Thrust production and chordal flexion of the flukes of bottlenose dolphins performing tail stands at different efforts

Dolphins are powerful animals capable of high-performance aquatic locomotion. These behaviors include high-speed swimming, agility and maneuverability, porpoising, leaping and tail stands. Tail stands describe a behavior in which a vertically oriented dolphin uses horizontal oscillations of its tail flukes to lift an anterior portion of its body out of the water (Fish et al., 2018). Tail stands are similar to a behavior known as spy-hopping, a common natural event that has been observed and recorded in many wild cetacean populations as well as in some captive odontocete species (Williams et al., 2002; Costa et al., 2007; Clegg and Delfour, 2018; Würsig and Whitehead, 2018). While spy-hopping, a vertically oriented animal will project its head and anterior body out of the water to obtain a better view of its surface surroundings, or in anticipation of training sessions that provide food as a reward (in captive situations). When performing tail stands, the dolphin must be able to balance propulsive forces generated by the oscillating tail flukes with the weight of the animal that is supported above the surface of the water.

Dolphins swim with a thunniform mode in which lift-based thrust is produced by the vertical oscillations of the caudal flukes (lunate tail) from movement of the posterior third of the body (Lang and Daybell, 1963; Lighthill, 1969; Webb, 1975; Lindsey, 1978; Videler and Kamermans, 1985; Fish, 1993, 1998; Rohr et al., 1998; Fish and Rohr, 1999; Sfakiotakis et al., 1999; Rohr and Fish, 2004; Fish et al., 2014, 2003). As opposed to the tail stand, dolphins swim by vertical oscillations of the tail flukes moving along a sinusoidal pathway (Fish, 1993; Fish et al., 2014). The downstroke describes the movement from the maximum elevation of the fluke to the horizontal position, and the upstroke describes the movement from the maximum depression back to the horizontal position (Videler and Kamermans, 1985). In the horizontal submerged swimming of dolphins, the buoyant force of water counters gravity so that muscular power is unnecessary to support the body (Noren, 2023). However, muscular effort is required to overcome gravity during spy-hopping and tail stands for the vertically positioned dolphin.

Thrust production of bottlenose dolphins (Tursiops truncatus) has been measured during tail stands using digital particle image velocimetry (DPIV) (Fish et al., 2018). It was determined that the dolphins could generate a downward force from oscillations of their tail flukes that was equal to the weight of the portion of the animal held above the surface of the water. In that study, the dolphins maintained a position with half their weight above the center of gravity out of the water. In this state, gravitational potential energy and kinetic energy remain unchanged, but energy is consumed in the oscillations of the flukes (Xia et al., 2022). However, the experiment conducted by Fish et al. (2018) was limited as only one level of effort was examined without regard for a wider range of performances. The study was initiated to validate the use of bubbles as the particles being tracked with DPIV.

The goal of the present study was to examine the kinematic differences of various degrees of effort (load) during the tail stand for the bottlenose dolphin. Swimming dolphins increase speed by modulating stroke frequency but maintain a constant stroke amplitude (Fish, 1993, 1998). In addition, the flukes show some chordwise flexibility (Bose, et al., 1990; Fish and Rohr, 1999; Fish et al., 2006). Dolphins performing tail stands show both chordwise and spanwise flexibility of the flukes (Fish et al., 2018). It was hypothesized that the kinematics of tail stroke and fluke flexibility during a tail stand would vary with increased effort. Specifically, it was expected that with increased effort (i.e. a greater percentage of the body held out of the water), the oscillatory frequency and flexibility of the flukes would increase.

Experiments were conducted on four female and two male adult bottlenose dolphins, Tursiops truncatus (Montagu 1821), at the National Aquarium in Baltimore, MD, USA. Each individual's body mass (m), body length (BL), number of trials and number of trials per effort were measured or recorded (Table 1). Body length was measured as the linear distance from the tip of the rostrum to the fluke notch. Data for body length and mass were provided by the National Aquarium. The dolphins were held in a large, indoor, marine pool (holding 4.9 million liters of water) with an underwater viewing window that spanned the front of the pool. Filming was conducted through this window as it provided an acceptable underwater view of the dolphins. Attached to the large pool were two separate, identical smaller pools which kept the males and females separate, to limit any sort of distraction that could occur during the tail stand performances. The pool was large enough that the dolphins would not interact with each other during the trials, but to further limit any distractions, the dolphins were kept out of the way by the trainers when not performing tail stands. The males and females were recorded during two separate filming sessions per visit, separated by more than 1 h.

Dolphins were trained to perform a tail stand at specified heights above the water's surface under trainer control with the use of a hand or target (Fig. 1). The heights were based upon the length of the dolphin's body held out of the water relative to the center of mass (COM) of the animal. The COM is located at the anterior insertion of the dorsal fin and accounts for roughly 41% of body length from the tip of the rostrum (Fish, 2002). The height of the body above the water's surface was associated with three levels of effort: low (Movie 1), medium (Movie 2) and high (Movie 3), which were based on the position of the COM relative to the surface of the water. Low efforts were categorized by trials in which the COM was below the surface of the water, medium efforts occurred when the anterior insertion of the dorsal fin was in line with the surface of the water, and high efforts occurred when the COM was above the surface of the water (Fig. 2).

During each trial, the dolphin was positioned so that the body faced laterally parallel to the portion of the viewing window where the video camera or cameras were positioned. Having two cameras positioned at slightly different angles ensured that the majority of the trials recorded were useable for analysis. The videos were recorded at 60 frames s⁻¹ on a Canon EOS 5D Mark III equipped with a Canon EW-88C zoom lens (1:2.8, f 24–70 mm).

The research on the dolphins was approved by the West Chester University IACUC for protocol 201701.

The peak-to-peak amplitude (A_p-p) is the maximum distance between the tail fluke's dorsal-most and ventral-most positions within a single stroke cycle. A_p-p was determined by taking the maximum positions to which the flukes extended during the ET and EB and measuring the distance between the locations of the fluke notch. For comparison of animals of different sizes, A_p-p is displayed as a proportion of BL.

For comparison of f and A_p-p among the various sized dolphins, the force (F_d) developed during a tail stand was scaled as the dimensionless thrust-to-weight ratio (F_d/W_b), where W_b is the body weight of the animal (in N) calculated as the animal's mass times the gravitational acceleration of 9.8 m s⁻² (m×g). F_d/W_b is used in engineering to assess the performance of a propulsive system. If the dolphin could hold its complete weight out of the water, its F_d/W_b would be equal to 1. F_d/W_b>1 would allow a dolphin to launch itself completely out of the water, becoming airborne.

Variation about the means and medians was expressed as ±1 s.d. One-way ANOVA (analysis of variance) tests were performed at the 95% confidence interval for the data concerned with stroke frequency versus tail stand effort level, and peak-to-peak amplitude versus tail stand effort level. Additionally, a one-way ANCOVA (analysis of covariance) was used for the frequency dataset to adjust for F_d/W_b. All ANOVA, ANCOVA, associated assumptions tests (i.e. Shapiro–Wilk, Levene's) and post hoc tests were run using IBM SPSS Statistics software [v.29.0.0.0 (241)]. Least-squares regressions and correlation coefficients (r) were determined with KaleidaGraph software (v.4.5.4, Synergy Software, Reading, PA, USA).

For the FI dataset, Statistica 6.1 (StatSoft, Tulsa, OK, USA) was used for analysis and was significantly different from a normal or lognormal distribution (Kolmogorov–Smirnov). As such, the Kruskal–Wallis (KW), a non-parametric one-way ANOVA, was conducted (α=0.05) to compare the individual dolphins with the FI. This analysis was repeated for effort level versus FI. As there were no significant differences for FI between individual dolphins (P=0.072) or between effort levels (P=0.912), the data for all dolphins and effort levels were pooled. The combined data were used to compare stroke cycle versus FI using the KW test (α=0.05) followed by the multiple comparisons test. Graphic analyses were used to elucidate patterns in the dataset.

A total of 136 trials for tail stands were recorded over six separate filming sessions. Only 100 trials were used for analysis in which the dolphin remained in the vertical position for at least two stroke cycles while laterally positioned perpendicular to one of the two cameras, or when it was positioned inside the viewable fields of the cameras. The useful trials were divided amongst six individual adult bottlenose dolphins (T. truncatus) with the morphometrics and number of trials provided in Table 1.

During a tail stand, the dolphin maintained a vertical position with the anterior body projecting out of the water. The dolphins maintained their position in the water, although in some trials, the dolphin would shift its position backward slightly relative to the trainer (Fig. 1). The tail stand was accomplished by actively oscillating the tail and flukes in the horizontal plane. The angle between the peduncle and the flukes was nearly perpendicular at midstroke (Fig. 3). At the transition between the upstroke and downstroke, the flukes displayed a large flexion (see below) as the downward faces of the flukes were alternately flipped between the dorsal and ventral surfaces.

Among the 100 analyzed trials, 27 accounted for low effort, 33 accounted for medium effort and 40 accounted for high effort. The mean proportions of body length above the surface of the water were 0.33±0.08, 0.47±0.06 and 0.61±0.08 m for low, medium and high effort, respectively. The mean weights supported above the surface of the water were 531.9±139.5, 773.4±133.8 and 976.9±133.7 N for low, medium and high effort, respectively (Fig. 2).

Frequency increased as the level of effort increased, with mean values of 1.75±0.43, 2.20±0.50 and 2.56±0.53 Hz for low, medium and high effort, respectively. The residuals of the data were normally distributed (W=0.960, P=0.004), and homogeneity of variance was met (F=0.442, P=0.644). There were significant differences between the mean frequencies at the different levels of effort (F=21.753, P<0.0001), such that frequency was significantly greater with increased effort group (P<0.01). The pooled frequencies showed a linear increase when compared with F_d/W_b ratio (Fig. 5) with a regression line described as f=0.73+3.06 F_d/W_b (r=0.71). Residuals of this dataset were normally distributed (W=0.979, P=0.115) and showed no significant differences between the means of the different groups (F=0.505, P=0.605). A one-way ANCOVA revealed that there were no significant differences in mean frequency between the effort levels, when adjusting for F_d/W_b (F=0.851, P=0.430).

The frequencies measured at medium and high effort also gave statistically similar results to those provided in Fish et al. (2018), with a mean f of 2.70±0.12 Hz. The thrust generation measured by Fish et al. (2018) ranged from 560.0 to 997.3 N with a mean value of 739.7±137.8 N.

The A_p-p remained consistent throughout all levels of effort, with mean values of 0.82±0.22, 0.84±0.17 and 0.84±0.17 m for low, medium and high effort, respectively, with an overall mean of 0.82±0.04 m. With respect to body length (BL), mean A_p-p was 0.34±0.07 BL with an overall range of 0.20–0.56 BL. At low, medium and high effort, A_p-p was 0.33±0.08 BL, 0.34±0.06 BL and 0.34±0.06 BL, respectively (Fig. 6). A_p-p rarely dropped below 0.25 of an individual's BL (only observed in 10% of all trials). As there was little to no variation for the amplitudes regarding effort, the values were not significantly different from one another (F=0.093, P=0.912 for overall A_p-p, and F=0.150, P=0.861 for A_p-p relative to BL). Both sets of data were normally distributed (W=0.967, P=0.014 for overall A_p-p, and W=0.975, P=0.059 for A_p-p relative to BL) and showed equal variance amongst groups (F=0.558, P=0.574 for overall A_p-p, and F=0.480, P=0.620 for A_p-p relative to BL).

Significant differences (Table 2) were observed among FI values between the four stages of the stroke cycle (CU, CD, ET and EB) (P<0.001). The mean values of FI for each stage were recorded as 0.89±0.03 for CU, 0.87±0.04 for CD, 0.83±0.05 for ET and 0.77±0.07 for EB (Table 2). The Kruskal–Wallace test showed that there were significant differences in FI during the stroke cycle (P<0.0001; Table 2). ET and EB were both significantly different from CU and CD (P<0.0001), and CU was significantly different from CD (P=0.0125). EB also showed a significant difference from ET (P=0.0002). The multiple comparisons test results shown in Table 2 indicate the significant differences between the different phases of the stroke cycle.

As noted in Materials and Methods, the KW test failed to show a significant difference when comparing the individual dolphins with one another in terms of their FI (P=0.0719). Additionally, the KW test also failed to show any significant difference in FI as the level of effort increased for the overall combined dataset (P=0.912; see Table 2). Median values of FI for each stage in the stroke cycle are shown in Fig. 7 and median values of the FI for each stage of the stroke cycle with respect to the level of effort are shown in Fig. 8.

Estimates of the propulsive power of cetaceans have been controversial (Gray, 1936; Webb, 1975; Fish, 1993, 1998, 2006). Despite studies that demonstrated that dolphins could swim at high speed with high power output (Lang and Daybell, 1963; Lang and Norris, 1966; Lang and Pryor, 1966; Fish, 1993, 1998), the presumption of a reduced power effort to swim rapidly by dolphins, whales and fishes has been perpetuated (Gray, 1936; Kermack, 1948; Kramer, 1960; Blake, 1983; Romanenko, 2002). However, direct measurement of thrust and power outputs of swimming dolphins had not been performed.

Goforth (1990) examined the forces produced by the swimming actions of bottlenose dolphins trained to push against a static load cell. Dolphins produced maximal forces during static swimming of 1.1–1.6 times body mass and forces of 0.3–0.6 times body mass at maximum oxygen consumption with minimum lactate production (Goforth, 1990; Williams et al., 1993). However, the force measured from the load cell was not regarded as equivalent to the thrust generated during forward swimming. The water acting on the flukes did not have an initial velocity to generate the lift-based thrust of actual swimming.

More recent analyses of the power output of dolphins utilized DPIV (Fish et al., 2014, 2018). DPIV is a video-based analysis technique in which the displacement of particles suspended in a fluid is tracked to make direct measurements of the flow field (Willert and Gharib, 1991; Ryerson and Schwenk, 2011). Typical examination of the flow field about swimming organisms using DPIV relies on the use of a laser sheet to illuminate neutrally buoyant reflective particles (Drucker and Lauder, 1999; Nauen and Lauder, 2002; Stamhuis and Nauwelaerts, 2005; Fish et al., 2014, 2018). To avoid harm to dolphins that were swimming in a large pool, a high-speed video was used to record the trajectory of microbubbles (1 mm) in the wake of bottlenose dolphins (Fish et al., 2014). It was found from the bubble DPIV that swimming dolphins could produce large amounts of thrust.

To validate the bubble DPIV results, experiments were performed with dolphins executing tail stands (Fish et al., 2018). During a stable tail stand, the dolphin hovers in a state of dynamic equilibrium (Xia et al., 2022). The equilibrium is maintained through a combination of gravitational (weight), buoyant and fluid (thrust) forces. The weight of the dolphin supported out of the water must match an equal and opposite downward force produced by the oscillating flukes. The force is the vertical downward-directed thrust component that was measured from the displacement of microbubbles. It was found that the corresponding measurements of thrust from the DPIV test were in line with the estimated proportion of weight of the animal suspended in the air. The study by Fish et al. (2018) corresponded to the medium effort of the dolphins in the present study and the thrust generated was found to be similar.

The propulsive oscillatory movements of the dolphin require that the flukes are canted at an angle of attack to generate lift with each stroke, during a tail stand (Fish et al., 2014). Momentum is generated through vortex shedding into the wake (Fish et al., 2014; Feng et al., 2021). As the body is held stationary during the tail stand, only minimal drag is produced along the body dorso-ventrally due to oscillations of the peduncle and on the flukes; however, the dolphin is still generating a lift for thrust. Even though the individual is holding position, and not accelerating in either direction, a force (i.e. gravity) must still be overcome through the application of thrust. Thrust is obtained from both leading-edge suction and lift force where an increase in the angle of attack directly relates to an increase in lift (Fish, 1993). Thrust generation measured in the present study ranged from 289.0 to 1262.8 N with a mean of 789.6±224.3 N. The maximal values of force generated during tail stands were consistent with the swimming efforts by delphinid species (Fish et al., 2014, 2018; Tanaka et al., 2019).

Another parameter used to study the propulsive power of the dolphins is the F_d/W_b ratio. Because of the nature of the tail stand, F_d/W_b values of 1 or greater would be impossible as some part of the body (e.g. flukes) would have to be immersed and thus have a supporting buoyant force. The maximum F_d/W_b ratio achieved by a dolphin in the present study was 0.81. Mean F_d/W_b at the low, medium and high effort was 0.33±0.08, 0.47±0.06 and 0.61±0.08, respectively. As the dolphin performing a tail stand is static in relation to water flow around the body, there is no equivalency between thrust generation in a tail stand and active swimming (Fish et al., 2018). The propulsive kinematics of a swimming dolphin does not exhibit the exaggerated motion of the flukes during the tail stand (see below; Fish, 1993; Fish et al., 2018). However, experiments on dolphins pushing against a load cell have similarities with the kinematics and force production of a dolphin performing a tail stand as its position is held static (Goforth, 1990; Williams et al., 1993). In an 8 s test where a 309 kg bottlenose dolphin pushed against a load cell, a F_d/W_b of 1.08 was achieved (Goforth, 1990). Using the load cell technique, Williams et al. (1993) showed a male dolphin had a maximum F_d/W_b ratio of 1.26. Above a F_d/W_b ratio of 0.59, oxygen consumption reached a plateau and lactate production increased for the dolphin.

Stroke frequency for the tail stand increased with increased load held above the surface of the water. Relative to the speed of a horizontally swimming bottlenose dolphin (Fish, 1993), the frequency of the tail stand was equivalent to 3.5, 4.7 and 5.6 m s⁻¹ for low, medium and high effort, respectively. These levels of speed performance were below the maximal speeds attainable by the species. A maximum swimming speed of 8.3 m s⁻¹ was reported for a 7.5 s burst by a Pacific bottlenose dolphin (Lang and Norris, 1966).

During a tail stand, the oscillations of the flukes are directed horizontally with a large pitch angle and A_p-p directing the thrust vertically (Fish et al., 2018). Pitch angle varied between 73 and 78 deg and mean A_p-p was 0.34 BL with a maximum of 0.56 BL (Fish et al., 2018). The vertical static position of the dolphin during the tail stand required a high pitch angle to cant the flukes at an angle of attack to the self-generated flow. The angle of attack describes the angle formed between the axis of the tail flukes and the tangent of their direction of travel (Fierstine and Walters, 1968; Fish et al., 1988, 2006; Fish, 1993). Control of the angle of attack can adjust propulsive efficiency and thrust production for lift generation (Long et al., 1997; Prempraneerach et al., 2003; Fish et al., 2006). Movement of the wing-like flukes generated an upward lift to hold a proportion of the weight of the dolphin above the water surface.

The kinematics of a stroke (i.e. frequency and peak-to-peak amplitude) during an acceleration are similar to those of a tail stand (Fish et al., 2018). During horizontal swimming, an acceleration represents an unsteady motion in which there is an unbalanced thrust force that is greater than the resistive drag. In an investigation of thrust production using bubble DPIV, bottlenose dolphins accelerating from rest had average A_p-p values of 0.28 BL (Fish et al., 2014). Skrovan et al. (1999) found large amplitude strokes with A_p-p values of 0.20 to 0.50 BL were used for accelerations at the start of horizontal swims and at the beginning of ascent and descent phases of dives. These values of A_p-p are close to or overlap the A_p-p for tail stands.

The tail stand of the dolphin shows similarity with hovering maneuvers performed by winged organisms (e.g. bees, moths and hummingbirds) (Alexander, 2003; Fish et al., 2018). These small animals and the larger dolphins each produce a vertically oriented lift to overcome gravity and support their weight in a fluid environment. The wake shows similarities among the hovering animals in the production of downward convected periodic vortices (Fish et al., 2018). Like the wing movements of hovering animals, the dolphin flips its flukes over during reversal from the upstroke and downstroke (Dickinson and Götz, 1996; Alexander, 2003; Fish et al., 2018). In contrast, lift generation during the downstroke in hummingbirds is typically greater than lift generated from the upstroke, whereas thrust generation is equal throughout the stroke cycle in dolphins (Warrick et al., 2005; Fish et al., 2018). In addition, the weight of aerial hovering animals is low as the low density of air provides little positive buoyancy, whereas the large weight of the dolphin is partially supported by the buoyancy of the aquatic medium.

The COM for each individual was approximated to be at the anterior insertion of the dorsal fin, which was assumed to measure the first 41% of the body length (Fish, 2002). Potential error may have arisen from this assumption, however, as there were slight discrepancies in overall morphologies amongst the individuals. Resulting calculations involving these values may have produced slight errors in the data concerned with the amount of mass held above the surface of the water. Because the position of the COM was used to categorize the trials based on effort, any calculations that compared low, medium and high effort would be most affected by these discrepancies. Additional calculations that depended on the COM include the mean weight supported above the surface of the water (thrust), and F_d/W_b ratio. In addition, the animals were not axisymmetric about the longitudinal body axis, so the mass distribution would vary along the body length. This affects the weight distribution on the body that is perceived to be above the surface of the water. Also, because of the unsteady nature of the behavior, the dolphins would vary vertically, in which a given vertical position could only be held for a short period of time. The oscillatory motions of the flukes produced during tail stands induced a change in thrust force throughout the stroke cycle.

The lateral caudal flukes of dolphins are composed of dense arrays of spanwise and chordwise collagen fibers without bony skeletal support (Felts, 1966; Gough et al., 2018). The collagen fibers provide enough structure and rigidity within the flukes to allow effective thrust production. In addition, the flukes are flexible and become cambered under load (Romanenko, 2002; Fish et al., 2006). Flexion through cambering promotes maintenance in thrust production throughout the stoke cycle, while also promoting smoother transitions between changes in the oscillatory direction, effectively limiting stall (Fish et al., 2006).

Increases in thrust and propulsive efficiency result from flexibility with the chord and span of the flukes (Yamaguchi and Bose, 1994; Heathcote et al., 2008). Chordwise flexibility in oscillating propulsors has been shown to increase efficiency when compared with rigid, oscillating foils and plates (Katz and Weihs, 1978; Bose, 1995; Prempraneerach et al., 2003; Rohr and Fish, 2004; Barannyk et al., 2012; Dai et al., 2012; Cleaver et al., 2013; Iverson et al., 2019; Brousseau et al., 2021; Li et al., 2021). Katz and Weihs (1978) found that chordwise flexibility of an oscillating foil could increase propulsive efficiency above that of a rigid propulsor with similar oscillations, although there was a moderate decrease in thrust. However, compared with a rigid wing, Li et al. (2021) asserted that a 28.3% greater propulsive efficiency of a flexible oscillating wing was due mainly to increasing thrust within the whole period of motion. A flexible foil undergoing heaving and pitching motions produced a maximum efficiency of 0.87 (Prempraneerach et al., 2003).

The issue of whether flexibility of the flukes of cetaceans is purely passive or has some contribution of an active mechanism of control is still unresolved. Pabst (2000) indicated that the extensor caudae lateralis muscle could control the angle of attack of the flukes while swimming. The anterior insertion of the flukes with the body is forward of the major flexion point with the caudal vertebrae (Watson and Fordyce, 1993; Long et al., 1997; Tsai, 1998; Fish et al., 2006). In spanning the main flexural joint, muscular control of the angle of attack would cause a smooth cambering of the flukes (Fish et al., 2006). In addition, it was observed that the extensor caudae lateralis tendons in the peduncle of cetaceans inserted exclusively on the caudal vertebrae posterior of the fluke insertion (Adams and Fish, 2019). The muscles pulling on the tendons could possibly control the spanwise and chordwise flexibility of the flukes (Adams and Fish, 2019). This potential control was evident by the maintenance of the degree of flexion of the flukes regardless of the load exerted during the tail stand.

The ability to perform tail stands by dolphins is a compromise between propulsive (thrust), buoyant and gravitational (weight) forces to lift a proportion of the body above the water surface. The degree of flexion in the tail can be measured by the flex index (FI): a dimensionless value that compares the chord and camber lengths of the caudal flukes. The present study measured the FI at the four defined stages of the stroke cycle (center stroke up, center stroke down, extreme top and extreme bottom) over the three effort levels. For increasing levels of effort, a greater proportion of the body was held out of the water, supported by greater thrust production. Increasing thrust results from an increased oscillatory frequency with consistent amplitude of the flukes. Furthermore, there was substantial bending of the flukes. However, there was no difference in flexion as the level of effort increased. This maintenance of flexion of the flukes may indicate active control of fluke stiffness in combination with the arrangement and mechanical properties of the constituent collagen fibers.

We are grateful for the cooperation of the National Aquarium (Baltimore), their staff and their dolphins. We would also like to thank Dr Jennifer Chandler of West Chester University's Department of Biology for her help with our statistical analysis.