The Collegiate Peaks (“the Avenue of Fourteeners”) are a section of the Sawatch Rangein Colorado. For this project we chose to focus on trails up to the peak Mount Harvard and Mount Princeton. Our goal was to determine the steepest and least steep parts of the pre-established trails. To do this we used contour maps, average gradients, and average directional derivatives. There is only one trail to the peak of Mount Princeton listed on Alltrails and that was the trail that we looked at. There are multiple trails up to the peak of Mount Harvard, we looked at the trail up the south face of the mountain.
We used the contour maps in Alltrails to determine where the trails for each hike were the steepest and least steep. For both Mount Harvard and Mount Princeton the steepest sections of the hike were where the trail was perpendicular to the contour lines. Due to this we were able to calculate an average gradient (change in elevation/distance traveled) for those steeper sections. For Mount Harvard the least steep section of the trail is closer to the trailhead where the contour lines are farther apart and the trail is more parallel to the contour lines. The least steep sections of the Mount Princeton trail are in the switchbacks and the place in which the trail follows the contour line. For these portions of the trail we calculated the average directional derivative using the same formula that was used to calculate the average gradient.
