&Bullet; physics 14, p89

A new experiment finds that a ball with “fins” maintains its orientation in a flowing liquid, despite a 19th century prediction that it would spin.

G. Voth / Wesleyan University

In 1871, Lord Kelvin proposed a hydrodynamics brain teaser: Is there an object that looks the same from any direction and rotates naturally when it moves through a liquid? Kelvin thought there was one, and he provided a recipe for making this “isotropic helicoid”. Over the next century and a half, the idea spread in textbooks and scientific publications, but no experimental test has been reported to date. Now Greg Voth of Wesleyan University in Connecticut and his colleagues have tested the idea with a 2 cm wide helicoid that they created with a 3D printer [1] . The team dropped the object through a viscous liquid under gravity and observed no rotation.

Kelvin’s recipe for making an isotropic helicoid is as follows. Take a sphere and draw three circles around it: one at the equator, one around 0 ° longitude, and one around 90 ° longitude. Place four wings or “fins” along each circle, each angled at 45 degrees to the circle. This arrangement, which is similar to a motorboat propeller, has several discrete rotational symmetries that ensure isotropic interactions with the liquid.

Voth and his colleagues modeled the movement of a helicoid through a liquid and found – as a first approximation – that the torques on each blade cancel each other out. However, their model shows that hydrodynamic interactions between the guide vanes can allow a net torque to develop, but that torque was too small to observe for the helicoid the team made. They suggest that by optimizing the design of the helicoid, the researchers could increase the hydrodynamic interactions to the point where the net torque becomes observable.

–Michael Schirber

Michael Schirber is the corresponding editor for physics based in Lyon, France.


  1. D. Collins et al., “Lord Kelvin’s Isotropic Helicoid”, Phys. Rev. liquids6th, 074302 (2021).

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