Land area measurement

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In conducting detailed land surveys or other agricultural and forestry production processes, it is often necessary to understand the area of ​​a piece of land. At this time, land area measurements should be made frequently. At present, the land area measurement methods we use mainly include grid method, vertical distance and method, planimeter method and control method. However, generally, in real life, the land we need to measure is irregular and can't be drawn out in the topographic map. At this time, we can use the method of edge-by-side calculation—direct calculation method. The area of ​​land required.

Here we focus on the method of measuring the area under the side-by-side method:

When the shape of the measurement zone is rectangular, only the length and width are measured and the area is obtained. If the shape of the survey area is a non-rectangular irregular polygon, the survey area needs to be divided into many triangles. As shown in Figure 1, measure the length of each triangle, calculate the area of ​​each triangle, and accumulate all the triangles to obtain the measured area. The area. The formula for calculating the triangle area of ​​the three sides is known as: S = √ p (pa) (pb) (pC). (1) where: a, b are three sides long, p is the triangle's half perimeter.

Figure 1 Shape of the measured land

From the above calculations, we have obtained the area of ​​the land to be measured. Then we need to carry out the precision analysis of the area calculation based on the results of the land area measurement.

Differentiating the three sides from the two sides of (1) is:

, Into the error form, the triangle area of ​​the error ms

Among them: a, b, c are the trilateral length of the triangle, A, B, C are the internal angles of the three sides, md/d is the relative error of the distance measurement, and S is the area of ​​the triangle.

When the triangle is equilateral, the relative measurement error of the area caused by the edge measurement is

To achieve the relative accuracy of 1/10 00 area, the relative accuracy of the horizontal distance measurement is 1/1 155.

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