Abstract
Rowing is demanding, in part, because drag on the oars increases as the square of their speed. Hence, as muscles shorten faster, their force capacity falls, whereas drag rises. How do frogs resolve this dilemma to swim rapidly? We predicted that shortening velocity cannot exceed a terminal velocity where muscle and fluid torques balance. This terminal velocity, which is below Vmax, depends on gear ratio (GR = outlever/inlever) and webbed foot area. Perhaps such properties of swimmers are 'tuned', enabling shortening speeds of approximately 0.3Vmax for maximal power. Predictions were tested using a 'musculo-robotic' Xenopus laevis foot driven either by a living in vitro or computational in silico plantaris longus muscle. Experiments verified predictions. Our principle finding is that GR ranges from 11.5 to 20 near the predicted optimum for rowing (GR ≈ 11). However, gearing influences muscle power more strongly than foot area. No single morphology is optimal for producing muscle power. Rather, the 'optimal' GR decreases with foot size, implying that rowing ability need not compromise jumping (and vice versa). Thus, despite our neglect of additional forces (e.g. added mass), our model predicts pairings of physiological and morphological properties to confer effective rowing. Beyond frogs, the model may apply across a range of size and complexity from aquatic insects to human-powered rowing.