Investigation of the curved trajectory formation mechanism of a curling stone focusing on the contact area with ice

In the sport of curling, various mechanisms in curl of rotating stones have been proposed; however, the essential understanding of the mechanism has not been clarified. In this study, we attempted to explain the curl of a rotating stone by focusing on the contact area between the stone and many small ice protrusions known as pebbles which artificially produced by spraying water droplets onto the flat ice surface of lane. Specifically, a novel model so-called contact area model, which assumes that the contact area between the stone and pebbles differs between the front and back side of the stone, was proposed to explain the curl of stone. It has been experimentally shown that the heights of pebbles decrease an average 1.1 μm with each pass of the stone. The sliding stone and pebbles contact each other firstly in the front side of the stone and then in the back side. Pebbles contacted in the front side of stone may also contact in the back side, resulting in a potentially larger contact area in the back side of stone compared to that in the front side. The difference in contact area between the front and back side creates a frictional force difference between the front and back side of rotating stone, creating the force that causes it to form a curved trajectory. We evaluated the force required for a rotating stone to curl based on the relationship between a stone-trajectory experimentally obtained and time estimated by solving the equation of motion of the stone, and investigated whether the magnitude of the force could be explained using the contact area model. The result shows that the difference of contact area between the front and back side probably contributes to the curl of rotating stones.