Definitions

Pinnacle points are a points from which no higher elevation point can be seen. Across the globe, 885 have been found. These are all pinnacle points with more than 300 m (~1000 ft) of prominence or more than 160 km (~100 miles) of isolation. The curvature of the Earth, atmospheric refraction, and local topography are taken into account. Two summits are defined to have line-of-sight if light can theoretically travel from one to the other under ideal atmospheric conditions. For more, refer to the What is a Pinnacle Point? page.

Prominence is the minimum vertical distance one must descend to reach a higher point.

Isolation is the distance to the nearest higher point.

Atmospheric refraction is the bending of light in the atmosphere due to varying temperatures and pressures.

Local topography is the specific shape of the terrain surrounding a point.

Links

My journal of summitted pinnacle points

My github for pinnacle points

An explanation of the algorithm used to find pinnacle points

An article by the Relative Hills Society on OTOTWs and pinnacle points

Contact me

Data Sources

1. Mountains by Prominence

Andrew Kirmse and Jonathan de Ferranti found all 11,866,713 summits on Earth with over 100 ft (~30 m) of prominence. I use this dataset to find all pinnacle points with more than 300 m (~1000 ft) of prominence.

2. Mountains by Isolation

Andrew Kirmse and Jonathan de Ferranti found all 24,749,518 summits on Earth with over 1 km (~0.6 miles) of isolation. I use this dataset to find all pinnacle points with more than 160 km (~100 miles) of isolation.

3. On-Top-Of-The-World Mountains

An on-top-of-the-world mountain (OTOTW) is a summit where no land rises above the horizontal plane from the summit. Since any land that rises above the horizontal plane would have higher elevation than the summit itself, if a summit is not an OTOTW then it can not be a pinnacle point either. In other words, pinnacle points are a subset of OTOTWs. Kai Xu found all 6,464 OTOTWs on Earth with over 300 m (~1000 ft) of prominence. I identify which of these 6,464 summits are pinnacle points. Andreas Geyer-Schulz deserves mention as well for his extremal peaks.

4. Atmospheric Refraction

The exact path light takes in the atmosphere depends on many factors. However, according to the San Diego State University, a ray's path can be approximated as the arc of a circle with radius seven times greater than Earth's. I use this when determining if two summits have line-of-sight.

5. Open-Meteo and Copernicus

Open-Meteo provides a free elevation API that uses the Copernicus DEM. I use this API to find the elevation of points that are not in any of my datasets.

Sources of Error

1. The Earth is approximated as a sphere instead of an ellipsoid. This is done for simpler math.
2. There is some inherent error in the data. The datasets have resolutions ranging from of 30 m (1 arcsecond) to 90 m (3 arcseconds). All data sources are surface elevation models, so trees and buildings are included.
3. Only 100 equidistant points are sampled when determining if two summits have an obstructed line-of-sight. Some points that could block line-of-sight may not be captured in this sample. By increasing the number of sampled points, more pinnacle points could be found.
4. The algorithm assumes there to be no land below sea level, which is not quite true. Any pinnacle points below sea level would not have been identified. It is possible for some identified pinnacle points that are near basins below sea level to not truly be pinnacle points. This is because these points can see farther across their basin in reality than they could if the basin did not descend below sea level.
5. Only summits with more than 300 m (~1000 ft) of prominence or more than 160 km (~100 miles) of isolation are considered. The promience threshold is determined by the OTOTWs dataset since I only consider points in Source 1 that are OTOTWs. When finding pinnacle points in Source 2, high isolation points are obvious strong candidates when identifying pinnacle points. The specific value for the isolation threshold was decided arbitarily. Computation time increases considerably as the isolation threshold is lowered.
6. To take atmospheric refraction into account, light rays are approximated as arcs of circles (Source 4). The path light takes in the atmosphere is in fact much more complex and depends on many factors. Since the distance you can see from a given point depends on temperature and pressure, the distance you can see from a point technically changes with the seasons and even the time of day. Additionally, the approximation of light following the arc of a circle only holds true for altitudes that are small compared to the 8 km height of the homogeneous atmosphere. This project is slightly outside of this scope.

App Download

Since the app is only available by downloading the APK, only Android devices are currently supported. Follow these steps to get the app on your Android device:

1. Open this page on your Android device.
2. Click the button that looks like [...] (three dots).
3. Click [Download]. Open the APK on your device when it is done downloading. You may get a message similar to "For your security, your device is not allowed to install apps from this source". You'll have to go to your settings and allow unknown installs from this source. I recommend changing this setting back after completing these steps.
4. Click [Install].