Proposed kinematic model for fish-like swimming with two pitch motions

• Kinematics of a flapping foil with two rotational motions is considered.
• The proposed kinematics model is generalized model.
• The optimum Strouhal number and pitch amplitude are obtained.

In the present investigation a new kinematic model for a fish-like swimming is presented. In this model the foil has two rotational motions in order to approach of the fish swimming performance. This kinematic model is a generalized model for flapping foil because it introduces caudal-to-heave ratio (is ratio of caudal length to heave amplitude) which has not been considered. In the present work the proposed kinematic model can be evaluated in Cylindrical coordinate, while it involves with nonlinear hydrodynamic and propulsion models. This kinematic model can switch to Cartesian coordinate when the caudal-to-heave ratio is infinitive value. The foil experiences the diverse effective angle of attack profile due to the influence of the caudal length in association with other kinematic parameters. It is shown that increase in foil-pitch amplitude decreases the angle of attack and hence, thrust reduces in thrust-based condition. Extreme increasing of foil-pitch amplitude leads the angle of attack to switch to drag-based condition and high drag production results from these changes. Moreover, it is shown that in the limited caudal-to-heave ratio the foil may have the better propulsive performance with reasonable thrust. Furthermore, the optimum Strouhal number and foil-pitch amplitude for fish-like swimming are computed from 0.2 to 0.4 and from 30° to 40°, respectively, which are in agreement with observed results in the nature.