Effects of Body Elasticity on Stability of Underwater Locomotion

TL;DR

This paper investigates how body elasticity influences the passive stability of underwater fish-like locomotion, demonstrating that appropriate spring stiffness can stabilize otherwise unstable straight-line motion in a fluid environment.

Contribution

It introduces a deformable articulated body model with torsional springs to analyze passive stability based on geometry and elastic properties, highlighting the stabilizing role of elasticity.

Findings

Proper spring elasticity can passively stabilize fish-like coast motion.

Body geometry and spring stiffness are key factors in stability.

Passive stabilization reduces the need for neurological control.

Abstract

We examine the stability of the "coast" motion of fish, that is to say, the motion of a neutrally buoyant fish at constant speed in a straight line. The forces and moments acting on the fish body are thus perfectly balanced. The fish motion is said to be unstable if a perturbation in the conditions surrounding the fish results in forces and moments that tend to increase the perturbation and it is stable if these emerging forces tend to reduce the perturbation and return the fish to its original state. Stability may be achieved actively or passively. Active stabilization requires neurological control that activates musculo-skeletal components to compensate for the external perturbations acting against stability. Passive stabilization on the other hand requires no energy input by the fish and is dependent upon the fish morphology, i.e. geometry and elastic properties. In this paper, we use a deformable body consisting of an articulated body equipped with torsional springs at its hinge joints and submerged in an unbounded perfect fluid as a simple model to study passive stability as a function of the body geometry and spring stiffness. We show that for given body dimensions, the spring elasticity, when properly chosen, leads to passive stabilization of the (otherwise unstable) coast motion.