Optimization of energetic advantages of burst swimming of fish

It is well‐known that fish can swim more efficiently by alternating periods of accelerated motion and powerless gliding. It has been shown numerically that this strategy is most effective for small velocities and very small variations of the accelerating and gliding mode. In the paper presented here, this has been reinvestigated analytically. By that means, the maximum energy saving obtained can be evaluated. Knowing the cheapest swimming mode in terms of energy of fish enables knowing its minimal oxygen need. In calculating the volume a fish crosses using this cheapest mode, we are able to estimate the least required oxygen concentration of the surrounding water. Therefore, we can also calculate the restriction on the size of fish schools due to oxygen limitations. The theoretical value for the maximum size of a school increases if one considers energetic advantages of schooling. These evaluations are of special interest for the estimation of fish stocks and for fishery. Copyright 2001 John Wiley & Sons, Ltd.