The Swimming Speed of Fish in Relation to Fish Size and Frequency of Tail Beating

Abstract

Tail beat motion was considered to be simple harmonic oscillation. The swimming speed of fish in relation to the size and frequency of tail beating was investigated with a simple hydrodynamic model. These relationships were measured with rainbow trout remaining stationary in a circular tank in which water flowed at a speed of 15 to 80cm/s. The amplitude of tail beating was a constant proportion of fish length at all speeds, but the frequency of tail beating changed with speed. The fish have a minimum tail beating frequency (ƒ₀) and a minimum swimming speed (V₀) below which they cannot swim by movement of the caudal fin. This minimum tali beat frequency is a function of the length of the fish. The minimum swimming speed is constant for various sizes of a particular kind of fish, but changes according to the species of fish. Thus, the swimming speed depended on the frequency of the tail beat, the fish size and the body type.
The general form of the formula was V=0.40√^S₂/^S₁L(F-ƒ₀)+V₀, where V is the speed of the swimming fish, F is the frequency of the tail beat, V₀ is the minimum speed of swimming at the minimum frequency of the tail beat ƒ₀, L is the total length of the fish, S₁ is the frontal area of the fish, S₂ is the lateral area of the fish from center of mass to tip of tail. This formula provided accurate estimates of swimming speed according to frequency of tail beating and fish size when the fish were stuck in a mesh of gill net.