Scaling of swim speed and stroke frequency in geometrically similar penguins: they swim optimally to minimize cost of transport

It has been predicted that geometrically similar animals would swim at the same speed with stroke frequency scaling with mass−1/3. In the present study, morphological and behavioural data obtained from free-ranging penguins (seven species) were compared. Morphological measurements support the geometrical similarity. However, cruising speeds of 1.8-2.3 m s−1 were significantly related to mass0.08 and stroke frequencies were proportional to mass−0.29. These scaling relationships do not agree with the previous predictions for geometrically similar animals. We propose a theoretical model, considering metabolic cost, work against mechanical forces (drag and buoyancy), pitch angle and dive depth. This new model predicts that: (i) the optimal swim speed, which minimizes the energy cost of transport, is proportional to (basal metabolic rate/drag)1/3 independent of buoyancy, pitch angle and dive depth; (ii) the optimal speed is related to mass0.05; and (iii) stroke frequency is proportional to mass−0.28. The observed scaling relationships of penguins support these predictions, which suggest that breath-hold divers swam optimally to minimize the cost of transport, including mechanical and metabolic energy during dive.