The Physics of Curling

The Sport

The Olympic sport of curling comprises of two teams taking turns sliding granite stones of uniform shape and density across a sheet of ice in order to land in the middle of the bullseye. Teams earn points based on which team is closest to the center of the bullseye or if they have more stones within the bullseye than the opposing team. Teams can use their stones to knock the other teams' stones out of the bullseye, or block the path of the other teams' stones. While the stone is travelling down the sheet, teams may also commit two players to sweep the ice with brooms in order to melt the ice in front of the stone and alter its path. The motion of the stone itself also plays a part in its trajectory, as putting a spin on the stone causes the stone's path to "curl" - where the sport derives its name. Using a combination of spinning, sweeping, and bouncing from other stones, skilled teams can create an exciting and complex game for spectators and competitors alike.

The Science

From a physiciti's standpoint, most of the mechanics of curling can be easily explained with the kinematic equations. The most basic element of the game, the stone's linear translation from one end of the sheet to the other, can be explained with Newton's second law:

$F=\mathrm{ma}$

With $F$ being the net force on the stone, we can further break down this equation. Because there are two opposing forces on the stone - the thrower pushing the stone and the friction of the ice pulling the stone backwards - this equation better models the stone:

$F_{\mathrm{curler}}-F_{\mathrm{friction}}=\mathrm{ma}$

If we take into consideration that there is also friction as the stone is travelling along the ice, it is proven that the stone will come to a stop. We can also take into consideration that the ice in front of the stone is being swept as it is moving, so the force of friction is lower as the melted water has a lower coefficient of friction than the solid ice. This explains in a more scientific sense the reason that a stone being swept travels further than a stone not being swept.

The most interesting part of the game, in my opinion, is using the stones' momentum in order to push opposing stones out of the bullseye or friendly stones into the bullseye. This can be modeled using the equation for linear momentum:

$p=<mi>mv</mi>$

To model a collision between stones, we need to recognize Conservation of Momentum, meaning that the momentum of objects in the system may be exchanged but remains constant. Because the second stone will be sitting motionless further down the sheet, $v_2=0$. Also, it should be noted that all stones have equal mass, so $m_1=m_2$. With all of these elements, the equation for the objects during collision should be as such:

$p_1=p_2$

$m{v}_{\mathrm{1i}}=m{v}_{\mathrm{1f}}+m{v}_{\mathrm{2f}}$

This equation, and the concept of conservation of momentum in general, show that after the collision both stones will be moving slower and in opposite directions.

The Controversy

The previous equations do well to explain the mechanics behind the collision and linear motion of the stones, but we have yet to explain the namesake of the sport - the curl of the stones as they travel down the sheet. This is quite a bit harder to define, though.

Before getting into the nitty-gritty of this topic, however, we need to note something special about the stone itself. The stone does not have a flat bottom, but rather a small ring on which it travels down the ice (as shown in the picture above). If you were to take any typical object with a surface such as this (like a mug turned upside down) and slid it along a surface, you would see that the object would begin to curl in the direction opposite of the direction of the rotation. This baffled early scientists, but it is now a well-explained phenomena. Curling stones, on the other hand, behave in the exact opposite way. If you were to slide a curling stone down the ice while it is rotating clockwise, it would curl clockwise - the same direction as the direction of rotation. Furthermore, the curl of the stone is independent of the speed of its rotation.

Two teams of researchers are currently at the forefront of explaining this phenomena - and both fervently disagree with each other. One team is lead by physicist Harald Nyberg from Uppsala University in Sweden, while the other is led by Mark Shegelski from the University of Northern British Columbia. Neither team has directly reached out to the other, instead publishing and refuting findings through a series of technical papers. So, what are the conflicting ideas in these theories?

The theory posited by the Swedish team is that as the curling stone spins, the irregularities in the granite creates a series of scratches in the ice that help to guide the stone in the direction of the spin. This theory was tested by the team by scratching a sheet of ice with sandpaper, and then sending a stone without spin down the sheet. As predicted, the stone traveled in the direction of the scratches. While this supported the theory that the stone travels in the direction of the scratches, further proof was needed. This proof came in the form of an invention by the team - the Frankenbroom. The Frankenbroom was a curling broom that not only melted the ice like typical brooms, but scratched the ice as well. This broom proved so effective in guiding the stone's trajectory that it was banned from competitive use by the international curling community. This seemed to prove the ideas of the Swedes, but across the globe, other ideas were taking form.

At the University of Northern British Columbia, Mark Shegelski hypothesized that the curling was caused by a mechanic dubbed "asymmetric friction melting". This mechanic boils down to the stone pushing downward more towards the front than the back due to the stone's tendency to tip over. This uneven downward force causes the ice to melt more near the front than the back, thus lubricating the surface in the direction of rotation. Another mechanic that he proposed could explain the curl is the nature of the ice sheets. Typically, ice sheets used in curling are not one uniformally flat surface such as for hockey or ice skating. Instead, the ice is a flat sheet studded with microscopic "pebbles" formed from misting the ice with water. These pebbles serve to decrease the friction with the stone compared to a stone travelling on a completely flat surface. Shegelski's theory regarding these pebbles is that the stone, when coming into contact with a pebble, is briefly stuck on the pebble and pivots around it as it glides over the pebble. As the stone travels over thousands of these microscopic pebbles during the course of its slide, the total pivoting on the pebbles could account for over a meter of curl.

Conclusion

Although neither team can definitively say that their theory reigns supreme, both agree that more work is necessary to truly understand what goes on under the hood in curling. Furthermore, regardless of unknown mechanics at play, what we do know about curling shows that it is a complex sport both scientifically and competitively.