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The kinematics of the California sea lion foreflipper during forward swimming

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2014 Bioinspir. Biomim. 9 046010

(http://iopscience.iop.org/1748-3190/9/4/046010)

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The kinematics of the California sea lionforeflipper during forward swimming

C Friedman and M C Leftwich

Department of Mechanical and Aerospace Engineering, School of Engineering and Applied Sciences, TheGeorge Washington University, 801 22nd St, NW Washington, DC 20052, USA

E-mail: chenfriedman@gwu.edu and mleftwich@gwu.edu

Received 2 June 2014Accepted for publication 3 September 2014Published 7 November 2014

AbstractTo determine the two-dimensional kinematics of the California sea lion foreflipper during thrustgeneration, a digital, high-definition video is obtained using a non-research female sea lion at theSmithsonian National Zoological Park in Washington, DC. The observational videos are used toextract maneuvers of interest—forward acceleration from rest using the foreflippers and bankedturns. Single camera videos are analyzed to digitize the flipper during the motions using 10points spanning root to tip in each frame. Digitized shapes were then fitted with an empiricalfunction that quantitatively allows for both comparison between different claps, and forextracting kinematic data. The resulting function shows a high degree of curvature (with acamber of up to 32%). Analysis of sea lion acceleration from rest shows thrust production in therange of150–680 N and maximum flipper angular velocity (for rotation about the shoulder joint)as high as −20 rad s 1. Analysis of turning maneuvers indicate extreme agility and precision ofmovement driven by the foreflipper surfaces.

S Online supplementary data available from stacks.iop.org/bb/9/046010/mmedia

Keywords: sea lion, kinematics, video analysis

1. Introduction

California sea lions are highly maneuverable swimmers,capable of generating high thrust and agile turns. Their mainpropulsive surfaces, the foreflippers, feature multiple degreesof freedom, allowing their use for thrust production (througha downward, sweeping motion henceforth referred to as a‘clap’), turning, stability and station-holding (underwater‘hovering’).

Generally, when large animals swim in a straight line—both fish and mammals—thrust is generated by the animalʼstail or caudal fin as it sweeps side-to-side (fish) or up-and-down (mammals). The California sea lion, however, reliespredominantly on its foreflippers for thrust production. Thelarge flippers move through the water in a clapping motionthat ends with each flipper adducted against the animalʼstorso. The clapping motion involves more than one rotationaxis, allowed for by the multiple degrees of freedom flipper.This flipper-based motion differs significantly from otherlarge fish and marine mammals, which typically have adominant oscillation frequency [1, 2]. Each clap is followed

by a prolonged glide, particularly unusual for large, highthrust producing swimmers, and is assisted by the animalʼslow drag coefficient [3].

Qualitative studies, while scarce, show that the flippersare used both for thrust and stability during the motion. Sealion locomotion has been studied by Godfrey using video-graphy for straight and turning maneuvers [4], describing acomplete stroke cycle and a horizontal banked turn usingseries of hand drawings. The drawings clearly show the sealions using the pectoral flippers for thrust generation, stability,and as control surfaces.

Quantitative studies have mainly concentrated on mea-surements of sea lions properties. Fish reports sea lion cost oftransport to be approximately 1 Kcal Kg−1 Km−1 (similar tothat of seals) [5]. Feldkamp calculated sea lion drag coeffi-cients for juvenile sea lions of approximately Cd = 0.07 [6].Fish et al used video recordings to analyze tight (up to 5.1 g)horizontal plane turning performance of sea lions, at bankangles of °90 [7]. The sea lion was found to have highmaneuverability with the foreflippers providing multipledegrees of freedom for various motion patterns. Additionally,

Bioinspiration & Biomimetics

Bioinspir. Biomim. 9 (2014) 046010 (8pp) doi:10.1088/1748-3182/9/4/046010

1748-3182/14/046010+08$33.00 © 2014 IOP Publishing Ltd Printed in the UK1

Fish et al found that the sea lions’ highly flexible bodies allowfor added maneuverability, as exemplified by high turn rates,up to ° −690 s 1 [7].

In this work, the existing qualitative studies are advancedby a quantitative, digital, investigation of the clap motion.Comparison between different clap cases and maneuvers isperformed, highlighting correlation between several kine-matic features (angular velocity, flipper curvature, etc.) andthe resulting thrust generated by the clap motion.

2. Experimental setup

The Smithsonian National Zoological Park (SNZ) is home tofour non-research, female sea lions. The quantitative datapresented here is based on a single individual. She waschosen for two practical reasons: the ability to positivelyidentify this individual, and her willingness to perform themaneuvers of interest, resulting in many useful maneuvervideos. The location features two viewing windows, onepartially and one fully submerged, both providing a sizableviewing area, considerably larger than a typical sea lion withits foreflippers abducted (shown in figure 1).

Videography is used to study foreflipper kinematicsusing a high definition camera (JVC GC-PX100BU) filmingthe sea lions at 60 frames per second (fps). A stationarycamera passively observes the sea lions while they swimfreely in their habitat. Claps are analyzed when the flipperfaces the camera during the thrust phase. Thus, allowing thetwo dimensional flipper shape to be characterized by a singlecurved line.

Typical Reynolds numbers, based on animal length, werebetween = ×Re 1.3 106 and = ×Re 6.8 106, based on thesea lionʼs length of 1.77 m (nose to hind flippers tip).Although the sea lion uses a form of unsteady propulsion, aStrouhal number or reduced frequency are hard to define, andless relevant because the claps are followed by a prolongedglide, and thus do not have a well defined frequency. Atypical clap lasts less than one second, while the animal willoften glide for up to 5 s before beginning the next maneuver.

3. Analysis and results

3.1. Assumptions and validity

3.1.1. Two dimensional analysis. The videos analyzed herewere collected using a single camera, which implies two-dimensional analysis. The flipper is therefore represented by asingle curve. Subsequently, pitch angle distribution along theflipper, and flipper thickness and cross section shapes arecurrently neglected. The spanwise shape of the flipper is themain feature captured using this analysis, as well as flippermovement speed (rotational speed about the root, see below).While not yet a comprehensive description of sea lionkinematics, this two-dimensional view provides importantinsight into the role of the sea lion foreflipper flexibility as apropulsive surface. It can also serve as basis for mechanicaland computational studies of sea lion-type aquatic motion.

3.1.2. Single subject analysis. As mentioned above, theanalysis was carried out using only one of the four subjectsfrom the SNZ. The individual (Sophie) was highly engagedand thus yielded a large number of usable maneuvers. Wewere particularly interested in obtaining videos of the clapmotion while facing the viewing window, thus allowing a 2Danalysis of the flipper as described below. While it is desiredto obtain videos form multiple subjects to allow comparisonbetween different sea lions, this was not deemed possible asthese are not research animals, and may not be trained toperform any specific action. Furthermore, Sophie was theonly individual that could be positively identified from thevideo footage. The calculated quantities (acceleration, angularrotation, thrust) required the animalʼs biological data (mass,circumference, length, etc.), in ways that could not always benormalized. Although the analysis is quantitatively based on asingle test subject, the limited data of the three other sea lionsdoes show qualitative agreement in terms of foreflippercurvature, high angular velocities, and rapid accelerations.The precise values will differ from individual to individualbased on animal size and biomechanics, but it is likely that thegeneral kinematic mechanisms will still apply.

Figure 1. The two viewing windows at the SNZ provide ample area to observe a variety of sea lion maneuvers. Left: partially submergedwindow. Right: fully submerged, underground access.

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Bioinspir. Biomim. 9 (2014) 046010 C Friedman and M C Leftwich

3.2. Clap motion analysis

Sea lions produce thrust with their large foreflippers. Theforeflippers clap motion is comprised of thrust generation andrecovery phases. During the thrust generation phase, theflippers are raised relative to the animals midline and drawndownwards to meet at the abdomen. The recovery phase isused to either reposition the flippers for an additional clap oradduct the flippers to streamline the body and reduce drag.

3.2.1. Digitized flipper motion. A two dimensional analysiswas performed to extract foreflipper shapes during the clapmotion. Analyzed cases featured the flippers’ center linesfacing the camera during the bulk of the thrust generatingphase (as in figure 2). This allows for quantitative comparisonbetween different claps and different maneuvers. Trackingwas performed using image analysis software [8]. Thesoftware allows for converting pixel-based positions(marked on an image) to metric positions using a user-defined reference length that is captured in the video frames.

Each analyzed video contained a single sea lion subject.The pixel based digitized points were converted to metricmeasurements using the sea lionʼs length from nose to hindflipper tips as the reference length. This length was measuredin each video to account for different distances of the sea lionfrom the camera, slight changes in camera positions betweendifferent experiments, etc. Only maneuvers where the planeof motion was perpendicular to the camera axis wereanalyzed.

In this work, flipper tracking is performed manually byfollowing the flipper center line in each frame, using a total of10 points spanning root to tip, as seen in figure 2. The numberof points was chosen after a short study that shows theadequacy of the points in representing different flipper shapeswith little error. The center line was chosen as the baseline fortracking the flipper since it was the easiest to discern from thesurroundings. Of the total frames in each video, only frameswhere the flipper centerline faces the camera are analyzed inorder to maintain a two dimensional analysis capability.

In order to study the foreflipper shape, the extractedpoints are then fitted with an empirical function which is acombination of a sinusoidal term and an exponential term

given by:

= +( )f x C C x C( ) e sin . (1)C x1 3 4

2

The extracted shapes are all rotated to approximately thesame orientation to facilitate fitting similarity across differentcases. An initial guess for the coefficients C1–C4 is given to anonlinear optimizer embedded in Matlab® (version 2010b, byMathworks), and the optimized results yield the function thatbest fit the extracted flipper shape. A least squares based costfunction is used in this process, given by:

∑= + −=

( )( )FN

C C x C y1

e sin , (2)i

NC x

i ip 1

1 3 42

i

p

2

where F is the total cost, Np is the number of digitized pointsin each frame (in this study, Np = 10 for all cases), and xi andyi are the coordinates of the digitized points in the x and ydirections, respectively. A single flipper shape fitted with anoptimized empirical function is shown in figure 3, showingthe digitized points (connected by a blue line) and the fittedfunction (red line). An example of a digitized foreflipper clapmotion fitted with optimized empirical functions is given infigure 4, presenting the fitted functions (plotted only up to theflipperʼs tip in each frame). The flipper root (the sea lionʼsshoulder joint) is located at (0, 0) extending to the right of thefigure. Functions were fitted to frames that allowed properrepresentation in two dimensions. Only the downstroke iscaptured and analyzed, as the upstroke happens almostcompletely out of plane (through a rotation of the shoulderjoint).

3.2.2. Flipper spanwise bending. The snapshots sequencepresented in figure 5 shows a sea lion starting at rest, and

Figure 2. Flipper tracking using 10 points along the centerline,marked as white circles.

Figure 3. A single digitized frame. The 10 digitized points appear inblue circles, connected by a blue line. The red line is the optimizedfitted empirical function. Flipper tip is the last blue circle, at x = 0.44.The empirical function was extended for visual reference.

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Bioinspir. Biomim. 9 (2014) 046010 C Friedman and M C Leftwich

performing a full foreflipper clap motion. The motion startsby raising the foreflippers above the sea lionʼs body, with theflipper showing relatively high curvature. The foreflippers arethen pulled downward, during the thrust generation phase.After the flipper tips are brought below the sea lionʼs body,the adduction begins, bringing the flippers closer to thebodyʼs centerline, thus streamlining the sea lion for thefollowing gliding phase. In this example, a crossover betweenthe two flippers is observed, a phenomenon correlated withrelatively high thrust production [4].

When compared to clap motion hand drawings byGodfrey [4], we see significantly higher flipper bendingduring the clap motion. This bending, a result of the flexibilityin the biomechanical structure of the flipper, is characterizedby the flipperʼs camber—defined as the largest distance of apoint along the flipperʼs centerline from an imaginary line thatconnects the flipperʼs root to tip, in percents. Measurementsshow camber values between 18% and 32%, which is muchlarger than that observed by Godfrey [4]. No strongconnection was found between camber and either accelerationor flipper angular rate. However, it was found that timehistory of the maximum camber value typically has a peakduring the thrust phase.

3.2.3. Flipper angular rate. The angular rate is determinedbased on the angle formed by the first digitized segment andthe horizontal axis (i.e. flipper root segment). The average and

the maximum angular rates are therefore defined as:

ωθ θ

Δ=

−t

, (3)avgF I

ωθ θ

Δ=

−+⎛⎝⎜⎜

⎞⎠⎟⎟t

max , (4)j

j j

jmax

1

where θI and θF are the root segment angles in the initial andfinal analyzed frames, respectively, Δt is the time passedbetween these two frames, θj and θj+1 represent two angles intwo sequential frames, and Δt j is the corresponding time

passed between these two frames (i.e. Δ = −t 1 fpsj1).

It is expected that higher angular rates will generallycorrelate with higher animal acceleration. Acceleration isestimated based on the sea lion passing one body length,using the nose and the caudal flipper tips as markers. Bothmarkers were timed when crossing a well defined point. Thesea lions typically flex their neck and back in the desireddirection, and so timings begins only after initial neck flexinghas been completed (typically when the flipper is fullyabducted and begins moving downwards). This results inacceleration measurements that correspond only to the flippergenerated forces. Acceleration in this case is thereforecalculated as:

Δ=L a t1

2, (5)2

Δ=a

L

t

2, (6)

2

where L represents one sea lionʼs body length, a isacceleration, and Δt is the time between the nose and thecaudal flipper tip crossing the same defined point in a givencase. The cases considered were all measured on one sea lionindividual. Therefore, ignoring relatively small sea lion massfluctuations and water density changes, the acceleration isdirectly proportional to the force generated by the flipper clapmotion.

Figure 6 presents the results for average angular rates(n = 39) plotted against acceleration values from rest. Asexpected, higher acceleration values correspond to higherflipper angular rates. While there is some scatter in the results,the average angular velocity trend appears to flatten for higheraccelerations, likely due to the sea lionʼs biomechanics and/orphysiological limits. The observed scatter is also attributed tothe fact that acceleration is not only a function of angularvelocity, but of flipper pitching angle as well. The magnitudeof the maximum angular rates was often quite impressive,reaching values of up to ω = −20 rad smax

1.The angular rate is upper bounded by muscular

capability. The trend in figure 6 fits a quadratic behavior, aslong as one considers the point (0, 0) as a constraint,representing zero acceleration for zero angular rate. This canbe quantified using the coefficient or determination, R2, whichyielded a very low =R 0.092 for a linear regression fit and amuch more reasonable =R 0.582 for a quadratic fit (bothconstrained to pass through the (0, 0) point).

Figure 4. Digitized foreflipper shapes during a full clap maneuver(blue circles and lines), fitted with the empirical function (red lines).Presented timeframe corresponds to the flipper positions that allowed2D analysis during the downstroke. Time difference between shapesis Δ =t 0.0167 s. The flipper root (the sea lionʼs shoulder joint) islocated at (0, 0) extending to the right of the figure.

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Bioinspir. Biomim. 9 (2014) 046010 C Friedman and M C Leftwich

3.2.4. Comparison to Cetaceans. Fish and Rohr [9, 10]report morphological data for dolphins, with values of up to3 Hz and °40 for the frequency and pitching amplitude,respectively. This yields an average flipper angular rate ofapproximately 4 rad s−1 (240 deg s−1), which is approximatelyhalf of the average angular rate values presented here. Theacceleration values achieved by the sea lions are also quiteimpressive, reaching values higher than −10 m s 1.

Measurements performed by Lang and Pryor [11] onporpoises showed acceleration values of 5.5 m s−1 (reportedvalues are a final velocity of 11 m s−1 over a period of 2 s).

The relatively high acceleration values obtained by thesea lions may be explained when considering the relative sizeof thrust producing surfaces to body mass. Compared tocetaceans, female sea lions have a higher ratio of flippersurface area to body mass. The subject in this current studyhas a total flipper area of Sf = 0.16 m2, with a total weight ofM = 65 Kg, yielding a ratio of η = =M S 406f Kgm−2. Incomparison, Videler and Kamermans report numbers for a2.5 m Tursiops dolphin, weighing 235 Kg, with a flipper areaof Sf = 0.1 m2 [12]. This yields a significantly higher value ofη = 2340 Kgm−2. The dolphin therefore has a much lowerthrust producing area relative to its own body mass.

However, it is important to note that while cetaceansmaintain their flipper angular rate over prolonged periods oftime, the sea lion angular rates are typically for a singleisolated clap, followed by a prolonged glide when the musclescan rest.

3.3. Average clap

The digitized data was utilized in this work to achieve anaverage clap motion. Clap motions for a single sea lionindividual accelerating from rest were subdivided based onmotion direction, with only cases where the sea lion accel-erated from left to right considered (n = 14), eliminatingdifferences in camera viewpoint relative to the sea lionindividual.

Figure 5. Clap motion from rest to full foreflipper adduction and glide phase. (a) Start from rest; (b) flippers abduction; (c) start of clapmotion; (d) mid-clap; (e) clap end; (f) begin ripper adduction; (g) flippers crossover (high thrust related phenomenon); (h) full flipperadduction to body centerline; (i) glide motion.

Figure 6. Flipper average angular rate versus resulting accelerationfrom rest values. Results for a single sea lion individual (n = 39),showing an initial increase and the existence of an upper bound dueto muscular physiological limits.

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Bioinspir. Biomim. 9 (2014) 046010 C Friedman and M C Leftwich

To maintain uniformity between different clap cases, clapduration was made dimensionless by dividing each time axisby its own final time. Dimensionless time is henceforthdenoted by t̃ . Since each video allowed for a different timespan to be analyzed in 2D, time shifting was employed on allconsidered clap cases. Time axes were aligned based on asingle common value such that = =C t(˜ 0) 42 for all case.The coefficients C1–C4 were then averaged across all cases.Figure 7 presents the average coefficients’ time history, withtheir corresponding upper and lower bounds (black and redlines, respectively), and standard deviations in dashed lines.All cases showed good agreement in both trend andmagnitude.

It was found that all claps generally produce the samebehavior for all four coefficients. Note that the first coefficientC1 is mainly used for scaling between the different cases, andtherefore its scatter is larger. However, all C1 data showsimilar trend, with relatively small negative values at thebeginning of the clap ( <t̃ 0), approaching zero in the mid-clap phase, and growing more negative toward the end ofthe clap.

The C2 coefficient values show the degree of dominancefor the exponential term over the sinusoidal term inequation 1. The clap begins with relatively high values, as theflipper is raised above the sea lionʼs body. The C2 values thenbegin to decrease, as the flipper is lowered during the thrustphase, and finally drop below zero toward the end of the clap.This means the exponential term dominates at the beginning,followed by a more pronounced sinusoidal shape at the mid-stroke (neutral exponential term for C2∼0) and then the finalstages of the thrust phase are dominated by a decayingexponential term shape. The flipper shape at the midway

through the thrust phase may therefore be described as aninverted sinusoid (since C1 is negative), which is clearlyvisible in figure 4.

The coefficient C3 which represents the spacial wavelength of the sinusoidal term also shows similar trendsbetween the claps, with values that increase until =t̃ 0, andthen decrease steadily. The phase coefficient C4 also showssimilar behaviors throughout the different claps with all theclap cases converging to the same trend and magnitude. Theinitial value of C4 is approximately °180 for all cases, and it isreduced to approximately =C 04 at the end of the clap.Statistically, the standard deviation for C2–C4 for >t̃ 0 waslower than 10% of their corresponding peak values (10 forboth C2 and C3, and °180 for C4). The scaling coefficient C1

shows a standard deviation of less than 20%.The resulting clap based on the averaged coefficients is

presented in figure 8 for five dimensionless times: =t̃ 0.1,0.2, 0.3, 0.4, and 0.5. All averaged clap shapes thereforecorrespond to times after the time shifting baseline value hasbeen achieved. The shapes appear to transition between theneutral exponential term phase and the negative exponentialterm dominance. The sinusoidal term is well pronounced forall the mid-clap averaged lines.

3.4. Thrust

The propulsive force generated by the foreflippers can becalculated using the above results. This requires using theacceleration values calculated above, multiplied by the sealionʼs mass, neglecting the drag force that acted on the sealion for Δ⩽ ⩽t t0 . This means that the thrust results pre-sented here represent a lower bound. Drag was neglected dueto the absence of drag estimation for a turning sea lion withabducted flippers. Additionally, the relatively low averagevelocity during the clap motion (of the order of 1–2 m s−1)

Figure 7. Time-shifted equation coefficients used to form the averageclap. Average coefficients line shown as thick solid blue line, upperand lower bounds shown by thin black and red line, respectively.Dashed lines show single standard deviation bounds.

Figure 8. Average clap motion for cases with similar motiondirection by the same sea lion. The five clap shapes correspond onlyto the time overlap available for all different cases (n = 14).

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Bioinspir. Biomim. 9 (2014) 046010 C Friedman and M C Leftwich

likely results in relatively little drag. Added mass effects arealso neglected in the absence of good estimates for addedmass effects for non-streamlined sea lions [6].

The sea lion whose results are presented above had amass of approximately 65 Kg. The propulsive force T istherefore simplified to:

=T Ma, (7)

where M is the sea lionʼs mass, and a is the acceleration from(5). Propulsive forces were thus calculated, showing valuesbetween approximately T = 150 N and T = 680 N.

3.5. Banked turn

Figure 9 presents snapshots from a common banked turnmaneuver, frequently performed by the sea lions (similar tothe banked turn of an aircraft). In this maneuver, also sur-veyed by Godfrey [4], the foreflippers are used both as liftgenerating surfaces and as thrust generating elements duringthe entire turn. Here, we assume that the sea lions are close to

being neutrally buoyant. Actual buoyancy values differdepending on the subject [13]. The subject explored here wasobserved multiple times floating in the tank without move-ment which suggests that itʼs relatively neutrally buoyant.

The near neutral buoyancy cancels most of the require-ment to generate forces that oppose gravity (which is requiredfor banked turns in aircraft). This enables roll angles ofapproximately °90 to be maintained throughout the turn. Theflippers are abducted at the beginning of the turn (figures 9(b),(c)), and pitched so that a centripetal force is generated, whichcauses the sea lion to enter the turn, and also controls the turnradius (together with flipper pitching angle). During the turn,the flippers are fully abducted to both sides (figures 9(d)–(h)),generating all the required centripetal force. The hind flippersact as secondary lifting surfaces.

When depth changes are involved, or when the buoyancyis not completely neutral, the sea lions use roll angles dif-ferent than °90 to orient their abducted flippers so that verticalforces are generated. This may be observed in figure 9(g)

Figure 9. Banked turn featuring a clap to generate the thrust required to exit the turn. (a) End of previous glide phase; (b) begin flipperabduction (to both sides), and initiate body roll; (c) flipper abduction begins to generate centripetal force, body roll almost complete; (d) rollangle at °90 , flippers fully abducted; (e) hind flippers providing secondary control surfaces; (f) mid turn; (g) end of turn; (h) begin of clapmotion to maintain desired velocity while exiting the turn; (i) mid-clap; (j) end of clap, turn complete; (k) full flipper adduction; (l) beginglide phase.

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Bioinspir. Biomim. 9 (2014) 046010 C Friedman and M C Leftwich

where the flippers span is clearly seen pointing upwards. Thisresults in a certain depth change which can be see whencomparing the depth between figures 9(d) and (l).

The body in this maneuver does not play a major role,and is only bent into the turn to streamline itself with thechanging direction of motion. In this case, toward the end ofthe turn, the sea lion produces thrust in order to maintain itsdesired velocity. The foreflippers are therefore clapped(figures 9(i)–(k)), and the centripetal force vanishes as the sealion orients itself in the final desired direction, while main-taining its desired velocity. In this case, body orientationreturns to its previous level condition, however, it is notuncommon for sea lions to exit the turn with a different rollangle than the initial one. While executing this maneuver, thesea lionʼs roll rate about its longitudinal axis was approxi-mately = °ϕ −170 s

t

d

d1. The roll motion is initiated by the head

and neck, followed by the torso with the foreflippers and thenthe tail section with the hind flippers.

4. Summary and conclusions

Sea lion videos were digitized and analyzed to study kine-matic features required for further studies of its thrust gen-eration mechanism. Two dimensional image analysis hasbeen performed for tracking the sea lion flipper centerlineduring the thrust phase of the clap maneuver. The digitizeddata was then fitted with empirical functions describing theshapes during the clap motion by means of an exponential andsinusoidal terms, governed by four coefficients (scaling,exponential, wavelength, and phase). The extracted coeffi-cients allow for appropriate comparison between differentclaps.

The results showed the ability to extract and characterizesea lion flipper shapes using non-intrusive videos of sea lionsliving at the Smithsonian National Zoological Park inWashington, DC. Marker-less tracking of sea lion flippers isdesired as it reduces experimental complexity involved inplacing markers on the animals. Tracking was performed onlyfor frames where the flipper faces the camera, allowing fortwo dimensional analysis.

Different flipper clap motions were quantitatively char-acterised by emperical function fits of the flipper shape. Allfour coefficients presented with similar trends across all cases(n = 39). Flipper angular rates showed good correlation withthe generated acceleration (or thrust). Angular rates at highacceleration levels presented with an upper bound stemmingfrom the limit on sea lionʼs muscular capabilities. Flippercamber was shown to be significantly higher as compared tothe drawings made by Godfrey [4], with camber valuesreaching as high as 32%.

A total of 14 clap motions that resulted in the samedirection of motion were also combined to form an averageclap by synchronizing the coefficients’ time histories. Thestandard deviation was less than 10% for C2–C4, and lowerthan 20% for C1 which is the general scaling coefficient.

These results may help characterize the flipper motion inmore detail when the flipper shape is known, and provide agood stepping stone toward performing 3D motion capture, tobetter characterize the full flipper kinematics.

Acknowledgments

The authors would like to thank the American Trail staff atthe Smithsonian National Zoological Park for access to theanimals, as well as much assistance in getting to know andsuccessfully work with the sea lions. We are specificallygrateful to Ed Bronikowski for arranging our partnership andhis invaluable logistical and zoological help. Finally, wethank Sophie the sea lion (and her fellow SNZ sea lions Calli,Summer and Sydney) for being such a great subject.

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