Hydrodynamic modulation via cupping in a crustacean-inspired propulsor

TL;DR

This study uses a robotic model to show how the cupping angle of shrimp-like appendages optimally balances thrust and lift during swimming, revealing a geometric control mechanism for efficient propulsion.

Contribution

It introduces a robotic pleopod system to systematically analyze the effect of cupping angle on hydrodynamic forces, highlighting its role in modulating thrust and lift independently of kinematics.

Findings

Moderate cupping angles optimize thrust-lift balance.

Exopodite contributes over half of the lift force.

Leading-edge vortex remains attached at optimal angles.

Abstract

Shrimp, like many invertebrates swimming at intermediate Reynolds numbers ($Re$), rely on the interplay between morphology and kinematics to generate thrust while producing sufficient lift to overcome their negative buoyancy. Shrimp pleopods branch into an endopodite and an exopodite, whose relative motion varies the projected surface area during the swimming cycle. For this mechanism to function, the exopodite must be cambered relative to the endopodite at a set cupping angle $\zeta$, which partially decouples the effective angle of attack of the exopodite from the overall leg kinematics. Here, we investigate the role of $\zeta$ in modulating thrust$-$lift balance during steady forward locomotion. Using a dynamically scaled (40$\times$) robotic pleopod, we systematically varied $\zeta$ from $0^\circ$ to $80^\circ$, measured hydrodynamic forces, and performed particle image velocimetry at $Re = 968$. Moderate cupping angles ($\zeta = 20^\circ-40^\circ$), consistent with biological observations, provide optimal thrust$-$lift balance. At these angles, the exopodite abducts rapidly during the power stroke, maximizing projected area at peak flow velocity, and adducts early during the return stroke, minimizing resistive drag. A reduced-order force model reveals that the exopodite contributes 52$-$62\% of total lift, particularly at intermediate $\zeta$, where a leading-edge vortex (LEV) forms and remains attached throughout the power stroke. At extreme cupping angles, LEV coherence degrades and force production weakens. These findings demonstrate that shrimp pleopods function as hybrid propulsors exploiting both drag- and lift-based forces, and that $\zeta$ serves as a geometric control parameter capable of tuning thrust$-$lift balance independently of stroke kinematics.