Friday 9-12
Go Forth and Measure
Experimental Determination of the Effect that the Number of Revolutions has on a Curling Stone
Ben Peters
10/21/18
2.671 Measurement and Instrumentation
Prof. Derek Rowell
Abstract
The once obscure sport of curling has, in recent years, begun to draw the attention of the public eye. As the number of curlers grows, competition has begun to heat up. The ability to “curl” a rock—or slide a rock in a non-linear, arcing path—is a great advantage in the sport of curling. This study determined how the number of revolutions a curling rock undergoes can effect the distance that rock will curl— that is, how far it will move off its initial linear trajectory as it spins. One hundred typical curling shots were analyzed and it was found thatgenerallythe less the rock is allowed to rotate, the more it will curl. However, when a rock is given very little rotation (less than ¼ revolution), it is much more unstable, and is likely lose its rotation and drift off target.
1. Introduction
The sport of curlingwas invented in 16th century Scotlandwhen rough-hewn rocks were slid across the tops of frozen lakes in a simple strategy game.Modern curling is an international, Olympic sport, played primarily indoors at special curling rinks. There are more than 135 of these clubs in the U.S., with about one million curlers worldwide.1
Curling is a game of strategy, often called “chess on ice.” A curler’s objective in curling is to slide his team’s rocks across a 138’ foot slab of ice to land in a 12’ wide target at the other end. The closer a team’s rocks are to the center of the target, the more points are scored in a round. Curling, in this way, has a very unique game play: one has to understand the special interaction between a heavy granite rock and a sheet of ice in order to slide rocks in the correct locations and outscore the other team.
Curlingowes its unique name to the effect that occurs when heavy granite stones are spun and slid on ice. Typically, when a stone is given a push across the relatively frictionless surface of ice, it follows a linear path. However, when a rock is pushed and spun it can follow an arcing path. This arcing path can be used to curl around objects that would be impossible for a linearly moving rock to avoid. In Figure 1, a yellow rock is seen to take an arcing path to “curl” around the red stone. This is a great advantage to the yellow team because they have used the opposing team’s red rock to guard the direct path to their scoring rock. In this way, the ability to curl rocks is very strategically important for the sport of curling, hence its apt name.
Very few experiments have been conducted on the movement of curling rocks—probably due to the relative obscurity of the sport—and no hard evidence exists that shows exactly how the number of rotations that are given to a curling rock affect the final curl of the rock. A general rule of “about 2.5 rotations” is normally taught to beginning curlers, but this appears to be based on qualitative insight. The present study is to experimentally determine approximate relationship between the number of spins a curling rock undergoesand the amount of curl that results.
2. Curling Theory
The curling motion of a curling rock has baffled physicists for many years. This is primarily because the curl of a curling stone is non-intuitive when compared to other near-frictionless spinning objects. For example, when one spins an empty glass counter-clockwise on a wet table, the glass will follow a clockwise arcing path.3
As seen above in Figure 2, the front of the glass (labeled “F”) has a higher normal force downwards then the back of the glass (labeled B). This is because of the direction of travel of the glass—it is sliding with its front leading. This forward motion makes the glass “tip” forwards—making the front push down more on the sliding surface than the back.3 This difference in normal forces results in a difference in frictional forces on the front and back of the glass from the following equation:
Since the glass is spinning, the frictional forces on the front and back of the glass are not parallel to the direction of motion, but rather have a component in the opposite direction that the glass is turning. Figure 3, below, shows clearly the unbalanced frictional forces (in pink) on a spinning glass. This unbalance causes the glass to follow an arcing path in the opposite direction it is spinning.
A curling rock, however, makes an arcing path in the same direction as it is spinning. A curling rock’s bottom is a beveled ring—not flat—just like the edge of a spinning glass described above. However, a curling rock is heavy, and spun on ice—two important differences to a spinning glass. The important fact is this: the friction caused by the bottom of a spinning rock results in the melting of the ice. This melted ice lubricates the bottom of the rock, allowing it to turn more easily4. So, on ice, a heavier downward force will result in less friction then a lighter downward force. Looking back at figure 2; we find that a spinning rock on ice will have less friction in the front of the rock than on the back because the normal force on the leading edge of the rock will be higher, as illustrated in figure 4.
This lubrication effect of the ice results in the opposite of the unbalancing of forces in figure 3 and a resulting arc path in the same direction as the spinning of the rock.
With this knowledge, it initially make sense that by increasing the number of spins, the overall distance the rock curls would be greater—the frictional forces would become more and more offset as the speed increases, resulting in a steeper arcing path. However, all professional curlers spin their rocks at a lower speed (about 2.5 revolutions per length of the sheet). The question is clear: what is the exact relationship between the number of revolutions and the curl of a curling stone? The following section outlines the experiment that analyzed a range of typical curling shots to answer this question.
3. Measuring Curl
To measure the number of revolutions a rock undergoes, I affixed paper rotary gauges to several rocks with tape; see Figure 5 below. When each rock was slid down the sheet, the initial gauge measurement was recorded, the number of complete revolutions was counted, and the final gauge measurement (parallel to the center-line) was recorded. This was an easy and accurate (to +/- 10 degrees) process and the paper gauges did not interfere with the rock’s handle or its normal motion.
To measure the distance each rock curled, I recorded footage from an overhead camera stationed above the target area. By analyzing this footage, I was easily able to determine and record the final position of each rock with respect to the center line—and therefore the distance each rock curled.
By keeping careful track of the order the rocks were thrown, the number of turns measured by the gauge could be compared to the video footage of the curl.
Only data from the rocks that landed in the 12’ target were used, for these rocks would have similar initial velocity and they are the only rocks that are actually important when the sport is played.
4. Results and Discussion
The number of turns for each rock was compared to the distance curled and the results are plotted below in figure 7.
These results shown in Figure 7 are surprising; I had expected to see a direct relationship between the number of spins to the amount each rock curled; that is, for greater numbers of revolutions, more curl will result. Instead, I found that the best fit line is clearly negatively sloped—it seems that the more spins put on a rock, the less it will curl.
The shaded region in the graph above indicates that a rock given less than ¼ rotation is almost certain to lose its spin over time because of its low momentum. It was found that losing the stabilizing effect of the spin results in an unpredictable and usually worthless shot. Therefore, fewer rotations result in a greater distance curled, but very low values of rotation can result in unstable rocks that can yield unpredictable results.
So what is the cause of this unpredicted result? Looking back at section 2, we find that, on ice, greater downward force from the rock actually causes less friction because of the lubrication effect of the melting ice. If this same phenomenon is applied to the friction caused by the spinning of the rock, it makes sense that a quickly spinning rock (with more rotational frictional force) will generate more lubrication on the ice, resulting in less friction than a slower spinning rock. The rock’s friction caused by its rotation apparently also has an affect on the path of the rock, just as the friction caused by the rock’s weight does. This would explain why the rocks do not curl as much when rotated at higher rates—they simply cannot “grip” the ice because of the greater amount of lubrication being generated.
5. Conclusion
A simple setup was used to measure the number of rotations a curling rock underwent versus the distance curled. Only rocks that landed in the scoring zone were compared, so that each rock was known to be traveling at nearly the same speed down the ice. When rotations and distances curled were compared, it was found that the greatest distances curled were a result of lower numbers of rotations and higher values of rotation resulted in less distance curled. Furthermore, a rock given less than ¼ rotation was found to almost certainly to lose its spin over time because of its low momentum. Losing the stabilizing effect of the spin resulted in an unpredictable and usually worthless shot. Therefore, fewer rotations result in a greater distance curled, but very low values of rotation can result in unstable rocks that can yield unpredictable results. This is probably why the average curling rock is thrown with about 2.5 rotations and not a lower value—a rock given 2.5 rotations is not likely to lose its momentum and go out of control, but still has enough curl to be useful for game play.
Acknowledgments
- We would like to thank Professor Rowell and Dr. Hughey for their help in setting up and designing the experiment.
- We would like to also thank David Tax and Broomstones Curling Club for their patience during testing.
References
1Potomac Curling Club. History of Curling and its Place in the World
2Sticker, Markus. Come Around
3Shegelski, Mark. What Puts the Curl in a Curling Stone
4Jensen, E.T.; Shegelski, Mark, Curling
Ben Peters 12/10/2009