A PORPOISE FOR POWER

摘要

Frank Fish writes about James Gray's 1936 publication on the power output of a swimming dolphin.Sometimes the most innocent of scientific endeavors can have the most far-reaching and profound ramifications. For James Gray, a simple calculation to determine the power output of a swimming dolphin(Gray, 1936) would launch a contentious argument known as `Gray's Paradox'. Gray's classic study would provide the impetus for studies of bio-hydrodynamics and would affect the fields of material science, hydrodynamics, biorobotics, and diving physiology.The Gray's Paradox controversy resulted from the first attempt to evaluate swimming energetics in animals (Webb,1975). In his 1936 study, Gray used a rigid-body hydrodynamic model to calculate drag power and applied it to a dolphin and a porpoise swimming at high speeds (>7.6 m s-1). The results indicated that the estimated drag power could not be reconciled with the available power generated by the muscles. Gray(1936) stated: `If the resistance of an actively swimming dolphin is equal to that of a rigid model towed at the same speed, the muscles must be capable of generating energy at a rate at least seven times greater than that of other types of mammalian muscle.'Gray's calculations assumed that turbulent flow conditions existed in the boundary layer between the dolphin's skin and the water, because of the speed and size of the animal. His resolution to the problem was that the drag on the dolphin would have had to be lower than the turbulent conditions dictated, and that this could be achieved by maintenance of a fully laminar boundary layer against the dolphin's skin. In other words, the water against the dolphin skin flowed in orderly, parallel streams over the entire body, although this ran counter to accepted hydrodynamic theory. Gray proposed that the motion of the dolphin's flukes, which are the broad, lateral extensions of the tail used for propulsion, accelerated water flow over the posterior half of the body and that this action could provide a mechanism to laminarize the boundary layer. This mechanism was largely ignored in subsequent work, but the basic premise that dolphins could somehow maintain a laminar boundary remained and became the focus and justification of much of the work on dolphin hydrodynamics for the next 60 years (Fish and Hui,1991; Fish and Rohr,1999).This basic premise of Gray's Paradox, however, was flawed, because of potential errors in estimation of dolphin swimming speed and inconsistencies between dolphin swimming performance and data on muscle power outputs. To measure drag power, Gray used a shipboard observation of a dolphin swimming along the side of the ship from stern to bow in 7 s. If the dolphin was swimming close enough to utilize the flow pattern around the ship, its speed may have been artificially enhanced and energetic effort reduced due to freeriding behaviors (Lang,1966; Williams et al.,1992; Weihs,2004). More important than the actual speed of the dolphin, the duration of this high performance swimming was for a sprint and Gray used measurements for muscle power output of sustained performance (3-5 min) by human oarsmen (Henderson and Haggard,1925). Muscle fibers specialized for quick bursts of anaerobic activity can produce maximum metabolic power output 2-17 times greater than muscle fibers using a sustained aerobic metabolism(Hochachka, 1991; Askew and Marsh, 1997). The higher muscle power outputs produced by anaerobic mechanisms offset the power required to overcome the drag when the boundary layer is turbulent.In effect, the dolphin has the capacity to swim at high speeds for short durations while maintaining a fully attached turbulent boundary layer between itself and the surrounding water. These turbulent boundary flow conditions would delay separation of the boundary layer from the dolphin's skin surface. When the boundary layer separates from the skin surface and interacts with outer flow, this results in a broader wake and i