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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.
[18] [19] Today, the degree, 1 / 360 of a turn, or the mathematically more convenient radian, 1 / 2 π of a turn (used in the SI system of units) is generally used instead. In the 1970s – 1990s, most scientific calculators offered the gon (gradian), as well as radians and degrees, for their trigonometric functions . [ 23 ]
Stream gradient (or stream slope) is the grade (or slope) of a stream. It is measured by the ratio of drop in elevation and horizontal distance. [ 1 ] It is a dimensionless quantity , usually expressed in units of meters per kilometer (m/km) or feet per mile (ft/mi); it may also be expressed in percent (%).
As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge. The divergence of a tensor field of non-zero order k is written as =, a contraction of a tensor field of order k − 1. Specifically, the divergence of a vector is a scalar.
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.
To compensate for this, the gradient should be a little less steep the sharper the curve is; the necessary grade reduction is assumed to be given by a simple formula such as 0.04 per cent per "degree of curve", the latter being a measure of curve sharpness used in the United States. On a 10-degree curve (radius 573.7 feet) the grade would thus ...