WEBB and KEYES: SWIMMING KINEMATICS OF SHARKS 



(1926), and has been more recently updated by 

 Lindsey (1978). The definition of common loco- 

 motor patterns, or modes (Lighthill 1975), for 

 undulatory swimming movements of the body 

 and caudal fin are based on the number of one- 

 half wavelengths contained within the body 

 length and the pattern of increasing amplitude 

 along the body. The elongate eel, Anguilla, is 

 definitive for the anguilliform mode where the 

 body contains more than one-half wavelength 

 within the body length, and often one or more 

 complete waves. The lateral amplitude of body 

 movements rises early and is large over most of 

 the body length. Jacks, in the family Carangidae, 

 are representative of the carangiform mode 

 where the body length contains less than one-half 

 wavelength, and lateral displacements increase 

 rapidly over the posterior third or half of the 

 body. Breder (1927) used the term "sub-carangi- 

 form mode" for fish with wave patterns of the 

 anguilliform mode and amplitude changes simi- 

 lar to the carangiform mode. So far, detailed 

 studies of fusiform teleosts have been on sub- 

 carangiform swimmers. 



The six species of shark are also subcarangi- 

 form swimmers according to these definitions; 

 the body contained more than one-half of a wave 

 (Table 1, Fig. 5) and the amplitude of body move- 

 ments increased predominantly over the poster- 

 ior half of the body (Fig. 6). However, the maxi- 

 mum rate of increase in amplitude occurred over 

 the third quarter of the body, intermediate be- 

 tween the situation for elongate and fusiform 

 teleosts. Therefore, although the sharks swam in 

 the subcarangiform mode, they were more eel- 

 like than fusiform teleosts. This is consistent 

 with the unaided visual impressions of shark 

 swimming. 



Among teleosts, trends in swimming kinemat- 

 ics from the anguilliform mode towards carangi- 

 form modes are associated with changes in body 

 form from an elongate, flexible body to a more 

 fusiform, less flexible body. This is coupled with 

 a larger caudal fin depth increasingly separated 

 from the body by a narrow caudal peduncle, a 

 morphology defined as narrow necking (Light- 

 hill 1975). The same trends are seen in the six 

 species of sharks studied here (Fig. 1, Table 1). 

 The more fusiform species were those with 

 longer propulsive wavelengths and a larger tail 

 depth swimming in a more carangiform mode 

 than the elongate sharks. In terms of the classifi- 

 cation of shark functional morphology by Thom- 

 son and Simanek(1977), group 1 is most carangi- 



form and groups 3 and 4 are most anguilliform. 

 Group 1 representatives were not studied here. 



The two factors of increasing wavelength and 

 caudal fin depth in the carangiform swimmers 

 are known to increase thrust and Froude effi- 

 ciency (Lighthill 1975). However, thrust is re- 

 duced by a decrease in tail-beat amplitude. 

 Among the sharks, increasing wavelength and 

 tail depth were found with smaller amplitudes. 

 Thus, the more fusiform, more carangiform spe- 

 cies show features that would both enhance and 

 decrease performance. Stride length increased 

 in these more fusiform sharks so that overall the 

 larger wavelength and deeper caudal fins must 

 generate more than enough thrust, perhaps 

 more efficiently, to offset reduced amplitudes. 



The details of kinematic movements appear 

 very different for sharks compared with bony 

 fish. In the teleosts that have been studied to date 

 (see Hunter and Zweifel 1971; Aleyev 1977) tail- 

 beat frequency is the major kinematic variable 

 with speed, and over most of the range of swim- 

 ming speeds, it is the only variable. In contrast, 

 the blacktip shark modulated all three of the 

 kinematic variables that influence thrust: tail- 

 beat frequency, tail-beat amplitude, and the 

 length of the propulsive wave. Teleosts vary one 

 morphological parameter with speed that would 

 also affect thrust. This is the depth of the caudal 

 fin trailing edge (Bainbridge 1963; Webb 1971) 

 to vary the mass of water accelerated by propul- 

 sive movements (see Alexander 1968; Lighthill 

 1975). The skeleton of shark fins is based on car- 

 tilaginous ceratotrichia, rather than bony rays, 

 which cannot be individually controlled. As a 

 result, shark fins lack the flexibility to substan- 

 tially modify fin depth during swimming. 



The differences in locomotor kinematics with 

 speed of the sharks illustrated by the blacktip 

 shark, compared with teleosts, may be related to 

 hydrodynamic interactions between the median 

 dorsal fins and the caudal fin. This interaction 

 was first described by Lighthill (1970) and has 

 been developed in detail using hydromechanical 

 theory for inviscid fluids by Sparenberg and 

 Wiersma (1975). A vortex sheet is shed by the 

 trailing edge of any sharp fin or body edge. This 

 vortex sheet travels downstream, but it also has a 

 lateral velocity component determined by the 

 motion of the trailing edge; i.e., the wake follows 

 a sinusoidal path (see illustrations in Rosen 1959; 

 Aleyev 1977). The vortex sheet carries momen- 

 tum determined by the motions and dimensions 

 of the body and fin at the fin trailing edge. 



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