Propulsive efficiency of frog swimming with different feet and swimming patterns

Aquatic and terrestrial animals have different swimming performances and mechanical efficiencies based on their different swimming methods. To explore propulsion in swimming frogs, this study calculated mechanical efficiencies based on data describing aquatic and terrestrial webbed-foot shapes and swimming patterns. First, a simplified frog model and dynamic equation were established, and hydrodynamic forces on the foot were computed according to computational fluid dynamic calculations. Then, a two-link mechanism was used to stand in for the diverse and complicated hind legs found in different frog species, in order to simplify the input work calculation. Joint torques were derived based on the virtual work principle to compute the efficiency of foot propulsion. Finally, two feet and swimming patterns were combined to compute propulsive efficiency. The aquatic frog demonstrated a propulsive efficiency (43.11%) between those of drag-based and lift-based propulsions, while the terrestrial frog efficiency (29.58%) fell within the range of drag-based propulsion. The results illustrate the main factor of swimming patterns for swimming performance and efficiency.