Conservation of energy in competitive swimming

Energy conservation in swimming is formulated in terms of four functions of the swim speed v: the consumed power K, the mechanical power P used for horizontal propulsion, the remaining expended mechanical power N, and the thermal power loss H. K is well-known (from O2) and P = FDv, where the drag force FD is not known with certainty but represents a small effect. Estimates of the nonpropulsive components of a swimmerʹs body motions reveal that N is small, less than 3 watts per kg of body mass. H is estimated by using the theory of convective heat transfer to express the heat loss in terms of the difference between the swimmerʹs skin temperature and the water temperature. This temperature difference was measured for the NYU menʹs swim team and found to be 0.033 K per kg of body mass, giving H ≈ 34 W kg−1. The results are seen to be in good agreement with the asymptotic (large swim time tf) form of energy conservation. The further requirement that energy conservation is valid to order 1/tf, and use of the 1993 world record race times, is shown to imply that the initial energy available in a swimmerʹs body is 963 ± 231 joules per kg of body mass.