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[1] [2] as a ratio of one part rise to so many parts run. For example, a slope that has a rise of 5 feet for every 1000 feet of run would have a slope ratio of 1 in 200. (The word "in" is normally used rather than the mathematical ratio notation of "1:200".) This is generally the method used to describe railway grades in Australia and the UK.
The Universal Soil Loss Equation (USLE) is a widely used mathematical model that describes soil erosion processes. [1]Erosion models play critical roles in soil and water resource conservation and nonpoint source pollution assessments, including: sediment load assessment and inventory, conservation planning and design for sediment control, and for the advancement of scientific understanding.
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 (%).
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.
Simpson's paradox says that even if a vector (in orange in figure) has a smaller slope than another vector (in blue), and has a smaller slope than , the sum of the two vectors + can potentially still have a larger slope than the sum of the two vectors +, as shown in the example.
For example, a 3-variable parameter space which is explored one-at-a-time is equivalent to taking points along the x, y, and z axes of a cube centered at the origin. The convex hull bounding all these points is an octahedron which has a volume only 1/6th of the total parameter space.
Due to the normal cross slope and the interaction with grade, road sections with insufficient drainage gradient are few and short. Still, they account for an unacceptable number of skid accidents. These hot spots are found at the entrances and exits of banked curves, where the cross slope changes direction in order to create superelevation.
In general, if an increase of x percent is followed by a decrease of x percent, and the initial amount was p, the final amount is p (1 + 0.01 x)(1 − 0.01 x) = p (1 − (0.01 x) 2); hence the net change is an overall decrease by x percent of x percent (the square of the original percent change when expressed as a decimal number).
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