The load against which the swimming muscles contract, during the undulatory swimming of a fish, is composed principally of hydrodynamic pressure forces and body inertia. In the past this has been analysed, through an equation for bending moments, for small-amplitude swimming, using Lighthill's elongated-body theory and a ‘vortex-ring panel method’, respectively, to compute the hydrodynamic forces. Those models are outlined in this review, and a summary is given of recent work on large-amplitude swimming that has (a) extended the bending moment equation to large amplitude, which involves the introduction of a new (though probably usually small) term, and (b) developed a large-amplitude vortex-ring panel method. The latter requires computation of the wake, which rolls up into concentrated vortex rings and filaments, and has a significant effect on the pressure on the body. Application is principally made to the saithe (Pollachius virens). The calculations confirm that the wave of muscle activation travels down the fish much more rapidly than the wave of bending.

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