Abstract
The best swimmers have a streamlined shape that ensures an attached flow pattern and a laminar boundary layer at rather large values of the Reynolds number. Simple expressions may be obtained for the volumetric drag coefficient of an ideal body of revolution under laminar unseparated flow conditions together with estimations of a critical value of the Reynolds number. A measure, the capacity-efficiency factor, calculated for different organisms and underwater vehicles, shows that information about animal shapes and locomotion is of utmost biological interest and could be useful to improve robot fish and underwater vehicles as well.
Highlights
From the hydromechanical point of view fish swimming is a very complicated unsteady phenomenon
A description of the diversity of fish locomotion and a classification of swimming modes, categories, and styles can be found in Blake [1]
From the first equation of (3) the value of U will be equal to unity; that is, the rotationally symmetric boundary layer on a slender body can be reduced to the flat plate one [11]
Summary
From the hydromechanical point of view fish swimming is a very complicated unsteady phenomenon. This study focuses on the most simple estimations of fish drag and power requirements during quasisteady motion when changes in body shape can be neglected. This approach would not be very reliable in the case of anguilliform propulsion, but it is acceptable for the carangiand thunniforms of the best swimmers (see [2,3,4]). The pressure drag can be reduced almost to zero when the boundary layer does not separate from the body surface In this case the d’Alembert paradox applies; that is, a closed rigid body in unbounded flow of ideal incompressible fluid has zero drag (see, e.g., [5]). In this paper the drag coefficient and the capacity characteristics of a corresponding slender body of revolution (with a small ratio of maximum diameter D to length L) have been calculated for different animals, human athletes, and submarines in order to compare them in terms of swimming efficiency
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