The complex physics of a fish swimming through water can be simplified into the same basic math used to describe a weight bouncing on a spring.
April 29, 2026
Original Paper
Dynamics of Fish Swimming
SSRN · 6661342
The Takeaway
Fluid dynamics are notoriously difficult to calculate because water moves in chaotic, swirling patterns called vortices. This paper proves that the way fish move these vortices follows a simple, linear mechanical equation. Engineers can now ignore the complex swirls and use basic spring math to design underwater vehicles. This makes it possible to build robotic fish that are just as efficient as the real thing without needing massive supercomputers to control them. It changes how we think about propulsion in everything from drones to submarines.
From the abstract
Although fish achieve high-efficiency propulsion by harvesting energy from self-generated vortex rings, a unified, predictive physical model that maps vortex-ring evolution to measurable net thrust has remained elusive. Most seminal and state-of-the-art research either reconstructs wake dynamics via high-fidelity numerical simulations or compresses fluid-structure interactions into quasi-steady coefficient approximations, yet neither yields an explicit, identifiable mapping between vortex dynami