Map Profiles Are Morbid Hallucinations
On a vertically exaggerated elevation profile, it is notoriously easy to exaggerate the perceived difficulty of a mountain trail. Vertical exaggeration can compress an innocent set of connected points into a lugubrious series of evil towers. The problem arises from our need to see a vast, bumpy chunk of the world represented by a tiny, smooth graph on paper. Unfortunately we tend to lose something in the translation from reality to hand-sized.
Map elevation profiles typically measure distance in miles or kilometers along a horizontal axis, and plot the corresponding elevation gains and losses in feet or meters from a vertical axis at specific points. Assuming an ample set of vertical points, the resulting picture emulates the summits and gaps along the trail's distance. However, keep in mind, an elevation profile only has limited inches of space to represent dozens of miles of distance horizontally and thousands of feet of elevation vertically. It is more art than science.
The design of an elevation profile's horizontal distance scale is fairly straight forward. An inch is one mile or ten kilometers or some other appropriate scale unit. On the other hand or axis, the creation of the vertical elevation scale is ripe fodder for morbid hallucinations. If one inch is one mile horizontally and we keep the same scale for elevation, then 528 feet of gain over one mile is .1, or 1/10th, of an inch vertically. Such a depiction is difficult to see, and creates an opportunity for an imaginative mind. For example, our humble tenth of an inch representation pumped up five times stretches the 1/10th inch to 1/2 inch making the 528 feet look like 2,640 feet, or a half mile rise over a mile run. The creative result is easy to see, but grossly distorted. While a picture may be worth a thousand words, a vertically exaggerated profile earns its weight in speechlessness.
After we vow our abstinence from vertically exaggerated elevation profiles, we still do have a couple of ways to scan the vague unknown of a mountain trail's ups and downs. One measurement is the percent gradient of a slope. The other measures the degrees of a slope. Either measurement will give us consistency and spare us from exaggerations. Although a slope's gradient and the degrees of a slope are related, they are not the same.
Gradient is expressed as a percentage. It tells us how the average elevation changes over every hundred feet of our total distance. For example, a 10% gradient means that we have an average elevation increase of 10 feet for every 100 feet. Assume we hike 400 feet and our elevation increases 40 feet. That's a 10% slope gradient. Here's the calculation:
40 ft. / 400 ft. * 100 is 10%
slope gradient is the elevation change divded by the distance multiplied by 100
The degrees of a slope measure the upward or downward angle of the slope. Using a bit of trigonometry, we can calculate a slope's angle in degrees of the elevation change over a distance. We divide the elevation change by the distance, and then find the arctangent of the result. We can use calculators to get the arctangent or Google: 'arctangent of (40/400) in degrees'. The degrees of slope of the 40 feet increase in elevation over the 400 feet distance is:
arctangent (40/400) in degrees is 5.7 degrees
We see from our calculations that the slope gradient, 10%, is a different measurement than the 5.7 degrees of the slope. However, there is a relationship between the slope gradient and degrees of slope. For example, if we increased our elevation gain to 80 feet over 400 feet, then the gradient of the slope would be 20% and the slope's angle would be about 11.3 degrees. We doubled our elevation increase which doubled our gradient and likewise doubled our degrees of slope. Likewise tripling, a gradient of 30% is a slope of 16.7 degrees. A good way to grasp their relationship is to think about walking up stairs with the same height and width. From the bottom to the top of the stairs, we average a 100% gradient or a 45 degree slope ( total horizontal distance / total vertical distance = 1 times 100 = 100% gradient, or arctangent of (1) = 45 degrees).
Enjoy a vertically exaggerated elevation profile if you wish, but make sure you understand that it is merely a smooth, hand-sized illusion of an awesome, incomprehensible world that we choose to hike on. Don't let an elevation profile intimidate you with its vertical exaggeration. Those evil towers only exist in fearful minds. If you desire to learn about the challenges of a mountain trail's ups and down, then peruse the gradients or degrees of its slopes. Neither percentages nor degrees will stretch the truth.
Here's an example of a 7.26:1 vertically exaggerated profile from a 2004 Maine Appalachian Trail Club map marked up to show distance and elevation measurements (points A, B, C, D, E, and F). The artwork's profile measures from 50 to 70 degrees, or a gradient well over 100 percent to convey dramatic steepness. The real trail varies between about four to 15 degrees, or 8 to 26 percent gradients. That's a challenging hike, but not as intimidating as the picture looks. See the table for the slope gradients and degrees from points A, B, C, D, E, and F.
