Elastic properties of structures in the tails of cetaceans (Phocaena and Lagenorhynchus) and their effect on the energy cost of swimming

A swimming whale must do work against hydrodynamic forces, to move its fluke through the water. In addition, it must do positive work at some stages of the swimming cycle and negative work at others, to accelerate and decelerate the fluke. The energy cost of swimming could be reduced by means of elastic elements in the tail.
A mathematical model predicts the work required of the muscles, when they have elastic compliances in series with them. It is shown that there is an optimum compliance that minimizes the energy cost of swimming, for any given ratio of peak hydrodynamic force to peak inertial force.
Anatomical measurements have been made on flukes, tail muscles and tendons of Phocaena and Lagenorhynchus . Mechanical tests have been made on the tendons, fluke and vertebral column. It is shown that the important compliances are those of the tendons, and the axial compliance of the vertebral column, and that these compliances should be regarded as being in series with the muscles.
Calculations using these data, and Lang & Daybell's (1963) observations of a Lagenorhynchus swimming at 5 m/s, seem to show that the compliances greatly exceed the optimum value for this swimming speed. They increase the energy cost of swimming, rather than decreasing it.