Why do curling stones curl?

Drs. Wilfred T. Tysoe & Nicholas D. Spencer | TLT Cutting Edge August 2013

Swedish tribologists debunk old theories and offer a new one that fits all the facts!
 


CURLING IS AN OLYMPIC SPORT PLAYED ON ICE that is enormously popular in northern countries such as Canada, Scotland and Sweden. It involves two teams that slide a series of 16 stones along a 28-meter stretch of ice, aiming to get them as close to the target as possible. Once the stone is released at one end of the ice sheet, the trajectory is governed purely by sliding friction.

The subtlety of the game is that by rotating the stone upon release (producing 1-3 rotations over the entire 28 meters), the stones can adopt a curled trajectory, thereby avoiding "guarding" stones that would otherwise prevent the moving stone from accessing the target, as shown in the figure.

Harald Nyberg of the Angstrom Tribomaterials Group. University of Uppsala, Sweden, along with colleagues Sture Hogmark, Staffan Jacobson and Sara Alfredsson, have recently published two landmark papers on this inherently tribological sport. One [1] of these discounts old theories, while the other [2] proposes a novel theory that appears to account for all observations to date. It is important to know that the bottom of the stone is hollowed out such that the contact with the ice is made with an annulus that is around 6 mm wide and 120 mm in diameter.

The surface of this annulus is intentionally roughened during stone preparation, and the degree of roughness is known to influence both friction and degree of curl, which can be as much as 1.2 meters lateral deviation from a straight trajectory. The preparation of the ice is also important as the surface is presprinkled with water, resulting in the formation of bumps or "pebbles" (0.2 mm high and up to 5 mm wide) whose tops are flattened by a special tool prior to the game.

In their first paper [1], the authors point out that most theories to date have been based on the idea of a friction asymmetry between the leading and trailing halves (as seen in the direction of the motion) of the annulus. This may seem reasonable at first, but it should be borne in mind that if. for example, an inverted drinking glass is slid along a table with a rotating component to its motion, the resulting curl is exactly opposite to that observed for a curling stone. In other words, there must be another much greater effect at work.

Previous studies have explored the influence of meltwater layers on the friction, as they become dragged around with the rotating annulus, but there remain many open questions about exactly how this may lead to a curl.


Courtesy of Springer

Nyberg et al. decided to construct a numerical model that checks whether a friction asymmetry, irrespective of its origin, could ever lead to the curling effects observed in practice. They found that even in the most extreme case imaginable, where all friction force was acting on the trailing half of the stone annulus, the observed curls could not be reproduced. Furthermore, their model showed a pronounced dependency of curl on rotational speed, which curlers know to be a non-significant parameter.

In the second paper [2], the authors invoke a completely new mechanism that takes into account the roughness of the stone, since they made the experimental observation that polished stones do not curl at all. They also found, by electron microscopic analysis of ice replicas, that the surfaces of the ice pebbles are scratched following the passage of a curling stone. Furthermore, they noticed that non-rotating stones could be given a curl by prescratching the ice in a particular direction. This latter effect appeared to diminish with repeated experiments, suggesting that the scratches were being worn away.

The mechanism that leaped out from these observations was as novel as it was all-encompassing: The roughness asperities on the leading edge of the stone were scratching the ice-pebble surfaces. Then, as the stone rotated, the asperities on the trailing edge encountered the scratches formed in the ice, and were guided by them, thereby leading to a curl in the correct direction. The forces encountered by the asperities contacting the scratches could be calculated by simple mechanics, and were shown to be indeed of sufficient magnitude to induce the curl. The mystery of how curling stones curl appears to have been laid to rest.

FOR FURTHER READING
1. Nyberg, H., Hogmark, S. and Jacobson, S. (2013), "Calculated Trajectories of Curling Stones Sliding under Asymmetrical Friction: Validation of Published Models," Tribology Letters, 50 (3), pp. 379-385.
2. Nyberg, H., Alfredsson, S„ Hogmark, S. and Jacobson, S. (2013), "The Asymmetrical Friction Mechanism that Puts the Curl in the Curling Stone." Wear. in press, available here.


Eddy Tysoe is a Distinguished Professor of Physical Chemistry at the University of Wisconsin-Milwaukee. You can reach him at wtt@uwm.edu.


Nic Spencer is professor of surface science and technology at the ETH Zurich, Switzerland. Both serve as editors-in-chief of STLE-affiliated Tribology Letters journal. You can reach him at nspencer@ethz.ch.