AMER. ZOOL., 17:343-354 (1977).
Body Form and Locomotion in Sharks
KEITH STEWART THOMSON AND
DAN E. SIMANEK
Department of Biology and Peabody Museum of Natural History, Yale University,
New Haven, Connecticut 06520
SYNOPSIS. A revised interpretation of the mode of action of the heterocercal tail in sharks
shows that the upturned tail axis tends to produce a thrust directed downwards behind the
centre of balance of the fish and thus gives a moment turning the head upwards. This is
countered in two ways—by the rotation of the tail along its longitudinal axis during each
lateral beat, and through the action of the ventral hypochordal lobe. The shape of the tail
and the mode of action of the tail in all sharks so far considered reflects a balance between
these three factors, in all of them the net effect being the production of a forward thrust
from the tail that passes directly through the centre of balance of the fiish. There is
normally therefore no tendency for the fish to turn around the centre of balance in a
sagittal plane but there is a net sinking effect that is countered by the planning effect of the
pectoral fins and the ventral surface of the head.
A study of 56 species of sharks shows that the tail is constructed according to a
remarkably consistent common plan, the extremes being the high angled rather symmetrical tail of pelagic sharks such as hums, Lamna and Rhincodon and the straight tails of
benthic sharks such as Ginglymostoma in which a ventral hypochordal lobe is absent. When
the general body shape of sharks, including the position of insertion of the median and
paired fins and the pattern of growth of fin surface areas is considered, the uniformity of
the shark body plan and locomolor function is further emphasised.
Four patterns of body form in sharks are recognised: 1) The fast swimming pelagic
sharks and the whale sharks have a tail with a high aspect ratio, a conical head, a lateral
fluke on the caudal peduncle. 2) The generalised sharks typified by the Carcharhinidae,
have lower heterocercal angles, a flattened ventral surface on the head and lack the caudal
fluke. 3) The demersal sharks typified by the catsharks (Scyliorhinidae) have a very low,
almost straight tail. The ventral hypochordal lobe is absent and the first dorsal fin is
posterior in position. 4) The squalomorph sharks are distinct in the absence of the anal fin,
presence of a marked epicaudal lobe in the tail and often an elevated insertion of the
pectorals.
The anal and second dorsal fins are always the smallest fins and the pectorals grow at the
fastest rate. In general there is an inverse relationship between size and rale of growth of
all fins and the ventral surface of the head. In hammerheads the growth data confirms that
the head has a significant planing action in swimming. The pectoral, second dorsal and
anal fins show an extreme constancy of position of insertion in all sharks studied. The
locomotor mechanism of sharks is adapted for an efficient cruising swimming but at the
same time, the potential instability in the sagittal plan allows for the production of turning
moments that are used in attack and feeding.
INTRODUCTION
In all the great fasc.nat.on that sharks
have for man what strikes us most forcibly
We are grateful to Professor Karel Liem of the
Museum of Comparative Zoology and Dr. Donn
Rosen of the American Museum of Natural History
for permission to study specimens in their care.
Walter Dunwiddie, Karin Muraszko and loan Darling
gave technical assistance. Linda Price Thomson preg
pared the illustrations. Studies supported by NSF
grant BMS 74-07759.
j s n o t t h e feeding behavior, much as it is
promoted in the nopular press; the most
v i v i d i r n p r e s s i o n t h a t one gets of any enc o u n t e r w i t n a shark is of the ease and
grace, the latent power of his swimming.
Dolphins are superb swimmers, as are
marlin, tuna, barracuda or pike, but they
seem to reveal their exertions in their gait,
T h e y are like racehorses in a magnificent
,,
cu i
.u
,u
u A -^- I;L-«,
S a l l °P- S h a r k s > O n t h e o t . h e r h a n d ' *™ l l k e
sinuous torpedoes, moving apparently etfortlessly through the water.
343
344
KEITH STEWART THOMSON AND DAN E. SIMANEK
All this may, of course, be a subjective
impression that we owe subconsciously to
popular myth and legend. But it certainly
is the case that shark swimming has long
been a subject of interest to the scientist
and layman alike. Here we would like to
examine some of the basic mechanisms of
shark swimming and to examine different
plans of body shape in sharks in terms of
functional considerations. We cannot explain those subtleties upon which we base
our aesthetic judgements of shark swimming but we hope to outline their
biomechanical foundation.
In the discussion that follows, the group
of sharks from which we have drawn data
is that described by Bigelow and Schroeder
(1948) in the classic volume The Fishes of the
Western North Atlantic, Volume 1. We have
not considered the squatinoids, which have
a very different body form from the "typical" sharks that we wish to discuss. The
reason for this choice is not only that these
are the best known sharks in terms of
external morphology and also those sharks
of which most specimens are readily available to the authors, but also because the
information on the general biology and
life histories is more uniform and complete than for any other group of sharks
that could be chosen.
NM
STL
het
FIG. 1. Idealised shark tail showing the upturned
notochordal axis (NM), the ventral (VHL) and longitudinal (LHL) hypochordal lobes, the subterminal
lobe (STL) and the heterocercal (het) and hypochordal (hyp) angles.
liver a symmetrical thrust and the fish
swim on an even keel, or, if the thrust is
asymmetrical it is necessary to describe this
exactly and then to see how it is balanced
by forces produced elsewhere in the fish.
The standard view has always been that
the heterocercal tail produces a forward
thrust that is directed in a line passing
above the centre of balance of the fish (the
actual angle proposed varies widely). Such
a line of thrust would produce a turning
moment around the centre of balance that
would tend to raise the tail and drive the
head downward in forward swimming.
This epibatic moment, according to the
standard account {e.g., Alexander, 1965) is
countered by vertical forces generated by
THE HETEROCERCAL TAIL
the pectoral fins and the inclined plane of
Every student in an introductory biology the "throat" region, acting in front of the
course learns that the sharks have a special centre of balance (Fig. 2). The net upward
type of asymmetrical tail called heteroceral components must then be balanced by the
with an upturned notochordal axis (Fig. 1). weight of the fish in water.
The same tail is found in early fossil representatives of most major groups of
fishes, but the Chondrichthyes are the only
group to have retained it intact for 350
million years. An understanding of the
heterocercal tail is fundamental to any
treatment of shark locomotion.
The mechanical significance of the
heterocercal tail has been discussed many FIG. 2. Standard model of shark swimming. The tail
times in the past: Breder (1926), Gray is thought to produce a net lifting effect (L) which
(1933), Grove and Newell (1936), Affleck causes a turning moment (here anti-clockwise)
(1950), Alexander (1965), Aleev (1963), around the centre of balance (CB). This moment is
by the planing effects of the pectoral fins (P)
Simons (1970) and Thomson (1971, 1976). opposed
and the ventral surface of the head (H). The comThe central problem has always been to bined vertical forces are thought to be opposed by the
discover how an asymmetrical tail can de- weight of the fish in water (W).
345
SHARK LOCOMOTION
There are several features of this model
that strike one intuitively as unsatisfactory.
For example, the vertical components will
vary in magnitude with the forward speed,
while the weight remains constant. Further, many sharks have recently been shown
to be effectively weightless in water due to
accumulation of tissue water and liver oils
(Bone and Roberts, 1969; Baldridge, 1970,
1972; Corner, et al. 1969). And, as the
magnitude of the turning moment produced by the tail will increase with the
forward speed, the opposing action of the
pectoral fins, if it causes any drag, will
produce more drag just when drag ought
to be kept to a minimum.
A recent study of the problem (Thomson, 1976) starts with the familiar point
that the forces acting in the tail can be
separated into two distinct components—
forward (F) and transverse (T)—during
each lateral beat of the tail (Fig. 3). The
forward component is necessarily directed
downwards in sharks because of the
heterocercal angle (Fig. 4A). This is clearly
shown by Affleck (1950). Any upward
component of thrust produced by the tail
must come from rotation of the tail along
its long axis (as predicted in the standard
account), but is separately generated, coming from the transverse component (T) of
the tail thrust alone (Fig. 4B). In order to
understand the balance between the various forces acting within the tail it is therefore necessary to know the magnitudes of
the angles by which the tail is upturned
(the heterocercal angle het) and by which it
is rotated during each beat (angle rot, Fig.
4), together with the relative magnitudes
of the forward and transverse thrusts produced in the tail.
From the data presented by Gray (1933)
an estimate has been obtained for the
relative magnitudes (and the upper and
lower limits) of forces F and T in swimming sharks. During each lateral stroke of
the tail the ratio F:T changes, as the lateral
speed of the tail and angle of inclination 9
change. The maximum value of F:T in the
main dorsal portion of the tail is in the region
of 2.10. In the ventral lobe of the tail,
which can for the purposes of analysis be
considered a separate fin (see discussion
FIG. 3. Schematic drawing of a tail in dorsal view to
show the resolution of the oblique thrust (Q) and its
resultant (R) into forward (F) and transverse (T)
components of thrust, the value of which are related
according to the angle of inclination 8.
below), the maximum value of F:T is 2.68.
The average values for F:T over one complete dorsal stroke are 1.85 for the upper
lobe and 1.50 for the ventral lobe.
It must be emphasised that the ratio F:T
does not change with the heterocercal
angle or the angle of rotation. However,
the vertical components of force produced
by the tail will be a direct function of the
heterocercal angle (downward component) and angle of rotation (upward component). The fact that F is always greater
than T means that the range of values for
the upward component of force (from T)
will tend to be less than that for the downward component (from F).
We can add to the calculation of F and
T, data on the angles of rotation (from
motion pictures of living sharks) and the
heterocercal angles readily obtained from
properly preserved museum specimens),
and can work out the balance between the
four sets of force components shown in
Figure 4 as F, F', A and B (see Thomson,
A-F»nhet
B
FIG. 4. A Side view of shark tail to show the resolution of the forward thrust (F) which is directed
downwards by the heterocercal angle (het), into horizontal (F') and vertical (A) components. B Rear view
of shark tail to show resolution of the transverse
thrust (T) into horizontal (T') and vertical (B) components when the tail is rotated along its long axis by
angle rot.
346
KEITH STEWART THOMSON AND DAN E. SIMANEK
1976, e.g., Fig. 3, for more elaborate
analysis). We can also predict that the
greatest possible angle of rotation is 45°.
Simple geometry and elementary
mechanics show that the optimal line of
net thrust from the tail would be one
passing directly through the centre of balance of the fish. This would eliminate any
turning moments in the sagittal plane and
would thus reduce to a bare minimum the
drag from production of lift by the pectoral fins. It would be the most stable
swimming configuration. We can calculate
a simple equation that would give such a
line of thrust. We can define an angle of
elevation (elD) which is the angle between
the line from the centre of effort of the
principal, dorsal, lobe of the tail to the
centre of balance and the horizontal. (The
centre of effort is difficult to measure
accurately on any shark but given the
distance between the tail and the centre of
balance, the angle of elevation is always
small and errors in its estimation can be
tolerated.) This angle also defines a dorsal
thrust angle (thD, Fig. 5). For the forces
acting in the upper lobe of the tail to
produce a net thrust aimed through the
centre of balance, the following balance of
forces is needed:
FIG. 5 Lateral view of shark to show the line of
"balanced" thrust from the centre of effort of the tail
(C of E) to the centre of balance of the fish (C of B).
Also shown are the dorsal angle of elevation (elD), the
dorsal thrust angle (thD) and the heterocercal angle
(het).
tail. It has its own ventral thrust angle and
its action is exactly opposite that of the
dorsal lobe of the tail. The values of F:T
are higher in this lobe, as we have seen, but
its area and transverse speed are less and
the forces generated in it are therefore
smaller. Its action is to modify the line of
action of the dorsal lobe, specifically so that
the net line of thrust from the whole tail
can be brought back "in balance" through
the centre of balance. This is accomplished
in two ways—by a lowering of the centre
of effort of the whole tail and by production of a modifying line of thrust that
passes upwards behind the centre of balD
F tan Th = T' tan rot
ance. The ventral lope is thus a "trimThis equation allows us to calculate a ming" device.
table of values of F:T and the angles of
This model of tail action can be tested by
rotation and thrust that would give such a predictions arising from the above ac"balanced thrust." This table then allows us count. 1) The ventral hypochordal lobe is a
to discuss the mechanics of the shark tail. necessity in sharks with a dorsal thrust
According to this model, a fully balanced angle of more than 26° (heterocercal angle
thrust from the dorsal lobe of the tail alone more than 33°). 2) A ventral hypochordal
is only possible at thrust angles of less than lobe would be extremely useful at lower
26° (equivalent to heterocercal angles of ranges, say 15° to 26°, because it would
less than 33°). At values of the thrust angle reduce the angle of rotation needed for
and heterocercal angle above those given, "balance." 3) Similar consideration of the
or at lower angles of rotation, an addi- epicaudal lobe (developed in squalomorph
tional balancing factor is needed or else sharks, for instance) which greatly dethe line of action must necessarily pass creases the possibility of generating strong
behind the centre of balance and thus upward force components in the tail, make
produce a moment forcing the head up- us predict that a ventral hypochordal lobe
wards (this is an unexpected contradiction is essential if there is an epicaudal lobe. 4)
of the 'standard account). This additional We can also predict that the theoretical
factor is, of course, produced by the vent- maximum dorsal thrust angle must be
ral hypochordal lobe which, where pre- close to 26° and that beyond this point, the
sent, forms the distinct ventral lobe of the- tail should move to a different configura-
SHARK LOCOMOTION
tion and a different mode of action. 5)
Finally, the model predicts that for optimal
effect, the centre of effort of the tail, the
centre of balance and the pectoral fin
insertions should lie close to the same
plane so as to minimise vertical turning
moments in swimming.
All these predictions seem to be borne
out by the data presently available. In any
case, they are now available to be tested in
the future and the model of heterocercal
tail action can be modified if necessary. A
survey of shark body types (Thomson,
1976) shows that tail construction is remarkably uniform. Of 56 species of sharks
measured only 5 had dorsal thrust angles
exceeding 30° (heterocercal angles between 32° in Carcharhinus milberti and 51° in
Rhincodon). In these forms the tail has a
high aspect ratio and narrow caudal
peduncle and probably works in the same
manner to the superficially similar tails of
scombroid teleosts (see Webb, 1975, for an
excellent review of tail structure and function). Ventral hypochordal lobes are absent in many fishes but are absent in none
in which the dorsal thrust angle exceeds
18°. A ventral hypochordal lobe is present
in all forms with an epicaudal lobe. Predictions 4 and 5 are more difficult to test but
seem to be confirmed by the data available.
When we compare the mode of action of
the tail in sharks of different types, some
important new features show up. As
shown elsewhere (Thomson, 1976; cf., Simons, 1970), the ventral hypochordal lobe
moves to a leading position during the
later parts of each transverse beat. This is
due in part to the fact that the ventral
hypochordal lobe is inserted in front of the
main part of the tail and thus finishes its
transverse stroke before the rest of the tail.
In posterior view this gives the effect of
leading. However, the same sort of effect is
seen in the anterior ventral parts of the
longitudinal hypochordal lobe in the nurse
shark. In part this may reflect the action of
the ventral hypochordal lobe (or its equivalent) in trimming the thrust produced by
the dorsal part of the tail, particularly as
the ratio F:T changes at the end of each
stroke. But it may also reflect a more simple
mechanical matter—for the tails of all
347
fishes, symmetrical or asymmetrical, seem
to assume this concave shape. As the tail
moves through the water, it may be most
efficient for it to assume a slightly concave
shape so that it pushes backwards a "tube"
(or section of a tube) of water, rather than
a convex shape from which water may
"spill" over the dorsal and ventral margins.
Motion picture analysis also shows that
the subterminal lobe always flexes to an
inclined trailing position during each
stroke. We suggest that it acts somewhat
like the tail of a kite, passively helping the
fish maintain the correct angle of rotation
along the whole of the caudal fin and
protecting the tip of the fin from fluttering. It is significant that the subterminal
lobe is reduced or lost in forms with a very
high dorsal thrust angle presumably because, in these forms, a balance of forces
acting within the tail as a whole is a balance
between dorsal and ventral lobes rather
than a balance of forces principally within
the upper lobe. In forms with a lower
dorsal thrust angle, a subterminal lobe
would be essential and this is confirmed in
a survey of shark tail shapes (Thomson,
1976, Fig. 14).
From a review of shark tail structure it is
clear that all sharks, even those with very
high values of dorsal thrust angle, have an
extremely similar type of tail and the differences among sharks essentially represent variations within a single common
theme. Within this common theme we can
identify four different extremes of tail
development (Fig. 6); most sharks falling
into somewhat intermediate positions.
1) A high aspect ratio tail with a narrow
caudal peduncle and high heterocercal
and hypochordal angles (high total angle),
the subterminal lobe is reduced or absent.
This is characteristic of large pelagic
sharks feeding near the surface and capable of high swimming speeds. 2) A moderate heterocercal angle (between 12° and
24°) equivalent to dorsal thrust angles between 10° and 18°, a well-developed ventral
hypochordal lobe, a moderate to welldeveloped subterminal lobe. Such a tail is
characteristic of Family Carcharhinidae. 3)
A tail with a very low dorsal thrust angle,
little or no separate ventral hypochordal
348
KEITH STEWART THOMSON AND DAN E. SIMANEK
H
FIG. 6. Drawings of four different patterns of shark Ginglymostoma cirratum; LScyliorhinus boa; M Aprislurus
tail architecture, as defined in the text. A Lamna profundorum; N Pseudotnakis mtcrodon; O Mustelxts
nasus; B Isurus oxynnchus; C Carcharodon carcharias; D canis; P Squalus acanthias; Q Centroscylhum fabncii; R
Celorhinus maximus; E Rhincodon typus; F Carcharias Etmopterus hilhanus; S Centroscymnus coelolepis; T histius
laurus; G Galeocerdo cuvieri; H Scolwdon terrae-novae; I brasiliensis. (All after Bigelow and Schroeder, 1948).
Negaprion brevirostns, J Carcharhinus falciformis; K
lobe, usually a large longitudinal lobe. This tures of the body. Here we present addiis characteristic of demersal sharks such as tional data on the position of insertion of
the nurse shark Ginglymostoma. 4) The tail the median and paired fins, the surface
in squaloid sharks is characteristic in the areas of these fins and of the ventral represence of a well-developed epicaudal gion of the head, and the rates of growth
lobe, moderate to low dorsal thrust angles, of these surfaces.
a moderately well-developed ventral
The first result of such a survey is that
hypochordal lobe and the subterminal lobe the positions of the fin insertions are exis either large or not well separated from tremely consistent within a given species
the rest of the dorsal tail structure. There and do not change with absolute size
is usually only a small longitudinal (length) of the fish. Secondly, the range of
hypochordal lobe. The squatinoid tail (not possible positions of insertion for the five
considered here) would represent a fifth sets of fins (first dorsal, second dorsal,
pattern—with a straight notochordal axis. pectoral, pelvic and anal) is remarkably
small (Fig. 7). The positions of insertion of
the pelvics and anals are particularly conSHARK BODY PLANS
stant within the 56 sharks surveyed (note
The next logical step in an analysis of that in two sharks, Hexanchus and Heptranshark body form is to attempt to correlate chias, the second dorsal is absent and the
characters of tail structure with other fea- anal is absent in all squaloids).
349
SHARK LOCOMOTION
Carchariui taurui
FIG. 7. Schematic drawing to show the relative position of insertion of the first and second dorsal fins,
pectoral, pelvics and anal is 56 species of sharks. The
data are presented as frequency histograms, the horizontal axis showing the relative position along the line
from the tip of the snout to the end of the caudal
peduncle. Drawing of shark superimposed for comparison.
In 12 of the 56 species under consideration, specimens were available spanning a
broad enough body-size range (standard
length range of at least three) to allow
measurements of fin area to be fitted to the
allometric growth curve, y = axb, where
"y" is the fin area, "a" is the proportionality
constant, "x" is the standard length (measured from the tip of the nose to the
insertion of the ventral—or longitudinal-hypochordal lobe), and "b" is the
rate constant for fin growth as a function
of standard length. The growth curves for
the fin areas of each species can be plotted
as straight lines on log-log coordinates as
shown in Figure 8. (The ventral surface
area of the head is included as a "fin" area
measurement.)
The relative order of fin sizes as determined by the growth equations proved to
be quite variable among the species, and
the growth constants, "b," cluster very
close to the value 2 for all fins in all species
(actual range 0.82-2.75). To simplify
analysis of the growth curves each line is
characterised by two parameters. The first
is the coefficient "b," already described.
The second is the x-intercept (Figure 8)
which bears an inverse relation to the
absolute fin area across species. This last
statement is generally true because the
growth lines are so very nearly parallel and
over a realistic range of body sizes there is
little crossing over.
In each species the fin areas were ranked
by the value " b " and then by the
x-intercept. The rank value of each area is
summed across all species for both
= 2.0-
1.0
2.0
Log Standard Length
3.0
FIG. 8. Fin surface area, SA, as a function of Standard Length, SL, for Carchanas laurits: log (SA) = log
(a) + b log (SL). Fin designations: Pc, pectoral; Pv,
pelvic; Dl, first dorsal; D2, second dorsal; A, anal; H,
ventral head surface; H + pc, ventral head surface
plus twice pectoral area.
parameters. The sums of rank order
scores are shown in Table 1. Pectoral fin
surface heads the "b" column. This indicates that, when all species are considered
together, the pectoral surface tends to be
the most consistently fast-growing fin area.
Likewise, ventral head area, at the bottom
of the list, increases more slowly in relation
to the other fin surfaces.
The relative sizes of the fin areas are
indicated by the x-intercept column of
Table 1. Here we see that the anal and
second dorsal are the smallest fins, while
the ventral head surface usually provides
the greatest area.
Rather than grouping the fins by species
one can alternatively look at one fin type
across all species. For this we have plotted
"b" and the x-intercept against each other
and in so doing have reduced the growth
characteristics of each fin of each species to
a single point. The results of this approach
are shown in Table 2 and Fig. 9. The
figure shows that fin size and growth rate
are related to one another in a linear
manner. The information derived from
these plots is that within fin types there
exists an inverse relation between fin size
and growth rate; in other words, large fins
350
KEITH STEWART THOMSON AND DAN E. SIMANEK
tail) parameters used in this study (details
of programs available from the authors
upon request). The bivariate comparisons
show that, over all sharks, high values of
x-intercept
b
the total tail angle of the tail (heterocercal
A
31
Pc
22
plus hypochordal angles) are accompanied
Pv
47
D2
22
by
a forward position of the first dorsal fin
Pv
Dl
52
36
and a posterior position of the pelvics.
52
Pc
51
H + Pc
H
56
D2
73
Lower heterocercal angles with a ventral
64
79
H
H + Pc
hypochordal lobe present are correlated
•Species listed in Figure 9. Within each species the with a relatively anterior position of the
values of the parameters are ranked in ascending second dorsal and relatively posterior posiorder. The rank order score of the parameter for tion of the pectorals and pelvics. However,
each fin type is summed across all specis. (Lowest reduction of the ventral hypochordal lobe
possible score = 12; Highest =84.)
(which only occurs in tails with a low dorsal
thrust
angle) is accompanied by an ingrow more slowly while smaller fins grow
crease
in the longitudinal hypochordal
faster. Fin size and growth rate do not
appear to be a simple function of adult lobe, relatively posterior position of the
first dorsal fin and a more anterior posibody size.
The species points do not cluster into tion of the pelvics.
groups, as might have been expected, but
Multivariate analysis confirms the above
rather they form straight lines, an observa- and also distinguishes four discrete pattion which in itself indicates that a similar terns of body shape that coincide fairly
regime of constraints mediates the fin well with the four extremes of tail shape
growth in all species. That each fin type mentioned above. The 56 species of sharks
plots as a discreet line suggests a strategi- for which data are available break down
cally different role for each fin, but into four groups (Table 3) which correnevertheless, a role which does not change spond well to the four types defined by tail
across species lines.
shape alone (cf., Klausewitz, 1962):
Group 1 (Fig. 10A) consists of sharks
Figure 9 shows that certain species occur
predominately in the upper or lower re- with a high aspect ratio caudal fin and high
gion of each fin plot. It would be interesting values of the dorsal thrust angle and
to relate this distribution of fin characteris- heterocercal angle. In terms of body protics to the factors of swimming dynamics portions these fishes are not significantly
such as size-weight and size-buoyancy rela- different from the sharks of the next
tions, center of balance, and angle of tail groups except in two important aspects.
thrust. This is not presently possible. The body is extremely deep in these sharks
However, it may be instructive to note and the caudal peduncle bears the lateral
the interplay of ventral head area and fluke that is characteristic of all vertebrates
pectoral fin area in the two species of with a high aspect ratio tail and narrow
hammerhead—Sphyrna tiburo and S. caudal peduncle (scombroid fishes and
zygaena. S. tiburo has the larger head area dolphins, for example). The head is coniand a smaller total pectoral fin area but the cal and not prominently flattened ventralcombined area of head and pectoral fins is
virtually the same for both species. This
Group 2 (Fig. 10B) is obviously closely
may confirm the importance of the head similar to group 1, but is characterised by
and pectoral fins as planing surfaces and significantly lower heterocercal angles in
adds a swimming function to the sig- the tail. The body is less deep, the caudal
nificance of the "hammerhead" design.
fluke is absent. The head is more blunt
A series of bivariate and multivariate than in group 1 sharks and the ventral
(principal components) analyses were surface is very much flattened. Sharks in
made in order to test for correlations both groups 1 and 2 have very large pecamong the various body shape (trunk and toral fins.
TABLE 1. Sums of rank order values for the parameters "b"
and "x-intercept" as calculated for twelve species of
sharks. *
,,
351
SHARK LOCOMOTION
TABLE 2. Regressions for growth rate, b, on fin surface area, SA:b = a(SA) + c*
a
c
r
P
Pv
Pc
3.15
-1.79
0.86
0.001
2.75
-0.52
0.86
0.001
A
3.27
-2.50
0.51
>0.10
D2
3.05
-2.43
0.53
>0.10
Dl
1.79
0.18
0.94
0.001
H
H +Pc
1.58
0.94
0.91
0.001
1.60
1.12
0.93
0.001
* The values reported are based on the twelve species of Figure 9. The equations for fins A and D2 are not
statistically significant and do not appear in Figure 9.
Group 3 (Fig. IOC) consists of sharks Etmopterus, Isistius and Somniosus have parwith a very low tail, a small to absent ticularly high pectoral insertions and this is
ventral hypochordal lobe, large longitudi- interpreted as evidence that the tail is
nal hypochordal lobe, and a large subterm- delivering a horizontal thrust from a centre
inal lobe. In addition, the pelvic fins are of effort on a horizontal plane with the
inserted significantly more anteriorly than centre of balance (see also Thomson, 1976).
in any other group of sharks and the first
In the above scheme the following
dorsal is inserted significantly further sharks do not fit well: Hexanchus, Heptranback. The head is very large and the snout chias, Paragaleus and Alopias. T h e first two
is blunt.
fall in with the group 3 sharks on many
Group 4 (Fig. 10D) is distinguished by multivariate plots, but are, of course, disthe fact that the anal fin is totally lacking. tinct because of their lack of the second
These are the squaloid sharks. The dorsal fin and the presence of a ventral
squaloids are further characterised by a hypochordal lobe in the tail which sigtail with a large epicaudal lobe. In all this nificantly increases the total tail angle.
group the pectoral fin gives the impression Paragaleus essentially falls with the sharks
of being inserted somewhat higher up the in group 2, but is distinguished by a lower
flank, more in line with the external heterocercal angle. Alopias obviously can
branchial openings than in any other be made to stand apart from any other
sharks. Centrolepis, Centroscymnus, Dalatias, shark but in most respects is remarkably
3.0-.
2.5-
2.5-
2.0-
2.0-
1.5-
1.5-
1.0
1.0
.5
1.0
X Intercept
1.5
FIG. 9. Fin growth rate as a function of fin size. Fin
size across species is estimated by use of the
x-intercept of the growth equation for the particular
fin-species combination. See text. Species plotted: 1,
Sphyrna tiburo; 2, Mustelus canis; 3, Scoliodon terrae-
1.0
X Intercept
1.5
novae; 4, Carcharinus limbatus; 5, Sphyrna zygaena; 6,
Prionace glauca; 1, Carcharinus falciformis; 8, Carcharinus obscurus; 9, Carchanus taurus; 10, Alopias vulpinus; 11, Gateocerdo cuvier; 12, Carcharinus teucas.
352
KEITH STEWART THOMSON AND DAN E. SIMANEK
TABLE 3. List of shark by genus in the four groups defined in the text on the basis of general body and tail shape.
Group 1
Carcharodon
Cetorhinus
Isurus
Lamna
Rhincodon
Group 2
Group 3
Group 4
Alopias
Aprionodon
Carchanas
Carcharhinus
GaUocerdo
Hypoprton
Negapnon
Paragaleus
Prionace
Scoliodon
Sphyrna
Apristurus
Galeus
Ginglymostoma
Mustelus
Pseudotriakis
Scyltorhinus
Triakis
Centroscyllium
Centroscymnus
Dalattas
Echinorhinus
Elmopterus
Isistius
Somniosus
Squalus
similar to the group 2 sharks, despite the
elongate tail. Carcharias taurus deserves
special mention as being almost intermediate between groups 1 and 2. Similarly,
of those species placed in group 3, Mustelus
cants most closely approaches those in
group 2.
The four groupings do not equate with
the taxonomic assignments of the fishes
concerned. Comparison with the latest
classifications of sharks (e.g., Campagno,
this volume) will show that patterns 1, 2
and 3 may be developed convergently in
sharks of different major groups. The four
morphological groupings accord better
with differences in mode of life. Group 1
presents a bit of a puzzle because it includes both very fast and rather slow
swimming sharks. They are, however, all
pelagic and all attain relatively large size.
Group 2 shows the body pattern for
generalised feeders and swimmers. Group
3 is basically the pattern of slow swimming
dermersal and benthic sharks. Group 4
sharks are essentially concentrated in
deeper waters and, within this group, the
genus Squalus which is mostly found in
shallower depths can be distinguished by a
tail of higher aspect ratio, more like those
seen in group 2.
The uniformity of position of fin insertion in all sharks is remarkable in the light
of the observed differences in the shapes
of the caudal fins. It seems to be further
confirmation of the hypothesis that all
sharks are capable of producing the same
type of "balanced" thrust from the caudal
fins—i.e., a line of thrust passing through
the centre of balance. One would expect
that the first dorsal fin lies close to the
vertical plane containing the centre of balance and our data fit with published observations of the constancy of the centre of
balance of sharks (Magnan, 1939; Baldridge, 1972). The more posterior position of the first dorsal fin in group 3 sharks
is probably associated with the elongation
of the tail itself. A very curious feature
brought out in this analysis is that, although the squalomorph sharks lack the
anal fin, the position of insertion of the
other fins is essentially the same as in other
sharks. The same is true for Hexanchus and
Heptranchias, which lack the second dorsal.
This serves further to emphasize our lack
of solid information concerning the function of the median and paired fins in
fishes.
DISCUSSION
From our analysis, although it is too
early to attempt a complete explanation,
we believe that it is possible to develop
some useful generalisations concerning tail
shape, body plan and locomotion in
sharks. The presence of the heterocercal
tail gives a potential instability in the sagittal plane while swimming, due to the possibility of producing powerful turning
moments around the centre of balance.
This instability is either a liability or an
asset, depending upon the way one views
it. In terms of making sudden changes of
direction, particularly in a vertical plane,
the system is probably very advantageous.
A shark of group 1 or 2 is specially capable
of using its tail to deliver a very powerful
SHARK LOCOMOTION
turning moment: by reducing the angle of
rotation of the tail it can direct the thrust
in a line behind the centre of balance and
cause the snout to be rotated strongly
upwards. This would be extremely useful
in feeding actions (see for example Moss,
19726, 1977).
By use of the large pectoral fins, such
vertical moments can be changed into
moments turning the fish suddenly in any
direction. At the same time, the fish can
adjust its angles of rotation (in upper and
lower lobes of the tail) to produce a balanced swimming on an even keel. Fishes of
group 2 are probably capable of the most
wide range of swimming speeds among the
sharks, retaining "balance" at all speeds.
There is, however, considerable reason to
suppose that an efficient cruising speed is
the customary mode of locomotion in all
sharks.
Even a "balanced thrust" mechanism of
swimming, as outlined here, requires
compensating actions of the pectoral fins
and ventral head surface. This places some
upper limit on maximum speeds and again
suggests that each shark will be adapted
for a given, rather narrow, range of cruising speeds. It is for this reason that the
subterminal lobe can act as a passive rather
than active control for the angle of rotation, supplementing muscular efforts.
A
353
In hindsight, it seems that the potentially negative aspects of the swimming
mechanism in sharks have been reduced
through several means. In sharks of group
1, (the large pelagic sharks), the external
symmetry of the tail which gives a high
aspect ratio and makes possible either high
speeds or very efficient slower cruising
speeds (as in the whale shark) also makes
possible a lowering of the centre of effort
of the tail. The closer the centre of effort is
to the same horizontal plane as that containing the centre of balance, the less the
pectoral fins and ventral head surfaces are
needed for compensation. In fact, in these
sharks, the ventral head surface is not as
flattened as it is in group 2 sharks and the
head is more streamlined and conical (see
also Klausewitz, 1962, 1965). An alternative way of lowering the centre of effort is
to reduce the heterocercal angle but this
gives a quite opposite set of adaptations
because it produces lower absolute speeds.
The adaptations of group 3 are therefore
more suited to slow speeds and bottom
living where extreme mobility in the vertical plane is not as important as efficiency in
cruising. A third possible modification of
the generalised group 2 plan is that seen in
squalomorph sharks. Here the centre of
effort is lowered by the addition of an
epicaudal lobe: this requires a ventral
D
FIG. 10. Drawings of four sharks, typifying the four Carcharinus leucas; C Scyhorhinus torrei; D Centroscylgroups discussed in the text. A Isurus oxyrhynchus; B liumfabricii. (After Bigelow and Schroeder, 1948)
354
KEITH STEWART THOMSON AND DAN E. SIMANEK
hypochordal lobe, the net result being a
more symmetrical tail. It is interesting that
in this group the heterocercal angle remains relatively high and this must mean
that considerable versatility in producing
moments of thrust around the centre of
balance is retained. The squalomorph pattern thus combines many useful features
of both groups 2 and 3. However, again
the multiplicity of control surfaces used in
forming a balanced thrust necessitates a
slow cruising speed and prevents the attainment of high speeds.
Finally, it must be noted that there is a
paucity of information in the literature on
the swimming habits of sharks. Some aspects of attack have been documented but
little is known of the patterns of swimming, cruising speeds, or method of feeding in many sharks. The following is a
sample of some useful recent sources in
this growing field: Baldridge and Williams
(1969); Barlow (1974); Clarke (1971);
Cousteau and Cousteau (1971, a more
popular account but well-documented);
Fellows and Murchisen (1966); Gilbert
(1962); Hobsen (1963); Johnson and Nelson (1973); Moss (1972a,b); Springer
(1961) and Strasburg (1958).
Bone, Q. and B. L. Roberts. 1969. The density of
elasmobranchs. J. Mar. Biol. Assn. U.K. 49:913937.
Clarke, T. A. 1971. The ecology of the scalloped
hammerhead shark, Sphyrna lewini, in Hawaii.
Pacific Sci. 25:133-144.
Corner, E. D. S., E. J. Denton, and G. R. Forster.
1969. On the buoyancy of some deep-sea sharks.
Proc. Roy. Soc. London B171:415-429.
Cousteau, J. Y. and P. Cousteau. 1971. The shark:
Splendid savage of the sea. Cassell, London.
Fellows, D. P. and A. E. Murchison. 1966. A noninjurious attack by a small shark. Pacific Sci. 21:150151.
Gray, J. 1933. Studies in animal locomotion. I. The
movement of fish with special reference to the eel.
J. Exp. Biol. 10:88-104.
Gilbert, P. W. 1962. The behaviour of sharks. Scient.
Amer. 207:60-68.
Grove, A. J. and G. E. Newell. 1936. A mechanical
investigation into the effectual action of the caudal
fin of some aquatic vertebrates. Ann. Mag. Nat.
Hist. (10) 17:280-290.
Hobsen, E. S. 1963. Feeding behaviour in three
species of sharks. Pacific Sci. 17:171-194.
Johnson, R. H. and D. R. Nelson. 1973. Agonistic
display in the gray reef shark, Carcharmus menisorrah, and its relation to attacks on man. Copeia
1973:76-84.
Klausewitz, W. 1962. Wie schwimmen Haifische? Nat.
Mus. Frankf. 92:219-226.
Klausewitz, W 1965. Die Bewungsweise der Geigenrochen aus funkioneller und stammegeschichtlicher Sicht. Nat. Mus. Frankf. 95:97-108.
Magnan, A. 1929. Les charactenstiques geometriques
et physiques des poissons. Ann. Sci. Nat. Zool.
12:5-133.
Moss, S. A. 1972a. Nurse shark pectoral fins: An
unusual use. Amer. Mid. Nat. 88:496-497.
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