speeds greater than 30 m/s risk death, regardless of impact orientation (20⇓⇓⇓⇓⇓–26). Understanding the bird plunge-dive may further explain methods of injury prevention in human diving.
In this present study, we investigate how birds are able to dive at high speeds and sustain no injury, given the morphology of the head and neck. Due to its long, slender geometry, the seabird’s neck is the region with the greatest potential for mechanical failure or instability under high dynamic loading. In reduced-order experiments, we simplify the seabird system as a long, thin, elastic beam attached to a rigid cone, which represent the bird’s neck and head, respectively. By modeling the bird’s neck as an elastic beam, we can use the buckling and nonbuckling behaviors of the elastic beam to represent the stability of the seabird’s neck. A linear stability analysis is used to obtain a theoretical prediction of the buckling transition. The effect of neck muscles is discussed in terms of modifying the buckling criterion. We then show that plunge-diving seabirds have a unique morphology, appropriate diving speeds, and strong neck muscles that will allow them to dive safely at high speeds.
Results
Plunge-Diving Seabirds.
To characterize the plunge-diving mechanism of seabirds, a salvaged northern gannet is prepared in the diving posture and is released into a water tank as shown in Fig. 1A (Materials and Methods). Upon water entry, in which momentum carries the bird through the water (11), three different phases become apparent: (i) the impact phase, (ii) the air cavity phase, and (iii) the submerged phase, which is characteristic of a classic water entry problem (27). The impact phase occurs when the tip of the beak first makes contact with the water surface until the head becomes submerged (
(A) A deceased, frozen northern gannet impacts the water surface vertically at
The air cavity phase [
A nondimensional number representing a ratio of hydrodynamic drag to the neck’s elasticity [
Physical Experiment to Mimic Plunge-Diving.
To further explore this fluid–neck interaction, we design a reduced-order experiment by approximating the neck (a composition of bone, muscle, and skin) as an elastic beam and the head as a rigid cone. A cone–beam system was fabricated to effectively model the head–neck interaction during impact (Materials and Methods). Various geometric parameters (i.e., cone angle, cone radius, and beam length) and impact velocities were tested, producing a range of drag to elasticity ratio to be
Fig. 2A shows the dynamics of a cone–beam specimen remaining stable through the air cavity phase,
Time sequence images of cone–beam specimens impacting the water surface as inspired by a diving seabird. Here, β = 30°,
Forces on Cone or Head.
Hydrodynamic drag is the main force that acts on the cone during impact. When the cone first enters the water (during the impact phase), the drag force is primarily induced by a change in added mass. Hence, the drag force increases in time during the impact phase;
Force data on a cone with
Force on the cone and 3D-printed northern gannet skull during impact. Force data are collected at four different impact velocities ranging from 2.1 to 3.2 m/s. The forces are normalized by
Next, we consider the force on a 3D-printed skull of a northern gannet. Based on the geometry of the skull, three distinct sections are identified (Fig. 1B and SI Appendix, Fig. S3). The first section is between the tip of the beak to its base, where a hinge [naso-frontal hinge (28)] runs along the dorso between the beak and the forehead (Fig. 1); the second section is between the naso-frontal hinge and small protrusions near the back of the skull (zygomatic process of the Os squamosum); the third section is between the protrusions and the end of the skull (Prominentia cerebellaris) (29). Assuming that the skull is two cones of different angles in tandem, the force measurement during the impact phase shows two distinct time-dependent curves as predicted by our analytical expression described above (Fig. 3B). This result indicates that the axial force acting on the neck of the plunge-diving bird increases with the skull radius, the impact velocity, and, most importantly, the beak angle.
Transition to Buckling.
The transition from stable to unstable beams depends on the impact velocity, geometric factors, and material properties of the beam and the cone. The critical compressive force to buckle the beam is calculated from a linear stability analysis resulting in the dispersion relation. In order for the beam to buckle, the highest growth rate at some given time must lie in the unstable region (Fig. 4A), in our case nondimensional wavenumber greater than π (
(A) Growth rate vs. nondimensionalized wavelength. Each curve represents a different time. The black curve is the moment when
Using morphological and material properties obtained from the salvaged bird, we find that the plunge-diving birds dive in the stable region of the transition diagram. However, this analysis neglects the effects of the neck muscles, which leads to another question addressed in the next section. What role does the neck musculature play in preventing neck injuries during the plunge-diving behavior?
Effect of Muscles.
The motion and strength of an animal’s neck result from the coupling between bone and muscles (32, 33). The total force generated by the muscle bundle will depend on the length and cross-sectional area of muscle fibers. Neck muscles in plunge-diving birds are mostly concentrated near the head and the thorax of the bird, as shown in Fig. 4C. The muscles connect the body, the vertebrae, and the skull by a series of thin muscle sheets and tendons (34). Additionally, the necks of gannets and boobies, similar to those of other birds, have an S shape, due to their vertebrae morphology and connecting design (34, 35), increasing the complexity of biomechanical analysis. One may note that the S shape would serve as a primary mode of buckling in the neck. However, the fact is that the musculature plays an important role in stabilizing a straight neck as a whole, and also maintaining the S shape of the spine. Therefore, we simplified the complex network of muscles using segmentation and reconstruction of computed tomography (CT) images of the lateral, dorsal, and ventral musculature (Fig. 4C). By muscle contraction, the tendons put some stabilizing tension on the bones, straightening the neck out and fixing the bones into place before the impact. We approximate the effect of the muscles as a continuously distributed load acting tangentially along the neck (Fig. 4D) (36). The muscle force
Discussion
The results help to reveal the mechanisms (in addition to visual accommodations) by which plunge-diving birds are able to dive at incredibly high speeds with no injuries (19). This is primarily attributed to the neck length and chosen diving speeds, which stay in parameter regimes that prevent the neck from bending under compressive loads. The neck muscles move plunge-divers further away from the buckling transition. In fact, it would take about 80 m/s for the plunge-diving seabird to sustain a neck injury based on our analysis.
Furthermore, this study may elucidate safe diving speeds for humans. We consider feet-first dives, which gives a higher survival rate (20). Human feet are flat with large surface areas; average foot areas for males and females are 0.06 and 0.05 m2 (38), respectively. At a diving speed of 24 m/s, the compressive force that a human would experience is about 14 kN, which well exceeds a range of maximum compressive forces (0.3–17 kN) to cause neck injury (39). The impact force exceeds the critical maximum compressive force (17 kN) at a diving speed of about 24 m/s (for trained individuals, i.e., stunt divers). This critical diving speed is consistent with the maximum speed (≈26 m/s) for spinal fractures reported in case studies (SI Appendix, Table S2).
Materials and Methods
Salvaged Bird.
A salvaged northern gannet (M. bassanus) was obtained for analysis. The elastic modulus of the neck (
Skull Specimens.
Several skull specimens for different species of gannets and boobies were acquired from the Smithsonian Museum of Natural History (M. bassanus, n = 14; Morus capensis, n = 5; Morus serrator, n = 2; Sula dactylatra, n = 2; Sula sula, n = 3; and S. leucogaster, n = 3). Two distinct regions are noted: (i) between the tip of the beak to the naso-frontal hinge having a half-angle of
Muscle Cross-Sectional Area.
The northern gannet’s neck musculature was divided in dorsal, ventral, and lateral (Fig. 4C; red for dorsal muscle and yellow for ventral muscle). Mesh masks were created using threshold selection (Hounsfield unit: −140, 299) and cleaned for segmentation and reconstruction in Mimics program. To measure the cross-sectional area of the dorsal and ventral musculature, the neck was divided in anterior (five vertebrae close to the skull) and posterior (vertebrae 9–14, closer to the thorax) portions; vertebrae 6–8 comprise the midsection of the S-shaped neck. After segmentation, seven points along the anterior and posterior portions of the neck were selected to extract the cross-sectional area measurements. Mask area measurements (square millimeters) of 10 sequential slice images were averaged for each of the seven points. Values from the seven points were averaged (anterior musculature: ventral, 195.87 ± 41.22 mm2 and dorsal, 319.21 ± 186.78 mm2; posterior musculature: ventral, 88.79 ± 23.76 mm2 and dorsal, 181.40 ± 68.44 mm2) to determine musculature forces to avoid neck buckling.
Physical Experiment.
To simulate the plunge-diving seabird’s head–neck coupling, a cone–beam system was developed (SI Appendix, Fig. S5). Cones with radii of 1.27 cm and 2.0 cm were either 3D-printed (Makerbot Replicator 2X, ABS plastic) or manufactured (acrylic). The cone half-angles, β, were 12.5°, 30°, 35°, 40°, 45°, 50°, and 58°. Rectangular elastic beams were created using vinylpolysiloxane (Elite Double 22; Zhermack Co.) (E = 0.95 MPa and
The cone–beam system is dropped from various heights, resulting in impact velocities ranging from 0.5 to 2.5 m/s, and recorded using a high-speed camera (IDT-N3, 1,000 frames per s). At least five trials are conducted for each set of the experimental parameters. The changing vertical distance (
After processing all high-speed videos for both amplitude and velocity data, our experiments exhibit three states: stable, unstable, and transitionally unstable. Quantitatively, these states can be characterized by distinct ranges of the nondimensional amplitude. The stable state is characterized by a nondimensional amplitude range less than one, which corresponds to the nonbuckling behavior of the beam; conversely, the unstable state has a nondimensional amplitude greater than one, which corresponds to the unstable buckling behavior. After repeated trials of a single case, the case is considered stable if fewer than 20% of the trials buckle. If more than 80% of the trials buckle, then the case is unstable. If 20–80% of the trials buckle, then the case is characterized as transitionally unstable.
Derivation and Measurement of Forces.
The drag force during the impact phase is derived from the Euler–Lagrange equation. The Lagrangian is defined as
A rigid steel rod connects the cone/bird skull to the force transducer (LCM-105-10; Omegadyne, Inc.). The force transducer is connected to a signal conditioner (2310; Vishay), which collects data at a sampling rate of 1 kHz. The high-speed camera was used again to determine the impact velocity at 1,000 frames per s. At least five trials were taken for the cone with β =12.5° and the 3D-printed northern gannet skull impacting the water from 2.0 to 3.2 m/s (SI Appendix, Fig. S6).
Derivation of Dispersion Relation.
Under an axial force, the lateral displacement,
Fig. 4A shows the dispersion relation between the integrated growth rate (
Spatial Stability.
If we assume force is time-independent (SI Appendix, Fig. S8), the most unstable mode is given by
where
In experiments, we chose a reference moment for the instability of the beam as when the cone reaches two cone heights (or
Neck Muscle Resistance.
The results from the previous sections indicate that the plunge-diving seabirds are able to dive safely at high impact speeds. The analysis, however, neglects the role of neck muscles. We consider the neck muscle force as a distributed follower load acting tangentially along the beam:
To simplify the analysis, the muscle force can be approximated as a constant force per unit length,
Acknowledgments
We thank Alex Ochs, Grace Ma, Andrew Marino, Thomas Moore, and Yuan-nan Young for their initial contributions. This work was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico Grant 246819/2013-8 (to L.S.), Virginia Tech Institute for Critical Technology and Applied Science, and National Science Foundation Grants CBET-1336038 (to B.C., S.G., and S.J.) and PHYS-1205642 (to S.G. and S.J.).
Footnotes
↵1B.C., M.C., and L.S. contributed equally to this work.
- ↵2To whom correspondence should be addressed. Email: sunnyjsh{at}vt.edu.
Author contributions: B.C., M.C., L.S., S.G., C.D., J.G., and S.J. designed research; B.C., M.C., L.S., S.G., and S.J. performed research; B.C., M.C., L.S., and S.J. analyzed data; and B.C., M.C., L.S., S.G., C.D., J.G., and S.J. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1608628113/-/DCSupplemental.
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