Velocity fluctuation of self-propelled manta-ray vehicles under flapping–twisting pectoral fin motion: The role of the effective angle of attack

Manta rays are prototypes for biomimetic vehicles, but how flapping and twisting affect velocity fluctuation under limited degrees of freedom remains unclear. Five-degree-of-freedom simulations with only pitch fixed are paired with one-degree-of-freedom rail experiments to test flapping frequency and flap and twist amplitudes. Flap amplitude and frequency set the mean speed, twist controls fluctuation, and the effective angle of attack is the key link. When the angle stays below 20°, thrust has two peaks, fluctuation is small, and the wake is compact and nearly symmetric (8.25°). The best case gives a maximum mean speed of 7.53 BL/s at 1 Hz for 1.4–1.6 rad flap and 0.2 rad twist. When twist exceeds 0.6 rad, the angle rises above 22°, the leading-edge vortex sheds early, and the fin stalls. The thrust then becomes single-peaked, fluctuation grows, and the mean speed drops to 3.42 BL/s. Experiments confirm numerical trends, with a maximum mean-speed error of 15.81%. This study shows how flapping and twisting control the effective angle of attack and thus fluctuation, and offers design rules for degree-of-freedom-constrained biomimetic manta-ray vehicles. • Flapping–twist coupling governs self-propelled manta-ray velocity fluctuation. • At 1 Hz, raising flap amplitude from 0.8 to 1.6 rad raised mean speed by 190%. • A 1.6 rad flap with 0.2 rad twist gave the peak cruising speed of 7.53 BL/s. • Effective angle of attack links fin kinematics to thrust efficiency and stability. • The optimal wake stayed compact (8.25°, 8.67°).