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The Speed of Swimming of Fish as Related to Size and to the Frequency and Amplitude of the Tail Beat
1 The Zoological Laboratory, Cambridge
1. An apparatus is described in which it is possible to study and record the continuous swimming of fish at speeds up to 20 m.p.h.
2. Records made of the swimming at different speeds of dace, trout and goldfish measuring up to 30 cm. in length are reproduced.
3. Speed at any particular frequency of tail beat is shown to be directly related to the length of the specimen, measured from the tip of the snout to the most posterior extremity of the tail.
4. Above a frequency of 5 tail beats per second speed is directly dependent upon frequency up to the maximum values recorded. The results for all sizes and species recorded may be adequately expressed by the formula V = 
{L(3f - 4)}, where V is the speed in cm. per sec., f is the frequency in beats per sec. and L is the body length in cm.
5. The distance travelled per beat (and hence the speed) is directly dependent upon the amplitude of the tail beat.
6. The amplitude increases with increasing frequency up to a maximum reached at about beats per second. This maximum amplitude is the same for all fish tested and is about one-fifth of the body length.
7. The maximum frequency attainable decreases with increasing size of the specimen. This decrease is slight in the trout and more pronounced in the dace and goldfish. Estimation of the possible maximum frequencies of much bigger fish allows for prediction of the maximum speeds they may be able to attain. Such predicted speeds are in accord with the few measurements that have been made and are of the order of 10 body lengths per second up to a size of 1 m.
Submitted on June 14, 1957
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