Swimming of a waving plate
The purpose of' this paper is to study the basic principle of fish propulsion. As a simplified model, the two-dimensional potential flow over a waving plate of finite chord is treated. The solid plate, assumed to be flexible and thin, is capable of performing the motion which consists of a progressing wave of given wavelength and phase velocity along the chord, the envelope of the wave train being an arbitrary function of the distance from the leading edge. The problem is solved by applying the general theory for oscillating deformable airfoils. The thrust, power required, and the energy imparted to the wake are calculated, and the propulsive efficiency is also evaluated. As a numerical example, the waving motion with linearly varying amplitude is carried out in detail. Finally, the basic mechanism of swimming is elucidated by applying the principle of action and reaction.
"Reprinted with the permission of Cambridge University Press." (Received 23 September 1960). This work is sponsored by the Office of Naval Research of the U.S. Navy. The assistance rendered by Mr D. P. Wang, Mrs Zora Harrison and Mrs Luna Fung in the computations and by Mrs Rose Grant in preparing the manuscript is greatly appreciated.