This chapter describes the kinematics of cownose ray swimming, relating it to fin geometry and skeletal structure. The equation of the deformed fin surface is presented, and the influence of different kinematic parameters on fin movement is analyzed. The numerical implementation of the CFD model of cownose ray swimming is presented, and finally, the results are analyzed, highlighting how the swimming performances and the wake structure change according to different kinematic parameters. The main parameters that affect swimming performances are frequency and wavelength of fin motion and frequency resulted in being proportional to the swimming velocity, and it did not affect the dimensionless parameters like energy efficiency and the Strouhal number, whereas a variation in wavelength implies changing the angle of attack of the fin, resulting in a different flow and strongly affecting all swimming performances. The vortices in the wake form a Reverse Karman Street, and vortex rings are connected like in a chain, similarly to other swimming animals, and for some wavelengths, a leading-edge vortex can be observed too. The energy efficiency is one of the highest among fishes, reaching 89% for the best combination of parameters, and the Strouhal number of most analyzed swimming motions is comprised between 0.2 and 0.4.
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