AMER. ZOOL., 36:567-581 (1996)

Pectoral Fin Locomotion in Fishes: Testing Drag-based Models UsingThree-dimensional Kinematics1

GEORGE V. LAUDER

Department of Ecology and Evolutionary Biology, University of California,Irvine, California 92697

AND

B R U C E C. JAYNE

Department of Biological Sciences, University of Cincinnati, P.O. Box 210006,Cincinnati, Ohio 45221-0006

SYNOPSIS. Paired fin propulsion in fishes has classically been divided intotwo categories which represent biomechanical extremes in the use of ap-pendages for propulsion: lift-based and drag-based mechanisms of thrustproduction. Theoretical models predict that fishes using drag-based propul-sion should have wedge-shaped fins with relatively blunt distal edges, a finbeat cycle that is oriented along the anteroposterior (x) axis, feathering ofthe fin to reduce drag during the protraction phase, and maximal fin areaduring the retraction phase as the fin sweeps posteriorly perpendicular to thebody. In this paper we use a three-dimensional analysis of pectoral fin pro-pulsion in the largemouth bass, Micropterus salmoides, to (1) evaluate theextent to which bass pectoral fin kinematics fit predictions of drag-basedpropulsion, and (2) demonstrate the complexity of fin movement when thetraditional two-dimensional analysis is extended into three dimensions. Weattached small markers to visualize the diaphanous distal fin edge, and wevideotaped lateral and ventral views from which we could measure x, y, andz coordinates from the fin and body. We divided the fin into two triangularelements for which we calculated planar (three-dimensional) angles relativeto each of three reference planes (XY, YZ, and XZ) during the fin beat cycle.We show how angles of attack based only on two-dimensional data mayresult in gross errors that severely compromise understanding of the me-chanics and hydrodynamics of pectoral propulsion. Furthermore, three-di-mensional analysis revealed that bass fin kinematics are much more complexthan expected on a rowing model of drag-based propulsion, and that thepectoral fins may produce drag-based thrust even during protraction. Three-dimensional kinematic data are critical to understanding the hydrodynamicsof aquatic animal propulsion. Such data are a necessary foundation for re-constructing patterns of movement, modeling (both theoretical and empiri-cal), and for assessing the extent to which motion is under active control ora passive consequence of fluid resistance.

INTRODUCTION from protozoa to mammals and a conse-Although the study of aquatic locomo- <luent w i d e diversity of hydrodynamic en-

tion has involved numerous taxa ranging vironments and modes of propulsion (Gray,1968; Lighthill, 1975; Wu et al., 1975;Maddock et al., 1994; Vogel, 1994), fishes

' From the Symposium Aquatic Locomotion: New h a y e , d a p r o m i n e n t r o l e j n our at-Approaches to Invertebrate and Vertebrate Biome- . . . .chanics presented at the Annual Meeting of the Society t e m P t s t o Understand how animals generatefor Integrative and Comparative Biology, 27-30 De- propulsive forces in the aquatic mediumcember 1995, at Washington, D.C. (Webb, 1975; Hoar and Randall , 1978;

567

568 G. V. LAUDER AND B. C. JAYNE

Blake, 1983; Videler, 1993). Two facts ac-count for much of this focus on fishes. First,fishes exhibit a considerable diversity of in-terspecific locomotor morphology. Differ-ences in external body shape and axial mus-culo-skeletal structure, such as those foundin eels, trout, and tuna underlie different hy-drodynamic mechanisms of generating pro-pulsive forces and facilitate investigatingalternative locomotor methods at moderateto high Reynolds numbers. Second, individ-ual fish possess both a variety of body sur-faces that interact with the surrounding wa-ter and a concomitant array of locomotorbehaviors. Any one fish may use the bodysurface and caudal fin for steady undulatorylocomotion at moderate to high speeds, pec-toral fins for low speed movement or hov-ering, caudal and median fins during rapidescape (c-start) responses, and caudal, pec-toral, and median fins for braking and ma-neuvering. This array of body surfaces andbehaviors provides an excellent system forinvestigating mechanisms of aquatic pro-pulsion over a variety of speeds and con-ditions while controlling for inter-individualvariation.

Given the broad interspecific and intra-specific diversity in fish locomotor struc-tures and behaviors, it is not surprising thatmany investigators have focused on a rel-atively few components of this variation inorder to conduct more thorough analyses ofphysiology and mechanics: myotomal mus-cle structure and function, swimming kin-ematics of steady undulatory swimming,and a few phylogenetically diverse "ex-emplar" taxa such as eel, trout, carp, andscup (e.g., Wardle et ai, 1995). One con-sequence of this approach is that many as-pects of fish locomotor mechanics, such asthose of low speed swimming, remain poor-ly understood from an experimental per-spective. Many fishes swim slowly by usingthe pectoral fins, and although some exper-imental data have been obtained (Webb,1973; Blake, 1979a, Blake, 1980; Geerlink,1983, 1989; Archer and Johnston, 1989;Gibb et al, 1994; Drucker and Jensen,(1996); Westneat, 1996), much of the prog-ress in understanding this form of locomo-tion has occurred by theoretical modelingof fin movements (Blake, 1981a, ft; Daniel,

1984, 1988; Webb and Blake, 1985; Danieland Webb, 1987; Vogel, 1994). Blade ele-ment theory (Blake 1979a, 1981ft), actuatordisc theory (Blake, 1919b), and unsteadyairfoil theory (Daniel, 1988) have all beenused to estimate force production by pec-toral fins in fishes. In addition, while theanalysis of phylogenetically disparate taxahas been helpful in understanding basic fea-tures of pectoral propulsion, to date no sin-gle clade of fishes has been studied to pro-vide an historical perspective on fin func-tion.

In this paper we provide kinematic dataon pectoral fin propulsion for taxa withina monophyletic clade of fishes, the sunfishfamily Centrarchidae, with the overallgoal of examining the biomechanics ofthis mode of fish locomotion in detail. Wepresent three-dimensional kinematic datato demonstrate the complexity of finmovements even in a "simple" case oflow speed swimming using the pectoralfins. We also evaluate the extent to whichtheoretical models of pectoral propulsionare applicable to sunfishes and discuss thevalue of detailed kinematic data for un-derstanding the diversity of locomotormodes in fishes.

THRUST PRODUCTION BY PECTORAL FINS

Paired fin propulsion in fishes has clas-sically been divided into two categorieswhich represent biomechanical extremes inthe use of appendages for propulsion: lift-based and drag-based mechanisms of thrustproduction (Blake, 1981ft; Daniel, 1984,1988; Webb and Blake, 1985; Vogel, 1994).In lift-based propulsion the pectoral fins areused as wings (Westneat, 1996) and moveprimarily along a dorsoventral axis. The an-gle of attack of the fin is adjusted duringthe fin beat cycle so that positive thrust isproduced during both the upstroke anddownstroke, and this requires reorientingthe fin at the upper and lower limits of itsexcursion. As noted by Vogel (1994, p.285), lift-based propulsion generates posi-tive thrust throughout most of the fin beatso that the duty factor is effectively 100%,and this mode of propulsion is most effi-cient at moderate to high swimming speeds.Lift-based propulsion is relatively ineffi-

PECTORAL FIN PROPULSION IN FISHES 569

Protraction Retraction

Watermovement

FIG. 1. Schematic diagram of model drag-based pro-pulsion in fishes. During retraction (shown on the rightside), the fin is vertical (at a 90° angle to the bottom)and water is pushed posteriorly generating thrust andmoving the fish anteriorly in the direction of the solidarrow shown at the midline. The fin is thus drawn asa line during retraction as it would appear in dorsalview. During protraction (shown on the left side) thefin is feathered to a 0° angle relative to the axis offorward travel and hence experiences relatively littledrag. During retraction the fin appears as a wedge-shaped plate in dorsal view. The direction of watermovement resulting from fin retraction is schematical-ly indicated by the posteriorly-pointing arrow attachedto the fin element. Modified from Blake (1981b).

cient at very low speeds due to the low in-cident fluid velocity over the appendage(wing) and hence a greatly reduced mag-nitude of the lift force on the fin.

In drag-based propulsion the pectoral finsmove primarily along an anteroposterioraxis in a "rowing" mode of propulsion(Fig. 1). The fins are retracted posteriorlywhile oriented perpendicular to the frontalplane and impart momentum to the water ifthe velocity of fin retraction is greater thanthe velocity of water movement. At the startof the recovery (protraction) stroke, the finis tilted so that it is parallel to the frontalplane and brought forward to begin the finbeat cycle again. Feathering the fin duringprotraction greatly reduces drag on the fin,but there is no positive thrust generated dur-ing this return stroke: hence the duty factorof this locomotor mode is about 50%. Drag-based propulsion is most efficient at lowspeeds and decreases in efficiency as body

velocity approaches the velocity of fin re-traction.

The acceleration reaction is also a poten-tially important aspect of pectoral fin pro-pulsion as changes in fin velocity may im-part additional thrust in a direction parallelto the direction of fluid motion over the finand reduce the magnitude of lift forces(Daniel, 1984; Daniel and Webb, 1987).The acceleration reaction depends on un-steady (time dependent) movement of thefins, and becomes significant when the re-duced frequency parameter a (=a>L/U,where u> is the frequency of oscillation, Lis the length of the fin, and U is the speedof fin movement through the water) isgreater than about 0.1 (Daniel, 1984). De-celeration of the fin at the end of both pro-traction and retraction will result in thrustdue to the change in velocity of the addedmass of water associated with the pectoralfin. For example, as the fin decelerates atthe end of the retraction stroke (Fig. 1), wa-ter accelerated by the fin will tend to keepmoving posteriorly as fin velocity decreas-es. The magnitude of this thrust will dependon the rate of change of fin velocity, theshape of the fin, and the stroke angle (Dan-iel, 1984). Gibb et ai, (1994) estimated thatfor the pectoral fin of bluegill sunfish op-erating at a Reynolds number of 5 X 103,a may be as high as 0.85 suggesting thatunsteady effects might be quite importantin contributing to thrust production duringpectoral locomotion.

The shape of the fin may also affectthrust production during pectoral locomo-tion. Blake (1981a) has modeled the effectof pectoral fin geometry on thrust produc-tion and concluded that a wedge-shapedblunt fin (with the apex of the wedge at-tached to the body and the blunt edge form-ing the distal fin margin; as in Fig. 1) is ahydrodynamically more efficient fin shapefor drag-based propulsion than a rectangu-lar shape due to reduced interference dragnear the body. Within the sunfish familyCentrarchidae, such blunt-edged fins char-acteristic of drag-based propulsion are pres-ent in primitive clades such as Micropterus(bass) and Pomoxis (crappie) (Fig. 2). Out-group taxa to the Centrarchidae also pos-sess relatively short blunt fins suggesting

570

Outgroup

CP

G. V. LAUDER AND B. C. JAYNE

Centrarchidae

Morone

cyanellus microlophus macrochirus

Micropterus Pomoxis

Lepomis

FIG. 2. Phylogenetic relationships of representative taxa within the North American teleost fish family Cen-trarchidae (following Mabee [1993, 1995] and Wainwright and Lauder [1992]) and an outgroup clade (Perci-chthyidae: Morone) to show evolutionary patterns to pectoral fin shape within this clade. Images of the leftpectoral fin above each clade have been scaled proportionally to the size of the fin in that clade, and all taxaare drawn to the same total length. Note the trend in the Centrarchidae from a primitive short and blunt fin(suggested to be characteristic of drag-based propulsion) to the longer wing-like fin used in lift-based propulsion.Images of fishes modified from McGillis (1984), Freshwater Fishes of California, © 1984 by the Regents of theUniversity of California.

that this condition is primitive for sunfishesas a clade.

Lift-based propulsion is associated withmore "wing-like" fin shapes where the dis-tal tip is tapered and the fin as a whole ismore "diamond-shaped." Species withinthe sunfish genus Lepomis possess morewing-like pectoral fins (Fig. 2) with greaterrelative area than the blunt fins character-istic of basal groups in this clade.

METHODS FOR THREE-DIMENSIONALANALYSIS

The most basic data needed for an anal-ysis of pectoral fin locomotion in fishes arekinematic. Without an understanding ofhow the fin moves in three-dimensionalspace we lack the ability to conduct accu-rate modeling (either empirical or theoreti-cal), estimate thrust production, or under-stand the extent to which fin movements areunder active muscular control. Fin motionis inherently three-dimensional as the pec-toral fin typically moves in both dorsoven-

tral and anteroposterior directions duringswimming due to the oblique orientation ofthe base of the fin with the body. Therefore,it is essential that kinematic data be mea-sured in three-dimensional space and thatspecific marked points on the fin be fol-lowed through time. Tracking the move-ment of individual markers allows both thevisualization of parts of the fin that can notnormally be seen due to the diaphanous na-ture of the fin membrane, and also permitsdivision of the fin surface into smaller unitsthat can be analyzed individually. A fullthree-dimensional analysis also allows cal-culation of 3D angles of attack of differentportions of the fin surface, rather than re-stricting angular calculations to their pro-jection onto one plane. As we will showbelow, two-dimensional analyses can resultin gross errors that severely compromiseunderstanding the mechanics and hydrody-namics of pectoral propulsion.

In order to analyze movement of thepectoral fin, it is useful to visualize the fin

PECTORAL FIN PROPULSION IN FISHES

posterior lateral

FIG. 3. Schematic representation of the three-dimensional space used to analyze pectoral fin kinematics inlargemouth bass. Movements of the fin are defined with respect to three planes: YZ, XY, and XZ. The base ofthe pectoral fin is located on the XY plane, and the pectoral fin surface is shown lying within a plane that makesa three-dimensional angle with each of the three reference planes: YZ, XY, and XZ angles. The fin surface isdivided into two triangles (A and B). The planar angles of intersection are reflected by the pie wedges shownfor the YZ, XZ, and XY angles. These angles are measured orthogonally to the reference planes and are notprojections of one plane onto the other. Note that as this figure is drawn, the fin plane intersects the XZ andYZ planes. The XY planar angle is shown for completeness, but would actually lie behind the fin plane asdrawn. See text for further explanation.

in three-dimensional space. Figure 3 illus-trates a left pectoral fin oriented within aschematic cube defined by three referenceplanes: YZ, XY, and XZ. In anatomicalterminology, YZ is equivalent to thetransverse plane, XY the sagittal plane,and XZ the frontal plane. If these refer-ence planes are viewed as part of a flowtank in which a fish is swimming by pec-toral fin propulsion, then water is movingfrom anterior to posterior perpendicular tothe YZ plane as indicated by the solidblack arrows, and parallel to the XYplane. The XZ plane would then corre-spond to the bottom of the flow tank. Thebase of the pectoral fin is drawn as beinglocated just lateral to the XY plane withthe fin extending at an angle into the flow,and the fish would be oriented with itslong axis parallel to the XY plane facinginto the YZ plane. For graphical conve-

nience the surface of the pectoral fin isindicated as lying entirely within a planeextending out from the fin base towardeach of the three reference planes (Fig. 3).The outer edge of the fin is indicated bya thin line and surface of the fin lyingwithin this line has been divided into twotriangles, A and B, by a three markers (in-dicated by black dots). These markers areon the distal edge of the fin while a singlepoint defines the base of the fin. While thefish is anesthetized, it is possible to attachsmall pieces of black plastic to mark thedistal fin allowing visualization of specificpoints on this otherwise largely invisibleregion of the fin (Fig. 4; also see Gibb etal., 1994).

The location of each of the points onthe fin is specified by x, y, and z coordi-nates (Fig. 3). The values of these coor-dinates are obtained experimentally by us-

572 G. V. LAUDER AND B. C. JAYNE

FIG. 4. Video images showing the pectoral fin beat cycle in largemouth bass. The last three digits at the topof each panel indicate elapsed time in ms. Each panel contains two views obtained simultaneously with separatecameras: the ventral mirror-image view is on the left and shows movement in the Z and X dimensions, whilethe lateral view is on the right and shows movement in the Y and X dimensions. Three small markers havebeen placed on the left pectoral fin: Left and Right labels in panel B indicate the respective fins, and the D, M,and V labels in panel F indicate the Dorsal, Middle, and Ventral markers respectively. The background grids inboth views are 2 X 2 cm. In this figure the three markers on the left fin are most easily seen in lateral view (D)and ventral view (F), although during data acquisition all markers generally could be followed throughout thefin beat cycle. The original video images have been cropped and contrast-enhanced for clarity using AdobePhotoshop.

ing two synchronized high-speed (200fs~") video cameras (Fig. 4) that providelateral (XY plane) and ventral (XZ plane)views of the fin. These two orthogonal im-ages (Fig. 4A) allow measurements of thethree-dimensional position of each mark-er: the XZ view provides the z coordinate,while the XY view provides the x and ycoordinates. All coordinates were initiallymeasured in the earth frame of reference,although many of the movements illus-trated in this paper are presented relativeto the position of the fin base. The fin baseshowed minimal oscillation in the X, Y,and Z planes through the fin beat cycle,

and the XY plane was thus assumed to beparallel to the anatomical sagittal plane.The video cameras showing both viewshave equal magnification and are alignedto minimize parallax errors.

The x, y, and z coordinates for each pointallow calculation of the surface area of thetwo triangular elements of the fin (Fig. 3)which may change throughout the fin beatas the spacing among adjacent fin rays isaltered cyclically by the fin musculatureand water pressure. Most importantly, thethree-dimensional planar angle that each tri-angle makes with each of the three refer-ence planes can be calculated. Each fin el-

PECTORAL FIN PROPULSION IN FISHES 573

ement defines a plane which extends be-yond the borders of the fin to intersect thethree reference planes. For, example, theplane defined by triangle B makes an XZangle with the frontal (XZ) plane and a YZangle with the transverse (YZ) plane. Asthe fin beats all three angles will changewith time, and Figure 3 illustrates the con-ventions used to define these angles. TheXZ angle is 90° when the fin triangle is per-pendicular with the XZ plane, less than 90°(acute) when the triangle is tilted to the left(as shown in Fig. 3), and greater than 90°(obtuse) when the triangle is tilted to theright. We use a similar convention for theYZ plane. If fin triangle B stays perfectlyvertical throughout the fin beat cycle, it willalways form a 90° angle with the XZ planebut the YZ angle will oscillate from about90° when the fin is against the body to avalue of about 40° at peak abduction. Val-ues of 0° for the XY angle indicate when atriangular fin element is parallel to the XYplane, negative values (between 0° and-90°) indicate that the fin markers are lat-eral to the fin base (as shown in Fig. 3),while positive values (between 0° and+90°) indicate that the distal fin markers arelocated medial to the fin base (this lattercondition does not occur for the left pec-toral fin which sweeps through an XY angleranging from 0° to about —75° during thefin beat cycle). Note that these planar anglesare measured orthogonally to each plane,and do not represent projections of the finedge onto each plane. Also, these planar an-gles measure the orientation of the surfaceof the fin, and hence are not equivalent tofin angles estimated by projection of linesegments located on the fin onto orthogonalreference planes.

We also calculated an instantaneousmovement vector for each triangle and eachtime increment of movement (see Fig. 8).Movement vectors were oriented perpen-dicular to the triangle surface with theirbase located at the triangle centroid. Vectororientation may thus be used as a visualguide to the orientation of the surface ofthat triangle. Vector magnitude was scaledin proportion to the area of the triangletimes the component of squared velocity ofcentroid movement along the normal to the

triangle surface. Longer vectors in Figure 8thus reflect either greater triangle area,greater velocity, or both.

3D KINEMATICS OF THE BASS PECTORAL FIN

The shape of the pectoral fin of large-mouth bass, Micropterus salmoides, is char-acteristic of fishes that presumably usedrag-based propulsion (Fig. 2). First wepresent kinematic data to document thecomplexity of movement of the pectoral finin bass, and then we provide comparisonsto other taxa.

Three-dimensional excursions of finmarkers

Video images of one fin beat cycle inbass are shown in Figure 4. Markers onthe distal fin edge are labeled dorsal, mid-dle, and ventral. Movements of the fin inthe negative and positive directions of thex, y and z axes are designated as: protrac-tion and retraction, depression and eleva-tion, and abduction and adduction, re-spectively.

Beginning with the fin maximally ab-ducted (Fig. 4A), the fin sweeps posteriorlyand medially during adduction (Fig. 4C)until the fin surface is oriented nearly par-allel to the body (effectively a 90° angle toboth the XZ and YZ planes). At the end ofadduction (Fig. 4D), the three markers onthe distal fin edge are clearly visible in lat-eral view. Fin abduction then begins and thefin moves anteriorly and ventrally (Fig. 4F)prior to starting a new cycle. Fin beat fre-quencies range from 1.8 to 2 Hz and do notchange significantly over a speed range of0.3 to 0.75 Lsec"1.

The complexity of the fin movements isillustrated by a plot of the displacement ofthe dorsal marker in each of the three di-mensions (Fig. 5) relative to a fixed pointon the bass. During early adduction the dor-sal marker moves dorsally and posteriorly,whereas after maximal adduction of thismarker, it moves anteriorly while continu-ing to move dorsally (Fig. 5). Ventralmovement begins during abduction and an-terior movement. A consequence of thephase differences among the three-dimen-sional movements is that quantifying move-ment in any one dimension will not allow

574 G. V. LAUDER AND B. C. JAYNE

Adduction

0.3 0.4

Time (sec)

FIG. 5. Displacement in three dimensions of the most dorsal marker on the bass pectoral fin relative to thebody during locomotion at 0.5 Lsec"1 (equivalent to 10.5 cmsec"1). Abduction and adduction phases of finmovement are defined by extreme displacements in the Z dimension. Negative slopes for plots of Y (•) , Z ( • ),and X (H) indicate, fin depression, adduction, and protraction respectively. Z-values are measured relative to afixed point on the fish; hence, decreasing z-coordinates reflect fin adduction. Note that the maximal speed of finretraction (X dimension) exceeds the speed of fish movement.

inference of movement in the other two di-mensions. The maximal speed of fin retrac-tion exceeds the speed of the bass (Fig. 5)suggesting that a drag-based mechanism isone of the thrust production mechanismsused during locomotion.

Movement of all three markers in the fishframe of reference is illustrated in Figure 6.All markers move in a loop with an axis ori-ented anteroventrally, and this contradicts ex-pectations of a simple rowing pattern duringwhich the fin would retract along the anter-oposterior axis, feather while protracting, andthen expand anteriorly prior to retraction. In-stead, these complex movements include acounter-clockwise loop of the dorsal markerand a clockwise loop for the middle and ven-tral markers. This movement pattern at 0.3Lsec"1 is consistent with a relatively passiveventral portion of the fin following activelycontrolled leading dorsal rays. This hypoth-esis is corroborated by electromyographicanalyses of fin muscles (Lauder and Jayne,unpublished). At higher speeds (e.g., 0.5Lsec"1), all markers move in counter-clock-wise loops.

Three-dimensional angles of fin elementsAnalysis of the three-dimensional orien-

tation of fin triangular elements A and B(Fig. 7B, C, D) shows that at the start offin adduction, both fin elements make anacute angle with the XZ plane indicatingthat they are oriented with their most dorsalvertex located anterior to the ventral verti-ces. As the fin moves posteriorly, triangleB reorients to achieve nearly a 90° angle tothe XZ plane and maintains a value closeto 90° until the fin is fully adducted. Tri-angle A, however, moves through the 90°angle to reach nearly a 120° angle to theXZ plane. In this orientation, triangle Awould be expected to exert a force on thefluid in a posterior and ventral direction.When the fin is against the body at mid-beat, both triangles are oriented at 90° tothe XZ and YZ planes and at a nearly 0°angle to the XY plane. During abduction,both triangles maintain nearly a 90° angleto the YZ plane (Fig. 7B, C) while formingincreasingly acute angles to the XZ (hori-zontal) plane.

Three-dimensional planar angles pro-

PECTORAL FIN PROPULSION IN FISHES 575

3.0 -

2.5 -

U 2.0 -

1.5 -

8-&'•6 i.o -Ho

r

o --0.5

Dorsal

Anterior^

0 0.5 1.0 1.5 2.0 2.5

Longitudinal displacement(cm)

FIG. 6. Loop plot for swimming at 0.3 Lsec~' (equiv-alent to 6.3 cm/sec) showing the vertical (Y) and lon-gitudinal (X) displacements of three markers on thebass pectoral fin ( • dorsal, 0 middle, and • ventral)relative to a fixed point on the fish. Arrows show thedirection of marker movement during one fin beat cy-cle within each loop. Numbers next to selected pointsindicate homologous times on each marker loop. Timebetween successive points is 0.05 sec.

vide an indication of the orientation ofeach fin element with respect to referenceplanes, and hence measure a geometricalangle of attack. However, nearly all pre-vious analyses of fish swimming haveused single camera views that precludesuch three-dimensional calculations. Towhat extent could two-dimensional meth-ods be in error? For pairs of markers onthe distal edge of the fin of a bluegill,Gibb et al., (1994) compared angles cal-culated from a two-dimensional (lateral)view versus angles derived the intersec-tion of the XY plane and the plane con-taining a three dimensional triangular finelement (similar to triangle A in Fig. 3).Table 1 shows the large discrepancies inangles (ranging from 22° to 83°) resultingfrom these different methods. These er-rors are so large as to suggest that seriousmisinterpretation of fin function is likely

if only two-dimensional data are used asa basis for estimating the hydrodynamicenvironment of the pectoral fin. Further-more, even the signs of various anglesmay be in error. For example, early in thefin beat cycle at 1.1 Lsec~', a line segmentformed by a (two-dimensional) projectionof the fin edge onto the XY plane formsa positive 58° angle relative to the pathtraveled by the fin, whereas the intersec-tion of the planar fin element and XYplane forms an angle of —11° relative tothe direction of fin movement in the XYplane (Table 1).

The excursions, angles of the triangularfin elements discussed above, and move-ment of the triangle centroids are visualizedin a three-dimensional reconstruction of finposition shown in Figure 8. During mid-adduction (T,), fin elements A and B movedorsally, posteriorly, and medially as re-flected by the direction of triangle centroidmotion. At mid-abduction (T2) both fin el-ements are moving ventrally, anteriorly, andlaterally. Movement vectors attached to thecentroid of each triangle show that duringprotraction (time T2) the lateral surface ofboth triangles is facing posteriorly (Fig. 8):the distal tip of the vector attached to thecentroid of triangle A is located posterior(along the x dimension) to the centroid ofthat triangle. The surface of triangle B hasa slightly less posterior orientation, with theresult that the entire fin is slightly concavedownward at this time. Thus, the fin is"feathered" to some extent during protrac-tion, and this configuration of the fin mayprovide lift-based propulsive force duringthis portion of the fin beat cycle. Note thatthe lateral fin surface is not oriented ante-riorly during protraction as would be ex-pected if the fin were exhibiting a primarilytranslational motion.

Figure 8 also illustrates the important re-sult that the bass fin may produce drag-based thrust even during protraction. Attime T2, as triangle A centroid is movinganteroventrally, there is still a positive com-ponent of centroid velocity that projectsonto a line perpendicular to the fin surface.Hence, triangle A is capable of pushing wa-ter posteriorly at this time even though thecentroid is moving anteroventrally, due to

576 G. V. LAUDER AND B. C. JAYNE

10-,

0.0I • • ' ' I

0.2 0.3 0.4Time (in sec)

0.5 0.6

FIG. 7. Plots of three-dimensional kinematic parameters for the bass pectoral fin during a single fin beat cyclefrom locomotion at 0.6 Lsec"1 (equivalent to 12.6 cm/sec) relative to the earth frame of reference as shown inFigure 3 (hence increasing Z values reflect adduction). A, lateral (z) excursion of the three distal fin markers;B, C, D three-dimensional angles of the two triangular components of the bass pectoral fin with the XY, XZ,and YZ planes. In C and D, horizontal dashed lines mark the 90° angle to each plane. Note that when the finis fully adducted against the body, both triangles make nearly a 90° angle to the XZ and YZ planes. The • andA symbols indicate kinematic parameters for the upper (A) and lower (B) fin triangles respectively. T, and T2refer to times during adduction and abduction of the fin for which three-dimensional reconstructions of finposition are presented in Figure 8.

the orientation of the line of centroid mo-tion relative to the fin surface. This resultmay at first appear counterintuitive, but isin fact analagous to a sailboat tacking up-wind. A sailboat can sail into the wind viathe judicious orientation of the sail surfacerelative to wind velocity. In a similar man-ner, the bass can generate positive drag-

TABLE 1. Comparison of angles derived from two-dimensional methods versus three-dimensional meth-ods for the two most dorsal markers on the bluegill(Lepomis macrochirus) pectoral fin.*

Swimmingspeed

0.3 Ls '0.3 Ls"1

1.1 Ls '1.1 Ls '

Phase within finbeat cycle

5-10%65-75%11-16%58-63%

Two-dimensional

angle

86°43°58°23°

Three-dimensional

angle

3°65°

-11°- 1 °

*Note how poorly the two-dimensional calculationsestimate the actual three-dimensional angle. Data from(Gibb et at, 1994.) See text for more detail.

based thrust during fin protraction by an ap-propriate orientation of the fin surface rel-ative to its path of motion.

The difficulty in appreciating the three-dimensional configuration of the fin derivesin part from our tendency to view move-ment in two dimensions only. Even thoughFigure 6 depicts motion only in the XYplane, the anteroventral orientation of themovement loop is clear. The major axis ofpectoral fin movement is not oriented hor-izontally, and during protraction, the fin ismoving ventrally to the same extent that itis moving anteriorly (Figs. 5, 6). Further-more, the orientation of the surface of finelement A is an essential parameter to con-sider when attempting to visualize move-ment. Note that in Figure 8 (time T2) thebase of triangle A is located medial and an-terior to the distal fin markers while themost dorsal marker is located laterally tothe middle marker. At time T2, the surface

PECTORAL FIN PROPULSION IN FISHES 577

FIG. 8. Three-dimensional reconstruction of the position and movement of the bass pectoral fin during adductionand retraction (times T, and T2 see Fig. 7). Note that the fin has been enlarged relative to the body to illustratetriangle and vector orientations. This reconstruction is based on the X, Y, and Z coordinates of the three finmarkers and a point at the base of the pectoral fin; small spheres indicate the location of fin markers and thebase of the fin used for three-dimensional calculations of triangle position. Vectors originating at the centroidof each of the two fin triangles show the orientation of the triangular surface: each vector is oriented perpen-dicular to the fin triangle plane. The length of each vector is proportional to the squared velocity of the trianglecentroid in the direction normal to the triangle surface (see text for further discussion). Note that at time T2 thesurface of the upper triangle (A) is oriented posteriorly. Triangle B is not visible in dorsal view at time T,because it is hidden beneath triangle A. The direction of triangle A centroid movement in shown by the arrowbelow each fish image. At time T2 the centroid of triangle A is moving anteriorly and ventrally as seen in lateralview.

of triangle A is moving laterally, ventrallyand anteriorly, folding the fin along the bor-der between triangles A and B.

One likely cause of the complexity of finmovements in bass is the oblique articula-tion of the fin with the body. The axis ofthe fin base is inclined from anterodorsal toposteroventral (Fig. 2) and the path of finmotion may thus be largely determined byanatomy. The orientation of the fin ray bas-es, their attachment to the underlying radialelements, and the lines of action of abduc-tor and adductor muscles may render purelytranslational motion along any one axis im-possible.

COMPARISONS TO OTHER TAXA

While three-dimensional kinematic dataof this kind are not yet available for anyother fish taxon, a basic three-dimensionaldescription of fin movement in bluegill, Le-pontis macrochirus, with marked pectoralfins was presented by Gibb et ai, (1994).A comparison between bluegill and bass isinstructive because although both speciesare members of the same sunfish clade, they

possess patterns of fin structure that wouldbe expected a priori to conform to lift-based and drag-based kinematic patterns re-spectively (Fig. 2). In addition, both specieswere studied under the same experimentalconditions and are size-matched by totallength: bluegill averaged nearly 18 cm intotal length (Gibb et al., 1994) while thebass used for the experiments reported inthis paper had a mean length of about 21cm.

At a similar total length, bluegill possesspectoral fins of greater maximum lengthand area than bass: the distance from themost dorsal marker to the fin base is 4.3 cmin bluegill compared to 2.8 cm in bass,while the respective total fin areas are 6.5cm2 and 4.0 cm2.

Bass show little change in fin beat fre-quency with speed, and over a speed rangeof 0.3 to 0.75 Lsec"1 use significantly high-er frequencies than bluegill. For example,at 0.5 Lsec"1, bluegill pectoral fin beat fre-quencies average about 1.35 Hz, while bassbeat frequencies reach almost 2 Hz. Blue-gill beat frequencies are strongly speed de-

578 G. V. LAUDER AND B. C. JAYNE

pendent (Gibb et ai, 1994) while those ofbass are not. In addition, the percent of cy-cle spent in protraction is much greater forbass (55%) than for bluegill (35%) at aspeed of 0.5 Lsec"1.

For bluegill and bass swimming at 0.3Lsec"1, one similarity in the movement ofthe pectoral fin (as seen in the XY plane)is that the most dorsal marker moves in acounterclockwise fashion whereas the ven-tral markers move clockwise [Fig. 6; Gibbet al., (1994)]. This suggests that for bothspecies the ventral fin rays are passivelyfollowing the leading dorsal rays at slowspeeds. In both species, the path traveled bydorsal and ventral fin markers in the XYplanar projection becomes counter-clock-wise at speeds above 0.5 Lsec"1 suggestingthe recruitment of additional muscles con-trolling the ventral fin rays. Previous workby Webb (1973) and Geerlink (1983) alsohas indicated that the dorsal fin rays maylead fin movement during the beat.

Compared to bluegill at the same rela-tive speed, bass have greater phase lagsamong dimensional excursions for a sin-gle marker, and this is most easily seen bycomparing the anteroventral and postero-dorsal movements of the dorsal marker. Inbluegill, maximal depression of the dorsalfin marker (minimum y) is nearly syn-chronous with maximum abduction (max-imum z) of the fin, whereas in bass max-imum depression is reached approximate-ly 20% cycle later than maximum abduc-tion (Fig. 5). In bass, phase lags approach30% cycle for maximal posterior move-ment compared to maximal dorsal finmovement, whereas in bluegill thesephase lags are much less, ranging from0% at 0.3 Lsec-1 to about 11% at 1.1Lsec"1.

Both bluegill and bass pectoral fins pos-sess a reduced frequency parameter CT ofabout 0.33 at a speed of 0.5 Lsec~', butbluegill swim at significantly higher speedsup to 1.1 Lsec~' prior to switching gait toinclude undulation of the body and caudalfin. At these highest speeds bluegill reducedfrequencies approach 0.85. The transition tobody and caudal fin undulation in bass oc-curs at about 0.8 Lsec1 in a fish of 20 cmtotal length.

CONCLUSIONS

Models of drag-based propulsion

The development of theoretical modelsof fish fin hydrodynamics has been a majorstimulus to the field and has provided ex-perimentalists with an extremely usefulframework for interpreting descriptions offish fin kinematics. The models of Blake[(1979a, 1980, 1981a, b), also see Webband Blake (1985), Webb (1988), Daniel(1984), and Vogel (1994)] have been par-ticularly fruitful in defining precisely thetheoretical extremes of lift- and drag-basedpropulsion. For example, modeling drag-based propulsion (Fig. 1) provides a well-defined extreme against which the kinemat-ics of the bass fin can be compared. Doesthe bass fin function in a drag-based man-ner? Bass possess fin shapes and a generallocomotor mode that qualitatively appearsto be drag-based, especially when com-pared to taxa that seem to more closely ap-proach the lift-based end of the propulsivespectrum such as Coris and Cymatogaster(Webb, 1973; Geerlink, 1983).

However, the results of three-dimension-al kinematic analyses in both bass and blue-gill show that it is very difficult to charac-terize pectoral fin locomotion in these taxaas fitting either a drag- or lift-based model.Our data show that the fin movements areextremely complex and defy both simplecharacterization and easy inference of hy-drodynamic regime or thrust productionmechanism. This conclusion is based onfour points.

First, the pectoral fin does not correspondto rigid plate-like element. Triangles A andB move along different paths and theymake different planar angles with the threereference surfaces. The division of the pec-toral fin into these two elements representsa minimal level of analysis in which the finis divided into a section that is controlledprimarily by the leading (dorsal) fin rays(element A) and a section that is increas-ingly passive with decreasing speed (ele-ment B). For a more complete analysis rel-evant to hydrodynamic modeling, the fincould be divided into spanwise strips, butthere are considerable practical difficultieswith achieving this.

PECTORAL FIN PROPULSION IN FISHES 579

Second, even our division of the fin intotwo triangles assumes that these trianglesthemselves do not bend. This is clearly anoversimplification as fin rays are flexible(Arita, 1971) and bend along their lengthduring locomotion. This flexibility may beimportant in thrust generation. For example,as the fin is abducted early during protrac-tion, the proximal ends of the fin rays movelaterally before the distal ends because theabductor musculature attaches to the baseof the rays. As the distal portions of the finfollow, they make an obtuse angle to theYZ plane (Fig. 3) which will generate pos-itive thrust as the distal portions of the finrays move laterally. In addition, bending ofthe fin rays may result in more posteriorlydirected thrust than would be possible with-out ray bending. For example, in Figure 8,at time T,, if the fin rays bend as the fin isretracted, the movement vectors would bemore posteriorly oriented than shown inFigure 8, enhancing thrust. To date, nostudy has quantified fin ray bending duringlocomotion and discussed the potential im-pact that bending may have on fin hydro-dynamics, but this is clearly an area for fu-ture investigation.

Third, the pattern of fin movement de-scribed here for bass does not match themotions expected of a fish swimming undera drag-based hydrodynamic regime. The finis not protracted and retracted with a majoraxis of movement oriented in the x dimen-sion. Instead, motion of the fin is extremelycomplex in three dimensions with an anter-oventrally inclined axis of motion.

Fourth, the value of the reduced frequen-cy parameter (about 0.35) suggests that un-steady effects are important but of unknownimpact. Undoubtedly during deceleration ofthe fin at the end of protraction and retrac-tion the acceleration reaction does play animportant role in providing additionalthrust. However, the changing area of thefin, the oblique and changing orientation ofthe fin to the flow, and the difficulty in cal-culating an added mass coefficient for thefin under these conditions, make it very dif-ficult to experimentally assess the impor-tance of unsteady effects. Given the in-creasing amount of data that implicate un-steady effects as having a significant impact

on moving appendages (Daniel, 1984,1988; Dickinson and Gotz, 1993), it seemsunlikely that simple vector analyses of liftand drag components under a quasi-steadymodel of locomotion will accurately de-scribe the hydrodynamic environment ofthe fish pectoral fin.

Three-dimensional kinematic analysis infish locomotion

The vast majority of kinematic analysesof fish locomotion have been conducted intwo dimensions. For many purposes such asdetermining the frequency of the tail beatand lateral (z) excursion of points along thebody, a two-dimensional approach is fullyappropriate. However, in some cases thetwo-dimensional approach may prove ex-tremely misleading. Analysis of pectoral finmovement provides one such case in whichthree-dimensional data are essential. Evenfor determining such basic hydrodynamicparameters such as the angle of attack,three-dimensional data are critical as shownby Table 1. Furthermore, determining theorientation of the surface of the body orappendage (crucial to understanding howforce is exerted on the water) depends onobtaining three-dimensional coordinates forpoints on that surface so that planar anglesmay be calculated.

The value of three-dimensional data ex-tends to influencing how we choose to char-acterize basic locomotor patterns. Relyingon two-dimensional data to characterizemovements that occur in three dimensionswill give an inaccurate characterization offin motion and imprecise inferences offunction. Such errors are likely to be par-ticularly consequential in comparative stud-ies where differences in three-dimensionalmotion among taxa may be critical to un-derstanding evolutionary diversification infunction.

Finally, although kinematic studies alonemay not possess the cachet of analyses ofmuscle physiology, studies of flow dynam-ics, or the production of mathematical mod-els of function, the value of detailed kine-matic data for studies of locomotor functioncannot be overestimated. Without such datawe are unable to estimate the hydrodynamicenvironment of locomotor structures, and

580 G. V. LAUDER AND B. C. JAYNE

we will not be able to construct accuratemathematical models because the input tosuch models (patterns of movement) willnot be available. Kinematics derived froma two dimensional view only are likely tocontain gross errors. Resolving a funda-mental problem of aquatic locomotion, ex-plaining how a moving body generatesforce on the fluid medium, is critically de-pendent on understanding how movementoccurs and the extent to which such motionis under active control.

ACKNOWLEDGMENTS

We thank H. Nguyen for many hoursspent digitizing images of fish, and HeidiDoan for all her help with digitizing anddata analysis. We thank Paul Webb and BillSchultz for very helpful discussions aboutfish locomotion, and Mark Westneat for alively exchange on angles of attack. Prep-aration of this manuscript was supported byNSF grants IBN 9507181 to GVL and IBN9514585 to BCJ. Most of the data discussedhere were originally collected under NSFBNS 8919497 to BCJ and GVL. NSF BSR9007994 to GVL provided funds for com-puter program development. Additionalsupport was provided by the University ofCincinnati to BCJ.

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