Hydromechanics of lunate-tail swimming propulsion. Part 2

Abstract

This paper investigates the propulsive performance of the lunate tails of aquatic animals achieving high propulsive efficiency (the hydromechanical efficiency being defined as the ratio of the work done by the mean forward thrust to the mean rate at which work is done by the tail movements on the surrounding fluid). Small amplitude heaving and pitching motions of a finite flat-plate wing of general planform with a rounded leading edge and a sharp trailing edge are considered. This is a generalization of Chopra's (1974) work on model rectangular tails. This motion characterizes vertical oscillations of the horizontal tail flukes of some cetacean mammals. The same oscillations, turned through a right angle to become horizontal motions of side-slip and yaw, characterize the caudal fins of certain fast-swimming fishes; viz. wahoo, tunny, wavyback skipjack, etc., from the Percomorphi and whale shark, porbeagle, etc., from the Selachii. Davies’ (1963, 1976) method of finding the loading distribution on the wing and generalized force coefficients, through approximate solution of an integral equation relating the loading and the upwash (lifting-surface theory), is used to find the total thrust and the rate of working of the tail, which in turn specify the hydromechanical swimming performance of the animals. The physical parameters concerned are the tail aspect ratio ((span)2/planform area), the reduced frequency (angular frequency x typical length/forward speed), the feathering parameter (the ratio of the tail slope to the slope of the path of the pitching axis), the position of the pitching axis, and the curved shapes of the leading and trailing edges. The variation of the thrust and the propulsive efficiency with these parameters has been discussed to indicate the optimum shape of the tail. It is found that, compared with a rectangular tail, a curved leading edge as in lunate tails gives a reduced thrust contribution from the leading-edge suction for the same total thrust; however, a sweep angle of the leading edge exceeding about 30° leads to a marked reduction of efficiency. Another implication of the present analysis is that no negative work is involved in the actual oscillation of the tail.The present results are used to obtain an estimate of the drag coefficient for the motion of the animals, based on observed data and the computed thrust. The results show some evidence of differences between the CD's for cetacean mammals and scombroid fish respectively. Some discussion of this difference is also given.

Measurement of hydrodynamic force generation by swimming dolphins using bubble DPIV

“…Thrust calculated from the vortices during small amplitude swimming at V swim below 1.5 m s −1 compared closely with previously reported thrust values for T. truncatus, based on calculations from lifting wing theory (Chopra and Kambe, 1977;Fish, 1998a). Above 1.5 m s −1 , the thrust from the present study increased to a maximum that was approximately 2.7 times higher than the calculated thrust at 3.4 m s −1 .…”

Effects of added drag on cetaceans : fishing gear entanglement and external tag attachment

“…Locomotor power requirements were similar to those calculated by Fish (1993b) with a hydromechanical model [i.e. following Chopra and Kambe (1977)]. …”

“…For example, thrust increases, but, beyond a certain threshold, efficiency decreases with flukestroke frequency (Daniel, 1991) and, again, beyond a certain threshold, with the angle of attack (Chopra and Kambe, 1977). Increasing frequency is commonly observed in swimming animals in response to changes in force balance (Skrovan et al, 1999;Williams, 1999;Cornick et al, 2006;Aoki et al, 2011).…”

“…Swimming animals adjust their fine-scale movements to optimize their performance, addressing trade-offs between thrust generation and efficiency (Chopra and Kambe, 1977;Bose and Lien, 1989;Daniel, 1991;Fish and Rohr, 1999). Whales and other marine mammals make repetitive or transient gait changes; for example, employing intermittent swimming strategies (Williams, 2001) or reducing thrust production to take advantage of net buoyancy on dive descents or ascents (Webb et al, 1998;Fahlman, 2008;Aoki et al, 2011;Miller et al, 2012b).…”

Swimming kinematics and efficiency of entangled North Atlantic right whales

“…For example, thrust increases, but, beyond a certain threshold, efficiency decreases with fluke-stroke frequency (Daniel 1991) and, again, beyond a certain threshold, with the angle of attack (Chopra & Kambe 1977). Swimming animals often increase fin-beat frequency in response to changes in force balance (Skrovan et al 1999, Williams 1999, Cornick et al 2006, Aoki et al 2011.…”