# Line of greatest slope

A surface showing one example (approximate) of a path of greatest slope (red path).

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.[1]

## 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.[citation needed] 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.[citation needed]

## Applications

### Mountain biking

A mountain biker riding a trail which follows the line of greatest slope, or fall line.

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,[1] 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

The line of greatest slope defines the path (red) a climber will take to gain the most elevation with the shortest possible path.

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.