## Baseline

In triangulation, the basic length on which the initial side length of the triangulation (lock) is estimated is called the baseline. When it is difficult to directly measure the starting edge of the triangulation network due to conditions, measure a shorter baseline, and then pass the baseline network (usually a diamond, the baseline is a short diagonal) based on the observed horizontal angle value and baseline length Calculate the length of the initial edge of the triangulation network (the expanded edge of the baseline network) as well as the corner relationship.

## The baseline ruler

The baseline ruler is a tool to accurately measure the length of the baseline. The baseline measurement usually uses the Invar baseline ruler, which is made of nickel-iron alloy with an expansion coefficient of less than 0.5×10^{-6}/℃. It is generally a linear ruler with a length of 24m and a diameter of 1.65mm. Each set of linear rulers is usually equipped with four main rulers and an 8m or 4m supplementary ruler. The compensation ruler is used to measure the ruler section that is less than a full foot.

There are three-sided reticles at both ends of each line ruler, and one of the edges is consistent with the center axis of the line ruler. The scale range of the reticle is generally 8cm, the minimum reticle spacing is 1mm, and there is a note for every 1cm. The marking directions of the front and back reticles are the same, and the distance between the reticles of the same name on the two reticles is the length of the baseline. The complete set of baseline ruler is equipped with accessories such as heavy hammer, tension frame, shaft frame (also known as marker frame) and so on.

The baseline ruler is factory-verified, with ruler length equation. The baseline ruler length must be verified before and after the operation period for measuring the baseline length. Through verification, determine the length correction number and expansion coefficient of the baseline ruler. The expansion coefficient (also known as temperature coefficient) of the baseline ruler is measured by the electric heating method in a verification room with special equipment, and measured at least once every three years. Baseline ruler length verification is carried out indoors by a special measuring unit, and it can also be carried out in the field baseline field. The length of the baseline field is generally 600m. Each baseline ruler shall be verified once before and half a month after the end of the operation, and the average value of the two verifications shall be taken as the length of the baseline ruler.

The length equation of the baseline ruler is:

_{t}is the actual chord length of the baseline ruler at temperature t; l

_{0}is the nominal length of the ruler (24m); Δl Is the length correction number of the whole length section when the temperature is t

_{0}; t

_{0}is the standard temperature when the baseline ruler is checked, generally t

_{0}=20℃; α, β and γ are the temperature primary, secondary and tertiary expansion coefficients of the baseline ruler, respectively. Since the value of γ is very small, it can generally be omitted.

## Content method

The baseline measurement uses the Invar baseline ruler to measure the distance of each measurement section in the direction of the line connecting the two ends of the baseline to obtain the length of the baseline. The main contents of the baseline measurement are: (1) Align the line and set up the shaft frame. Arrange the shaft holder in the direction of the baseline according to the length of the baseline ruler as a mark for the measurement of the baseline ruler; (2) Level measurement of the shaft head; (3) Configuration and length measurement of the baseline ruler.

**Content**

(1) Before the baseline measurement, clean up and level the baseline site (measurement track), and then start from one end of the baseline A certain line station is set every 200～300m in the baseline direction. When the baseline is long, it can be measured in sections, and the section length is generally 0.5 to 1km. Each section point should be embedded with solid stakes or markers.

(2) At the alignment station, use theodolite and optical projector to accurately place the shaft holder head in the direction of the baseline according to the length of the baseline ruler, as the ruler mark for the baseline ruler measurement. The job is called alignment.

(3) Measure the height difference between adjacent shaft heads to calculate the measured tilt distance as a horizontal distance. This work is called shaft head leveling. After finishing 8 to 10 shaft holders, the shaft head level measurement can be carried out. Usually, the back-test is performed before the baseline measurement, and the back-test is performed after the measurement. In order to calculate the length measured along the shaft head to the geoid or other projection surface, the average elevation of the shaft head needs to be calculated.

(4) Measure the length between the heads (rulers) of two adjacent shafts one by one from the end of the baseline. The figure "Schematic Diagram of Measuring a Certain Ruler Section of Baseline" shows the i-th ruler section of the measurement, the number of the rear axle head is Z_{i-1}, and the number of the front axle head is Z_{i }, the zero division of the grading ruler at one end of the baseline ruler is placed at O, the reading at the rear end is a, the reading at the front end is b, and the temperature of the ruler section is t, then Z_{i-1} The slant distance between the i-th ruler and Z_{i} is:

_{t}is the actual chord length of the baseline ruler at temperature t, which can be obtained according to the ruler length equation. The remaining short span that is less than a full length shall be measured with a compensation ruler. In the process of measuring the baseline, the temperature is read every 10 to 15 minutes, and within the interval between two readings of the temperature, no more than 5 rulers are measured.

The number of baseline rulers used for baseline measurement and the number of round-trip measurements are determined according to the accuracy requirements of the baseline. When measuring the combination of the baseline ruler for each measurement section, this section should be used as the baseline ruler for the previous measurement and the next section as the back measurement.

**Calculation of baseline length**

Before calculation, the field data should be thoroughly checked, and then the results should be sorted out and the baseline length calculated. The baseline length is calculated by adding up the measurement results of the whole length and the remaining short span.

**Calculation of approximate baseline length**

According to the measurement results of each baseline ruler. The formula for calculating the baseline approximate length is:

**Calculation of tilt correction**

According to the height difference h of each measure, the following formula calculates the tilt correction Δh of each measure:

**Calculation of remaining short span length**

Since the approximate baseline length does not include the short span length, the ruler length must be calculated separately for each short span Correction, temperature correction and tilt correction, the corrected length is the field length of the short span.

**Calculation of three corrections**

Three corrections of catenary asymmetry, reticle tilt and gravity change should be added to the baseline length. The values of these three corrections are very small.

(1) Correction of asymmetry of catenary. Because the two ends of the wire ruler are not equal in height, the catenary is asymmetrical, so that the catenary chord length l_{0}' when the same wire ruler is inclined is not equal to the catenary chord length l_{0, the difference is called catenary asymmetry correction. The calculation formula is: }

_{0}is the chord length when the baseline ruler is checked; p is the tension applied to the ruler; h is the height difference between the two ends of the ruler. For a 24m line ruler, use the baseline ruler to check the pulling force, and take m as the unit. The correction number of catenary asymmetry over the full length of the baseline is:

(2) Correct the slanted line. Because the reticle is inclined, the inclination angle of the reticle is ψ, and the reading difference between the front and rear reticle of a ruler section should be (b-a) cosψ. Therefore, the correction of the inclination of the baseline full-length reticle is:

(3) Correction of gravity changes. The baseline ruler verification and baseline measurement generally use the same set of heavy hammers. Due to the different latitudes of the two places, the acceleration of gravity is also different. The same weight has different weights at different latitudes, which will cause slight changes in the length of the wire ruler. The correction of the baseline full-length gravity change is:

_{1}and g

_{2}are the acceleration of gravity at the location of the baseline verification field and the baseline field, respectively.

**Calculation of the final length of the baseline**

The field length of the baseline is the horizontal length on the average elevation surface of the baseline. It can be reduced to the reference ellipsoid surface (or geoid, average elevation surface of the mining area) and Gaussian projection surface as needed.

(1) The correction to calculate the baseline field length to the reference ellipsoid is:

_{m}is the average height of the baseline; h

_{m}Is the height difference of the geoid where the baseline is located relative to the reference ellipsoid; R

_{a}is the radius of curvature of the normal section of the baseline in the direction at the average latitude of the baseline. If h

_{m}is zero, the ΔS in the formula becomes the correction number for reducing the baseline to the reference ellipsoid. The correction to calculate the baseline to the average elevation surface of the mining area is:

_{m}' is the height difference between the average elevation of the baseline and the average elevation of the mining area.

(2) The correction for reducing the baseline to the Gaussian projection plane is:

_{m}is the average value of the abscissa (y coordinate) of the two ends of the baseline.

## Accuracy requirements

The relative median error of the baseline measurement calculated by the difference between each measurement result and its number is: the first and second class baselines shall not exceed 1:1 million, the first and second class The starting edge of the triangle lock net shall not exceed 1:700,000. The Invar baseline ruler used for baseline measurement should be compared with the set verification baseline before the annual test and after the fieldwork completes the measurement work to verify the accuracy of the length change of the verifier ruler.

Beijing and Xi'an, China have established calibration baselines. Two sets of 14 baseline rulers are used to measure each year, and the accuracy is better than 1:2 million. Since baseline measurement is restricted by topography and working conditions, it has been replaced by high-precision electromagnetic rangefinders since the 1960s.

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