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).
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.
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
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
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:
– 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.