Pectoral fin kinematics of Coris Formosa

ARCHIEF

Neh&lands Journal of Zoology

33 (4). 515-531 (1983)

PECTORAL FIN KINEMATICS OF CORIS FORMOSA (TELEOSTEI, LABRIDAE)

by

P. J. GEERLINK

(University of Groningen, Department of Zoology, P.O. Box 14, 9750 AA Haren, The Netherlands)

SUMMARY

A fish propelling itself by means of the pectoral fins, was filmed with a high speed cine camera. For each film frame the movements of the pectoral fins were analysed and the body velocity calculated. The fin beat cycle can be divided into three phases. The ef-fects of each phase on the body velocity are variable, but downstrokes generally cause deceleration and upstrokes acceleration. The intermediate phase sometimes showed acceleration possibly caused by a jet of water squirted out from the space between fin and body wall. The discrepancy between the observed fin shapes and the simplified representation of the fin as a flat plate is discussed. Estimates of drag and swimming force are made.

INTRODUCTION

Although a majority of teleost fishes use the pectoral fins for steering and auxiliary propulsion, in some fish species these fins are the main locomotive apparatus. Labridae, Chaetodontidae and Acanthuridae swim with their pectorals by means of rowing movements, where the fins act as paddles or hydrofoils. Waves are propagated along the pec-toral fins in Diodontidae, Tetraodontidae, some Balistidae as well as in Syngnatidae, where the frequency of these waves on the fins is high and the pectorals cooperate with the waving motion of the dorsal fin (BREDER, 1926; BLAKE, 1976; LINDSEY, 1978).

Special adaptations are found in bottom dwelling fish. Here the pec-toral fins serve for locomotion or support on the ground. Lophiiformés appear to "walk" on the base of their pectorals. Gobiidae and Scor-paenidae use the pectoral fins as a pair of crutches. Triglidae have separate fingerlike rays, independently movable, and other rays con-nected by the fin membrane, spread out horizontally when swimming by body and tail activity. Pectoral fins are also used to aerate eggs. Gasterosteus aculeatus is a well known example; the hole breeding mediterranean Blenniidae do it as well (J. J. VIDELER, J. DE JONGE,

Technische Hogeschoot

Deift

516 PJ.GEERLINK

unpublished). BAERENDS & BAERENDS-VAN RooN (1950) describe the role

of pectoral fins in the sexual display of some Cichlidae. An ex-travagant use of the pectorals is found in the mudskipper (Periopht/zalinus) which can walk or even climb on them on land. Its pectoral fin consists of two functional parts: a rigid, platelike, prox-imal region hinged to the pectoral girdle for the locomotion on land, and a fanlike distal part. Other examples of terrestrial locomotion on pectoral fins are known in Anabantidae and Clinidae (LINDSEY, 1978). Exocoetidae (flying fish) "glide" on their pectoral fins through the air. Some members of the Gasteropelecidae

even make flapping

movements while taxiing over the water surface and apparently con-tinue flapping when airborne (LINDSEY, 1978).

In this study Corisformosa, a species with prominent pectoral swim-ming, is discussed. A description is given of the external morphology of the pectoral fins and of their movements when the fish propels itself without using any other fins. To make an accurate description of the fin movements and the resulting displacement of the fish high-speed cine-film recordings have been analysed.

BREDER (1926) and HARRIS (1937) described general patterns of fin activity and WEBB (1973, 1975b) and BLAKE (1979, 1980) also studied the movements of pectoral fins. These authors resorted to simplified

models which enabled them to carry out calculations on

hydrodynamics and energetics. The present paper concentrates on giving a detailed description of the fin movements, showing variations and relating fish motions to the real fin activity.

MATERIALS AND METHODS

Unrestrained swimming movements of a commercially obtained specimen of Cons for-mosa (BENNET), 1834 were recorded on 16 mm film. This fish was 0.152 m long, its wet body mass 0.0495 kg, and the wetted surface area without the pectoral fins 9.63 x i0-m2. The following approach was used to establish the wetted surface area: the surface area A of the lateral projection of the anaesthetized fish was measured, as well as the circumference C and height H of the body halfway snout and tail. The wetted surface area S was calculated as S = (2Ah/2C)/(H).

The fish tank contained 120 1 of artificial seawater of 25°C. A buffer solution (Na2CO3:NaHCO3 = 1:6) kept the pH between 8.2 and 8.4 and a charcoal filter cleaned the water. A 5 cm thick layer of sand covering one third of the tank bottom allowed the fish to hide during the night. In the other two thirds of the tank, a mirror' was mounted at an angle of 45° with the horizontal plane, extending half way up the water column.

The fish was filmed using a high speed 16 mm camera with intermittant film

transport (Red Lake, Locam) in a fixed position. The camera had a built-in reference grid. Eastman Ectachrom VNF film (400 ASA) was exposed at 100 frs s'1 and two 500 W tungsten lamps were used for illumination. The films were analysed frame by frame on a Vanguard Motion Analyser. On the films a lateral view of one fin (by chance always the left one) and a ventral view of both fins were visible.

From each film frame a drawing of the fin shape was made in lateral view (fish-bound frame of reference).

The position of the body was plotted for each frame using a èoloured spot on the head as a mark. The regression line through the body positions was taken as the mean path of motion and called the X-axis. The 'instantaneous velocities in x and y direc-tions (U and U) were calculated as time derivatives of the displacements in the x and y directions using the five point differentiation formula of Lagrange. U, and U, at

ins-tant t = n were estimated to be the mean values of five dxldt values arbund t = n (ABRAMOWITZ & STEGUN, 1970). A correction was introduced for those cases in which the fish did not swim quite parallel to the plane of the film. In the saiüe way the

velocities of the fin tip (the distal end of the anterior edge) V, and V,, (as measured in lateral projection) were calculated.

Acceleration and deceleration rates were assumed to be the slopes of linear regres-sion lines through the velocity-time curves for (parts of) the various fin stroke phases (downstroke, upstroke, intermediate phase).

The ventral images were used to measure the angle between the body axis and the vertical projection of the anterior edge of both fins.

RESULTS

External Fin Morphology

The pectoral fin of C. formosa has 13 fin rays of different lengths con-nected by a fin membrane (fig. la). The skeleton of a fin ray consists of a lateral and a medial half, each consisting of a varying number of

bony segments. The most anterior or first ray, however, is not

segmented and is firmly attached to the second ray. The second and following rays are segmented and flexible, the fourth and following rays have a branched distal half. Each ray has an unsegmented prox-imal part which is of decreasing length in successive rays.

The proximal ends form a curved row of joints with the distal ends of four bony elements, the proximal radials. The first ray articulates directly with the scapula.

The drawing of the skeleton of the pectoral girdle (fig. ib) shows the position of the scapula and coracoid, the proximal radials and the fin rays. Scapula and coracoid, situated within the body of the fish, form the rigid basis of the fin which is firmly connected to the skull by means, of the cleithrum and some smaller bony elements.

The proximal radials and rays protrude from the body. The gap be-tween the proximal radials and the rays is filled with a cushion of con-nective tissue.

Principles of Fin Movements

The movements of the fin are the results of the movements of the prox-imal radials and of the individual rays. The joint between scapulalcor-acoid and proximal radials allows a movement of the proximal radials

1mn

Fig. 1A. External morphology of the left pectoral fin. x = horizontal axis generally coinciding with median line of progression. y = vertical axis. ant. = anterior, post. =

posterior.

Fig. lB. Skeleton of left pectoral fm. ci = cleithrum; cor = coracoid; pr = proximal radials; r = rays; sc = scapula.

over a maximum angle of about 900. They cannot move independent-ly, because they are attached to each other by connective tissue and covered with skin and muscles. The joint between proximal radials and rays allows a movement around the antero-posterior axis of pro-bably not more than about 90°. Around the transverse axis the max-imum angle of movement is estimated to be about 45-60°.

The fin membrane limits the independence of the movements of the individual rays and allows only small phase differences between adja-cent rays. The rays are stiff but bendable and due to their construction their degree of stiffness can be changed actively by muscle action (VIDELER, 1977). Because of the differences in fin ray lengths the fin does not have the outline of a rectangular plate (see fig. 1A).

Fin movements are potentially very complex because they are the results of movements of the different joints and of the flexing rays,

518 P.J. GEERLINK

cooperating in an almost infinite number of ways. Restriction of the observations to propulsive movements of the pectorals howeVer limited this number of variations.

Three filmshots were selected in which the fish used the pectoral fins exclusively for propulsion and no movement of the other fins or of the body could be observed. These shots contained at least one whole cycle of fin movement Analysis Of the three film sequences shows that three phases of movement can be distinguished in each example (figs. 2, 3

and 4): a downstroke, an upstroke and an intermediate phase

preceding the next downstroke (cf WEBB, 1973).

The downstroke stafts from a position in which the fin is kept dor-sally against the body wall. From this position the anterior edge starts to move rostroventrally in either of two ways:

Initially performing a latero-ventral movement, gradually chang-ing into a merely rostral direction at the end of the downstroke: the "downward-forward type" (dowristrokes Do Ia and Do lb - fig. 2 - and Do 3a-fig. 4);

Carrying out a rostral movement with .a gradually increasing ven-tral component: the "forward-downward type" (dowñstrokes Do 2 -fig. 3 - and Do 3b - fig. 4).

In both types the anterior edge leads the movement in forward direction while the fin spreads and moves downward. The posterior edge moves slightly upward, and also laterally. It lags in phase behind the anterior edge.

The upstroke is carried out as a dorsocaudal movement of the anterior edge, while the posterior edge moves slightly downward in-itially and then backward. The anterior edge is about V2ir to r in phase ahead of the posterior edge. The fin membrane in this way is spread and brought into a more or less vertical position in which it is swept backward and turned toward the body wall. The anterior and posterior edge lead during this movement, the intermediate rays lag behind. The fin membrane may thus assume a hollow shape as in the upstrokes Up 2 - fig. 3 - and Up 3b - fig. 4 -, or this hollow shape may be less pronounced as in the upstrokes Up la and Up lb - fig. 2 -. and Up 3a - fig. 4.

It is difficult to define the beginning and the end of the intermediate phase accurately. At the end of the upstroke the fin is brought to the body wall. The anterior edge comes nearto or even touches the body wall first, then the rest of the fin follows: The fin is sometimes turned to a more forward inclined position, before the downstroke starts (see downstroke Do 3b - fig. 4).

This general pattern of fin movement can be readily distinguished, but there are differences in the details of the movements during the

Fig. 2. Fin movements and body velocity; film shot 1. From top to bottom: -, shapes of left fin as seen in lateral view. Numbers represent frame numbers. Cross

bars indicate fish bound reference grid.

velocity along median line of progression,'U, of the fish as calculated for each film frame, and the velocity U perpendicular to U,.

velocity of fin tip in x direction, V,, and relative to the fish, (V-U), and (V-U). V,, is omitted because of small difference between V,, and (V-U). Note the dif-ference in scale between the graphs for U and V.

- angle a between anterior edge of fin and median plane of the fish body in vertical projection. 00 = fib backwards against body wall. a = angle for 'right 'fin

= idem for left fin. . V

520 P. J. GEERLINK

three phases of every fin stroke. At this level of precise observation each fin stroke appears to be unique.

Fin Stroke and body Velocity

The body velocity ,U and '? tip velocity V are plotted for the x and y

direction (U, U, V,, V; figs. 2,3,4). The angles between the pro-jection of the anterior edge of respectively the left and right pectoral fin on the horizOntal plane and the median plane of the fish, are called aj and a. The graphs of these angles against time show whether the left and right fins are beating simuItanously or not (lower graphs figs. 2, 3, 4). Theobserved U, values varied between 0.04 and 0.12 m s (0.3 and 0.8 body lengths s-i). Average velocities and accelerations are listed in table I.

During film shot 1 (fig. 2) the fins were beating simultaneously (note, however,, that the psitipn.pthe right fin was not recorced dur-ing downstroke Do la). Both downstrokes Do la and Do lb were associated with deceleration of different magnitudes: -0.066 m s-2 for Do la and.-0.280 m -2 for Do lb. Both downstrokes .were of the

"downward-forward type".

The first half of the upstrQke Up la showed a small acceleration rate of only 0.055 m 2, but the second half as well as upstroke Up lb were associated with acceleration rates of 0.470.and 0.420 m s2 respective-ly.

During intermediate phase In 1 the fish decelerated at a rate of -0.250 m s2.

U, was positive during downstrokes and negative during upstrokes. Figs. 2, 3, 4 also showthe fin tipvelocity in x and y directions relative

to the body, (V-U) and (V-U) respectively, and reveal the

rela-tionship between movements of the fin in x and y direction. During the downstrokes (VU) is negative, whereas (V-U) changes from

0.08- 0.07-0.06- 0.4- 005- 0.3- 0.04- 0.1-0.01 0 0 -0.01

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Fig. 3. As for fig. 2; film shot 2.

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524 P.J. GEERLINK

negative to positive values. The reverse can be said for the upstrokes. The changes during the intermediate phase are relatively small.

In film shot 2 (fig. 3) the downstroke Do 2 is of the

"forward-downward type". The first

half shows a slight decrease of U

(a= -0.014 m s-2), during the second half U increases (a=0078 m

s-2).

This increase persists during the following upstroke Up 2

(a=

0.078 m s2). The intermediate phase In 2is also associated with

a slight acceleration (ax = 0.022 m s-2), maybe because water is

squirted backwards between the body wall and the fin membrane. U,, is negative during the first half of the downstroke Do 2, and

becomes positive only in the second half. During upstroke Up 2 U,, decreases and becomes negative only in the last part of Up 2. During intermediate phaseIn2 it remains negative. The right fin is

apparent-ly beating simultaneousapparent-ly with the left fin, but aj * R. for most film frames. (V-U) is positive during the whole of downstrokeDo

2 and

(V-U) is negative, but to a varying degree.

Downstroke Do 3a(fig.4) is of the "downward-forward type" and is

associated with acceleration (a = 0.095 m s2), and only in the last

part with a deceleration (ax = -0.0 14 m s2). The fins were beating alternately, however:, the acceleration might be due to the action of an upstroke of the contralateral fin. During upstroke Up3a a strong

ac-celeration occurs (a = 0.5 10 m s2) which is followed by a deac-celeration during the intermediate phase In 3. During downstroke Do 3b the

deceleration continues (a= -0.115 m s2). The contralateral fin pro-bably changes from an alternating into a simultaneous movement which occurs during upstroke Up 3b. This upstroke is associated with

acceleration (a =0.280m s2). (V-U) is negative in the beginning of

downstrokeDo 3a, and then becomes positive, and remains so during

the first part of upstroke Up 3a. It is positive during intermediate

phaseIn 3and downstrokeDo 3b, and becomes negative just before the

start of upstroke Up 3b.

Summarizing the data of figs. 2, 3 and4we can say that various

ac-celeration and deac-celeration rates in the x direction were measured Most downstrokes of the left, pectoral Un. were accompanied by

deceleration, but in some cases(Do 2 andDo 3a)acceleration occurred

during parts of the downstrokes. During the upstrokes always an ac-celeration took place. The intermediate phase was accompanied either by deceleration or acceleration.

U,, can be expected to be positive during downstrokes and negative during upstrokes. Film shot 1 (fig. 2) is a good example of this

phenomenon, but in shot 2 (fig. 3) and 3 (fig. 4) this is not consistent.

Generally, negative values for (V-U) are associated with positive values for (V-U); the fin tip moves downward and forward during downstrokes, but sometimes negative values for (V-U) occur during the first part of the downstroke. The transition from one phase into another had to be established somewhat arbitrarily. The flexibility of the fin rays allows the proximal part of the rays to change their direc-tion of movement, whereas the tip still moves the other way. The upstroke is characterized by an upward-backward movement. Shot 1 shows some irregularities where the tip moves forward during part of the upstroke.

During intermediate phases (V-U) is close to 0, because then the anterior border of the fin is about parallel to the film plane. (V-U) was positive during In 2 and In 3, but negative during most of In 1..

Simultaneous as well as alternating movements of the fins could be observed.

Propulsive Forces of Pectoral Fins

The drag coefficient of the body (with the fins in passive position), Cd, was calculated from two filmshots, during which the fish was coasting with the pectoral fins in upright position against the body wall. The calculated deceleration rates were:

a= -4.8x 10-2 m s2(U= 0.130 ms-1, U, decreasing

from 0.150 to 0.110 m s-i)

and

a= -7.5 x 102 rn s2 (U,1= 0.175 m s-i, U decreasing from 0.195 to 0.155 m s-i)

The total drag for a coasting fish is:

- Ma= V2

SU Cd

(1)

(where M is the mass of the fish, a is the acceleration rate, is the density of the surrounding water (1024 kg m3), S is the wetted surface area (9.63 x 103 m2).

Cd was calculated to be 0.024 and 0.028 respectively. (In the calculations of table I the average value of 0.026 is used.) Theoretical drag coefficients can be calculated using HOERNER'S (1965) equations:

(where Cf is the coefficient of frictional drag, Re is the Reynolds number, L is the length of the fish, d is the mean of depth and width of the fish).

Cf lam 1.33 Re°5 (2)

Cf turb= 0.072 Re-0.2 (3)

526 P. J. GEERLINK

These equations treat the fish as a rigid streamlined body of revolu tion and give:

Cd lam = 0.012, Cd turb = 0.012 for U, = 0.130 m

s-C1O.0lO, CdturbO.Ol2 for U=0.175 ms-1

which is about half the measured value.

The corresponding Reynolds numbers were 1.8 x 10 and 2.4 x 10 respectively, defined on the basis of the snout-tail length of the fish. No definite prediction can be made whether the flow around the fish is laminar or turbulent. The theoretical Cd values for these two situa-tions hardly differ.

When the fish accelerates or decelerates, the total propulsive force F generated by the two pectoral fins can be calculated as the sum of the net propulsive force working on the body, and the drag on the body and the pectoral fins:

F= M.a+ 1/2 Q S Uc Cd+ Dpect.fins (5)

The net propulsive force generated by the pectoral fins can be express-ed as:

F = FDpect fins

Table I shows the calculated F values for (parts of) downstrokes, upstrokes and intermediate phases.

During the downstrokes positive as well as negative values of F oc-cur. In the case of Do la, lb and 3b a negative F was measured. These downstrokes were, as far

as could be

seen, accompanied by simultaneous dowristrokes of the contralateral fin. The effect of Do 2 was obscured by a slight stretching of the tail, which could possibly contribute to body propulsion. During Do 3a the contralateral fin

made an upstroke. The results

suggest, that downstrokes are

associated with a negative F of different magnitudes.

The upstrokes were all associated with positive values of F, though again of different magnitudes. The lowest value for the two pectoral fins together was 0.323 x 10-2 N (Up la), the highest for one fin

2.645x 10-2 N (Up 3a). Nomovement of the tail could be detected.

In two cases the intermediate phase shows a negative net propulsive fOrce (In 1, In3).There is not sufficient evidence that the contralateral fin was in the intermediate phase as well in these cases. One in-termediate phase (In 2) showed a positive F. It was not accompanied with an upstroke of the contralateral fin, nor with any detectable movement of other fins. The only explanation is a propulsive effect due to a jet of water squirting between fin and body wall.

The complex fin shapes during various parts of the fin strokes of-fered no opportunity to describe trajectories for blade elements of the

TABLE I

Values for body drag (Db) and net drag or propulsive force working on the pectoral fins (Fe)

during parts of the stroke.

Stroke U U,JL Re _x104 a ms-2 -+ M. ax N -+ Db (for 0.026) N F = M. ax + Db N -+ Do Ia Do lb Do 2 Do 3a Do3b Up Ia Up lb Up 2 Up 3a Up3b In 1 In 2 In 3 0.064 0.054 0.066 0.072 0.077 0.078 0.101 0.063 0.078 0.056 0.084 0.097 0.100 0.078 0.091 0.106 0.42 0.36 0.43 0.47 0.51 0.51 0.66 0.41 0.51 0.37 0.55 0.64 0.66 0.51 0.60 0.70 0.89 0.75 0.91 1.00 1.07 1.08 1.39 0.87 1.08 0.77 1.17 1.34 1.38 108 1.25 1.46 0.066 0.280 0.014 0.078 0.095 0.015 0.115 0.055 0.470 0.420 0.078 0.510 0.280 0.250 0.022 0.260 0.00327 0.01386 0.00069 0.00074 0.00569 0.01238 0.0 1287 0.00386 0.00470 0.00272 0.02327 0.02079 0.00386 0.02525 0.01386 0.00109 000053 0.00037 0.00056 0.00066 000076 0.00078 0.00131 0.00051 0.00078 0.00040 0.00090 0.00121 0.00128 0.00078 0.00106 0.00144 0.00274 0.01349 0.00013 0.00438 0.01160 0.01143 0.00453 0.00546 0.00004 0.00323 0.02404 0.021 19 0.00477 0.02645 0.01514 0.002 15

528 P. J. GEERLINK

fin. Only for the tip a trajectory could be described and the fin

velocities calculated. Therefore no direct hydrodynamic calculations could be made from fin movements.

The error in the calculated velocities was estimated in two ways. For one film shot the whole analysis was executed three times. Com-parison of the three U, curves showed, that the differences between U, values for each film frame varied between 0.0 and0.008

m s. It was

possible to estimate the errors made while plotting each individual frame. From these estimates the calculated resulting error for U, values was not significantly different from the result of the first ap-proach. So the error is assumed to be no more than about ±0.008 m

s-i.

DISCUSSION

WEBB (1973) reported for Cymatogater aggregata a positive angle of

at-tack during the downstroke and a resulting propulsive effect. Because of the complexity of the fin shape during various parts of the fin move-ment, it can not be concluded whether any part of the fin of Cons for-mosa has a positive angle of attack during the downstroke, nor what the simultaneous influence of other parts of the fin will be. The data in this

paper suggest that there is no net prosulvive effect during the

downstroke. BLAKE (1980)described for Pterophyllum eimekei a

horizon-tal forward recovery stroke, the pectoral fin being in a feathered posi-tion, only exerting drag forces. In C. formosa the downstroke or recovery stroke always contains a vertical component, and the fin can not be compared with a flat plate.

The upstroke of C. formosa shows only little resemblance with the

rowing movement described byBLAKE (1979) for P. eimekei, because it

has a vertical component and it shows a phase difference between suc-cessive rays. Even when the anterior and posterior rays are in phase the interjacent rays lag behind. The fin has a variable cup shape and again can not be compared with a flat plate. This means that force calculations considering the fin as a flat plate result in values which are

too low, because a hollow profile is associated with a higher drag coef-ficient than a flat plate at Reynolds numbers between 10 and 106

(HOERNER, 1965: 3-17). There is no disagreement about the presence

of a propulsive effect of the upstroke (or adduction phase) (WEBB,

1973; BLAKE, 1979; this paper). This paper provides some evidence for

a possible jet propulsion effect during the intermediate phase due to water being squirted out of the decreasing space between fin and body wall. The same conclusion was reached by WEBB (1973) for the

530 P. J. GEERLINK

The empirically determined drag coefficient for the body of the fish, Cd, was found to be twice as high as the theoretical one (table II). This is consistent with the findings of VIDELER (1981) for a gliding cod (Gadus morhua). WEBB (1975a, b)suggested that the body drag could be close to the theoretical value if the body was kept straight. From data for trout the.effect of fin fluttering was calculated by WEBB (1975b) as 0.34 x theoretical drag. This factor is not sufficient to explain,

however, the high value of Cd for cod and, C. formosa. Apparently the formula for the drag coefficients of rigid streamlined bodies is not ap-propriate for slender bodies of live fish.

For lower values of U, than those for which the experimental Cd was calculated we can estimate Cd by extrapolation if we assume from (2) and (3) that Cd lim aU05 and Cd turb aUo2. This was done for

U= 0.04 m s-1

(table II). The data shown in table I are not

significantly different when these extrapolated values of Cd are used. The versatile movements of the pectoral fin of C. formosa frustrate direct hydrodynamic calculations. Reduction of the fin toa flat plate and simplication of the movements violate the real process to such ri

extent that results must deviate from reality. Accurate description of the behavioürof the fins and of the resulting movements of the body give more realistic information about the function of the pectoral fins in locomotion.

ACKNOWLEDGEMENTS

I wish to thank Dr. J. J. Videler and an anonymous referee for their critical comments on the manuscript and their valuable suggestions. I thank Mrs. H: H. Videler-Verheijen for her stylistic support. I also

express my thanks to Mrs. J. Poelstra-Hiddinga for typing the

manuscript.

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angel-fish. -J. exp. Biol. 85: 337-342.

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Town, N.J., U.S.A.

LINDSEY, C. C., 1978. Form, function and locomotory habits in fish. In: W. S. HOAR & D. J. RANDALL (Eds): Fish Physiology, vol. VII: pg. 1-100. Acad. Press, New York.

VIDELER, J.J., 1977. Mechanical properties of fish tail joints. In: W. NACHTJGALL (Eds): Fortschritle der Zoologie, Band 24, Heft 2/3. Gustav Fisher Verlag,

Stuttgart/New York.

VIDELER, J. J., 1981. Swimming movements, body structure and propulsion in Cod

Gadus morhua. - Symp. zool. Soc. Lond. 48: 1-27.

WEBB, P. W., 1973. Kinematics of pectoral fin propulsion in Cymatogoster aggregata. -J. exp. Biol. 59: 697-710.

WEBB, P. W., 1975a. Hydrodynamics and energetics of fish propulsion. - Bull. Fish. Res. Bd. Can. 190: 159 pp.

WEBB, P. W., 1975b. Efficiency of pectoral-fm propulsion of Cymatogaster aggregata. In: T. Y. T. Wu, C. J. BROKAW, C. BRENNEN (Eds). Swimming and flying in nature: 573-584. Plenum Press, New York.

WEBB, P. W., 1978. Hydrodynamics: non-scombroid fish. In: W. S. HOAR, D. J. RANDALL (Eds): Fish Physiology Vol. VII: 189-237. Acad. Press, New York.

SYMBOLS

a acceleration rate in x-direction Cd coefficient of body drag

Cf coefficient of frictional body drag

Cf lam coefficient of frictional body drag for laminar flow

Cf turb coefficient of frictional body drag for turbulent flow d mean of depth and width

Do downstroke

net drag or propulsive force of pectoral fins In intermediate phase

L fish length M mass of the fish Re Reynolds number

Q density of surrounding water

5 wetted surface area Up upstroke

body velocity in x-direction average of U

U, body velocity in y-direction velocity of fin tip in x-direction V,, velocity of fin tip in y-direction