The magic motion of moguls

Gravity always wins, one might think. Avalanches roar and skiers plunge inexorably downhill. But moguls—or bumps, as they’re known by skiers—move uphill.

Just ask lead researcher David Bahr, a Regis University professor and former CU geological sciences PhD student; Tad Pfeffer, a professor of civil, environment, and architectural engineering at the University of Colorado; and Ray Browning, a professor at Colorado State University and former CU integrative physiology PhD student.

The three teamed up to confirm their hunch that moguls move uphill.

“I knew that moguls moved uphill,” says Bahr, “to a physicist, this was the only direction that makes sense, but nobody would believe such a counter-intuitive idea. I don’t think Winter Park believed me at first, but they were willing to find out, and they were quite generous in letting us do the research on their mountain.”

The results of that research, an article titled “The surprising motion of ski moguls,” was published in the November issue of Physics Today.

As the article explains, skiers cruise down fresh slopes, unimpeded, turning whenever and wherever they choose. With each cut, with each calculated turn, they push snow into small piles. These piles build over time, creating “bumps” that can’t be easily ignored.

To save knees and ligaments from extreme damage, skiers turn on the underside of moguls.

“To control speed, skiers turn and scrape the snow on the downhill side of the moguls they encounter,” the authors write. “In so doing, they push snow down the mountain and pile it onto the uphill side of the following mogul. As a consequence, each mogul loses material on its downhill side but gains new material on its uphill side.”

This process causes the moguls to migrate uphill. Each skier who traverses the mogul field adds new snow on the uphill side of bumps and shaves some snow off the downhill side.

Essentially, this pushes moguls up the hill. This process of “backward propagation” is not unique to moguls.

“Moguls are a type of kinematic wave, an entity rather different from the more commonly studied dynamic wave,” according to the study.

“The classic example of kinematic waves, and the setting in which kinematic wave theory was formulated, is the flow of cars on a highway,” said Pfeffer.

Furthering the analogy between car and mogul, the article states, “If a car taps its brakes, then the cars behind bunch up and the density of cars increases. That bunching travels backward through the traffic, even though the cars continue to move forward, and so the bunched cars, like moguls, are said to be backward-propagating.”

The study finds that moguls move uphill at roughly 8 centimeters meters a day, or about 10 meters a season. Using this observation along with data from Riflesight Notch in Winter Park, Colo., the authors calculate how much energy it takes to move a mogul each year.

“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 (kilocalories) expended. The field has about 200 moguls; that comes to 400 kcal per mogul each season.”

“An especially unique part of the collaboration was the realization that we were measuring calorie expenditure, and that’s a very hard thing to do without setting up specialized experiments, getting permission to work with human subjects, etc.,” according to Bahr.

It’s that collaboration that makes this project unique. Three outstanding specialists, from three distinct disciplines, each from one of the three top-tier Front Range educational institutions came together to collectively make this research happen.

“All three of us are skiers, so we share that common interest; but so many successful research collaborations these days are crossing discipline boundaries. It’s great to get three specialists in different fields all working together. We had a geophysicicist and computer scientist (Dave), a geophysicist and engineer (Tad), and a kinesiologist and specialist in physical activity (Ray),” says Bahr.

“This seemed like a fun opportunity to find out if they actually do migrate uphill and work on some new time-lapse photogrammetric methods at the same time,” adds co-author Pfeffer.

“We used one of Tad’s cameras to do time-lapse photography.  The camera was housed in a waterproof case and set up on the side of a building.  The camera took pictures every hour, all season long.  Each picture became the frame in a movie.  An entire season flies by in just a few seconds of the movie,” Bahr notes.

When the project started, Pfeffer was just starting to work on time-lapse photogrammetry, a process he now uses with some frequency for his work with the Extreme Ice Survey (http://www.extremeicesurvey.org).

The Extreme Ice Survey, founded and directed by CU alumnus James Balog, uses time-lapse photography to document the retreat of glaciers worldwide. His work has been featured on PBS and in National Geographic.

Viewing the video makes it clear that moguls do, in fact, move uphill. But experiments should be replicated, and skiers might well wish to do their own, first-person field research.