Slope is the steepness of the surface element. Usually, the ratio of the vertical height h of a slope to the horizontal distance l is called the slope (or slope ratio), which is represented by the letter I. The greater the slope, the greater the I, and the greater the horizontal distance I, and the greater the i=h/I, so the greater the slope, the steeper the slope.
Slope can also be regarded as the angle between slope and horizontal plane. The greater the slope, the greater the included angle, the greater the tangent of the included angle and the steeper the slope.
Extended data:
Slope is often expressed as a percentage or one thousandth of the tangent of trigonometric function, that is, "climbing height divided by moving distance on the horizontal plane".
Slope = tan α = h/d.
Where α is the angle between the slope and the horizontal plane; H is the slope height; D is the length of the slope.
Except tangent percentage, when the value of slope is large, the steepness of slope will be directly expressed by angle α. Mathematically, when the angle is less than 5, the error between sine function and tangent function is very small, so when the slope is very small (less than 10%), sine function can be used for approximate calculation, such as the hydraulic slope formed by running water.
The principle of slope marking method can be applied to topographic survey. Although using any of the above marking methods can bring out the same information, in order to avoid confusing readers who are not proficient in trigonometry, tangent percentage is most often used in public places.
In Britain and Hong Kong, tangent gradient is often marked by ratio instead of percentage, such as "1: 12" instead of "8.3%". In the railway transportation system, it is impossible for ordinary trains to climb steep slopes, and the slope will be expressed by one thousandth ratio (symbol ‰), which is smaller than the percentage. Since the denominator is 1000, it is more intuitive to show how many meters you have climbed per 1 km.
References:
Baidu encyclopedia-slope