Built on Facts

Unfortunately it’s rarely on TV more than once every four years, but I have to say I’ve really gotten to curling. Not only is it interesting to watch, it looks like it’s actually a sport that could be played for fun at the beginning level. Unfortunately there doesn’t seem to be a whole lot of curling in Texas for some reason, so I have to content myself with watching. And thinking about the physics.

The goal in curling is to end each round with your stones closest to the center of the ring. From the release point to the center of the ring is about 97 feet or so. Friction with the ice brings the stone to a stop in that period. Why not estimate the amount of friction of the ice against the stone?

Friction is intrinsically a very complicated phenomenon, but it’s frequently a good approximation to say that it’s a force in the opposite direction of the motion, with a magnitude proportional to the force holding the moving object against the surface – gravity, in this case. We generally call this latter force the “normal” force, because normal in this context means “perpendicular”, and the force is perpendicular to the surface. The ratio of those two forces (frictional force and the normal force) is the coefficient of friction.

So we can write the equation describing the frictional force:

Where Greek mu is the coefficient of friction, and the mass m of the stone times the gravitational acceleration g is the normal force. We also know, because we’ve used them so many times, that an object in 1d accelerated motion obeys the standard equations of accelerated motion:

and

Here d is the distance the stone travels, t is the time it takes for to stone to complete its travel, a is the acceleration due to friction, v0 is the initial velocity. When the stone completes its travel the velocity will be 0, hence the 0 for the final velocity in the last equation. We know that force is equal to mass times acceleration, so the accleration due to friction will be the frictional force divided by mass: a = -μ*g.

But we don’t know the initial velocity. We have no way of measuring it. But we do have the total time of travel. If I understand the announcers, 24 seconds or so is a typical “hog line to tee line” time. From that, we can algebraically manipulate the equations to eliminate the initial velocity and solve for the coefficient of friction:

As expected, the longer a stone takes to travel a given distance, the lower the friction. Curling tends to use English units, so with g = 32 feet/s^2, d = 97 feet, and t = 24 seconds, plugging in I get μ = 0.011. This is a terribly tiny amount of friction, smaller than teflon on teflon. It could be that the particular approximation we’re using for friction isn’t so great here, or it could be that granite on vigorously swept ice simply has a very tiny coefficient of friction.

Either way, best of luck to the Olympians as the curl their hearts out. Team USA needs all the luck they can get!

Comments

#1 Pablo
February 20, 2010

I have also found curling to be extremely compelling. Not so much for the physics, but from a game-theory perspective. On one hand, it is a target sport, like archery or bowling, but then you have the competitive aspect, with the opponents getting in the way. Scoring-wise, it’s like bocce, but I think it is more interactive between opponents. In the end, I sort of characterize as closer to something like pool or marbles. It requires a lot of skill, of course (ask Schuster from the US who choked away the match the other day with bad throws), and in that way is like your normal target sports. But it also requires an interactive strategy. I like that.
#2 Anon
February 20, 2010

Any thoughts as to the physics behind the actual curling? That is, the hook to the left or right, after the stone has slowed down a bit (it does not curl much or at all for relatively high speed throws). I also understand that the surface of the ice itself is slightly pebbled, and that this is important. I assume that the spin, as well as the speed, with which the rock is releases, probably matters.

Is it similar physics to the curve ball in baseball? Or a different thing altogether?
#3 Winter Toad
February 20, 2010

Up here in Canada, on regular cable we get hundreds of hours per season of curling. Our primary sports channel will show 50 hours of women’s or men’s curling over the space of 10 days, with the final match often being broadcast on the national network (CBC) so that everybody can see it.

The thrower releases the rock with a slow rotation, either clockwise or counter-clockwise. Perhaps counter-intuitively, releasing with a high rotation results in pretty well no curl at all, at least when I tried it. With a very slow rotation, the rock will curl in the direction of the leading edge. That is, if the thrower sees the leading edge of the rock as moving right to left, then the rock will curl to the left. Sweeping the path makes the rock run faster and straighter.

Yes, the pebbling is important. Late in a game, the rocks will have worn away the pebble where they passed, resulting in less curl. The players have to keep track of how much curl is available from which different paths down the ice, and have to adjust their throws based on how much curl they’re expecting on this particular trajectory.

It’s an interesting game, one in which players can be competitive at Olympic levels for decades. When Brad Gushue’s team won the gold medal at the last Olympics, Brad was 25 and Russ Howard, throwing second, was 50.
#4 derek
February 20, 2010

I’ve never liked that model of friction, because such a stone sliding on an inclined plane would have an infinite terminal velocity. I mentioned it to my physics teacher, who shrugged and agreed, but said I wasn’t meant to take the model that far.

Wouldn’t a better model be one that saw the friction as an inelastic interaction that transfers momentum to the ground while dissipating the lost kinetic energy as heat? The ground would of course gain exactly as much momentum as the stone lost, while gaining only a negligible fraction of the lost kinetic energy, so the sliding stone on an inclined plane would stop accelerating when it was dissipating exactly as much energy as frictional heat as it was gaining from losing height.
#5 david
February 20, 2010

I am watching curling and times a throw. I got about 8 seconds. If that is true, your answer is off by an order of magnitude since time is squared in the final equation. Given your comment on the answer, that is probably closer.
#6 chezjake
February 20, 2010

If you’re really interested in exploring curling, perhaps you should come up and visit Chad at Union. The Schenectady Curling Club (actually in Niskayuna) is one of the oldest and biggest in the US — founded in 1907.
http://www.schenectadycurlingclub.org/
#7 Flavin
February 20, 2010

This week’s episode of the Scientific American podcast Science Talk is about the physics of curling, specifically the counter-intuitive direction of the curl. If this subject interests you it’s a must-listen.

http://www.scientificamerican.com/podcast/episode.cfm?id=ice-ice-baby-the-physics-of-curling-10-02-18
#8 qetzal
February 20, 2010

Unfortunately there doesn’t seem to be a whole lot of curling in Texas for some reason, so I have to content myself with watching.

Texans don’t curl. They shuffleboard. (From College Station even!)
#9 steve s
February 20, 2010

http://faraday.physics.utoronto.ca/GeneralInterest/Harrison/Flash/ClassMechanics/Curling/Curling.html
#10 Nathan
February 20, 2010

I also have been thinking about the physics of curling quite a bit, but more the (nearly) elastic collisions between the stones. I still haven’t gotten my head around the strategy entirely, but it’s fun to try to predict where a shot will leave all of the stones involved.
#11 Matt Springer
February 20, 2010

Wow, lots of interest in curling! There’s more physics too, as has been mentioned there’s the curl itself as well as the collisions. They’re worth posts too; no sense in trying to do an entire interesting sport in one day!

I just timed a couple throws on the currently airing women’s US/UK match, and ~23 seconds seems to be pretty typical. Much shorter times are probably the hard shots meant not to stop on the bullseye but to knock another stone out.
#12 Winter Toad
February 20, 2010

So, timing the throws. The usual way throws are timed in the broadcasts up here is “hog to hog”. Since the thrower must release the rock before the first hog line, and it will be removed from play if it doesn’t reach the second hog line, this is a good standard interval over which the rock travels without being touched by a person. The hog to hog distance is about 22 metres, but can vary a bit while still being within regulations.

As I recall, the typical hog to hog times, which vary a bit by ice conditions, are about 9 seconds for a peel (hitting a stone and expecting the thrown stone to go out of play as well), 12 seconds for a hit (hitting a stone out of play while leaving the thrown stone in play), and 16 seconds for a draw (the stone comes to rest near the centre of the house without hitting any other stones).
#13 Mike
February 21, 2010

Interesting to see that I’m not the only one that’s been thoroughly enthralled by curling in these Olympics (I’d probably not watched more than 30 seconds of the game before 3-4 days ago). But as the physics go, I think the notion of ‘coefficient of friction’ is particularly inapplicable to this game, on account of the fact that such a thing is constantly changing. Sure, you can do a nice job of figuring out it’s average… but the sweeping, and spinning of the stone, and change of the ice as the game progresses, among other things, make the computation laid out in this article particularly unenlightening. (Fun, and useful in a teaching sense? Absolutely… but w/o much applicability to the game itself. Get on to the spin and the sweeping man!)
#14 Cyndy
February 21, 2010

Actually, there are two curling clubs in Texas. They play on hockey ice, not dedicated curling ice though.
Not sure what area you are in, but here are the links.

http://www.houstoncurling.com/
http://dfwcurling.com/

I recommend trying it out. I did 3 seasons ago and became hooked.

Cyn
#15 Matthias
February 21, 2010

The low friction coefficient is realistic; I think there will be a thin film of water between the stone and the actual ice on which the former slides.
#16 doug bennion
February 21, 2010

I just googled for “number of curlers in canada”, and found an estimate of 1.3 million, 3% to 4% of the population. America’s population is ten time greater, so the equivalent number in the US would be 13 million. I don’t curl myself, but I understand there is also much appeal in the post-game beer(s), win or lose.
#17 BroccoliOfDoom
February 21, 2010

You forgot the chemistry of curling. The stone is heavy with a fairly small footprint (sorry not awake enough for math). Ice isn’t actually too slippery, but water on ice is a different story. Ice is less dense than water, and so when you apply pressure to ice it turns into water. This is the reason that you can still slip on ice and why we concentrate out weight onto narrow blades to slide more easily on skates. It also explains the low friction.
#18 Uncle Al
February 21, 2010

“Enhance” performance! Add a remote control high voltage chargeable plate internally hard by the bottom stone surface. The freezing of supercooled water is charge dependent: Positive surfaces trigger crystallization at a dielectric electrode, negative charges at the opposite interface.

http://www.citeulike.org/user/rbaron/article/6631779

Remember the Eleventh Commandment and keep it wholly.
#19 Elfie
February 22, 2010

http://hypertextbook.com/facts/2004/GennaAbleman.shtml

According to that website, some guy found the coefficient of kinetic friction to be about 0.0168. So it seems you’re in the ballpark.

They also list rubber on ice as 0.15, and speed skates as 0.0059.
#20 John Milne
February 22, 2010

Hi
I live in Kinross in Scotland, Eve Muirheads father is from our local area, the World Curling rules are based on the rules of the Royal Caledonian Curling Club, and their rules are based on the rules of the Kinross Curling Club, which has been continous since 1668, and have minutes of the AGMs to prove it.
This area is probably the heart of curling in Scotland and have numrous World Champions from this are around Perth & Kinross in both the ladies and Mens curling.
#21 NJ Wedding Photographer
February 22, 2010

Curling is quite an interesting sport. It’s kind of like ice shuffleboard – but way more complicated. The concept that took me the longest to grasp was ownership of the hammer. It baffled me why it was good to end up with an empty ring versus scoring 1.
#22 nofaith
February 23, 2010

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#23 Cannonball Jones
February 23, 2010

To John Milne…

Another Kinrossian on ScienceBlogs? I’d never have believed it! I grew up there but left about 15 years ago, now living in Thailand. Somewhat less curling here…

(Sorry for the irrelevant threadjack, just don’t expect to see someone else from a wee Scottish town of about 6,000 people to pop up on a physics blog!)
#24 James
February 23, 2010

Besides the clubs listed above, there is actually a third curling club in TX, located in Austin: http://www.lonestarcurlingclub.org/

All three clubs will be hosting learn to curl sessions around the Olympics, and the Houston club will be hosting the Texas Open Bonspiel from April 16-18. There is still space available to enter teams, and spectators are welcome for free to come see teams competing from throughout North America!
#25 CCPhysicist
February 24, 2010

Bring back real brooms! I miss the slapping noise …

We used to watch Sunday afternoon curling every week on Canadian television from across the border. Now that US broadcasters have stopped making fun of it and provided appropriate commentary with an overhead telestrater (like they have been doing for decades in Canada), it is easier to appreciate good curling. A pro can do a multi-rock takeout or hit-and-roll that would make a billiards player applaud, putting it right on the line predicted by the commentary. Bad curling, on the other hand, is painful to watch. The only plus is there is a tradition in Canadian curling to call a bad shot a bad shot.

To a novice viewer, it is easier to focus on the conservation of momentum aspect of the sport; getting the impact parameter just right to get the effect you want. It takes more experience to appreciate a draw or the use (and evasion) of guards.

On the physics side, what makes curling work the way it does is that mu is not constant! Your value is just the median value. Sweeping reduces it, making the rock carry better and also affecting its curl. Similar complexities show up in other interesting areas, such as the interaction of a rubber tire with a racing surface. The friction increases from the static value when there is a tiny amount of slippage (the slip angle in a turn) but then falls rapidly to the kinetic value when the tire is truly sliding. Friction is complicated!
#26 Chris B
February 25, 2010

Curling was the first sport I was ever any good at. Back in the mid ’80′s, myself and a group of physics majors at Brandeis University were regular visitors to the local curling club and formed a college club to pursue our interests. Nothing like a bunch of physics majors on ice with brooms and 42 pound chunks of granite.

The best tradition, however, is that the winners buy drinks for the losers after each match — so you’re a winner either way. Now that’s a tradition I wish would catch on elsewhere!
#27 Anonymous
November 18, 2010

help wat does this have to do with bowling? UHHHHH its called hw and no one seems to have an answer!!
#28 Todd
January 12, 2011

This site is way helpful in understanding some of the physics ive been studying, THANKS!!!!
#29 Matt
January 14, 2011

I’m designing a curling board game and this site helped out in a few area I wasn’t sure on. Thanks!
#30 Sharon
April 13, 2011

Hans, I think you make a very valid point. Perhaps you could contact the Congregation and present to them both your questions and suggestions.
#31 anonymous
May 25, 2011

this has been very helpful thank you to all the people that have contributed to this article

sincerely: anonymous
#32 Anonymous
January 12, 2012

Curling FTW!