Line of greatest slope
steepest slope on a surface
In topography, the line of greatest slope is a curve following the steepest slope. In mountain biking and skiing, the line of greatest slope is sometimes called the fall line.
Definition
Mathematically, the line (or path) of greatest slope from a point is determined by the gradient of height, taken as a potential field with respect to an acceleration from the force of gravity. Lines of greatest slope are analogous to lines of force acting to accelerate an object downward at that point. These lines are orthogonal to contour lines. Discounting inertial forces and terrain roughness, a ball rolling down a slope, or water flowing down, will accelerate in the direction of greatest slope.
Applications
Mountain biking
In mountain biking the line of greatest slope defines the fall line, which is the path a trail will follow to descend a hill or mountain with the shortest path, and will also cause the rider to gain the most velocity (assuming brakes are not used, and other factors such as rolling resistance are equal).
Mountain climbing
In mountain climbing, the line of greatest slope defines the fall line, which is the path a climber will take to gain the most elevation with the shortest possible path.
Map reading
The line of greatest slope has practical significance in map reading. On the terrain it is often far more discernible, even intuitively obvious, rather than accurately picking out the consistent height level on what is likely the undulating uneven ground along the ground represented on the contour line.
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This entry incorporates text from “Line of greatest slope” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.