The Swimming Form of a Dolphin

Abstract

The paper seeks to determine what swimming form a dolphin can take when the from is balanced dynamically. The transverse oscillatory movements of slender fish had been theoretically analyzed by M.J.Lighthill. According to the theory, any movements attempted by the dolphin which does not satisfy the equation (3) will automatically produce reactions and recoils. To calculate the reactions and recoils it is convenient to represent the form of a dolphin in a mathematical form. The body is approximated to a paraboloid of revolution, the length-diameter ratio of which is 6.0. The position of maximum diameter is located at 0.4l from the nose (l is the length of the dody), and the caudal fin is replaced by a triangle. The span of the trailing edge is 0.25l. As regards the swimming movements, the follwing assumptions are made. The swimming form is represented by the equation (4) which contains six parameters. The progressive wave length of the swimming movement is equal to l and the amplitude of motion of the tail is 0.25l. To determine a balanced swimming form of the dolphin, calculations of reactions and recoils are worked out for various values of two parameters, b and d. The balanced form is found out approximately and shown in Fig. 12. The values of the parameters are b=0.66l and d=0.015l, respectively.