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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 ...
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.
The gradient of F is then normal to the hypersurface. Similarly, an affine algebraic hypersurface may be defined by an equation F(x 1, ..., x n) = 0, where F is a polynomial. The gradient of F is zero at a singular point of the hypersurface (this is the definition of a singular point). At a non-singular point, it is a nonzero normal vector.
A spatial gradient is a gradient whose components are spatial derivatives, i.e., rate of change of a given scalar physical quantity with respect to the position coordinates in physical space. Homogeneous regions have spatial gradient vector norm equal to zero.
In aerodynamics, climb gradient is the ratio between distance travelled over the ground and altitude gained, and is expressed as a percentage. The angle of climb can be defined as the angle between a horizontal plane representing the Earth's surface, and the actual flight path followed by the aircraft during its ascent.
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Stream gradient may change along the stream course. An average gradient can be defined, known as the relief ratio , which gives the average drop in elevation per unit length of river. [ 4 ] The calculation is the difference in elevation between the river's source and the river terminus ( confluence or mouth ) divided by the total length of the ...
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