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Studies in Animal Locomotion I STUDIES IN ANIMAL LOCOMOTION I. THE MOVEMENT OF FISH WITH SPECIAL REFERENCE TO THE EEL BY J. GRAY. King's College, Cambridge. (From the Laboratory of Experimental Zoology, Cambridge.) (Received 20th October, 1932.) (With Four Plates and Eleven Text-figures) WHEN a body is moving in water it encounters a resistance in the direction of its motion, and consequently the body must be supplied with energy if motion is to occur at a uniform speed. A study of the mechanism of propulsion of a fish falls therefore into two parts, (1) a study of the forces resisting motion through the water, and (2) a study of the mechanism whereby the fish utilises the energy liberated by its muscles for overcoming the forces of resistance. To some extent these two aspects of the problem are interdependent and involve considerable hydrodynamical difficulties, but in the present paper an attempt will be made to show that the move- ments of a fish's body1 are such as to generate forces capable of opposing the forces of resistance whatever be the nature or magnitude of the latter. The problem was attacked two centuries ago by Borelli and by Pettigrew in 1873; since then com- paratively little attention has been devoted to the subject except by Breder (1926), whose results will be considered later. Since all propellers operate by driving astern a volume of water, the reaction from which compensates the surface resistance of the moving object, the initial problem of the fish's movements consists in demonstrating that the fish moves its body in such a way as to drive water away from its surface in a backward direction. All inanimate propellers belong to one of three types: (1) The jet propellers—as exemplified by all reaction turbines which project a current of water from a nozzle. The reaction caused by the water moves the nozzle in a direction opposite to that of the movements of the water. (2) Paddles—whereby a backward thrust is exerted on the water, parallel to the direction of motion of the paddle and at right angles to the surface of the paddle. The paddle can only be submerged during one-half of its complete movement, or it must be capable of being rotated about an axis at right angles to its line of motion, in order that no appreciable thrust is exerted during the period which follows the effective phase of the movement. (3) Screws—the theory 1 The present paper deals only with the propulsive properties of the bodies of a selected number of fish whose appendages play little or no part in the propulsion when the fish are moving at reasonable speeds. The propulsive properties of the caudal fin will be considered in a subsequent paper. Studies in Animal Locomotion 89 of screw propulsion is essentially that of an inclined plate—which, by motion through the water, generates a force at right angles to its surface (see Fig. 1). This force (P) has a component (T) at right angles to the direction of motion of the plate, which tends to move the plate along a line at right angles to its original direction of motion. The mechanism of propulsion of a typical fish does not conform to the design of a jet or a paddle, and since all screws operate by means of a true rotary movement, the possibility of a screw is, at first sight, excluded. The object of this paper is to consider the motion of a fish's body and to compare the underlying mechanism with that of a typical screw propeller. During the whole of the work, an attempt has been made to record the form and position of the fish at known intervals of time by photo- Fig. 1. AB is a cross-section of the blade of a screw moving along cd in the direction of the large arrow. A force P is generated at right angles to AB. This has a component T which tends to move the screw in the direction of a. graphic means. An experimental tank was set up in the field of a timed cinemato- graph camera, so that the position of the fish could be determined by means of a graduated field placed immediately underneath the fish. The method of recording the interval between successive photographs has been described elsewhere (Gray, 1930). I am greatly indebted to Mr J. E. Harris for his valuable help in the preparation of these photographic records. I. OBSERVATIONS ON THE MOVEMENTS OF FISH. As observed by the human eye, the motions of various types of fish appear to vary considerably from one species to another. The most conspicuous features of a moving eel—as are seen in the photographs taken by Marey (1894)—are the waves of curvature which pass along the length of the body from head to tail. In the dogfish (and, still more, the mackerel and whiting), the presence of such waves is less obvious, and the visible movements appear to be due to transverse strokes 90 J. GRAY executed by the posterior end of the body across the axis of motion. It can be seen from the photographs reproduced in Figs. 2-10 (Pis. I—IV), however, that in all these cases waves of curvature pass along the body alternately on the two sides, but that they differ in the various fish in certain important characteristics. Firstly, their speed of propagation along the body varies greatly. In the examples illustrated the approxi- mate speeds of the waves and the rates of movement of the fish are as shown in Table I. Secondly, the form of the waves differs. In the reversing eel (Fig. 10) the amplitude of the waves is very large, and is of approximately the same value as their wave-length. In Ammodytes (Fig. 7) and the mackerel (Fig. 5), the relative amplitude is very much smaller, while the dogfish, glass-eel, butterfish, and rockling occupy intermediate positions. Thirdly, when the fish are swimming at a steady rate, the frequency of the waves per second varies in the different species. In the examples illustrated, the approximate number of waves passing down each side of the body are shown in Table II. Fourthly, the amplitude of the waves is always greatest at the posterior end of the body, but the variation between the amplitude of the head and tail varies very greatly in different types. In the small eel the amplitude of the movements of the head is relatively very much greater than those of the mackerel or whiting. Table I. Velocity of wave Velocity o cm. per sec. cm. per Gla9s eel (Anguilla vulgaris) 6-2 4-0 Butterfish (Centronotus gunnellus) I7-S 117 Whiting (Gadus merlangtit) 25-0 168 Dogfish (Acantlrias vulgaris) 55 29 Mackerel (Scot/tber tcombrus) 77 42-5 Ammodytes (A. lanceolatut) 160 80 Table II. Waves per min. Glass-eel 93 Butterfish 120 Whiting 120 Dogfish 54 Mackerel 170 Ammodytes 120 The movement of the muscular waves along an eel's body was recorded photographically by Marey (1894), who made no attempt to define the mechanical principles which are responsible for the forward movement of the whole fish. These principles have been considered by Breder (1926), whose description of "anguilli- form" movement is as follows: "The forward motion is certainly attained by the pressure of the fish's body against the water in the following manner. The mechani- cal forces brought to bear on the water are diagonally backwards (from the posterior surfaces of each of the curves of the body). As these are distributed symetrically about the line of progression, a forward resultant of reaction follows, for pressure Studies in Animal Locomotion 91 from a moving plane is always at right angles to its surface." That the fish's body exerts a pressure on the water at right angles to its own surface is in accordance with the analysis given later in this paper, but Breder goes on to state that " It might be objected that as the eel is moving ahead there is likewise adverse pressure diagonally forward from the anterior sides of these backwardly moving waves. The truth of this is evident and it simply makes it necessary for the fish to pass these waves posteriorly at a rate considerably faster than it expects to move forward The speed of the waves moving backward must exceed that of the forward motion of the animal as a whole. If the two speeds just equalled each other it would mean that any point on a wave such as its crest would be stationary with reference to the sea- bottom; but as one is dependent on the other this is obviously impossible." The mechanical principles involved by this explanation are by no means clear, for it is certain that the propulsive thrust of the moving body is due to the fact that each part of the body is executing a series of transverse movements. Although these movements can be expressed in terms of longitudinally moving waves of contraction, the principles of propulsion of a fish are much more readily derived from a study of the transverse movements of each section of the body than from a direct investigation of the propagated waves of contraction. In the present paper an attempt will be made to investigate the propulsive effect of those transverse movements which are induced in the various parts of the body by a series of muscular contractions which are of such a nature as to produce the phenomenon of a propagated wave. The movements of the body can be considered in two ways.
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