First, the principle of horizontal angle measurement

As shown in Figure 3-9, A, B and C are three points on the ground, and their elevations are not equal. These three points are projected on the PQ horizontal plane along the vertical line, and three points A 1, B 1 and C 1 are obtained on the horizontal plane, so the included angle β between the horizontal lines B 1A 1 and BlC 1 is defined as the level between the straight lines BA and BC on the ground. It can be seen that the horizontal angle between any two straight lines on the ground is the two-sided angle between the vertical planes passing through these two straight lines.

In order to measure the horizontal angle, a dial can be placed horizontally at any height 0 on the intersection of these two vertical planes. The intersection of BA and BC with a vertical plane is 0m and 0n, and the corresponding readings on the dial are B and A, so that the horizontal angle can be obtained.

β=a—b (3— 1)

According to the above analysis, the theodolite measuring the horizontal angle must have a horizontal dial with an indicator that can be read; In order to aim at targets with different heights, the telescope of theodolite can rotate not only in the horizontal plane, but also in the vertical plane.

Figure 3-4 Horizontal Angle Measurement

Second, the principle of theodolite

There are three kinds of theodolite: vernier theodolite, optical theodolite and electronic theodolite. Vernier theodolite is generally a metal dial, vernier reading and conical shafting, which is rarely used at present. Electronic theodolite has not been popularized, but optical theodolite is widely used for its advantages of high reading accuracy, small size, light weight, convenient use and good sealing performance. Here is a brief introduction to optical theodolite and electronic theodolite.

1.J6 optical theodolite

As shown in Figure 3-5, it is the second generation theodolite of Hongqi produced by Beijing Optical Instrument Factory. The names of all parts are marked on the drawing. Theoretically, the angle measurement error is 6 ",so it is called a 6-second theodolite. It belongs to low-precision theodolite, which is generally used for control survey below level 5 and other low-precision survey work.

J6 theodolite consists of three parts: base horizontal dial and aiming part.

There are three anchor screws 6 on the base for leveling the instrument. 5 is the connecting screw of the shaft seat. Tighten it to fix the instrument on the base. The screw should not be loosened to avoid the instrument falling off.

The horizontal dial is invisible outside. It is a ring made of glass, and the dial is engraved with scales clockwise, from 0 to 360, to measure the horizontal angle.

The aiming part consists of a telescope, a reading system, horizontal and vertical scales, and the observation direction value can be read by a reading microscope 9. Generally reading 1' is estimated to read 1 dot in 10, which is a multiple of 6 ". As shown in Figure 3-6, it is the reading window of J6 theodolite with micrometer, where HZ stands for horizontal dial and V stands for vertical dial. Here, the horizontal dial reads 2 14 54', 0, and the vertical dial reads 79 06', 4. Figure 3-7 shows the reading window of J6 theodolite veneer glass micrometer. Domestic Hongqi Ⅱ and Swiss T 1 optical theodolite belong to this reading mode. The meter reading window is in the reading window, the lower pane is the image of the horizontal dial, and the middle compartment is the image of the vertical dial. The double line in the middle of the reading board is the indicator line, the dial 1 or 30' is engraved with a dividing line, and the marked number is the degree. The upper window is an image of a micrometer, and the single line in the middle of the window is also an indicator line. The micrometer rotates the micrometer wheel every 5', so that the graduation or 10' on the dial is just sandwiched between the double-line indicators, so that reading can be made, as shown in the figure. In Figure 3-7b, the reading of the leveling dial is 430'+11'48 "= 441'48".

Figure 3-7J6 Theodolite Reading Window

2.J2 optical theodolite

Figure 3-8 is the outline of DJ2 optical theodolite produced by Suzhou Optical Instrument Factory. The name of the part is indicated on the drawing. Compared with J6, J2 instrument reading equipment has two characteristics: first, J2 optical theodolite adopts the average radial coincidence reading of dial, which eliminates the influence of eccentricity of sighting part and improves the reading accuracy; Secondly, in J2 optical theodolite reading microscope, only one image of horizontal dial or vertical dial can be seen. To read another image, you need to turn the image conversion handwheel 9.

As shown in Figure 3-9, when the reading window diagram of Su Guang J2 optical theodolite is aligned, turn the micrometer handwheel 7 to mark the main image (orthographic projection), the auxiliary image and the back projection, and put forward a relative scale line with the following three conditions and marked with degrees.

Figure 3-3-8 J2 Optical Theodolite Outline Diagram

Figure 3-9 J2 Reading Su Guang's Face

(1) The difference is180;

(2) The main image is on the left and the auxiliary image is on the right;

③ The closest.

Then the degree marked by the main image on the bisector is the degree to be read. When the integer 10' to be read on the dial is less than 10', half of the frames sandwiched between the main image dividing line and the sub-image dividing line are minutes and seconds. Read on the micrometer on the right. So the window reading is:

The degree on the dial is 163.

The integer 10' on the dial is 2× 10'= 20'.

Minutes and seconds on the micrometer 7 inches 32.5.

All readings are 163 27' 32. 〃 5

The reading method of T2 theodolite is the same as DJ2, but its micrometer mechanism adopts double-layer flat glass and archimedean spiral. The difference is that the main image is at the bottom, the auxiliary image is at the top, and the main image is still the main image when reading. As shown in Figure 3- 10, the reading of the horizontal dial is 0.09' 48.5.

The reading of the new T2 theodolite has been digitized. When reading, rotate the micrometer wheel to make the scribed lines of the primary and secondary images overlap, and its reading can be directly displayed in the reading window, which improves the reading speed, as shown in Figure 3- 1 1, and its reading is 94 12' 44'' 2.

Figure 3- 10 T2 theodolite reading window Figure 3- 1 1 new T2 reading

3. Electronic theodolite

At present, electronic theodolite, rangefinder and micro-shun together constitute a full-station electronic fast measuring instrument. It uses photoelectric angle measurement, and the angle measurement results are expressed in the form of photoelectric signals. That is, a new type of dial which uses photoelectric technology and electronic micrometer technology to determine the principle of photoelectric angle measurement. At present, there are three kinds of dials for photoelectric angle measurement, namely, grid dial, shed dial and coded dial. The following is just a brief introduction to the dynamic angle measurement principle of the grid disk.

As shown in figure 3- 12, it is a lattice glass dial. Light and dark intervals are engraved on the dial, and the width and number of intervals depend on the design requirements. The dial is also equipped with apertures LR and LS, and the apertures are equipped with LEDs. When the dial rotates, the photodiode in the fixed diaphragm will receive the bright and dark signal sent by the light emitting diode, which is the sign of the rotation size of the dial.

Figure 3- 12 Regional Format Dial Figure 3- 13 Marking Delineation

There are two kinds of dial division: marking division and general division. Figure 3- 13 has four groups of markers, A, B, C and D. Each marker is set in an interval with a starting position of 90 in different lines and different arrangements. Generally, the scribing is similar to Figure 3- 12, and it is distributed in the four intervals divided by scribing. Generally speaking, the width of dark stripes is twice that of bright stripes.

The total score of dial is 1024, as shown in Figure 3- 17, φ. = 360× 60× 60/1024 =1265.625 seconds.

Dynamic scanning obtains angle information through photoelectric signal scanning. In fig. 3- 12, the fixed diaphragm IS arranged inside the dial, and the movable diaphragm IR is arranged outside the dial and connected with the aiming part.

When measuring the angle, because LR rotates with the lighting part, a certain angle is formed between Ls and LR. Driven by the motor, the dial always rotates at a certain speed, so that the receiving diode intermittently receives the infrared light emitted by the light-emitting diode, and when it receives the optical signal, it sends out a high-level electrical signal, and when it does not receive the optical signal, it sends out a low-level electrical signal, thus completing the scanning of the dial.

As can be seen from Figure 3- 13, φ. Represents the angle represented by the width of the scribe line. That's φ. = 2π/n is a known value. For any angle φ, it can be expressed as:

φ= nφ∧+△φ(n is a positive integer, 0 ≤△φ

Measurement of △φ: From the waveforms of signal R and signal S in Figure 3- 15, it can be seen that the variation range is 0~T due to the existence of △φ. Because the motor speed is constant, there are:

△φ=φ3.5/T .△ti(i= 1，2，.....n)

Where: n is the total score of the dial, and △ti can be accurately determined by pulse filling. After the microprocessor calculates △φ i, it follows the following formula:

△φ=[△φI]/N

Finally, the final result is calculated and the angle measurement of the dial is realized.

Figure 3-/determination of kloc-0/4 signal Figure 3-3-/determination of kloc-0/5n signal

Determination of N: The four groups of marks on the dial are specially set for determining the value of N ... Their functions are shown in Figure 3- 15. Assuming the observation angle is φ, when measuring the angle, the dial rotates once, and A, B, C and DF all pass through R and S once, and the signals sent by R and S are RA, SA, RB, SD, RC, SC and DF. When a turns from r to s, the corresponding time is TA, so φ is included in φ. The numerical value nA of can be expressed by the formula na = ta/T. (rounding) (3-5). For the description of groups B, C and D, there are also ni = ti/t. (i=B, C, d) (3-6), that is, four values of n can be measured in one rotation, and the microprocessor will compare them. If differences are found, the value of n will be repeated automatically, thus ensuring the correctness of the value of n. ..

WidTC2000 total station adopts the principle of dynamic scanning absolute angle measurement. It can greatly eliminate the influence of scale error and eccentricity error of the dial, and the minimum reading of the observed value is 0.1". The observation error is 0.5 ″, and the horizontal zenith distance synchronous measurement time is 0.9 seconds. Please refer to the instruction manual for specific operation and use. I won't go into details here.

Third, the horizontal angle observation

1. The alignment, leveling and aiming of theodolite are vertical ball alignment and optical alignment. At present, all theodolites produced are equipped with optical alignment devices, which can generally be used for optical alignment. When the vertical ball is used for alignment, the alignment error should generally be less than 3 mm. Generally, the optical alignment error should be less than 1 mm. However, the longer the side length, the lower the centering accuracy and the shorter the side length. In order to ensure the same angle measurement accuracy, the higher the centering accuracy is required.

Leveling: Adjust the anchor screw (3) to center the bubble of the bulb level in the sighting part, so that the horizontal dial is in a horizontal position and the vertical axis is vertical.

Optical centering and leveling should be done alternately. Because the optical alignment will deviate from this point after leveling, the two steps of alignment and leveling need to be repeated until they are within the tolerance range.

The leveling error should not exceed one grid value of the leveling tube.

Aiming: first adjust the eyepiece to make the crosshair clear, then aim at the target and adjust the objective lens to make the object image clear. When observing the horizontal plane, aim at the bottom of the target as much as possible to improve the aiming accuracy.

2. The method of horizontal angle observation

The observation method of horizontal angle depends on the accuracy required by the measurement, the instruments used in the measurement and the number of observation directions. Generally, there are three methods: survey, retest and full circle survey. Let's briefly introduce the measurement method and the full circle measurement method.

(1) The survey method is shown in Figure 3- 16. Set the theodolite at 2 o'clock, set the left position of the dial (that is, the front mirror), pull up the measuring button, rotate the sighting part, and pull down the measuring button when the reading in the observation window is slightly greater than 0. At this time, the horizontal dial rotates with the sighting part to aim at the front viewpoint 3, tighten the horizontal brake screw and pull up the measuring button. Rotate the sighting point 1 clockwise and record the reading al in the notebook, then the angle value βleft:al-b 1 measured on the left disk is called the upper half measurement.

Figure 3- 16 Angle measurement by back measurement method

Loosen the horizontal brake screw on the right side of the disc (that is, the mirror), first aim at the rear viewpoint 1, and read a2, then aim at the front viewpoint 3 counterclockwise, and read a2, and then you can get the measurement angle value β right =a2-b2 in the lower half.

The main purpose of front mirror and inverted mirror observation is to eliminate or weaken the influence of instrument error on angle measurement.

Final angle value: β = (β left+β right) /2

The difference between two and a half back angles of J6 should be less than 40, and the vernier theodolite should be less than 2t, where t is the minimum reading of the vernier.

Table 3- 1 Measurement method on the back of observation manual

(2) The full circle survey method is generally used when a station needs to observe several angles, that is, there are more than three observation directions.

As shown in Figure 3- 17, Mengshan Station has four directions and is a fourth-order triangular network. In order to measure the angle value between two directions, the value of each direction can be measured by the full loop method first.

Fig. 3- 17 observation direction value by full loop method

Place a theodolite at Mengshan point and aim at the first target (the target with good visibility and clear imaging). Here, Matang is chosen as the first target, which is usually called zero direction. Tighten the horizontal brake screw, rotate the horizontal inching screw for accurate aiming, and rotate the dial converter to make the reading of the horizontal dial slightly greater than 0. Then check whether the telescope is aiming accurately, turn in the micrometer handwheel to make the reticle recombine and read it once, and then turn it back a little to coincide. Rotate the sighting department clockwise, then aim at Zhou Jia, Yishan and Da 'ao in turn, and finally record all the readings in the upper column of the hand panel in turn near the zero direction (Matang).

Rotate the telescope vertically, rotate the sighting part counterclockwise 1 ~ 2 weeks, then accurately sighting the zero direction, and read according to the above reading method.

Turn the sighting department counterclockwise and observe in the reverse order of the first half, namely, Matang, Da 'ao, Yishan, Zhou Jia and Matang. See Table 3-2 for manual records.

Table 3-2 Format of Horizontal Observation Manual (Full Circle Measurement Method)

Description of calculation in the table:

A. 2C value of twice aiming error

2C The left reading of two disks-(the left reading of the disk is 180), and the mutual difference of 2C within one measurement shall comply with the provisions in Table 3-3. Fill in the calculated value in column (2C).

Table 3-3 Provisions on Tolerance of Direction Observation

B. Calculate the average readings in all directions.

Average reading = 1/2[ reading on the left side of the disk-(reading on the right side of the disk 180)]. Since the general degree and minutes will not change, just average the second readings on the left and right sides of the disk surface and fill this value in the left and right /2 columns.

C. calculate the average value in the zero direction:

This value is recorded in the column of average value of crabgrass, as shown in Table 3-2.

D, calculating the direction value of each observation point.

The direction value of zero direction is 0.0000.0. Other direction values = average direction value-zero direction value, for example, the direction value of Zhou Jia is 6916' 51.5-0 00' 08.2 = 6916' 43.3.

If multiple measurement returns are observed, such as fourth-order triangulation, the Property Survey Code stipulates that six measurement returns must be observed with DJ2 theodolite, so the mutual difference of each measurement return in the same direction value shall comply with the provisions in Table 3-3.

In addition, each measured zero direction value should be configured according to the following formula, and then

Where n is the number of returns of the measurement.

In the first measurement, the position of the dial is 0 00, and the position of the micrometer is micrometer increment = the reading is in the zero direction of each measurement. Its purpose is to evenly distribute the readings of each measurement in different positions of dial and micrometer, so as to eliminate and reduce the influence of dial scale length, short-period error, micrometer scale error and line difference.

3. Matters needing attention in horizontal observation

(1) The height of the whole instrument should be suitable for easy operation.

(2) Before observation, adjust the focal length of the telescope and keep it unchanged within one measurement, because focusing will change the collimation axis and make 2c overrun.

(3) Only when the instrument temperature is completely consistent with the outside temperature can observation be started. During the observation, the instrument should not be exposed to the sun.

(4) When placing the instrument as a whole, the rotating shaft of the instrument should be as vertical as possible. In the observation process, for DJ2 instrument, the center position of the bubble shall not exceed one grid. Before each measurement, the instrument should be kept level.

(5) During observation, if it is found that the absolute value of double collimation difference (2C) is greater than 30 (for DJ2 instrument), the line of sight should be corrected between measurements.

(6) The rotation of the instrument should be smooth and symmetrical. When aiming at the target, rotate in the specified direction and place the target near the intersection of the crosshairs. When aiming at all targets, they should be in the same position. When aiming at the target with a inching handwheel or overlapping the dividing line with a micrometer handwheel, the final rotation direction should be precession.

4. Some provisions on reinspection in national standards.

(1) Any result beyond the tolerance specified in the specification shall be retested. Investigation returns abandoned due to wrong dialing, wrong direction, wrong reading or poor observation conditions found in the middle are not included in the second interview.

(2) If it is necessary to retest due to the reciprocity and overrun of measurement returns, in principle, the maximum and minimum paired returns should be retested except for obvious abnormal values.

(3) Calculation method of retest number: In the observation results of foundation section, one direction in a retest is called "direction survey", and all directions of a result (calculated according to the basic survey number) are equal to (m- 1) n, where m is the direction number and n is the survey number.

In the basic survey, when the number of directional surveys that need to be retested exceeds 1/ 3 of all directional surveys, all directional surveys should be retested.

(4) Zero direction overrun, repeated measurement.

(5) In one measurement, when the number of measurement directions exceeds 1/3, or when there are only three measurement directions and one of them exceeds the limit, the measurement must be re-measured. However, when calculating the number of repeated measurements, it is still calculated according to the number of out-of-gauge directions.

(6) When re-measuring the overrun direction, it is only necessary to jointly measure the zero direction.

(7) Re-examination scores and basic return scores do not take the median. That is, only one measurement result meeting the tolerance is used for each dial position.

(8) If it is necessary to retest due to triangle closure error and angle measurement error overrun, the results of the whole station shall be retested.

When observing, the instrument can't be placed in the marker stone with a certain distance from the marker stone center, or the calibrated marker stone center is not on a vertical line. At this time, the centering elements should be determined on site, and then the observation results should be attributed to the center of the marker stone.

1. Center calculation.

As shown in figure 3- 18, BIBK is the marking stone center, YI is the instrument center, and Tk is the marking center. Er, θr, called station centering blessing, er, θr called sighting centering elements. M represents the observation direction value without center correction.

Figure 3- 18 Alignment Correction

Add the correction number c to the actually measured YITK direction value and change it into the BITK direction value, and add the correction number r to change it into the BITK direction. This correction is called collimation and centering correction. that is

(BIBK)=(YIYK)+C+r

Among them:

It should be noted that Mr, er and θr are the direction values measured by this station and the centering correction number calculated by centering elements, while Mr, er and θr are the direction values and centering elements measured by K station where the sight point is located, which cannot be confused.

2. Determine the requirements for centering components.

When projecting (1), two positions with an included angle of 120 should be selected for projection, or three projection stations with an included angle of 60 or two projection stations with an included angle of 90 should be selected for two projections. In projection, the original point of projection and the drawing direction cannot be changed.

(2) The side length of the error triangle between the projection mark center and the instrument center shall not exceed 5mm, and the side length of the error triangle of the projection sighting center shall not exceed10 mm. ..

(3) The projection should use a special projection diagram. After the projection, two observation directions should be drawn on the projection paper, one of which is preferably the observation zero direction of the station.

(4) When projecting an aiming point on a point without an observatory, the two directions described should include the direction in which the observatory aims at the point.

(5) The second-class observation direction and centering elements should be measured once before and after the test; The central elements of the third and fourth points can only be projected once. However, the time difference between the determination of centering elements and observation at the station should not exceed 3 months.

(6) When measuring er and eT, it should be accurate to millimeter, QRQT to 15, and estimated side length DIK to meter. The larger e is, the higher the accuracy of 9 and d is required.

(7) Direct measurement method: measure the eccentricity twice with a steel ruler, and the difference between the two results is less than 10mm, and observe the eccentricity angle with a theodolite, and measure it back to 10 ".

5. Calculation of observation direction-direction curvature correction

The so-called observation direction transformation is to transform the measured direction between two points on the ellipsoid into the straight line direction between two points on the Gaussian projection plane, that is, to add a correction number to the observation direction value, which is called direction correction or direction curvature correction.

Six, the main error of horizontal angle observation

1. Influence of external conditions on observation accuracy

The main factors affecting the observation accuracy are atmospheric temperature, atmospheric movement, solar exposure, topography, ground features and line of sight height. The motion of the atmosphere affects the clarity of target imaging. The temperature difference makes the atmospheric density uneven, which leads to atmospheric refraction, thus bending the line of sight and bringing systematic errors to the observation direction value. Due to the sunshine, the light and dark sides of each aiming target are different, which leads to the deviation when aiming at the target. This deviation is called phase difference. In addition, the change of temperature will change the collimation axis of the telescope, and direct sunlight will distort the tripod of the instrument. Although these errors are small, they should be avoided or weakened as far as possible in slope control survey.

Therefore, it is necessary to choose a good observation time, such as sunny days, the image is the most stable, and the clear time is after sunrise 1 hour to 8: 00 am and after 3: 00 pm. On cloudy days, the observation time can be much longer than on sunny days. Don't observe when the horizontal refraction is large before and after sunrise and sunset or before and after heavy rain. For the phase difference of the sighting target, the observer should carefully identify the actual contour of the target to be sighted. If the impact is particularly significant, it can be compensated by the number of half-tests in the morning and afternoon. In addition, the sun's rays should try not to point at the tripod. At the same time, aiming at the target in the opposite order in the morning and afternoon can be expected to eliminate or weaken the influence of tripod torsion.

2. Error of the instrument itself

No matter how delicate the instrument is, it is impossible to make an instrument without errors. The errors of the instrument itself are mainly the geometric relationship error of the shafting, the marking error of the dial and the error of the optical micrometer, for example, the collimation axis is not orthogonal to the horizontal axis, the horizontal axis is inclined, the vertical axis is inconsistent with the vertical axis, and the graduation between the dial and the micrometer is uneven, which will affect the accuracy of the observed values.

In practical work, we use positive and negative mirrors to reduce the collimation axis error and eliminate the influence of horizontal axis error; Re-level the instrument part every time to eliminate the influence of vertical axis deviation; The dial is interchanged with each measuring back, and the position of the micrometer is configured to reduce the influence of indexing error.

3. Errors in instrument operation

The influence of elastic torsion of the instrument base and tripod is adjusted by measuring the sighting part in the same direction for half a time, so that the positive and negative errors are roughly offset. This method can also effectively eliminate the influence of the spiral socket gap of the base. In order to ensure that all observation directions are basically equally affected by the torsion of the observation part, the middle part of the inching screw should be used as much as possible. Therefore, before each measurement, the inching screw should be withdrawn to the middle position. In order to eliminate the influence of the failure of the horizontal inching spiral spring, the inching spiral must rotate in the precession direction to aim at the target.

4. Observe your own errors

Observation consists of aiming and reading, and its errors include reading error, aiming error, target eccentricity and centering error.

Reading error is mainly the error of judging the dividing line of coincidence dial. Generally speaking, for J2 instrument, the middle error of dial dividing line is not more than1″ and there are two overlapping readings.

mo= 1/2= 0.7

Collimation error is mainly related to eye resolution, telescope magnification and climate stability. It is generally considered that the collimation error mv of primary collimation is about

mv= 60/v

Where V is the magnification of the telescope, for J2 instruments, there is generally v=30x, so J2

mv= 60/30= 2.0

In addition, when aiming at the flower pole, it is difficult to ensure that the central axis of the flower pole strictly coincides with the vertical line passing through the center of the monument. Aiming at the target is often the main reason to damage the observation accuracy.

As long as the alignment accuracy of the instrument can reach millimeter level, the side length is generally large and has little influence on the control measurement. Under the condition of constant centering error, the greater the side length, the greater the influence.

Table 3-4 Influence of Alignment Error on Angle Measurement