The threads of your cotton shirts are not made of long continuous strands of cotton. Instead, individual centimeters-long fibers are kept together simply by twisting a bundle of them, a technique employed by prehistoric humans and even Neanderthals. In more recent history, scientists have figured out how the trick works- The tension in the coiled fibers creates forces normal to their curvatures, and frictional forces tangential to the fibers prevent sliding. (See the article by L. R. G. Treloar, Physics Today, December 1977, page 23.)

How well the strategy works depends on the twist angle. Tug on a yarn composed of a hardly twisted bundle of fibers, and it will easily slip apart. Tug on a yarn composed of highly twisted fibers, and the fibers won’t budge—although pulling hard enough will break them. But beyond that general trend, a detailed quantitative understanding of the relationship between twist angle and yarn strength has eluded researchers.

Now Antoine Seguin of the University of Paris–Saclay and Jérôme Crassous of the University of Rennes in France have investigated yarn strength through a combination of experiment and theory. They found not only the relationship between the frictional forces and the yarn’s twist angle but also a dimensionless parameter that predicts optimal yarn compositions.

In their experiments, Seguin and Crassous gathered cotton strands, twisted them together by some amount, and hung more and more weight on the resulting yarn, as shown in the photo, until the threads started to slide or break. They then replicated the observed maximum loads as a function of twist angle in numerical simulations and a mechanical model. They found that the frictional forces grew exponentially with the square of the twist angle. That amplification led to a sharp transition from a loose yarn whose strength is limited by sliding threads to a tightly coiled yarn whose strength is limited by snapping threads.

The transition happens for a critical value of what the researchers have named the Hercules twist number, which depends on the twist angle, the friction coefficient, and the length and radius of the yarn. Low Hercules twist numbers correspond to the sliding regime. But are higher numbers always better? Twisting too tight can elongate and thin the fibers, which renders them easier to break. And that tendency grows for thicker yarns. The thickest cotton yarn that can twist enough without breaking to reach the optimal value of the Hercules twist number has a radius of 80 μm, which turns out to be a typical value for cotton yarns.

Cotton and wool yarns have been more or less perfected through historical trial and error. But Seguin and Crassous’s work could help optimize blends and yarns made of new synthetic materials, including environmentally friendly ones. (A. Seguin, J. Crassous, Phys. Rev. Lett. 128, 078002, 2022.)