Elongated-body theory has been fruitfully applied over twenty years to the biofluiddynamic analysis of modes of locomotion of elongated fishes by means of body flexure, with special emphasis on the anguilliform mode using undulatory body movements, and on the carangiform mode where oscillatory movements of only a fish's posterior end(including the caudal fin) exhibit phase lag of posterior movements behind anterior movements just as in an undulation yet not nearly as much as a whole wavelength is apparent at any one time. The extension of elongated-body theory to analyse the locomotion of elongated fishes with elongated median fins (dorsal and/or anal) in modes where the body (together with any caudal fin) remains rigid, being propelled forwards by undulations or oscillations of those median fins, has long been recognized as desirable but is here presented for the first time.

In many large groups of fishes, evolutionary adaptation to limited environments (such as coral reefs) favoured a development of defensive ‘armour’ at the expense of speed, to such an extent that bodies became essentially inflexible, with locomotion achieved by fin movements alone. In one principal group of such fishes, however (the sub-order Balistoidei including the trigger-fishes), a later evolutionary development restored a capacity for relatively high-speed movement even though the body remained essentially rigid. The balistiform mode of locomotion, with propulsion achieved by synchronized movements of the dorsal and anal fins, exists in two alternative forms, with either undulatory or oscillatory movements of these median fins, that are analogous to the anguilliform and carangiform modes of body flexure, respectively.

Analysis in this paper throws light on the puzzling question of why trigger-fishes are able to move so fast notwithstanding the modest extent of their fin movements. A form of the large-amplitude elongated-body theory, specially adapted to balistiform locomotion, allows a direct comparison of thrust and efficiency for different modes of propulsion. The conclusions in brief are that thrust is dominated by the mean rate of shedding of backward momentum at the posterior end of the fish's propulsive apparatus and that, for movements of median fins attached to a deep, essentially rigid body, this momentum is increased (above the momentum expected for the same movements of the fins ‘on their own’) by a momentum enhancement factor β of around 3 or a little more. Yet there is no such enhancement of the rate of shedding of ‘unproductive’ energy into the wake; accordingly, overall efficiency is improved. Also, especially for the undulatory mode of balistiform locomotion, sideforces are minimized so that the fish body avoids sideslip and yaw; accordingly, the body drag which fm thrust must overcome is reduced by another large factor.

Alongside discussion of the Balistoidei, this paper reviews and analyses balistiform locomotion as observed in several other groups, including groups of flexible-bodied fishes that regularly use this mode as a low-energy-cost alternative to locomotion by means of body flexure. Finally, we similarly analyse gymnotiform locomotion, in which the body is again held rigid, being propelled by undulations in just a single (ventral) fin, and compare and contrast different interpretations of its advantages.