The scaling of swimming speed

Maximum swimming speeds increase with animal length up to about the size of wahoo or tuna, but increase little more beyond that: even the great whales do not appear much faster. Here, the scaling of top swimming speeds is considered in terms of meeting the power demands with muscle power and work. The power required to provide thrust to overcome drag scales with area (the square of length). Without other constraints, muscle power capacity would be proportional to volume (the cube of length) meaning that bigger animals should be able to swim faster - which they do, up to a limit. However, the capacity for muscle to produce work over a contraction is also limited, and animals are hindered in that they can contract locomotor muscles only once per gait cycle. Larger animals have lower frequency oscillations of their propulsive fins or flukes, presumably due to the geometric requirements of high hydrodynamic efficiency; and a reduction in efficiency equates to a loss of thrust for a given power supply at a given speed. It is proposed that, above a certain size - very approximately a length of 1 m - top speed does not increase with size because of the limited capacity of muscle to produce mechanical work, the geometry of hydrodynamic efficiency, and the resulting decrease in contraction frequency. However, a similar constant top speed limit is also predicted if cavitation - a phenomenon that damages propellers and would presumably hurt or injure fish or whales - is to be avoided.