SWIMMING SPEED, TAIL BEAT FREQUENCY, TAIL BEAT AMPLTrUDE, 



AND SIZE IN JACK MACKEREL, Trachurns symmetric^ 



AND OTHER FISHES 



John R. Hunter and James R. Zweifel' 



ABSTRACT 



The tail beat frequency and tail beat amplitude of jack mackerel, Trachnrus symmetricus, 4.5 to 27.7 

 cm were measured at speeds of 15 to 212 cm/sec. Tail beat amplitude was a constant proportion of 

 length at all speeds but tail beat frequency changed with speed; thus speed depended only on fre- 

 quency of the tail beat an<l length. A simple mathematical model for estimating swimming speed from 

 tail beat frequency and fish length was derived from the Trachurus data and applied to data for three 

 marine fish — Scomber jnponicus, Triakis henlei, and Sardinops sagax — and to data for freshwater 

 fish from the literature. The general form of the model was V — Vg = L(KF — Fg) where V is fish 

 speed, V'o is length-dependent minimum swimming speed at minimum tail beat frequency F„, and L is 

 fish total length. The model represented a major improvement over previous equations because it 

 provided an unbiased correction for length, was sensitive to specific diff'erences, and provided a more 

 accurate estimation of speed. 



Of the variables that determine the swimming 

 speed of a fish, the size of the fish, the frequency 

 of the tail beat, and the amplitude of the tail 

 beat are among the most important. Knowl- 

 edge of the relationships between swimming 

 speed and these variables is important not only 

 for an understanding of the mechanism of lo- 

 comotion in fish but because it may be used to 

 forecast maximum swimming speeds (Bain- 

 bridge, 1958) , to estimate swimming speeds 

 indirectly by analysis of tail beat frequencies, 

 and possibly to estimate fish size and make spe- 

 cific identifications of fish targets with doppler 

 Continuous Transmission Frequency Modulated 

 sonar (Hester, 1967). 



Bainbridge (1958) described the relationship 

 between tail beat frequency, tail beat amplitude, 

 and size for three species of freshwater fish: 

 dace, Leiiciscus leuciscus; trout, Salmo gairdneri 

 (S. irideus); and goldfish, Carassiiis auratus. 

 He concluded that the amplitude of the tail beat 

 increased with the tail beat frequency to about 

 5 tail beats/sec and thereafter became constant. 



' National Marine Fisheries Service Fishery-Ocean- 

 ography Center, La Jolla, Calif. 92037. 



Manuscript received January 1971, 



FISHERY BULLETIN: \0L. 69. NO. 2. 1971. 



Speeds above 5 beats/sec were dependent only 

 on the frequency of the tail beat and the length 

 of the fish. The relationship between speed, 

 frequenc.v, and length above 5 beats, sec was 

 nearly the same in the three species studied; 

 consequently, he used a single equation to ex- 

 press this relationship for all three species. No 

 similar study exists for marine fish although 

 some measurements of tail beat frequency and 

 amplitude have been made incidental to other 

 studies. Yuen (1966) measured the tail beat 

 frequency of ski])jack tuna, Katsuivomis pelamis, 

 and yellowfin tuna, Thmmus albacares, from 

 cine photographs taken from the viewing port 

 of a research vessel and Magnuson and Prescott 

 (1966) measured the tail beat frequency of 

 Pacific bonito, Sarda chiliensis, from cine pho- 

 tographs taken through a window in an ocean- 

 arium. The slopes of the lines relating tail 

 beat frequency to speed in body lengths per sec- 

 ond for skipjack and yellowfin tunas and bonito 

 were sufficiently different from those of Bain- 

 bridge (1958), for Hester (1967) to speculate 

 that species might be identifiable by this re- 

 lationship. The measurements were taken from 

 lateral photographs of free-swimming schools; 

 thus the tail beat amplitude and the absolute 



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