Explanation:

Angle Calculations

## Summit Analysis using the National Elevation Dataset

Which peaks have the steepest terrain within the area surrounding the summit? To answer this question, these web pages present analysis of digital data provided by the USGS in the form of the National Elevation Dataset.

### Angle Calculation:

In contrast to plugging geographical information into a complex formula to get a numerical rating, angle-based calculation reports steepness of the terrain surrounding a summit in terms of easy to understand figures: angle and vertical drop.

The following lists display maximum and minimum angles and vertical drops, with straight-line horizontal distances outward from the summit set at 100m, 800m and 1600m. All directions(360 degrees) outward from the summit are considered. For convenience and ease of understanding, angle units are in degrees. Drop is measured in feet. A negative angle figure indicates there is terrain higher than the summit within the given horizontal distance. A figure of -99 or greater in angle or drop indicates the summit was not evaluated due an error in the digital elevation data.

The simple figure below identifies the angle which is being considered. As can be seen, a higher angle figure indicates a steeper path to the summit from the given horizonal distance.

Three ranking criteria are presented at three horizontal distances(100m/800m/1600m):

1. Maximum angle of steepness in any direction outward from summit. This measures the steepest single line at the given distance.

2. Highest minimal angle of steepness in any direction outward from summit. Every other direction will have a more severe drop than the figure shown here. At 100m this measure favors sharp spires, at 800m and 1600m the most conically shaped summits will score near the top.

3. Average angle of steepness in all directions outward from summit. Best measure for all around sttepenss of a summit at the given distance interval. At 100m, sharp spires are identified, 800m/1600m favor large mountains with great vertical drop.

The Summit Steepness Master List is a normalized average of the average angle figures at the three given distances(100m/800m/1600m). This is the best measure for all around vertical drop, with all distances represented.

Use menu on left to view lists for each state

### Background:

The calculations above are related of the concept of Spire Measure, with the main difference here being that fixed distances from the summit are analyzed.

The rationale behind staying within a fixed distance is to focus on the area immediately surrounding the summit in order to identify peaks with steep terrain near the summit, as opposed to peaks which may not be particularly sharp, but have moderately steep slopes which go on and on into the distance, resulting in large relief over a local area. In Colorado, summits such as Antero Peak or Pikes peak are good examples of peaks which have large relief over a local area, but are not especially steep. Within the fixed distance framework, these summit do not grade out highly. Small, sharp peaks grade out highly at a fixed distance of 100m, while larger mountains with steep sides get high scores at a 800m distance.

While the algorithm to produce these lists is an original work, the general concepts are consistent with the Spire Measure framework. I wish to thank the creators(E Earl, D Metzler, B Bolton, and others) of the original Spire Measure. Also, thanks to the US Geological Survey, who produces the National Elevation Dataset.

Peak lists are courtesy of John Kirk, Listsofjohn.