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The surprising motion of ski moguls supplemental material

To capture mogul migration, one of us (Bahr) made time-lapse videos from a collection of pictures. At 11:00am every day from 4 December 2005 through 14 April 2006, an automated camera captured photographs of the Riflesight Notch run from the Utah Junction parking lot at the Winter Park Resort in Colorado. The camera took one photo every hour, but only one picture per day—the 11:00am shot— was considered for the video because the Sun casts different shadows at different hours. Thus, including several photographs per day would actually obscure the moguls’ movement. If an image was obscured by poor visibility due to a snowstorm or fog, then that photograph was not included in the video.

Each day in the movie corresponds to approximately 1/100th of a second of video. When a day is missing, the previous frame is scaled to last longer and cover the gap. In December and March, 4-day gaps occur; in those cases the movie includes frames that last roughly 1/25th of a second and yield a noticeable delay.

All three videos show the same uphill movement of the ski moguls. The portion of Riflesight Notch in the field of view is 100 m long and has an average slope of 40°. Moguls move uphill in the direction opposite to that in which skiers travel. Measurements show that the average mogul separation in the direction of skier travel is 5.7 m, and the videos reveal that the bumps move approximately two mogul lengths over the five-month-long ski season. The migration speed, therefore, is slow, roughly (2 × 5.7 m)/(150 days) = 0.08 m per day.

At the beginning of the 2007–08 season, Bahr took photographs every five minutes during the first few days that Riflesight Notch was open to skiers. That attempt to capture the formation of moguls was not successful. With hundreds of skiers in the first hour eager to ski fresh powder, the moguls formed within minutes. The large number of skiers was unusual, however. Although the number of skiers depends on the snow conditions and time of day, a simple manual count averages 10 skiers per hour on Riflesight Notch—fewer in the morning and afternoon, more at midday. In contrast, about 100 skiers per hour enjoy the nearby Mary Jane and Sleeper trails, both of which are groomed.