What can be eliminated by using anti directional observations in triangulation elevation measurement

Trigonometric elevation measurement can eliminate the influence of spherical aberration of the earth's curvature and atmospheric refraction, i.e., spherical aberration.

Trigonometric elevation measurement is a method of determining the elevation difference between two points by observing the horizontal distance between two points and the zenith distance (or altitude angle). It is a simple observation method and limited by topographic conditions, and is the basic method for determining the elevation of geodetic control points.

In order to improve the accuracy of trigonometric elevation measurement, the vertical angle of the opposite observation is usually used to calculate the height difference between the two points to weaken the influence of atmospheric vertical refraction.

More than 100 years ago, triangulation elevation measurement was the main method for determining elevation differences. Self-leveling.

Since the advent of the method, it has taken a back seat. However, because of its simple operation, it is still widely used in mountainous and hilly areas.

Zenith distance observations are heavily influenced by ground-level atmospheric refraction. If the density of the atmosphere is uniformly distributed.

, the light emitted by the light source will be in concentric spheres.

The form of the wavefront propagates in all directions, and its velocity corresponds to the density of the atmosphere. In fact, the density of the atmosphere generally decreases with increasing elevation, so the speed of upward propagation of light waves is greater than that in the horizontal direction. In this way, the wavefront is no longer a concentric sphere.

At this time, the light source is observed by the station, and the telescope is perpendicular to the wavefront, and the visual direction of the light source will be perpendicular to the wavefront. This phenomenon is called ground-level atmospheric refraction, and the angle between the apparent and true directions of the light source is called the refractive angle. In triangular elevation measurements, the refractive angle depends on the physical conditions of the atmosphere between the station and the observation target, in particular the upward rate of decline in atmospheric density.

It is not possible to fully grasp the physical conditions of the atmosphere to calculate the refractive angle in actual measurements, and generally only the approximate value of it can be estimated, or appropriate measures can be taken to weaken its influence on the final result.

Spherical gas difference is the difference between the effect of the curvature of the earth and the refraction of the atmosphere on the leveling readings in leveling. Since the earth is not a plane in the actual measurement, and the influence of atmospheric refraction makes the line of sight not a straight line, the influence of the two on the level measurement exists, and the spherical difference needs to be considered when the distance between the two points measured is too large. When the front and rear sight distances are equal, the ball gas difference can be eliminated.

Of course, it is the spherical aberration of the curvature of the earth and the air difference of the refraction of the atmosphere. That is, the ball gas difference.

When should trigonometric elevation measurements be used? How it observes, records, calculates.

Hello! I'm glad to be able to answer for you. Trigonometric elevation is suitable for undulating mountainous areas where it is not visible, and leveling measurements are suitable for flat land where the terrain is flat and can be seen.

As shown in the figure, the elevation of point A is known, and the elevation Hb of point B is to be determined, and the theodolite can be placed at point A, and the height of the instrument is measured. Erect a benchmark at point B, and measure its height to be called the elevation of B vb; Use the theodolite filament to aim at its top and determine the vertical angle. If the horizontal distance D between two points of AB is known (e.g., the total station can directly measure the horizontal distance), then the elevation difference between the two points of AB is calculated as follows: the above trigonometric elevation measurement formula (in it, let the geoid and the horizontal plane through points A and B be the planes of each other's Pingzhou sheds, which can be considered to be like this at a relatively close distance (e.g., 200 meters).

However, in fact, the starting surface of elevation, the geoid is a curved surface, and the influence of the curvature of the water level on the measurement of the height difference has been described in the first chapter, so it is shown by the trigonometric elevation measurement formula (the calculated height difference should be corrected for the influence of the earth's curvature, called spherical aberration correction f1, as shown in the textbook). Press (formula: where:

r is the average radius of curvature of the earth, and r=6371km is generally taken. In addition, because the line of sight is affected by the vertical refraction of the atmosphere, it becomes an upward convex curve, so that the tangent direction of the line of sight is raised upward, and the vertical angle is measured, as shown in the figure. Therefore, the correction of the influence of atmospheric refraction should also be carried out, which is called the air difference correction f2, and f2 is always negative.

Figure Trigonometric Elevation Survey The influence of the earth's curvature and atmospheric refraction on the atmospheric vertical refractive coefficient k varies with factors such as air temperature, air pressure, insolation, time, ground conditions and line of sight height, and the average value is generally taken so that k = . In the table, the correction value of spherical gas difference f for the horizontal distance d=100m-200m is listed, and f is always positive because f1 > f2. When considering the spherical gas difference correction, the formula for calculating the height difference of trigonometric elevation measurement is:

Due to the uncertainty of the refractive coefficient, there is a large error in the correction of the air difference in the correction of the spherical air difference. However, if the opposite observation is carried out between two points, that is, the average value of HAB and HBA is measured, then because F2 will not change in a short time, and the height difference HBA must be averaged with HAB against its sign, so F2 can be offset and F1 can also be canceled, so the error of F does not work, so the opposite direction observation must be carried out when the triangulation elevation measurement is carried out as an elevation control point. Table Trigonometric elevation measurement, earth curvature and atmospheric refraction correction (k = this is a bit complicated, you need to buy relevant materials for training and learning.

I hope mine can be helpful to you, thank you for your consultation, thank you! 

1. Leveling:

Pros: Fast speed.

Disadvantages: Affected by atmospheric refraction and curvature of the earth, corrections must be made to achieve high accuracy.

2. Trigonometric elevation measurement:

Advantages: The observation method is simple, not limited by terrain conditions, and is the basic method for determining the elevation of geodetic control points.

Disadvantages: large ranging error.

3. Trigonometric elevation measurement should generally adopt the method of opposite observation, that is, point A observes point B, and then point A is observed by point B, and the average of the absolute value of the height difference is taken as the height difference of A B, and the observation results are checked at the same time.

In triangular elevation measurement, the influence of () can be eliminated by using the antidirectional observation of Potato Xun.

a.Parallax. b.This error in the collimation axis.

c.Difference in the curvature of the earth and refractive difference in the hand base of the atmosphere.

d.Horizontal dial dividing error.

Correct answer: c

Answer] :d when the terrain fluctuates greatly and it is not convenient to carry out leveling, the elevation difference between the measuring station and the point to be measured can be measured by the method of triangular elevation measurement foci, and then the elevation of each point to be measured is calculated according to the elevation of the measuring station. Trigonometric elevation measurements, anti-directional observations can eliminate the effects of the Earth's curvature and atmospheric refraction. Too bright.

In trigonometric elevations, the effects of () can be eliminated by using counterdirectional observations as follows

First, the similarities.

Triangulation and leveling are both elevation measurements, mainly to measure the height difference between two points on the ground.

Second, the differences.

1. The measurement method is different.

Leveling, using a horizontal line of sight, with the help of a leveling ruler erected on the ground point to determine the height difference between two points on the ground.

Trigonometric elevation measurement, which determines the height difference between two points by observing the horizontal distance and height angle between two points.

2. The scope of application is different.

The leveling method is sophisticated, and it is mainly used to establish a national leveling network.

The triangular elevation measurement calendar is simple and the elevation transmission is fast, but the accuracy is not as good as that of level measurement, and it is mainly used in the elevation calculation of large places.

Answer]: a, b, c, e

Trigonometric elevation key god measurement, the measurement accuracy of the manuscript and the loss of factors: distance error, vertical balance right angle error, atmospheric vertical refractive error, instrument height and visual elevation error.

Answer] :d trigonometric elevation measurement requires the observation of the opposite direction, the round-trip elevation difference is calculated, and the main osmosis is to effectively compensate or eliminate the influence of the spherical gas difference.

Answer: Gao Meng]: b, c, d, e

According to the trigonometric elevation measurement principle (formula), the error sources include the right angle of the vertical bridge, the side length, the height of the instrument, the elevation of the eye, and the light coefficient of the atmospheric folded wax. The horizontal angle has nothing to do with trigonometric elevation measurements. Therefore, BCDE was chosen.