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l = slope length α = angle of inclination. The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line is either the elevation angle of that surface to the horizontal or its tangent. It is a special case of the slope, where zero indicates horizontality. A ...
Cant gradient is the amount by which cant is increased or decreased in a given length of track. The change in cant is required in order to connect a tangent track (no cant) to a curved track (with cant) through a transition curve. The rate of change of cant is used to determine the suitable cant gradient for a given design speed.
The gradient of the function is always perpendicular to the contour lines. When the lines are close together the magnitude of the gradient is large: the variation is steep. A level set is a generalization of a contour line for functions of any number of variables.
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
A level surface, or isosurface, is the set of all points where some function has a given value. If f is differentiable, then the dot product (∇f ) x ⋅ v of the gradient at a point x with a vector v gives the directional derivative of f at x in the direction v. It follows that in this case the gradient of f is orthogonal to the level sets of f.
Sergeant Chris D. Washington checking his Topographic map during a morning deer hunt in Kilgore, Texas A topographic map of Stowe, Vermont with contour lines Part of the same map in a perspective shaded relief view illustrating how the contour lines follow the terrain Sheet #535 (2013 version; second digital edition) of MTN50 Spanish National Topographic map series, covering Algete town (near ...
I–VI)–is used to grade the "overall" risk and difficulty of mountain routes (with the gradient of the snow/ice fields) (e.g. the 1938 Heckmair Route on the Eiger is graded: ED2 (IFAS), VI− (UIAA), A0 (A-grade), WI4 (WI-grade), 60° slope). The related "commitment grade" systems include the notable American National Climbing Classification ...
Analogue on a Cartesian grid by adding lines of slope −1. The scale of the c axis is that of the a and b axes. The cross denotes the point a = b = c. Cartesian coordinates are useful for plotting points in the triangle. Consider an equilateral ternary plot where a = 100% is placed at (x,y) = (0,0) and b = 100% at (1,0).