With the recent Winter Olympics in Milano-Cortina keeping many of us glued to our televisions, and the extensive worldwide broadcasting of curling, many of us have been left to ponder how the sport works. On the surface it seems fairly simple, with some going as far as claiming they could easily do it themselves, but is this true? And what is the maths behind this unique sport?
Curling is a sport where players slide a granite stone over ice towards a target area, called the ‘house’, giving it a slight twist so that it curls along the way. Other players in the team will sweep to control the stone’s path and influence its speed, with the goal being to get the stone closest to the center of the target, the ‘button’. While this may sound straightforward, the reasons why the stones move the way they do is far more complex – in fact, many physicists are still puzzled by them.
One of the key aspects of how the sport works is the design of the ice. Before matches, the ice surface is sprayed with water droplets to create a rough ‘pebbled’ surface. This pebbling reduces friction since it means there is less contact between the stone and the ice, therefore helping the stones reach the house. The vigorous sweeping performed by the athletes warms the ice and causes pebbles to melt, resulting in a water film that further decreases the friction. This is how the players dictate the speed and how much the stone curls.
There are three stages of the stone’s journey across the ice. The stone is at its highest speed when launched, so moves in a straight line, the distance of which is extended by the players sweeping the ice to melt more pebbles. The water lessens as it slows down so the friction increases and the stone begins to curl. Eventually, the water disappears so the stone experiences more friction, slowing to a stop.
Another detail behind the sport is the shape of the stones, which are particularly tough and water-resistant. The underside is not flat, with only the rims (running bands) staying in contact with the ice. But what puzzles physicists about all this?
Usually, when you rotate an object, it will curl counterclockwise along the surface. Unlike these, curling stones curl in the same direction they spin. This movement is not what would be expected typically and defies the conventional mathematical explanations. There are multiple theories about why the stones behave in the strange way they do.
One theory blames the surface of the ice, suggesting that the running band of the stone will pivot in the direction that it is spinning as it moves over a pebble, and this movement will increase exponentially as the stone moves toward the target over more pebbles. This theory noticed that the stones were moving in a somewhat pendulum like fashion, as they seemed to rotate around a certain point. According to a researcher, Jiro Murata of Rikkyo University, “The spinning itself isn’t what pushes the stone sideways. Instead, the spin creates a difference in friction, and that friction acts as a pivot point”. He compared it to grabbing a pole on the left while running, causing you to swing to the left around it.
Another theory suggests that the unusual curling has more to do with the running bands, or that the irregular ice surface along with the irregular surface of the band may be the driving force behind the direction of spin. The stone may be steered by the irregularities on the band scratching the ice. Researchers at Uppsala University in Sweden believe the stones curl due to them creating tiny scratches on the ice sheet which they then follow. This theory even influenced the creation of the ‘Frankenbroom’ which aided in scratching ice as well as heating it, which gave more control to sweepers and was even banned for being too effective.
Additionally, a different theory states that non-uniform melting of the ice is responsible for the stone’s odd curl. The stones press more strongly on the front end of the running band than the back as they travel, leading to ice in front melting quicker than ice at the rear side. This creates less friction at the front which in turn leads to the stone curling in the direction of induced rotation. This theory was originally backed by a physicist from the University of Northern British Colombia, however it couldn’t fully explain the degree of the curl observed.
To conclude, there is far more to curling than it might seem. From the applied mathematics of pebbles moving the stone to banned equipment, hopefully your next watch of the sport will be far more interesting. While the official maths behind the movement of the stones may be unclear, what is clear is that curling is far from simple. In a sport where athleticism meets calculation, is the motion magic or actually maths?