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Physics

Flexibility as a Universal Nature-Inspired Mechanism for Thrust Enhancement

Roberta Santoriello, Francesco Viola, Vincenzo Citro

Featured July 1, 2026

Original Paper

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Simply

Squids and jellyfish use flexible nozzles to push water, and this paper shows that when their nozzle "breathes" in and out perfectly in time with the water pulse, it creates a powerful standing wave that greatly boosts their swimming power.

In depth
The paper reveals that flexible nozzles in jet-propelled swimmers enhance thrust by exhibiting a standing-wave response, where the structure dilates and recoils synchronously with the fluid pulse. This mechanism optimally charges and releases energy, and the authors propose a physics-based model that precisely predicts the optimal nozzle stiffness for maximum thrust.

Key Takeaways

  • 1
    Flexible nozzles in jet-propelled swimmers achieve optimal thrust enhancement through a standing-wave response, where the entire nozzle expands and contracts in phase with the fluid pulse.
  • 2
    The optimal nozzle stiffness occurs when the structure's natural period precisely matches the effective duration of the fluid pulse, maximizing the energy transfer and hydrodynamic impulse.
  • 3
    A closed-form physics-based model is derived, providing a universal design rule for soft pulsed-jet propulsors by linking optimal stiffness to nozzle length and pulse duration.

Conceptual Flow

HIGH LEVEL
1
Methodology: How Flexible Nozzles Work

The researchers used computer simulations to watch how water and flexible nozzles interact, finding two main ways the nozzle moves: either all at once (good) or in a wave (less good).

Flexible Nozzle
Water Flow
Simulate Interaction
Nozzle Movement Pattern
Thrust Power
2
Results: The Power of Synchronized Movement

They discovered that the best way for the nozzle to move is by expanding and shrinking all at once, like a standing wave, which makes the animal swim much faster than a stiff nozzle.

Nozzle Breathes All At Once
Nozzle Breathes Like a Wave
Compare Power
Much More Thrust
Less Thrust