**PROCESSING THE RESULTS OF THE THEODOLITE SURVEY. CALCULATION OF THE THEODOLITH TRAVEL VERTEX COORDINATES. PLANNING**

**Main geodetic tasks**

**Direct task** : according to the coordinates x _{1} and y _{1 of} point 1, the directional angle α and the length *d* of the side 1-2, calculate the coordinates of point 2 (Fig. 8.1).

Decision:

1) Calculation of coordinate increments

2) Coordinate calculation

3) Calculation control

**Inverse geodetic problem:** given the coordinates of two points 1 and 2, find the directional angle and the length of the side 1-2.

*Solution* :

1) Calculation of coordinate increments

2) Calculation of rhumb and directional angle

When calculating points, the signs of coordinate increments should be taken into account and (Fig. 8.2).

Rice. 8.2. Dx and Dy signs

3) Distance calculation

4) Calculation control:

Tolerance 1 – 2 cm

**Sum of coordinate increments**

Rice. 8.3. Sum of coordinate increments

;

.

In a closed theodolite traverse

So

Residuals along the coordinate axes

**Processing a traverse**

*The purpose of processing* is to calculate the coordinates of the traverse points

*Initial data* :

1) coordinates of the start and end points of the theodolite traverse

2) start and end directional angle

3) results of field measurements – horizontal angles and side lengths

Table 8.1. Traverse processing sheet

*Treatment*

1) Extract horizontal angles and lengths of sides from the magazine

*Note* . All initial and measured linear values are written out with an accuracy of 0.01 m, and angular – with an accuracy of 0.1¢. Trigonometric function values are calculated with 5 digits after the decimal point. All further calculations are performed with the same accuracy.

2) Extracting the coordinates of the starting and ending points of the theodolite traverse, the starting and ending directional angles from the catalog of coordinates of geodetic network points. If there are no directional angles, their values are found by solving the inverse geodesic problem.

3) Calculation of the sum of the measured angles

4) Calculation of the theoretical sum of stroke angles

For open travel

theoretical sum of *n* right angles

theoretical sum of *n* left corners

.

Theoretical sum of the angles of a closed stroke ( *n* -gon)

5) Calculation of the resulting angular residual

6) Calculation of the allowable angular discrepancy

*t* is the error in measuring angles in one step; *n* is the number of measured angles

7) Ratio check

8) Calculation of corrections in angles

*Note* . Correction values are rounded up to 0.1′ and are written above each measured value of the horizontal angle as whole numbers. Due to rounding errors, the corrections may differ from each other by 0.1¢.

9) Control of the calculation of corrections to the angles: the equality must be fulfilled

10) Calculation of corrected angles

11) Control calculation of corrected angles

12) Calculation of directional angles

for right corners

for left corners

13) Control of calculation of directional angles

In open stroke

In a closed course

14) Calculation of increments of coordinates

15) Calculation of sums of increments of coordinates and

16) Calculation of the theoretical sums of coordinate increments

for open travel

for a closed stroke (because and )

17) Calculation of residuals along the coordinate axes

18) Calculation of the linear residual of the course

19) Calculation of the relative travel discrepancy

where *L* is the stroke length. The relative discrepancy is represented as a fraction with a numerator equal to 1, for which in the expression the numerator and denominator must be divided by the numerator.

20) Checking the fulfillment of the ratio

21) Calculation of coefficients

22) Calculation of the correction of increments of coordinates

*Note* . Correction values are rounded up to 1 cm and written as integers over the values of the calculated coordinate increments.

23) Control of the calculation of corrections and

24) Calculation of corrected coordinate increments

25) Control of corrected coordinate increments

26) Calculate the coordinates of the points of the move

27) Coordinate calculation control:

**8.4. Planning**

Actions:

– construction of a coordinate grid;

– overlay points of theodolite traverse;

– drawing pickets;

– drawing of the situation;

– drawing up the plan.

Rice. 8.4. Drobyshev ruler

Topographic plans are drawn in the form of separate sheets 50 * 50 cm in size. The coordinate grid – a grid of squares 10 * 10 cm is divided using the Drobyshev ruler (Fig. 8.4).

Rice. 8.4. Building a grid of coordinates

The construction of a coordinate grid consists of the following actions.

1) With the help of the Drobyshev ruler, points *A* and *B* are built with a distance between them of 50 cm (Fig. 8.4).

2) From points *A* and *B* , using the Drobyshev ruler, determine the position of points *C* and *D* (linear notch).

3) Check the distance between points *C* and *D.* Its value should not differ from 50 cm by more than 0.3 mm; mark all sides after 10 cm.

4) Draw a grid of squares and perform grid control. The dimensions of the squares should not differ from the nominal values by more than 0.3 mm.

Rice. 8.5. Construction of a non-standard grid

Draw diagonals and build points *A* , *B* , *C* , *D* , setting aside equal distances from the point of intersection of the diagonals. Then, at points *A* , *B* , *C* , *D* , a quadrilateral is built and its sides are marked. Connect the opposite labels on the sides of the quadrilateral and get the desired grid.

After drawing the coordinate grid, it must be signed. If the plan is placed on several sheets, then the coordinates of the boundaries of each sheet are chosen as multiples of 50 *M* cm, where *M* is the denominator of the scale.

*The traverse* points are superimposed according to their coordinates selected from the list of coordinates calculation. *The control* of drawing points of the traverse on the plan is carried out by measuring the distances on the plan between neighboring points of the traverse and comparing these distances with the lengths of the sides in the list of coordinates calculation.

Shooting pickets are placed on the plan according to the method used during their shooting. The field journal and outline serve as source materials.

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