How Skiers Move Moguls Uphill

BY Rebecca Jacobson  January 10, 2013 at 12:50 PM EDT



Here’s a little-known winter fact: Ski moguls, those tricky-to-navigate bumps on well-traveled ski runs, migrate slowly uphill.

Moguls are formed by skiers on virtually all ski trails that are not mechanically flattened with grooming equipment. They organize spontaneously as skiers move along a ski run, kicking up snow behind them as they turn. The kicked-up snow forms into piles, which eventually turn into moguls.

David Bahr, an avid skier and a professor of physics and computational sciences at Colorado’s Regis University, had suspected for some time that the moguls he slalomed around moved up the mountain. Testing that theory started as an experiment to demonstrate to his students how nature self-organizes.

So at the start of the 2005 ski season, with the help of some ski-savvy graduate students, he set up an automated camera on the Riflesight Notch run at Colorado’s Mary Jane Mountain. At 11 a.m. every day from Dec. 4, 2005 through April 14, 2006, the camera snapped shots of the run. They used these photographs to create a time-lapse video of the mountain’s movement over time. Each day corresponds to approximately a hundreth of a second of video.

And indeed, the video showed the moguls slowly creeping up the trail.

“You can actually see these things moving uphill,” Bahr said. “It’s pretty remarkable.”


Illustration by David Bahr.

The moguls, his team found, move in what’s known as a “backward-propagating kinematic wave.” Kinematic waves are traveling masses, Bahr explains in this study, which was released in the publication, Physics Today in November 2009. As skiers move down the mountain, they scrape snow off the downhill side of the moguls and push it to the uphill side.

The same phenomenon occurs with brake lights in traffic, he said. The cars are moving forward, but a car slamming on its brakes at the front of the line will send a wave of brake lights backward through traffic as everyone behind him is forced to stop.

Bahr’s study found that with an average of 10 skiers on the hill per hour, the moguls move about 33 feet throughout the season. That’s just under an inch per day.

See it yourself here, in this time-lapse video:

And here’s another:

Interestingly, as the bumps migrate uphill, they align with other bumps, and then together march up the mountain, Bahr explains on his website:

“Once a bump gets in line, it never gets out of line,” he writes. “Why? Because the skiers would preferentially ‘scrape and pile’ that misaligned bump until it was re-aligned. So each row of bumps marches in lockstep up the hill. Think of the bumps as a marching band. At first everyone in the band mills about haphazardly, then they organize into rows, and finally each row marches in sync.”

Moving that much snow takes energy, said Ray Browning, assistant professor of exercise science at Colorado State University, who contributed to the study. Browning calculated that each mogul requires 40 calories to move a meter up the hill. Here’s how the researchers explain the calculations:

Measurements show that recreational skiers expend about 20-25 kilocalories per minute. Skiers spend roughly 20 seconds of actual time skiing (as opposed to huffing and puffing) when traversing a 100-m mogul field such as the one shown in the figure, located at Riflesight Notch in Colorado. That means a skier expends 8 kcal in a run. About 10 skiers go down Riflesight Notch each hour, and the mogul field is open 50 hours per week for five months. So there are about 10 000 runs down Riflesight Notch per season and 80 000 kcal expended. The field has about 200 moguls; that comes to 400 kcal per mogul each season. Since moguls move about 10 m uphill over the course of a season, each one requires 40 kcal/m to move uphill.

As a public service for any beer-drinking skiers seeking to work off the calories consumed, the team concluded the study with some helpful calculations:

The amount of energy required to move a mogul one meter is roughly equivalent to the number of calories in a half a light beer, they say. Moving all 200 moguls on the ski run in the study, researchers say, would take about 1,000 beers worth of calories.

“More prosaically, skiers expend half a light beer for every meter of uphill mogul movement — a lot of work for not a lot of refreshment,” the study concludes.