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The paper seeks to determine what transverse oscillatory movements a slender fish can make which will give it a high Froude propulsive efficiency, (forward velocity) (thrust available to overcome frictional drag) { (work done to produce both thrust and vortex wake) }. The recommended procedure is for the fish to pass a wave down its body at a speed of around 5 4 of the desired swimming speed, the amplitude increasing from zero over the front portion to a maximum at the tail, whose span should exceed a certain critical value, and the waveform including both a positive and a negative phase so that angular recoil is minimized. The Appendix gives a review of slender-body theory for deformable bodies.
M. J. Lighthill (Sat,) studied this question.