Maximal Speed of Underwater Locomotion
Keywords:Water animal locomotion, Drag reduction, Unseparated shapes, Cavitation, High-speed underwater vehicles
Background. An increasing interest in unmanned underwater vehicles continues to draw attention to swimming in aquatic animals. Their high speed continues to surprise researchers. In particular, the high dolphin speed caused a series of attempts to explain its paradox, which continues to this day. Some researchers believe that even rigid bodies, shaped like water animals, provide an attached flow pattern, as opposed to the widespread view of the inevitable separation. The possible explanation may be in the perfect body form, which provides an attached flow pattern (without boundary layer separation). Elongated unseparated shapes can not only reduce the pressure drag but also delay the laminar-to-turbulent transition in the boundary layer, significantly reducing the friction drag. Thus, the highest possible swimming speeds are expected in aquatic animals.Objective. We will try to prove that the low drag and the high speed of aquatic animals can only be ensured by their unseparated shape (as a rigid body), neglecting flexibility and compliance.
Methods. We will use: a) shape calculations of special bodies of revolution with negative pressure gradients near the tail similar to fish trunks with the use of the developed before approach; b) the known drag estimations of such shapes for laminar and turbulent cases; c) the swimming power balance and the theory of ideal propeller; d) statistical analysis of available data about the length, the speed and the aspect ratio of aquatic animals.
Results. The swimming speed of most aquatic animals is proportional to the length of the body in power 7/9. The exception is whale locomotion that occurs in turbulent mode at supercritical Reynolds numbers.Conclusions. The perfect body shapes of most aquatic animals provide an attached laminar flow pattern. Estimated maximum speeds for laminar and turbulent cases show that the special shaped unseparated hulls can greatly increase the speed of underwater vehicles and SWATH ships. Further increase in speed can be achieved by using supercavitation and greater than animal capacity-efficiency.
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