There are four methods to express slope: percentage method, degree method, density method and fraction method, among which percentage method and degree method are more commonly used.
(1) percentage method
The most commonly used method to express the slope, that is, the percentage of the height difference between two points and its horizontal distance, is calculated as follows: slope = (height difference/horizontal distance) x 100%.
When expressed as a percentage,
That is, I = h/l× 100%
For example, a slope of 3% means that the horizontal distance rises (falls) by 3 meters every 100 meters; 1% means every 100m in the horizontal direction and every 1m in the vertical direction. And so on!
(2) degree method
The gradient is expressed in degrees and calculated by inverse trigonometric function, and its formula is as follows:
Tanα (slope) = height difference/horizontal distance
So α (slope) = tan- 1 (height difference/horizontal distance)
Tangent and sine slopes of different angles
Angular tangent sine
0 0% 0%
5 9% 9%
10 18% 17%
30 58% 50%
45 100% 7 1%
60 173% 87%
90 ∞ 100%
Example:
The gradient of a slope i= 1:2. If someone walks up the slope of 100 meters, how many meters will his height rise?
Solution: Because the slope-the ratio of the vertical height H of the slope to the horizontal width L is usually called the slope (or the slope ratio), which is represented by the letter I. It is usually expressed as a percentage.
Then, there is: the height rises to: x? +(2X)？ = 100?
5X？ = 100?
X√5= 100
X= 100/√5 because √5=√5/√5*√5.
X=20√5
Simplified as: 100 * √ 5/5 = 20 √ 5m.
In fact, the slope is simply the TAN value of a right-angled adjacent angle (the angle of the ground).
The professional committee of Geomorphology Survey and Field Surveying and Mapping of the International Geographic Society divides the slope into seven grades: 0-2 plain to slight slope, 2-5 gentle slope, 5-15 slope,15-25 steep slope, 25-35 steep slope and 35-55 steep slope. > 55 vertical slope
Chinese mainland stipulates that > 25 cannot be cultivated.
The northwest loess plateau15 and 25 are the lower limit and upper limit critical slope angles of slope water surface erosion respectively.