Dolphins have become famous for their ability to perform a wide variety of athletic and acrobatic behaviors including high-speed swimming, maneuverability, porpoising and tail stands. Tail stands are a behavior where part of the body is held vertically above the water's surface, achieved through thrust produced by horizontal tail fluke oscillations. Strong, efficient propulsors are needed to generate the force required to support the dolphin's body weight, exhibiting chordwise and spanwise flexibility throughout the stroke cycle. To determine how thrust production, fluke flexibility and tail stroke kinematics vary with effort, six adult bottlenose dolphins (Tursiops truncatus) were tested at three different levels based on the position of the center of mass (COM) relative to the water's surface: low (COM below surface), medium (COM at surface) and high (COM above surface) effort. Additionally, fluke flexibility was measured as a flex index (FI=chord length/camber length) at four points in the stroke cycle: center stroke up (CU), extreme top of stroke (ET), center stroke down (CD) and extreme bottom of stroke (EB). Video recordings were analyzed to determine the weight supported above the water (thrust production), peak-to-peak amplitude, stroke frequency and FI. Force production increased with low, medium and high efforts, respectively. Stroke frequency also increased with increased effort. Amplitude remained constant with a mean 33.8% of body length. Significant differences were seen in the FI during the stroke cycle. Changes in FI and stroke frequency allowed for increased force production with effort, and the peak-to-peak amplitude was higher compared with that for horizontal swimming.

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.

Experimental animals and effort determination

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.

Table 1.

Morphometrics, sex, total number of trials and number of trials per effort of each dolphin (Tursiops truncatus) tested

Morphometrics, sex, total number of trials and number of trials per effort of each dolphin (Tursiops truncatus) tested
Morphometrics, sex, total number of trials and number of trials per effort of each dolphin (Tursiops truncatus) tested

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).

Fig. 1.

Tursiops truncatus performing a tail stand under trainer control with a hand target. This represents a medium level effort as the center of mass (COM), the anterior insertion of the dorsal fin, is at the water's surface.

Fig. 1.

Tursiops truncatus performing a tail stand under trainer control with a hand target. This represents a medium level effort as the center of mass (COM), the anterior insertion of the dorsal fin, is at the water's surface.

Fig. 2.

Force to weight (Fd/Wb) ratio produced by dolphins at the three different levels of effort (low, medium and high). The mean±s.d. Fd/Wb values were 0.33±0.08, 0.47±0.06 and 0.61±0.08 for low, medium and high, respectively. The efforts are illustrated with respect to the surface of the water.

Fig. 2.

Force to weight (Fd/Wb) ratio produced by dolphins at the three different levels of effort (low, medium and high). The mean±s.d. Fd/Wb values were 0.33±0.08, 0.47±0.06 and 0.61±0.08 for low, medium and high, respectively. The efforts are illustrated with respect to the surface of the water.

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.

Scaling and analysis of videos

A calibration device (1.2 m×1.2 m×1.2 m) composed of metal rods with white plastic balls placed every 0.3 m was used for scaling. The device was dropped into the water at the location in which the tail stands were performed, whilst the dolphins were not in the larger pool. The measurements of the calibration device were performed with ImageJ software (Fiji) and used to scale the video footage. All dolphin measurements were determined using ImageJ. The length of the body underwater was determined by measuring the distance between the individual's fluke notch and the water's surface, following the curvature of the body. Because of the movements of the dolphins, the water's surface did not remain perfectly static during the trials. As a result, potential error in the measurements may have occurred during the time at which they were taken (see Discussion). For each video, the measurements were taken during the center stroke up (CU; see below). The length of the body below the water (LBW) was used to determine the proportion of the body above the water (PBAW), which was calculated using Eqn 1:
formula
(1)
When vertically oriented, a dolphin's swimming cycle could be broken into four separate stages relative to the longitudinal axis of the dolphin in a horizontal orientation: center stroke up (CU), extreme top (ET), center stroke down (CD) and extreme bottom (EB). CU describes the center of the stroke with the fluke moving dorsally, ET describes the flukes at their dorsal-most position, CD describes the center of the stroke with the flukes moving ventrally, and EB describes the flukes at their ventral-most position (Fig. 3). These different positions were captured from videos of each trial so that measurements of the chord length and camber length could be taken to calculate the flex index (FI) of the tail flukes. FI represents the degree of chordwise flexion in the tail flukes as a dimensionless ratio of the chord length to the camber length (Eqn 2):
formula
(2)
The chord length describes the shortest, straight-line path between the leading and trailing edges of a fluke measured from the anterior insertion of the fluke to the fluke tip, while the camber length is the distance that the curved path of the fluke takes between the leading and trailing edges (Fish et al., 2006). The edge of the fluke closest to the camera was used to measure the camber length (Fig. 4). A FI of 1.00 represents a perfectly straight fluke (no bending), while values lower than 1.00 represent greater bending of the flukes.
Fig. 3.

The different stages of a complete dolphin stroke cycle during a tail stand. These stages were the center stroke up (CU), extreme top (ET), center stroke down (CD) and extreme bottom (EB).

Fig. 3.

The different stages of a complete dolphin stroke cycle during a tail stand. These stages were the center stroke up (CU), extreme top (ET), center stroke down (CD) and extreme bottom (EB).

Fig. 4.

The flukes of a dolphin during a tail stand in the ET position. The chord line is represented by the straight, yellow line and the camber line is represented by the curved, red line. The lengths of these lines were used to calculate the flex index (FI).

Fig. 4.

The flukes of a dolphin during a tail stand in the ET position. The chord line is represented by the straight, yellow line and the camber line is represented by the curved, red line. The lengths of these lines were used to calculate the flex index (FI).

The peak-to-peak amplitude (Ap-p) is the maximum distance between the tail fluke's dorsal-most and ventral-most positions within a single stroke cycle. Ap-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, Ap-p is displayed as a proportion of BL.

The tail beat frequency (ƒ) was the inverse of the stroke period (T) (Eqn 4). T was obtained from the average number of frames for two complete stroke cycles multiplied by the time of each video frame (=1/60=0.0167 s) (Eqn 3):
formula
(3)
formula
(4)

For comparison of f and Ap-p among the various sized dolphins, the force (Fd) developed during a tail stand was scaled as the dimensionless thrust-to-weight ratio (Fd/Wb), where Wb 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). Fd/Wb 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 Fd/Wb would be equal to 1. Fd/Wb>1 would allow a dolphin to launch itself completely out of the water, becoming airborne.

The total force (Fd) that is equal to thrust generated by each dolphin (Eqn 5) was estimated by calculating the animal's total mass (m) compared with the proportion of the body length above the water (PBAW):
formula
(5)

Statistical analysis

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 Fd/Wb. 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 Fd/Wb ratio (Fig. 5) with a regression line described as f=0.73+3.06 Fd/Wb (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 Fd/Wb (F=0.851, P=0.430).

Fig. 5.

Scatter plot between stroke cycle frequency and Fd/Wb over different efforts. The trendline, with equation y=3.068x+0.738, shows a general increase with increasing effort. The mean values of frequency were 1.75±0.43, 2.20±0.50 and 2.56±0.53 Hz for low, medium and high effort, respectively, and the mean values of Fd/Wb were 0.33±0.08, 0.47±0.06 and 0.61±0.08 for low, medium and high effort, respectively.

Fig. 5.

Scatter plot between stroke cycle frequency and Fd/Wb over different efforts. The trendline, with equation y=3.068x+0.738, shows a general increase with increasing effort. The mean values of frequency were 1.75±0.43, 2.20±0.50 and 2.56±0.53 Hz for low, medium and high effort, respectively, and the mean values of Fd/Wb were 0.33±0.08, 0.47±0.06 and 0.61±0.08 for low, medium and high effort, respectively.

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 Ap-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 Ap-p was 0.34±0.07 BL with an overall range of 0.20–0.56 BL. At low, medium and high effort, Ap-p was 0.33±0.08 BL, 0.34±0.06 BL and 0.34±0.06 BL, respectively (Fig. 6). Ap-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 Ap-p, and F=0.150, P=0.861 for Ap-p relative to BL). Both sets of data were normally distributed (W=0.967, P=0.014 for overall Ap-p, and W=0.975, P=0.059 for Ap-p relative to BL) and showed equal variance amongst groups (F=0.558, P=0.574 for overall Ap-p, and F=0.480, P=0.620 for Ap-p relative to BL).

Fig. 6.

Scatter plot between the ratio of peak-to-peak amplitude to body length (Ap-p/BL) and ratio of force to total weight (Fd/Wb) of the individual over different efforts. Throughout the different effort levels, the Ap-p remained consistent, with a mean Ap-p/BL ratio of 0.34±0.07. The Fd/Wb ratio increased with each level of effort, with values of 0.33±0.08, 0.47±0.06 and 0.61±0.08 for low, medium and high effort, respectively.

Fig. 6.

Scatter plot between the ratio of peak-to-peak amplitude to body length (Ap-p/BL) and ratio of force to total weight (Fd/Wb) of the individual over different efforts. Throughout the different effort levels, the Ap-p remained consistent, with a mean Ap-p/BL ratio of 0.34±0.07. The Fd/Wb ratio increased with each level of effort, with values of 0.33±0.08, 0.47±0.06 and 0.61±0.08 for low, medium and high effort, respectively.

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.

Table 2.

Results of analyses of flex index

Results of analyses of flex index
Results of analyses of flex index

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.

Fig. 7.

The medium flex index (FI) at each stage of the stroke cycle. CU, center stroke up; CD, center stroke down; ET, extreme top; and EB, extreme bottom. Box plots represent all data within 25–75% of the median (indicated by the small black squares); whiskers represent all non-outlier values. The results showed that ET and EB were significantly different from CU and CD (P<0.0001), CU was significantly different from CD (P=0.0125), and ET was significantly different from EB (P=0.0002).

Fig. 7.

The medium flex index (FI) at each stage of the stroke cycle. CU, center stroke up; CD, center stroke down; ET, extreme top; and EB, extreme bottom. Box plots represent all data within 25–75% of the median (indicated by the small black squares); whiskers represent all non-outlier values. The results showed that ET and EB were significantly different from CU and CD (P<0.0001), CU was significantly different from CD (P=0.0125), and ET was significantly different from EB (P=0.0002).

Fig. 8.

Tail stand effort compared with median flex indices of each stage in the stroke cycle individually. Box plots represent all data within 25–75% of the median (indicated by the small black squares); whiskers represent all non-outlier values. All results were non-significant.

Fig. 8.

Tail stand effort compared with median flex indices of each stage in the stroke cycle individually. Box plots represent all data within 25–75% of the median (indicated by the small black squares); whiskers represent all non-outlier values. All results were non-significant.

Thrust generation

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 Fd/Wb ratio. Because of the nature of the tail stand, Fd/Wb 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 Fd/Wb ratio achieved by a dolphin in the present study was 0.81. Mean Fd/Wb 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 Fd/Wb of 1.08 was achieved (Goforth, 1990). Using the load cell technique, Williams et al. (1993) showed a male dolphin had a maximum Fd/Wb ratio of 1.26. Above a Fd/Wb ratio of 0.59, oxygen consumption reached a plateau and lactate production increased for the dolphin.

Kinematics

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 Ap-p directing the thrust vertically (Fish et al., 2018). Pitch angle varied between 73 and 78 deg and mean Ap-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 Ap-p values of 0.28 BL (Fish et al., 2014). Skrovan et al. (1999) found large amplitude strokes with Ap-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 Ap-p are close to or overlap the Ap-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.

Potential errors in analysis

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 Fd/Wb 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.

Flexibility

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.

Conclusions

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.

Author contributions

Conceptualization: F.E.F.; Methodology: F.E.F.; Validation: D.A.K.; Formal analysis: D.A.K., M.J.S.; Investigation: F.E.F.; Resources: F.E.F.; Data curation: D.A.K.; Writing - original draft: D.A.K., M.J.S., F.E.F.; Writing - review & editing: D.A.K.; Supervision: F.E.F.; Project administration: F.E.F.; Funding acquisition: F.E.F.

Funding

This research was funded by the Office of Naval Research (ONR), Multidisciplinary University Research Initiative (MURI) (N000141410533) to F.E.F. Open Access funding provided by West Chester University. Deposited in PMC for immediate release.

Data availability

Data are available from the West Chester University institutional data repository: http://digitalcommons.wcupa.edu/bio_data/9

Adams
,
D. S.
and
Fish
,
F. E.
(
2019
).
Odontocete peduncle tendons for possible control of fluke orientation and flexibility
.
J. Morph.
280
,
1323
-
1331
.
Alexander
,
R. M.
(
2003
).
Principles of Animal Locomotion
.
Princeton, NJ
:
Princeton University Press
.
Barannyk
,
O.
,
Buckham
,
B. J.
and
Oshkai
,
P.
(
2012
).
On performance of an oscillating plate underwater propulsion system with variable chordwise flexibility at different depths of submergence
.
J. Fluids Struct.
28
,
152
-
166
.
Blake
,
R. W.
(
1983
).
Fish Locomotion.
London
,
UK
:
Cambridge University Press
.
Bose
,
N.
(
1995
).
Performance of chordwise flexible oscillating propulsors using a time-domain panel method
.
Internat. Shipbuild. Progr.
42
,
281
-
294
.
Bose
,
N.
,
Lien
,
J.
and
Ahia
,
J.
(
1990
).
Measurements of the bodies and flukes of several cetacean species
.
Proc. R. Soc. Lond. B
242
,
163
-
173
.
Brousseau
,
P.
,
Benaouicha
,
M.
and
Guillou
,
S.
(
2021
).
Hydrodynamic efficiency analysis of a flexible hydrofoil oscillating in a moderate Reynolds number fluid flow
.
Energies
14
,
4370
.
Cleaver
,
D.
,
Wang
,
Z. J.
and
Gursul
,
I.
(
2013
).
Oscillating flexible wings at low Reynolds numbers
. In
51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
,
Grapevine, Texas
,
January 7-10, 2013
.
Clegg
,
I. L. K.
and
Delfour
,
F.
(
2018
).
Cognitive judgement bias is associated with frequency of anticipatory behavior in bottlenose dolphins
.
Zoo Biol.
37
,
67
-
73
.
Costa
,
P.
,
Piedra
,
M.
,
Franco
,
P.
and
Paez
,
E.
(
2007
).
Distribution and habitat use patterns of southern right whales, Eubalaena australis, off Uruguay
.
J. Cetacean Res. Manage
9
,
45
-
51
.
Dai
,
H.
,
Luo
,
H.
,
de Sousa
,
P. J. F.
and
Doyle
,
J. F.
(
2012
).
Thrust performance of a flexible low-aspect-ratio pitching plate
.
Phys. Fluids
24
,
101903
.
Dickinson
,
M. H.
and
Götz
,
K. G.
(
1996
).
The wake dynamics and flight forces of the fruit fly Drosophila melanogaster
.
J. Exp. Biol.
199
,
2085
-
2104
.
Drucker
,
E. G.
and
Lauder
,
G. V.
(
1999
).
Locomotor forces on a swimming fish: three-dimensional vortex wake dynamics quantified using digital particle image velocimetry
.
J. Exp. Biol.
202
,
2393
-
2412
.
Felts
,
W. J. L.
(
1966
).
Some functional and structural characteristics of cetacean flippers and flukes
. In
Whales, Dolphins, and Porpoises
(
ed.
K. S.
Norris
), pp.
255
-
276
.
Berkeley, CA
:
University of California Press
.
Feng
,
D.
,
Yang
,
W.
,
Zhang
,
Z.
,
Wang
,
X.
and
Yao
,
C.
(
2021
).
Numerical study on hydrodynamic behavior of flexible multi-stage propulsion foil
.
AIP Adv.
11
,
035326
.
Fierstine
,
H. L.
and
Walters
,
V.
(
1968
).
Studies of locomotion and anatomy of scombrid fishes
.
Mem. S. Calif. Acad. Sci.
6
,
1
-
31
.
Fish
,
F. E.
(
1993
).
Power output and propulsive efficiency of swimming bottlenose dolphins (Tursiops truncatus)
.
J. Exp. Biol.
185
,
179
-
193
.
Fish
,
F. E.
(
1998
).
Comparative kinematics and hydrodynamics of odontocete cetaceans: Morphological and ecological correlates with swimming performance
.
J. Exp. Biol.
201
,
2867
-
2877
.
Fish
,
F. E.
(
2002
).
Balancing requirements for stability and maneuverability in cetaceans
.
Integr. Comp. Biol.
42
,
85
-
93
.
Fish
,
F. E.
(
2006
).
The myth and reality of Gray's paradox: implication of dolphin drag reduction for technology
.
Bioinsp. Biomim.
1
,
R17
-
R25
.
Fish
,
F. E.
and
Rohr
,
J. J.
(
1999
).
Review of Dolphin Hydrodynamics and Swimming Performance (SSC Technical Report 1801)
.
San Diego, CA
:
SPAWARS System Center
.
Fish
,
F. E.
,
Innes
,
S.
and
Ronald
,
K.
(
1988
).
Kinematics and estimated thrust production of swimming harp and ringed seals
.
J. Exp. Biol.
137
,
157
-
173
.
Fish
,
F. E.
,
Peacock
,
J. E.
and
Rohr
,
J. J.
(
2003
).
Stabilization mechanism in swimming odontocete cetaceans by phased movements
.
Mar. Mamm. Sci.
19
,
515
-
528
.
Fish
,
F. E.
,
Nusbaum
,
M. K.
,
Beneski
,
J. T.
and
Ketten
,
D. R.
(
2006
).
Passive cambering and flexible propulsors: cetacean flukes
.
Bioinsp. Biomim.
1
,
S42
-
S48
.
Fish
,
F. E.
,
Legac
,
P.
,
Williams
,
T. M.
and
Wei
,
T.
(
2014
).
Measurement of hydrodynamic force generation by swimming dolphins using bubble DPIV
.
J. Exp. Biol.
217
,
252
-
260
.
Fish
,
F. E.
,
Williams
,
T. M.
,
Sherman
,
E.
,
Moon
,
Y. E.
,
Wu
,
V.
and
Wei
,
T.
(
2018
).
Experimental measurement of dolphin thrust generated during a tail stand using DPIV
.
Fluids
3
,
33
.
Goforth
,
H. W.
(
1990
).
Ergometry (exercise testing) of the bottlenose dolphin
. In
The Bottlenose Dolphin
(
ed.
S.
Leatherwood
), pp.
559
-
574
.
New York
:
Academic Press
.
Gough
,
W. T.
,
Fish
,
F. E.
,
Wainwright
,
D. K.
and
Bart-Smith
,
H.
(
2018
).
Morphology of the core fibrous layer of the cetacean tail fluke
.
J. Morph.
279
,
757
-
765
.
Gray
,
J.
(
1936
).
Studies in animal locomotion: VI. The propulsive powers of the dolphin
.
J. Exp. Biol.
13
,
192
-
199
.
Heathcote
,
S.
,
Wang
,
Z.
and
Gursul
,
I.
(
2008
).
Effect of spanwise flexibility on flapping wing propulsion
.
J. Fluids Struct.
24
,
183
-
199
.
Iverson
,
D.
,
Rahimpour
,
M.
,
Lee
,
W.
,
Kiwata
,
T.
and
Oshkai
,
P.
(
2019
).
Effect of chordwise flexibility on propulsive performance of high inertia oscillating-foils
.
J. Fluids Struct.
91
,
102750
.
Katz
,
J.
and
Weihs
,
D.
(
1978
).
Hydrodynamic propulsion by large amplitude oscillation of an airfoil with chordwise flexibility
.
J. Fluid Mech.
88
,
485
-
497
.
Kermack
,
K. A.
(
1948
).
The propulsive powers of blue and fin whales
.
J. Exp. Biol.
25
,
237
-
240
.
Kramer
,
M. O.
(
1960
).
The dolphins’ secret
.
New Sci.
7
,
1118
-
1120
.
Lang
,
T. G.
and
Daybell
,
D. A.
(
1963
).
Porpoise performance tests in a seawater
.
Nav. Ord. Test Sta. Tech. Rep.
3063
,
1
-
50
.
Lang
,
T. G.
and
Norris
,
K. S.
(
1966
).
Swimming speed of a Pacific bottlenose porpoise
.
Science
151
,
588
-
590
.
Lang
,
T. G.
and
Pryor
,
K.
(
1966
).
Hydrodynamic performance of porpoises (Stenella attenuate)
.
Science
152
,
531
-
533
.
Li
,
Y.
,
Pan
,
Z.
and
Zhang
,
N.
(
2021
).
Propulsive properties of a flexible oscillating wing with time-varying camber deformation
.
Ocean Eng.
235
,
109332
.
Lighthill
,
M. J.
(
1969
).
Hydrodynamics of aquatic animal propulsion — a survey
.
Annu. Rev. Fluid Mech.
1
,
413
-
446
.
Lindsey
,
C. C.
(
1978
).
Form, function, and locomotory habits in fish
. In
Fish Physiology: Locomotion
, Vol.
7
(
ed.
W. S.
Hoar
and
D. J.
Randall
), pp.
1
-
100
.
New York
:
Academic Press
.
Long
,
J. H.
,
Pabst
,
D. A.
,
Shepherd
,
W. R.
and
McLellan
,
W. A.
(
1997
).
Locomotor design of dolphin vertebral columns: bending mechanics and morphology of Delphinus delphis
.
J. Exp. Biol.
200
,
65
-
81
.
Nauen
,
J. C.
and
Lauder
,
G. V.
(
2002
).
Hydrodynamics of caudal fin locomotion by chub mackerel, Scomber japonicus (Scombridae)
.
J. Exp. Biol.
205
,
1709
-
1724
.
Noren
,
S. R.
(
2023
).
Building cetacean locomotor muscles throughout ontogeny to support high-performance swimming into adulthood
.
Integr. Comp. Biol.
63
,
785
-
795
.
Pabst
,
D. A.
(
2000
).
To bend a dolphin: convergence of force transmission designs in cetaceans and scombrid fishes
.
Am. Zool.
40
,
146
-
155
.
Prempraneerach
,
P.
,
Hover
,
F. S.
and
Triantafyllou
,
M. S.
(
2003
).
The effect of chordwise flexibility on the thrust and efficiency of a flapping foil
. In
Proc. 13th Int. Symp. on Unmanned Untethered Submersible Technology: Proc. Special Session on Bio-Engineering Research Related to Autonomous Underwater Vehicles
.
Lee, New Hampshire
:
Autonomous Undersea Systems Institute
.
152
,
152
-
170
.
Rohr
,
J. J.
and
Fish
,
F. E.
(
2004
).
Strouhal numbers and optimization of swimming by odontocete cetaceans
.
J. Exp. Biol.
207
,
1633
-
1642
.
Rohr
,
J. J.
,
Quigley
,
L.
,
Fish
,
F. E.
,
Gilpatrick
,
J. W.
and
Scardina-Ludwig
,
J.
(
1998
).
Observations of Dolphin Swimming Speed and Strouhal Number
. Space and Naval Warfare Systems Center Technical Report 1769.
San Diego, CA
:
Space and Naval Warfare Systems Center
.
Romanenko
,
E. V.
(
2002
).
Fish and Dolphin Swimming.
Sofia
:
Pensoft
.
Ryerson
,
W. G.
and
Schwenk
,
K.
(
2011
).
A simple, inexpensive system for digital particle image velocimetry (DPIV) in biomechanics
.
J. Exp. Zool.
317
,
127
-
140
.
Sfakiotakis
,
M.
,
Lane
,
D. M.
and
Davies
,
J. B. C.
(
1999
).
Review of fish swimming modes for aquatic locomotion
.
IEEE J. Oceanic Eng.
24
,
237
-
252
.
Skrovan
,
R. C.
,
Williams
,
T. M.
,
Berry
,
P. S.
,
Moore
,
P. W.
and
Davis
,
R. W.
(
1999
).
The diving physiology of bottlenose dolphins (Tursiops truncatus). II. Biomechanics and changes in buoyancy at depth
.
J. Exp. Biol.,
202
,
2749
-
2761
.
Stamhuis
,
E. J.
and
Nauwelaerts
,
S.
(
2005
).
Propulsive force calculations in swimming frogs II. Application of a vortex ring model to DPIV data
.
J. Exp. Biol.
208
,
1445
-
1451
.
Tanaka
,
H.
,
Li
,
G.
,
Uchida
,
Y.
,
Nakamura
,
M.
,
Ikeda
,
T.
and
Liu
,
H.
(
2019
).
Measurement of time-varying kinematics of a dolphin in burst acceleration swimming
.
PLoS ONE
14
,
e0210860
.
Tsai
,
W.-L.
(
1998
).
Dorsoventral bending of the tail and functional morphology of the caudal vertebrae in the bottlenose dolphin, Tursiops truncatus.
Master's thesis
,
Oklahoma State University
.
Videler
,
J.
and
Kamermans
,
P.
(
1985
).
Differences between upstroke and downstroke in swimming dolphins
.
J. Exp. Biol.
119
,
265
-
274
.
Warrick
,
D. R.
,
Tobalske
,
B. W.
and
Powers
,
D. R.
(
2005
).
Aerodynamics of the hovering hummingbird
.
Nature
435
,
1094
-
1097
.
Watson
,
A. G.
and
Fordyce
,
R. E.
(
1993
).
Skeleton of two minke whales, Balaenoptera acutorostrata, stranded on the south-east coast of New Zealand
.
New Zealand Nat. Sci.
20
,
1
-
14
.
Webb
,
P. W.
(
1975
).
Hydrodynamics and energetics of fish propulsion
.
Bull. Fish. Res. Bd. Can.
190
,
33
-
48
.
Willert
,
C. E.
and
Gharib
,
M.
(
1991
).
Digital particle image velocimetry
.
Exp. Fluids
10
,
181
-
193
.
Williams
,
T. M.
,
Friedl
,
W. A.
and
Haun
,
J. E.
(
1993
).
The physiology of bottlenose dolphins (Tursiops truncatus): heart rate, metabolic rate and plasma lactate concentration during exercise
.
J. Exp. Biol.
179
,
31
-
46
.
Williams
,
R.
,
Trites
,
A. W.
and
Bain
,
D. E.
(
2002
).
Behavioural responses of killer whales (Orcinus orca) to whale watching boats: opportunistic observations and experimental approaches
.
J. Zool., Lond.
256
,
255
-
270
.
Würsig
,
B.
and
Whitehead
,
H.
(
2018
).
Aerial behavior
. In
Encyclopedia of Marine Mammals, Edn 3
(
ed.
W. F.
Perrin
,
B.
Würsig
and
J. G. M.
Thewissen
), pp.
6
-
10
.
San Diego, CA
:
Academic Press
.
Xia
,
D.
,
Lei
,
M.
,
Chen
,
W.
and
Shi
,
Y.
(
2022
).
Hydrodynamics study of standing-and-hovering behavior of dolphins on the water surface
.
Ocean Eng.
264
,
112604
.
Yamaguchi
,
H.
and
Bose
,
N.
(
1994
).
Oscillating foils for marine propulsion
. In
Proceedings of the Fourth International Offshore and Polar Engineering Conference
, pp.
539
-
544
.
Golden, CO
:
International Society of Offshore and Polar Engineers (ISOPE)
.

Competing interests

The authors declare no competing or financial interests.

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