Nineteen kilos of Ailsa Craig granite leaves your hand at the hack, glides thirty-eight metres down pebbled ice, and in its last few seconds hooks a metre off the line you threw it on. Late. Certain. Almost alive.
A century of physicists have tried to explain that hook. They still disagree.
Spin a wine glass clockwise on a wet table and shove it forward. It veers left. Every coin, every hockey puck, every spinning object on Earth does this — the side moving with the slide drags harder than the side moving against it, and the spinner hooks away from its own rotation. It is the first rule of friction on a sliding spinner.
Throw a clockwise in-turn down a sheet of curling ice. The rock hooks right. Toward the spin. Against the rule.
“The curling stone is the only spinning object on Earth that breaks this rule. It has been breaking it, in front of physicists, for more than a hundred years.”
Mark Shegelski’s idea: the front half of the running band, plowing into fresh pebble tops, melts a slightly thicker water film than the trailing half. Less friction in front, more behind, and the rock pivots into its rotation.
Falsifiable: warm the ice. The asymmetry should collapse and the curl weaken. So far, every controlled trial agrees.
Harald Nyberg and Sture Hogmark at Uppsala photographed the ice after a stone passed and found tiny cross-scratches, etched by microscopic roughness on the running band, all leaning the same way. The next pass catches on those scratches like a needle in a record groove and is nudged sideways.
Falsifiable: scuff the sheet with sandpaper before each shot. The scratch-pivot model says curl drops to zero. Asymmetric melting says nothing should change.
Twenty years after the first paper, Shegelski returned with Edward Lozowski and a peace treaty. Maybe both are real. The pivot-slide model has the rock alternating between long stretches of asymmetric-melt sliding and brief scratch-driven pivots at the back of the band. The weight between the two depends on speed.
Falsifiable: high-speed video the last six metres. The blended model predicts a kink in the curl rate at a critical speed. Single-mechanism models predict a smooth curve.
“Three theories. One rock. We are not done arguing.”
A cross-section through the running band. Only a thin ring near the edge of the cupped underside ever rides on the pebbles.
A regulation stone weighs between 17.24 and 19.96 kilograms (WCF Rules of Curling, 2025). Almost every competition rock on Earth is cut from one of two quarries: Ailsa Craig, an uninhabited granite plug in the Firth of Clyde off the Scottish coast, or Trefor, on the Llŷn Peninsula in north Wales. Ailsa Craig has supplied stones for over 150 years; the island is now a bird sanctuary and the quarrying is rare and ceremonial.
Pick up a stone and turn it over. The bottom is concave. Only a thin ring touches the ice — the running band, about 6.4 centimetres in radius and a few millimetres wide. It is the only part of nineteen kilos of granite the ice ever knows about. Ailsa Craig granite manages two things almost no other rock on Earth can: it doesn’t crack from a thousand freeze-thaw cycles, and it doesn’t chip from a hundred clashes a year. That’s why the stone you throw on Tuesday night came from a bird sanctuary.
And here is the fact that breaks every intuition: even within the running band, the actual contact area at any instant is a few square millimetres. Not centimetres. Millimetres. The ice is sprayed with frozen droplets, and the rock balances on a few dozen droplet-tops at a time — a marble on a handful of grains of rice. The whole sport is the physics of a 13-centimetre ring of polished granite balanced on dewdrops.
“Most of a curling stone is decoration. The math is in the ring.”
Before every game, an ice technician walks the sheet with a watering can on their back and sprays warm water through a fine rose. The droplets freeze on contact into pebble— a field of tiny frozen domes, a few thousand per square metre, each a millimetre or two across. Without pebble, a curling stone wouldn’t curl. It probably wouldn’t even slide; the full bottom would suction down and seize.
Pebble lifts the rock onto a few mm² of contact area and gives it a steady supply of fresh droplet-tops to break and re-melt as it travels. Penner measured the resulting friction across forty-seven trials at the Calgary Olympic Park: μ = 0.0168 ± 0.0008 — about the same as a steel skate, on a stone that weighs as much as a small adult. (Penner, Am. J. Phys. 2001.)
The technician chooses a temperature, a stroke pattern, a droplet size. Two technicians on the same arena ice can produce sheets that play differently. The ice tech is the instrument maker — the closest thing curling has to a Stradivarius. Too few pebbles and the rock skates without grip. Too many and the meltwater films merge and the curl saturates. There is a sweet spot.
“A man with a watering can decides how your rock will curl.”
Slow-motion any draw. The rock travels nearly straight for thirty metres. Then, somewhere past the far hog, it hooks — sharply, not gradually. The last three metres carry more curl than the first thirty-five. Every skip knows it. Almost no skip can say why.
The rock is losing two things at very different rates. Forward speed dies fast: linear friction takes about 0.16 m/s² off it every second. The spin barely decays at all — angular drag on a thin granite ring is tiny. So as the rock travels, the slide dies but the spin survives, and the ratio of spin to slide climbs and climbs. The lateral force that bends the rock’s path depends on exactly that ratio. By the last three metres the ratio is enormous, and the rock hooks hard.
Watch the next game with this in your head: thirty-two metres of straight, six metres of hook. You will see it for the rest of your life.
Total hook: 0.20 m · Sheet covered: 23.2 m
Δy ∝ s³·shegelski_late_curl_cubic“The hook isn’t a surprise. It’s the inevitable consequence of the rock losing its momentum faster than its spin.”
A sweeper does one thing: warms the ice by a degree or two. Warmer ice means a thinner meltwater layer, which means less friction, which means the rock travels farther and curls less. That is the entire mechanism.
And the numbers are real. Penner clocked unswept friction at μ = 0.0168; hard sweeping drops it to about 0.0128. That is a 24% drop, worth five to fifteen feet of extra draw. Day and Reid measured the broom output of competition sweepers at the order of a hundred watts, sustained for the twenty seconds a draw spends between the near hog and the rings. (Penner 2001; Day & Reid 1994.)
Ten feet is the difference between freezing to a guard and clipping it. No other sport lets the team mates intervene this directly between the moment the projectile leaves the hand and the moment it stops.
“Sweeping isn’t magic. It’s a degree or two of warmth, twenty seconds of contact, and a hundred watts of will.”
Hammer is the last-rock advantage. At the start of a tied game it is worth about half a point per end. But that value is not constant — it grows as the game runs out, because end ten is the last chance to undo a steal. Give one up in end one and you have nine ends to climb back. Give one up in end nine and you have one.
Kostuk, Willoughby and Saedt modelled a curling game as a Markov chain in 2001 and back-solved the value of hammer for every end of a tied ten-end game. The table they produced is the foundation of every modern curling strategy book. (Kostuk, Willoughby & Saedt, Eur. J. Oper. Res. 2001.)
Blank with hammer in end one and you trade 0.45 expected points now for 0.45 next end — a wash. Blank in end nine and you trade 0.60 for 0.70 — a fifth of a point upgrade. The deeper the game gets, the more you should hoard hammer.
“Hammer in end ten is worth one and a half hammers in end one.”
Two thousand simulated shots — a thousand draws to the button on the left, a thousand hit-and-stick takeouts on the right — each one optimised under realistic release noise. The same parameter (launch speed) drives the outcome. The slopes go in opposite directions.
On the draw, more weight means more distance and more distance means closer to the button. The slope climbs. Every skip knows it: a light draw is a doomed draw, and the cure is more weight.
On the takeout, the same parameter does the opposite. Too much weight and the shooter rolls through the back of the rings into the backboards. The slope plummets. The optimiser rewards less weight, not more, inside the in-house range.
“Draw weight rewards more. Hit weight rewards less. Every coach who ever yelled ‘soft hands’ was teaching the same theorem.”
This page is a gift to anyone who has thrown a few hundred rocks and ever wondered why the last one did what it did. Every claim on it traces to a published measurement or a machine-checked proof. Nothing here is folklore.
If you want a piece of math built for your rock, your ice, your question, write to us. The first one is free.
Two free maths next door, on the same proof engine: Onitama — sixteen cards, twenty-five squares, ten to the seventeen positions — and Signal— Knuth’s 1976 information bound, kernel-checked.
“Curling deserves better than folklore.”
Good curling.