Equivalent laws of pectoral fin propulsion parameters of cownose ray based on kinematic and hydrodynamic analysis

Batoids achieve remarkable swimming efficiency through adaptive speed modulation. While previous studies have preliminarily linked pectoral fin kinematics to swimming speed in cownose rays (Rhinoptera javanica), the dynamic relationship between fin motion patterns and propulsive performance has remained unclear. By integrating kinematic analysis with hydrodynamic experiments, this study establishes a consistent framework that reveals their unique propulsion mechanism. Kinetically, we found that fin velocity exhibits a linear relationship with swimming speed via coordinated amplitude-frequency modulation. The Strouhal number (St) decreases with increasing speed, with most values falling within the optimal range of 0.2-0.4. A bio-inspired robot successfully replicated the figure-of-eight motion of biological pectoral fins. Hydrodynamic experiments demonstrated that the fins generate comparable instantaneous thrust during both upstroke and downstroke, with thrust in each half-stroke following a unimodal pattern - increasing to a peak before declining. A parameter equivalence law was identified: when the product of frequency and amplitude (fA) is held constant, different kinematic combinations yield consistent mean thrust, and thrust shows a significant positive correlation with fA. This confirms that the rays dynamically regulate swimming speed through fin velocity while maintaining high efficiency across conditions. These findings not only advance the understanding of cownose ray propulsion but also provide a theoretical basis for motion control in bio-inspired underwater robots.