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:
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.
(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 Zi-1, and the number of the front axle head is Zi , 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 Zi-1 The slant distance between the i-th ruler and Zi is:
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 l0' when the same wire ruler is inclined is not equal to the catenary chord length l0, the difference is called catenary asymmetry correction. The calculation formula 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:
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:
(2) The correction for reducing the baseline to the Gaussian projection plane is:
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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