Propulsion efficiency and cost of transport for copepods: a hydromechanical model of crustacean swimming

In the absence of direct measurement, costs of locomotion to small swimming Crustacea (<10 mm) have been derived exclusively through application of the fluid dynamic theory. Results indicate very low swimming costs, and contradict experimental data on larger Crustacea (15 to 100 mm) that suggest a three-fold increase in metabolic rate with increasing swimming speed. This paper introduces a swimming model that analyzes the hydrodynamic forces acting on a crustacean swimming at non-steady velocity. The model treats separately the hydrodynamic forces acting on the body and the swimming appendages, approximating the simultaneous solution of equations quantifying the drag and added-mass forces on each by stepwise integration. Input to the model is a time-series of instantaneous swimming-appendage velocities. The model output predicts a corresponding time-series of body velocities as well as the mechanical energy required to move the swimming appendages, dissipated kinetic energy, and metabolic cost of swimming. Swimming of the calanoid copepod Pleuromamma xiphias (Calanoida) was analyzed by extrapolating model parameters from data available in the literature. The model predictions agree well with empirical observations reported for larger crustaceans, in that swimming for copepods is relatively costly. The ratio of active to standard metabolism for P. xiphias was >3. Net cost of transport was intermediate to the values found experimentally for fish and larger crustaceans. This was a consequence of the predicted mechanical efficiency (34%) of the copepod's paddle propulsion, and of increased parasitic resistance resulting from non-steady velocity swimming.