We study hydrodynamic efficiency of a slender fish furnished a with separated caudal fin that swims by flexing its body (say, left-right). Most fish look and swim that way. Hydrodynamic efficiency of this fish obviously depends on the shape of its body and fins and on the way it flexes, but it also depends on elastic recoil of its fins (caudal fin in particular) and dynamic recoil of its body.
Under most circumstances, elastic recoil of the caudal fin has no detrimental effect on hydrodynamic efficiency; moreover, in many cases it improves it by placing the fin at a more favorable angle of attack. Because the elastic recoil increases with increasing thrust, under the same circumstances the efficiency also increases with increasing thrust. Indeed some fish prefer moving in short powerful bursts, rather than swimming at constant speed. We show that, under some circumstances, body recoil can significantly affect hydrodynamic efficiency, leading to cases in which rigid caudal fin is more effective than the flexible one, and swimming with low thrust is more effective than swimming with high thrust.