Enhancing Collective Efficiency of a Pair In-line Pitching Hydrofoils in a Stable Formation

Schooling fish exhibit remarkable efficiency as they swim together, dynamically adjusting their movements relative to one another. Recent research has demonstrated that passive hydrodynamic forces can create 1D and 2D stable arrangements for a pair of swimmers, leading to speed and efficiency benefits regulated by hydrodynamic interactions. However, in an in-line configuration, the highest efficiency position is not necessarily at the 1D stable location for swimmers. We postulate that stable formations can be tailored to coincide with high efficiency zones by controlling the amplitude ratio of leader and follower. To investigate this further, our study focuses on purely pitching in-line hydrofoils with matched and mismatched amplitudes between the leader and the follower hydrofoil. We employ direct force measurements and particle image velocimetry to analyze the efficiency benefits and 1D stability criterion. Additionally, we extend our research to consider different upstream velocities and in-phase and out-of-phase pitching synchronizations at multiple spacings, providing a comprehensive understanding of the hydrodynamic interactions and efficiency enhancement potential.