SWIMMING SPEED, TAIL BEAT FREQUENCY7 TAIL BEAT AMPLITUDE, AND SIZE IN JACK MACKEREL, Trucharzcs symmetricas, AND OTHER FISHES

The tail beat frequency and tail beat amplitude of jack mackerel, Trachurus symmetvicus, 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 frequency of the tail beat and 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 japonicus, Triakis henlei, and Sardinops sagas - and to data for freshwater fish from the literature. The general form of the model was V - V, = L(KF - Po) where V is fish speed, V, 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 differences, 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. Knowledge of the relationships between swimming speed and these variables is important not only for an understanding of the mechanism of locomotion in fish but because it may be used to forecast maximum swimming speeds (Bainbridge, 1958), to estimate swimming speeds indirectly by analysis of tail beat frequencies, and possibly to estimate fish size and make specific 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, Leuciscus leuciscus; trout, Salmo gairdneri (S. irideus) ; and goldfish, Carassius 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.