Estimate of Strouhal and Reynolds numbers for swimming penguins

Propulsion performance of swimming and flying animals is often evaluated by using dimensionless numbers, such as the Strouhal and Reynolds numbers. They have been shown to allow a better understanding of locomotion efficiency, using relatively simple approaches and avoiding overly complex computational models. Specifically, it has been reported that efficient propulsion is more likely to occur when Strouhal number values – estimated from propulsive frequencies and amplitudes – are within a relatively narrow range, depending on the corresponding Reynolds number, broadly expressing the fluid resistance to the animal motion. We have estimated both Strouhal and Reynolds numbers for seven species of penguins after analysing relevant kinematic data taken from the literature. The obtained values neatly indicate that, as expected, penguins employ efficient propulsion mechanisms. Additionally, by comparing these values with those for alcids – seabirds that can also fly – we have found that penguins swim at least as efficiently as alcids. However, we have also found that the swimming number – proportional to the product of Strouhal and Reynolds numbers – neatly correlates to the diving abilities of the considered species and apparently indicates, in a straightforward hierarchical manner, the gains in diving due to the loss of flying abilities. Within the penguin species, a clear correlation is also observed between diving performance and drag coefficient values.