grade (geography)

In topography, the slope of a hill, mountain, road or anything else inclined, is more often referred to as its grade (or, sometimes in the US and usually in the UK, gradient). The mathematical definition of slope is generally accepted as applicable in the topographic context. However, with regards to the angle of inclination, the following definitions of grade conflict:

The tangent - the ratio of the altitude change to the horizontal distance between any two points on the grade, and the mathematical definition of slope
The sine - the ratio of the altitude change to the surface length between any two points on the grade.

The difference between the two is small for gentle slopes. (See Small-angle formula.) The ambiguities and the small differences that result may permit these two inconsistent approaches to coexist unrecognized, especially where all grades considered are subject to engineering upper limits of 15% or less. Many of the mathematical principles of slope, that follow from the definition, are applicable in topographic practice. Grade is usually expressed as a percentage. Expressing it as the angle from horizontal carries the same information, but may lead to confusion for readers who are not proficient in trigonometry. For instance, on hearing the same ground described as having 50% grade and also having 30 degrees inclination, one might falsely infer that a 5:3 ratio exists between the grade and the angle of inclination. In vehicular engineering, various land-based designs (cars, SUVs, trucks, trains, etc.) are rated for their ability to ascend the slope of terrain. (Trains typically rate much lower than cars.) The highest grade which a vehicle can ascend while maintaining a particular speed is sometimes termed that vehicle's "gradeability" (or, less often, "grade ability") at that speed.

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