The science of sledding

By Ray FordRay Ford


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The snowy slope beckons, your heart pounds a tattoo like a hungry woodpecker, and a little-kid grin is smeared across your face. It’s toboggan time, and ain’t it amazing how winter changes everything?

Take the laws of physics: Last summer, friction was a drag and gravity a downer. When the screen door stuck open and mosquitoes invaded the cottage, you blamed friction. When it was too much effort to climb from dock to cottage, you cursed gravity. (Sloth probably played a role, too—but let’s not make this personal.)

When the world is cloaked with ice and snow, though, friction no longer chafes. Gravity becomes your friend. And the slope from cottage to lake is transformed into a white-knuckle, can’t-scream-because-your-face-is-covered-by-flying-snow toboggan run. Expert sledders don’t need an operator’s card or a clingy wardrobe from Lululemon (at least, not yet). But a little high-school physics helps you go faster, carve better turns, and maybe even stay on—or explain why you keep falling off—your sled. In case you weren’t paying attention back in physics class, avoid the school of hard knocks with this cheat sheet for sledders.

It’s all downhill from here

Notice how tough it was to climb up the sledding hill? That’s because gravity—the force that’s pulling you toward the earth’s centre—was working against you. But as soon as you plant your bum on your toboggan, gravity starts working for you—and fast.

How fast depends on the angle of the hill. A free-falling object accelerates at 9.8 metres per second, every second. So if cartoon character and noted physics demonstrator Wile E. Coyote flew off a cliff on his Acme toboggan, he would be falling at more than 35 km/h after one second. In another tick of the clock, he’d top 70 km/h.

As air resistance applies the brakes, Wile E. reaches terminal velocity, the point where his speed becomes constant. An expert skydiver in an aerodynamic position tops out at around 320 km/h. An obsessive coyote will be slower, thanks to his furry coat and flailing motions.

Cartoon characters aside, no one can sled on a vertical incline, at least not more than once. But “the steeper the incline, the fuller the effect of gravity you’re exposed to,” says Mark McDonald, a Memorial University graduate student in physics. Even a 15° slope offers about one-quarter the pull of gravity. Leaving aside the factors of snow friction and air resistance, that’s an acceleration of 2.5 metres per second per second—from zero to 45 km/h in just five seconds. Emissions-free, too.

Feel the burn

With speeds like that, thank goodness for friction, the force that slows moving things. Without some resistance, your toboggan would rapidly become dangerous and uncontrollable—or more dangerous and even less controllable.

Snow offers about a tenth to a quarter the friction of wood, but at the microscopic level, both the bottom of the sled and the top of the snow are rough and uneven. As the speeding toboggan encounters the jagged snow crystals, it grapples with and flattens the flakes, losing some of its speed in the process. An added bonus of this unseen wrestling match is that it could create enough heat to melt a thin layer of snow, helping to lubricate the sled. The struggle even produces its own soundtrack: that swishing sound that accompanies a good run.

There’s a Goldilocks factor at work here, too. Snow that’s either too cold or too warm offers more friction and makes for slower sledding. While a thin film of water helps a sled glide over uneven snowflakes, when the air temperature is close to the melting point, the sled sinks into the slush, exposing more surfaces to the grip of friction, and the run becomes slow and sticky.

When the temperature falls into the -20°C to -30°C range, snow crystals become stronger—so strong that, now, instead of squeezing and melting them, the toboggan pushes and rolls them over as if they were grains of sand. “You’re still generating heat, but not enough to melt much of the snow,” says Nirmal Sinha, a specialist in ice and snow, and a senior research officer at the National Research Council’s Institute for Aerospace Research in Ottawa.

So if near-zero is too warm and -30°C too cold, somewhere in the middle—say, -5°C to -10°C—is just right. The soft snow packs and melts beneath the toboggan but refreezes to form a thin glaze that makes the next run faster.

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Ray Ford