Triangulation is a common method to measure the relative height difference between two points on the ground. It is calculated according to the relationship between geometric principles and trigonometric functions.
In trigonometric leveling, we usually create a triangle with a horizontal baseline and two measuring points, one at one end of the baseline and the other at the other. We can measure the length of the baseline and the included angle between two measuring points with measuring instruments, and then calculate the height difference according to these measured values.
1, determine the measuring point and observation point.
Before trigonometric leveling, it is necessary to determine the points to be solved and the known points. The point to be solved is the target point whose elevation needs to be measured, and the known point is the reference point whose elevation is known.
2, horizontal measurement
Using rangefinder or other measuring tools, the horizontal measurement is carried out between the known point and the point to be solved, and the horizontal distance between the two points obtained by measurement is recorded, usually represented by the letter AB.
3. Elevation measurement.
Use altimeter or other measuring instruments to measure the elevation angle or depression angle between the known point and the point to be solved. The elevation angle is the angle measured upward from the horizontal plane, which is represented by the letter α; The depression angle is the angle measured downward from the horizontal plane, and is represented by the letter β.
4. Calculate the elevation difference
According to the measured horizontal distance AB and elevation angle α (or depression angle β), it is calculated by trigonometric function.
5, where h represents the height difference of the points to be solved.
Use the tangent function: h=AB*tan(α) or h=AB*tan(β).
Use sine function: h=AB*sin(α) or h=AB*sin(β).
In the calculation process, we should pay attention to the use of appropriate angular units (such as radian system or degree system) and unit conversion to ensure the accuracy of the calculation results. At the same time, in order to improve the measurement accuracy, it is necessary to consider the correction factors of geoid, such as geoid deviation or curvature of the earth.
Please note that in actual measurement, error correction, data processing and more complicated calculation methods may also be involved. Therefore, when carrying out trigonometric leveling, it is suggested to refer to relevant surveying manuals and documents or consult professional surveyors to obtain more detailed and accurate information.