Basics of geodesy and cartography. Basics of Geodesy. Relationship between magnetic azimuth and directional angle

Autonomous non-profit professional educational organization

"URAL INDUSTRIAL AND ECONOMIC TEKHNIKUM"

FOUNDATIONS OF GEODESY
Training manual for practical work

for students of the specialty

« Construction and operation of buildings and structures»

Yekaterinburg, 2015

Compiled by: TG Semenova, lecturer at the Academy of Sciences of the POO "Ural Industrial and Economic College".

FOREWORD

To consolidate theoretical knowledge and to acquire the necessary practical skills, the curriculum of the discipline "Fundamentals of Geodesy" provides for practical work, which is carried out after studying the relevant topic in lectures.

You should draw the student's attention to the fact that before starting to carry out practical work on each of the topics, you must study the appropriate sections from the textbook (study guide) and / or lecture materials recommended to you.

If the work is delivered later than the deadline, then it must be protected at consultations.

A control sheet is attached to this manual, which is filled in by the teacher after completing each practical work.

Work must be done carefully. The score may be downgraded for negligence.

As a result of studying the discipline and performing these practical works, the student must

Determine the position of lines on the ground;

Solve problems at scale;

Solve direct and inverse geodetic problems;

Take out the elements of the construction plan to the construction site;

Use instruments and tools used to measure lines, angles and point heights;

Conduct office work at the end of theodolite survey and geometric leveling;

know:

Basic concepts and terms used in geodesy;

Assignment of geodetic reference networks;

Scales, conventional topographic signs, scale accuracy;

A system of flat rectangular coordinates;

Devices and instruments for measurements: lines, angles and determination of elevations;

Types of geodetic measurements.

Practical work No. 1.2

Solving problems at scale. Numeric to named translation.

Determination of the lengths of the segments on the plan in measures of length on the ground.

View presentation # 1

The scale is the ratio of the length of the line on the map, plan (drawing) Sp to the length of the horizontal application of the corresponding line in nature (on the ground) Sm.

The numerical scale is 1 / M, a regular fraction in which the numerator is 1, and the denominator M shows how many times the terrain lines are reduced in comparison with the plan.

For example, a scale of 1: 10000 means that all terrain lines are reduced 10,000 times, i.e. 1 cm of the plan corresponds to 10,000 cm on the ground

or 1 cm of the plan \u003d 100 m on the ground,

or 1 mm plan \u003d 10 m on the ground.

Therefore, knowing the length of the segment Sp of the plan using the formula Sm \u003d Sp * M, you can calculate the length of the line on the ground, or using the formula Sp \u003d Sm: M, determine the length of the segment on the plan.

For example, the length of the line on the ground is 252 m; scale of the plan 1: 10000. Then the length of the line on the plan is Br \u003d 252m: 10000 \u003d 0.0252m \u003d 25.2mm.

And vice versa, the length of the segment on the plan is 8.5 mm; scale of the plan 1: 5000. It is required to determine the length of the terrain line. It will be 8.5 mm * 5000 \u003d 42.5 m.

Problem number 1 Calculate the length of the line on the ground, Sm, for the data given in Table 1. Record the results in the appropriate column of Table 1.

Table 1

Map scale	The length of the segment on the map, mm	Line length on the ground Sm, M	Map scale	Section length on the plan, mm	Line length on the ground, m
1:10000	62,5		1:1000
1:25000	20,2		1:500
1:5000	12,5		1:2000
1:50000	6,2		1:5000

table 2

Map scale	The length of the segment on the map, mm	Line length on the ground Sm, M	Map scale	Section length on the plan, mm	Line length on the ground, m
1:2000		80,4	1:50000
1:5000		380,5	1:1000
1:10000		536	1:500
1:25000		625	1:2000

Often in geodetic practice it is necessary to determine the scale of aerial photographs. To do this, measure the length of the segment on the aerial photograph and the length of the horizontal route of this line on the ground. The scale is then calculated using the scale definition.

For example: the length of the segment in the aerial photograph is 2.21 cm; the length of the horizontal laying of this line on the ground is 428.6 m.

Then, according to the definition:

Problem number 2 Determine the scale of aerial photographs, according to the data given in Table 3.The results are recorded in the appropriate column of Table 3

Table 3

N / a	Length of horizontal application on the ground m	The length of the segment in the aerial photograph	Ratio in appropriate units	Aerial photo scale
1	625 m	62.5 mm	62.5mm / 625000mm	1:10000
2	525 m	5.25 cm
3	125.5 m	2.51 cm
4	62.2 m	31.1 cm

Scale accuracy

The length of the lines on the ground, corresponding to 0.1 mm of the map (plan), is called the scale accuracy - tm. This is a value that characterizes the accuracy of determining the lengths of lines on the map (plan). For example: 1: 25000 scale accuracy is 2.5 m.

The calculation can be done as follows:

in 1 cm - 250m;

in 1 mm - 25 m;

in 0.1mm-2.5m

or to \u003d 0.1mm * 25000 \u003d 2.5 m.

Problem number 3

a) Determine the accuracy of the scales:

b) The accuracy of the scale of the map (plan) is equal to:

tm1 \u003d 0.5m; t2 \u003d 0.05M; t3 \u003d ___; t4 \u003d _______;

Determine the scale of the map (plan).

1 / M1 \u003d ______; 1 / M2 \u003d _______; 1 / MH \u003d _______; 1 / M4 \u003d _______;
Problem number 4 On a map with a scale of 1: 10000 (Fig. 1), the meter opening is shown equal to the distance between two points of the KL map. Using the linear scale graph below (Figure 2), determine the horizontal application lengths of the terrain lines for all options.




Picture 2

Problem number 5 On the graph of the transverse scale (Fig. 3) with a base equal to 2 cm, thickened lines with numbers indicate the meter solution equal to the distance between two points of the map

Figure 3

Determine the lengths of the horizontal runs of the terrain lines for the following options:

Option I, scale 1: 10000	Option II, scale 1: 5000
S 1 \u003d	S 1 \u003d
S 2 \u003d	S 2 \u003d
S 5 \u003d	S 5 \u003d
S \u003d	S \u003d
W option, scale 1: 2000	Option IV, scale 1:
S 2 \u003d	S 2 \u003d
S 5 \u003d	S 5 \u003d
S \u003d	S \u003d

Note: at the beginning, determine the distances on the ground (in the appropriate scale) for segments 0-2; a1b1; a2b2; aZvZ.

Problem # 6 Build a 1: 2000 scale diagram on drawing paper with a base of 2.5 cm; the number of divisions along the base and in height is taken equal to 10 (n \u003d m \u003d 10). Sign the divisions by base and height (one after another). Glue the diagram in the place left below.

Scale 1: 2000
Determination of rectangular coordinates of points

Task number 1 Determine the rectangular coordinates of all the vertices of the polygon, given on the training topographic map at a scale of 1: 10000 (1: 25000).

Instructions for implementation.

Rectangular coordinates of points are determined relative to the kilometer coordinate grid, which is a system of lines parallel to the coordinate axes of the zone, forming a system of squares. The outputs of the grid lines (sides of the squares) are labeled in the map frame in kilometers.

Let us consider the procedure for determining the coordinates of a point using a specific example. In this case, it is point 1 (see Fig. 7).

Figure 7
Point 1 (xi.yi) coordinates can be determined by the formula

1 \u003d x o + Δx
y 1 \u003d у 0 + Δу, where хо, уо are the coordinates of the vertex of the square, which are determined by the captions of the outputs of the coordinate grid (in this case, хо \u003d 6062 km; у 0 \u003d\u003d 4310 km)

or by the formula:
x 1 \u003d x "o + Δx";
y 1 \u003d y "o + Δy".
In this example, the rectangular coordinates of p. 1 are
x 1 \u003d 6062 km +720 m \u003d 6065720 m;

y 1 \u003d 4310km + 501m \u003d 4310501m.
or
x 1 \u003d 6063km-280m \u003d 6065720m;

yi \u003d 4311km-499m \u003d 4310501m.

When you define the coordinates of points, make a schematic drawing illustrating the position of the point relative to the coordinate axes.

Table 4

Schematic drawing T. number 1	x 0 \u003d
t # 2	x 0 \u003d
t. No. 3	x 0 \u003d
t. No. 4.	x 0 \u003d

Inverse geodesic problem

Task number 2 Determine the lengths and directional angles of the polygon sides by the coordinates of the vertices. Instructions for implementation: formulas for calculation


Calculations should be carried out in the scheme for solving the inverse geodetic problem (table 5).

Computing circuit

Table 23

Decision procedure	Quantity designation	Values \u200b\u200bof quantities
		line 1-2	line 2-3	line 3-4	line 4-1
1	y k
2	y H
3	Δy
4	x k
5	x H
6	Δx
7	tga
8	Δx signs
9	r
10	α
11	sin r
12	S "
13	cos r
14	S "
15	Δx 2
16	Δy 2
17	Δх 2 + Δу 2
18	S ""

Federal Agency for Education of the Russian Federation

State educational institution

Higher professional education

Norilsk Industrial Institute

Department of RMPI

Discipline: "Geodesy"

BASICS OF LECTURES GEODESY

Norilsk

Geodesy is a science that considers the methods and methods of measuring the earth's surface, the use of which makes it possible to determine the shape and size ... Geodesy includes higher and space geodesy, topography, photogrammetry and engineering geodesy.

Shapes and dimensions of the earth

A body bounded by a mid-level surface is called a geoid. Due to the uneven distribution of masses in the earth's crust, the surface of the geoid ... is the formula of polar compression. The dimensions of the earth ellipsoid, accepted as mandatory in our country:

Coordinate systems

· Planned coordinate systems. Geographical coordinates. The main surface of the projection is taken to be the surface of the ellipsoid and the geoid.

Line orientation

The true magnetic and axial directions are used as the initial directions ... The true azimuth is the angle between the north direction of the true meridian and the defined line, measured by ...

Relationship between true and magnetic azimuth

Аи \u003d Аm– δз Directional angle is the angle between the north direction of the axial meridian or a line parallel to it and is determined ...

Relationship between true azimuth and directional angle

Relationship between magnetic azimuth and directional angle

Rumb – it is an acute angle measured from the closest direction of the reference axis to the defined line.

The relationship between the directional angle and the bearing

Basic geodetic tasks

Direct geodetic problem

HA UA SAB αAB XB–? УB–? ∆Х and ∆У can be positive and negative, depending on the quarter in which AB is located.

Inverse geodesic problem

The signs ∆Х and ∆У determine the quarter in which the line is located and choose a formula for calculating the directional angle.

Basic geodetic drawings

The scale set for this map is called the main one - this is the average scale of the drawing, it is strictly executed only along some meridians and ... The plan is a similar reduced image of a small area of \u200b\u200bthe earth's surface ... The main difference between the map and the plan: the scale is constant on the plan, but not on the map.

Basic requirements for cards and plans

2. Accuracy of depicting situations and reliefs in accordance with the scale (the larger the scale, the more accurately and fully the situations are reflected and ... 3. Geographic correspondence and plausibility.

The scale

There are numerical and graphical scales. The numerical scale is a fraction, the numerator of which is always one, and in ... Example: 1: 25000, ie in 1 cm 250 m - named.

Ultimate graphic scale accuracy

Is the length of a segment on the ground corresponding to 0.1 mm for a plan of a given scale (0.1 mm is the minimum distance distinguishable by the naked eye).

Example:

in 0.1 mm 2.5 m

c 0.1 mm \u003d 0.05 m

t \u003d 0.05m

Relief

Is a set of irregularities on the earth's surface.

The relief in the drawings can be depicted with color, marks, strokes and contours. The method of contour lines is used in geodesy.

Horizontal Is a closed curved line that connects points with the same elevation.

Contour lines properties:

1. All points lying on the same horizontal have the same elevation

2. Contours with different elevations do not intersect

3. The steeper the slope, the smaller the distance between the contours.

The marks of the contour lines are signed in their break so that the lower part of the figure is turned towards the slope lowering; berg-strokes are used to determine the direction of the slope. Every fifth horizontal line is drawn with a thickened line.

Relief section height (h) - they call the difference in elevations of adjacent contours - this is a constant value for a given drawing.

The horizontal distance between adjacent contours - slope placement (d) .

Slope (i) Is the tg of the slope of the terrain ν or the ratio of the difference in the heights of the points to the horizontal distance between them.

Slopes are expressed in 100 decimal places, thousandths (%, ‰, respectively).

Example:

0.025 \u003d 2.5% \u003d 25 ‰

Basic landforms

All relief forms are formed from a combination of inclined surfaces - slopes, which are divided into flat, convex, concave and mixed. The figure shows that the horizontal lines depicting an even slope are located at the same distance from each other. When ...

Tasks solved by topographic plans

Determination of distance using scale.

The procedure for using the transverse scale: · fix the length of the line on the map with a measuring compass, · put one leg of the compass on a whole base, and the other - on any transversal, while both legs of the compass ...

Determination of elevations of points lying on the horizontal and between the contour lines.

To determine the height of a point located between two contours (lower and higher), between adjacent contours, draw through this point along ... Hb \u003d h-∆h

Determination of the slope steepness according to the schedule of laying on the plan

On the map with contours, you can determine the slope of the terrain line.

i \u003d tg v= h / s,

where h- excess between the ends of the line;

s - inception.

The slope is often expressed not in degrees of the angle of inclination, but in thousandths or percentages.

Drawing lines of the design or specified slope.

The value of the found position s with the meter is laid down sequentially between adjacent horizontals in the direction from point A to point B. ... In those cases when the meter solution does not intersect with the next ...

Determination of the catchment area

The boundaries of the catchment area are watershed lines crossing the contour lines at right angles. The picture shows the watershed lines ... Knowing the catchment area, average annual precipitation, evaporation conditions ...

Nomenclature of topographic maps and plans

In our country, an international system of drawing and nomenclature of topographic maps has been adopted; it is based on a map sheet at a scale of 1: 1 000 000. The entire surface of the Earth is conventionally divided by meridians and parallels on trapezoids ... The nomenclature of a sheet of a map of a million scale is composed of a row letter and a column number, for example, N – 37.

Main parts of geodetic instruments

1. Instruments for angular measurements - theodolites. 2. Instruments for linear measurements - tape measures, measuring tapes and wires, ... 3. Instruments for measuring elevations - levels.

Ray path in the telescope

Tubes with internal focusing are more advanced; they use an additional movable diffusing lens L2, which together with ... In technical devices, an increase of 20-30 times. The field of view of the tube is the space that is visible in the telescope when it is stationary.

Horizontal circle of theodolite

Limb - a flat, glass or metal ring along the beveled edge of which graduations from 0 ° to 360 ° clockwise are applied. Alidada is an auxiliary device that allows you to take readings by ... Reading is the arc of the limb from 0o to 0o clockwise alidade.

Vertical circle

The limb of the vertical circle can have different digitization from 0 ° to 360 ° clockwise or counterclockwise sector digitization, i.e. from 0 ° to ... The alidade of the vertical circle is usually equipped with a cylindrical level for ...

Readout devices

The scale microscope is an auxiliary scale on the alidade, the length of which is ...

Angle measurements

Measurement of horizontal angles, their essence: let the points A, B, C, located at different heights above sea level, be fixed on the ground. It is necessary ... Let's draw plumb lines through A, B, C, which when crossing with ... The horizontal angles are measured using the horizontal circle of the theodolite.

Classification of theodolites

Theodolites are divided in accuracy into:

1. High-precision, allowing you to measure angles with an average square error of 0.5 "-1"

2. Exact, UPC 2 "–10"

3. Technical, SKP 15 "–30"

Based on the materials for the manufacture of circles and the device of counting devices Vernier:

1.With metal circles and vernier

2. With glass circles - reading device - line or school microscope and optical micrometer.

By design on:

1. Simple theodolites, in which the limb and alidade can only rotate separately.

2. Repetitive, in which the limb and alidade have both independent and joint rotation.

By appointment for:

1. Mine surveying.

2. Design

Schematic diagram of theodolite

1- limb GK

2- alidada GC

3- columns

4- alidada VK

5- VK limb

6- telescope

7- cylindrical level

8- stand

9- lifting screws

10-head screw

II 1- the main (vertical) axis of the theodolite

NN 1- axis of rotation of the telescope

The theodolite must meet certain optical-mechanical and geometric conditions. The optical-mechanical condition is guaranteed by the manufacturer, and the geometric conditions are subject to changes during operation, transportation and storage of devices.

The geometric conditions must be checked after long-term storage of the device and regularly during operation.

Basic geometric conditions of theodolite

1. The main axis of the theodolite should be vertical

2. HA limb should be horizontal, the sighting plane should not be vertical. To comply with these conditions, theodolite is checked.

Theodolite checks

Verification 1.

The axis of the cylindrical level at alidade of the HA ( uu 1) should be perpendicular to the main axis of the theodolite zz 1.

Leveling

Before performing the rest of the checks, the theodolite is carefully leveled, i.e. its main axis is brought to a vertical position, for this level ... These actions are repeated until at any position of the ampoule the bubble is not ...

Verification 2.

Violation of this condition leads to a collimation error (s). To perform the verification, they sight at a distant point and take readings along the GK limb ... If the condition is violated, calculate the collimation error, a value that should not exceed twice the accuracy ...

Verification 3.

To perform verification, the theodolite is installed at a distance of 20–30 m from the building and the point is sighted at the top of the wall. The pipe is lowered to about ... The same steps are repeated with a different position of the VC. If center grid projections are ...

Verification 4.

To perform the verification, they point at a distant point and, acting with the alidade lead screw and acting with the alidade lead screw, the GK rotate the device ... If corrections were made, then repeat the verification 2.

Eccentricity of alidade

D - center of the circle of divisions of the limb, A - center of rotation of the alidade, L - center of rotation of the limb. In an ideal theodolite, all three points should coincide, but in reality ... Consider the effect of alidade eccentricity on dial counts. Line segment AD is called a line element ...

Horizontal angle measurement methods

Installing the device in the working position implies centering it, leveling it and installing the pipe over the eye. Centering is bringing the main axis of the theodolite to the top of the measured ... Leveling see verification 1.

Method of receptions

The second half-step is performed to control the measurement and reduce the influence of instrumental errors. Angle values \u200b\u200bin semi-receptions should differ by no more than double accuracy ...

Circular Technique

The theodolite is installed in T.O. and brought into working position. Orient the limb towards some point, for example A (direct 0o ... To do this, unfasten the alidade and set the countdown \u003d 0o by rotating it, fix it, unfasten the limb and sight on ...

Repetition method

The device is brought into working position at the apex of the corner and a measurement is performed during which the measured angle 2k is successively laid on the dial ... Suppose that the angle is measured in two repetitions. Orient the dial with a reading close to 0, at point A and record this reading (n1).

Measuring vertical angles

The measurement technique depends on the design and digitization of the theodolite VC.

Way

If the VC does not have a level at alidade, then after bringing the device to the working position, they sight at the determined point. For example, with KL, the vertical circle alidades are brought to the 0-point level at VC with a directing screw and the reading is taken along the VC limb.

The pipe is transferred through the zenith and the actions are repeated with a different position of the vertical circle.

Calculate the vertical angle and MO.

The control of the correctness of measurements is the constancy of the MO, the fluctuations of which can be within the double accuracy of the device. (MO \u003d const, ∆MO≤2t).

Way

In the event that alidade BE does not have a level, and its functions are performed by the level with alidade BG (T30, 2T30). The device is brought to the working position, pre-sighted at a certain point, with the lifting screw of the stand located closest to the sighting axis, bring the bubble of the level with the main body to the 0-point, make accurate sighting and take a reading along the vertical circle. The action is repeated with a different position of the VC.

Calculate the vertical angle and MO, control MO \u003d const.

Way

If the alidada VK does not have a level and a compensator is used instead (the alidada automatically becomes horizontal).

Measurement procedure:

The device is brought to the working position, sighting at the point to be determined and taking a reading from the VC. The pipe is transferred through the zenith and the actions are repeated. Calculate the vertical angle and MO, MO \u003d const.

Formulas for calculating the vertical angle and MO

1.from 0º to 360º (limb) clockwise: MO \u003d ½ (CL + KL) V \u003d KP – MO \u003d MO – KL \u003d ½ (KP – KL)

Vertical circle zero point

The zero point is the VC reading at the moment when the sighting axis of the pipe is horizontal, and the level bubble at VC is at the zero point. If geometrical conditions are observed, this reading is zero, in case of violation ... Geometric conditions. The place of zero is a constant value for the device, its fluctuations can be within 2t. ...

Zero spot fix

If the zero point turns out to be large, then with the basic position of the circle, you need to direct the pipe to the point and set the counting equal to the angle of inclination with the micrometer screw of the alidade; the bubble of the level will deviate from the zero-point. Adjust the level screws to zero the bubble.

Measuring the slope of the terrain

i is the distance from the axis of rotation of the pipe to the point above which the device is installed. At point B, a rail is vertically installed on which i is marked. Visiting ...

Measuring line lengths

Linear measurements are divided into direct and indirect. Direct measurements include such measurements in which the measured ... The gate is a vertical plane connecting the beginning and end of the measured line.

Measuring line lengths with a mechanical device (using a measuring tape as an example)

To measure the distance, it is usually not enough to fix the beginning and the end of the line to be measured on the ground, it is necessary to install additional landmarks in the alignment of the line, this process is called by hanging or hanging a line ... Hanging can be done with theodolite or by eye.

To hang line AB by eye, at points A and B, sticks are fixed, the observer stands near point A so that the sticks at points A and B coincide. His assistant moves from point A to point B and sets up additional landmarks at points 1, 2,…, n, guided by the instructions of the observer.

When hanging the theodolite at point A, set the theodolite, at point B, a pole. The vertical thread of the mesh is aligned with the pole at point B, the horizontal circle and the pipe are fixed, the auxiliary pole is installed along the vertical thread of the mesh.

If there is no line of sight between points A and B, hanging is performed as follows: two auxiliary points are selected so that they are both visible from both point A and point B, and poles are installed in them.

Using the method of successive approximations, the markers are moved from point D 1 to C 1, C 1 to D 2, D 2 to C 2, etc., until all the markers are on one straight line.

Line Measurement Procedure

After fixing, fix the points of inflection of the terrain that fall into the range of the line. Use a tape measure to measure sloped areas D 1, D 2, ... and slope angles ν 1, ν 2, ….

Calculation of horizontal projections of measured distances

d 1, d 2 - horizontal spacing:

d i \u003d D i cos ν i

The total amount of horizontal distance AB:

Each oblique distance is measured as follows: the zero stroke of the tape is applied to the beginning of the measured line, the tape is laid in alignment, shaken in the horizontal and vertical planes, pulled and inserted into the cutout at the end of the tape, remove the tape from the hairpin, put the zero tape cut on the hairpin and actions are repeated. At the end, the length of the incomplete span is measured. The measured slant length is calculated using the formula:

D 1 \u003d n ∙ l + r

r- partial span length

n - number of complete tape runs

For control the length is measured in the opposite direction D 2, the final value of the length is taken as the average of two measurements if the difference between them does not exceed 1: 2000 of the line length:

Corrections to be introduced to the line lengths measured by mechanical instruments:

1. Over temperature enter in cases when the measurement temperature differs from normal (+ 20 ° C). The nominal length of the measuring device is determined at normal temperature, its length increases or decreases depending on the external temperature:

D - measured length

l - length of the measuring device

α - coefficient of linear expansion

t- measurement temperature

t 0 - normal temperature

2. For tilt line is introduced in those cases. When the angle of inclination of the terrain exceeds 2º. Sometimes it is necessary to set the distance on an inclined surface so that its horizontal distance is equal to a given value.

First, horizontal distances are chipped from point A, and then lengthened to correct:

3. Comparing - this is the determination of the true length of the measuring prior, when comparing with a measuring device, a previously known line length is measured and the measurement results are compared with a known value, and then the correction of the measuring device is calculated. This correction is introduced if the nominal length differs from the length.

Distance measurement using physical-optical measuring devices

(for example, a filament rangefinder)

Filament rangefinder these are two auxiliary horizontal threads on the mesh.

Beam path in a filament rangefinder Field of view of a pipe

Determining distances with a filament rangefinder

P is the distance between the ranging filaments σ is the distance from the axis of rotation of the device to the optical center of the lens ... f is the focal length of the lens

Leveling

- determination of elevations between points on the earth's surface.

Leveling is performed with various devices and in different ways, they are distinguished:

- geometric leveling (leveling with a horizontal beam),

- trigonometric leveling (leveling with an inclined beam),

- barometric leveling,

- hydrostatic leveling and some others.

Hydrostatic leveling

h \u003d c1 - c2 Accuracy of hydrostatic leveling depends on the distance between the vessels, ...

Barometric leveling

The approximate value of the excess between points 1 and 2 can be calculated by the formula: h \u003d H2 - H1 \u003d ΔH ∙ (P1 - P2), P1 and P2 - pressure at the first and second points;

Trigonometric leveling

It is used in topographic surveys to create a survey justification and survey of the relief, as well as when transferring marks over long distances. ... Trigonometric leveling scheme

Geometric leveling

Leveling "forward" To determine the excess between points A and B to a point with a known elevation (back), set the level so ...

Simple and complex leveling

If this requires several stations, then leveling is called complex. The number of stations depends on the distance between points and the steepness of the slope. For… The excess of h1, h2,…, hn and the total are successively determined.

Classification and devices of levels

Levels are divided by:

- Accuracy for 3 groups:

–high precision- are intended for leveling the 1st and 2nd classes, allowing to determine the excess with a mean square error (RMS) of no more than 0.5-1 mm per 1 km of travel;

–accurate- are intended for leveling of III and IV classes with an RMS of no more than 5–10 mm per 1 km of travel;

–technical- designed for engineering and technical work, allowing to determine the excess with the SKP not more than 10 mm per 1 km of travel. For technical work, the permissible SKP is 15–50 mm per 1 km of travel.

- by design into 3 groups:

–Levellers with a cylindrical level;

–Levellers with a compensator;

–Levellers with an inclined sighting beam.

Leveling devices with a cylindrical level (for example, H3)

The main parts are a telescope with a cylindrical contact level fixed on it and a stand with leveling screws and a circular level. The pipe is secured with a clamping screw, a guide screw is used for accurate sighting. An elevation screw is used to accurately level the pipe sighting axis.

The circular level is intended for approximate leveling of the device, and the cylindrical contact level is intended for accurate leveling of its sighting axis. Therefore, the following geometrical condition must be met: the sighting axis of the pipe and the axis of the cylindrical level must be parallel.

Leveling battens

On the bottom of the rail there is a metal plate that protects the rail from abrasion, called the "heel" of the rail. Signed on the rail ...

Level checks with level

Verification 1.

The axis of the circular level must be parallel to the axis of the instrument. Verifications and corrections are performed similarly to the verification of a cylindrical level with an alidade of the horizontal circle of theodolite.

Verification 2.

The vertical line of the grid should be parallel to the axis of rotation of the level. To perform verification at a distance of 20–30 m from the level, a plumb line is suspended on a thin cord and the level is leveled along a round level. Align one end of the vertical mesh with a plumb line. If the other ends of the vertical thread deviated from the cord no more than 0.5 mm, the verification condition is met. Otherwise, the mesh is corrected in the same way as the theodolite mesh.

Verification 3.

Align the ends of the image of the level bubble and take a reading on the staff. If the verification condition is met, then b1 ’will be taken along the staff, and if ... h \u003d i1 – b1’ \u003d i1– (b1 + x) The level and the staff are swapped, i2 is measured and the b2 bar is read. Since the distance between points is constant ...

Geodetic networks

State Geodetic Network (GGS) Is a system of points fixed on the terrain by certain signs with known coordinates and marks. The state geodetic network is the basis for topographic surveys, alignment and survey work. GGS is divided into planned and high-altitude.

Planned networks

- by purpose: - support - designed to extend a unified coordinate system to ... - thickening network - designed to increase the density of points in the network of necessary areas;

Characterization of triangulation networks

At the beginning, the backbone network is developed in the form of chains of triangles of class 1, ... A network of class 2 is built in the form of a continuous network of triangles inside a polygon of class 1. To further thicken the network ...

High-altitude geodetic network

Planned filming networks

They are developed from points of geodetic networks of all classes and categories by laying theodolite, tacheometric and mensule moves, as well as by building geometric networks.

High Altitude Survey Networks

They are created by laying leveling moves with a horizontal beam (theodolite or kipregel with a level on the pipe) or trigonometric leveling. The residuals in the passages and polygons when leveling with a horizontal beam should not exceed ± 0.1m, for trigonometric leveling ± 0.2m, where l–Travel length in km.

Shooting. Types of filming

Survey is a complex of linear and angular measurements on the ground, as a result of which a plan or map is obtained. The survey consists of 2 stages: 1. Creation of the survey justification (survey network), i.e. determination of coordinates and marks of points of the survey network;

Office processing of measurement results of theodolite traverse

Calculation of the coordinates of the points of the theodolite traverse.

Σβph \u003d β1 + β2 +… + βn Calculate the theoretical sum of the angles Σβt \u003d 180º (n – 2) - for a closed stroke

Calculation of directional angles and points.

αn \u003d αn – 1 ± 180º – βn - for right angles αn \u003d αn – 1 ± 180º + βn - for left angles The control of the correctness of calculating the directional angles is the coincidence of the value of the directional angle of the initial side ...

Calculating coordinate increments

According to the values \u200b\u200bof the directional angles and horizontal distances of the sides of the theodolite traverse, coordinate increments are calculated with an accuracy of 0.01m:

∆х \u003d dcos r

∆у \u003d d sin r

Coordinate increment signs are determined depending on the rumba name.

Calculation of linear residuals along coordinate axes

And the theoretical sums of increments ΣΔхт \u003d хfin – хnach

Calculating the coordinates of traverse points

yn \u003d yn – 1 + ∆yn corrected Calculations are controlled by obtaining the coordinates of known points x1 and y1: x1 \u003d xпт + ∆xпт – 1 \u003d xV + ∆xV – I

Construction of a plan of theodolite survey.

Digitization of the coordinate network.

Produced in accordance with the scale of the drawing in such a way that the value of the coordinate lines are multiples of 10 cm at a given scale and all points of the survey justification fit on the drawing and are located, if possible, in its middle part.

Drawing points of survey justification.

The control of correctness will be the equality of the directional angles of the sides on the plan and in the statement and the equality of the lengths of the sides on the plan and statement.

Putting the situation on the plan.

The situation is drawn along the outline and is depicted with conventional symbols, while auxiliary lines are not transferred to the plan.

Registration of the inscription on the plan.

Along the northern frame, the name of the drawing is signed, along the southern one - the scale, at the bottom right - the year of shooting and the artist.

Tacheometric survey

Reducing the accuracy of survey justification 1. Theodolite-leveling moves Angles in the theodolite move are measured ... Devices used in tacheometric survey: 1. Theodolites-tacheometers: T30, 2T30

The order of work at the station of tacheometric survey

The crocs are the same as the outline, but in this drawing the arrows indicate the directions of the homogeneous slopes. The height of sight is noted in the magazine (usually sighting is at the height of the instrument ...

Office processing of measurement results

Calculation of coordinates and marks of points of survey justification.

Coordinates (x, y) are calculated as in the theodolite line, station marks - as in the high-altitude line.

Tacheometric survey log processing.

MO \u003d (CL + KP): 2 ν \u003d KL – MO \u003d MO – KP For | ν |\u003e 2º, the horizontal distance, with an accuracy of 0.1 m, is calculated by the formula:

The marks of the rack points are calculated.

H r.t. \u003d H st + h

The excess sign depends on the sign ν .

Building a plan.

Using the journal of tacheometric surveys and crocs, rack points are applied to the plan and marks are signed next to their numbers. Using the method of graphic or analytical interpolation, a relief is built in ...

Menzular shooting

It is carried out using a beaker set and kipregel. The beaker kit includes: a tripod, a stand with lifting screws and a tablet (beaker), ... Kipregel's checks. Before starting work with the kipregel, the following must be done ... 1. The beveled edge of the kipregel ruler should be a straight line.

Side serif

Menzula is set at point A, oriented towards point B, kipregel is applied to point a, sighted at point C and drawn ...

Shooting situations and relief

Phototopographic shooting

Since the photographs do not represent precise plans of the area, they are processed in accordance with the laws of correspondence of objects ... The great advantages of phototopographic surveys are their complete ... Phototopographic survey methods allow most of the operations to create a map to be transferred to office conditions. ...

Technical leveling along the axis of a linear structure

At the beginning, office tracing is performed, i.e. on the plan, several options for the future route are outlined, after reconnaissance on the ground, they choose ... The main points of the route are the points of the beginning, end, turning angles, leading points ...

Field tracing

The inflection points of the terrain between the pickets are fixed with stakes, on the gatehouses nearby ...

Circular curve scheme

To calculate the rounding on the theodolite terrain, measure the angle β , in order to calculate the angle of rotation of the track φ \u003d 180º – β (φ - the angle between the initial and subsequent direction of the route)

Bending radius R are chosen in accordance with the safety conditions for the operation of the structure and relief. By φ and R calculate the basic elements of the circular curve.

Tangent (T) - the distance from the apex of the angle (VU) to the beginning of the curve (NK) or the end of the curve (KK):

Curve (K) - the length of a circular arc with a radius R from NK to KK:

Bisector (B) - distance from VU to the middle of the curve (SK):

Domer (D) - the difference of paths along a broken line and an arc:

D \u003d 2T-K

After the end of the curve, all pickets move forward on D.

In order to break a circular curve on the ground, it is enough to fix its main points: beginning, middle and end.

In order to fix the NK and KK from the VU along the axis of the route, T is laid. In order to fix the SC, an angle is laid with the help of a theodolite β / 2 and in this direction B.

The picket value of NK and KK is calculated by the formulas:

NK \u003d VU – T

KK \u003d NK + K

Control: KK \u003d VU + T – D

For large R it is not enough just to secure the NK, SK, KK. In this case, a detailed breakdown of a circular curve is used, which is performed, for example, by the method of rectangular coordinates, continued chords, etc.

Then they start leveling the track, which begins with linking the track to the DHW benchmark. The binding consists in laying a leveling course about the benchmark to the beginning of the track (PK0). Next, pickets, "plus" points, cross sections, main points of curves are leveled. Leveling is performed geometrically "from the middle", and the pickets are leveled as tie points (on both sides of the rails), and the rest as intermediate (along the black side). Leveling ends by binding the route to the datum of the high-altitude network.

Methods for detailing roundings

To calculate the coordinates x, y of the points of detailed breakdown, the central angle θ corresponding to a given arc k is preliminarily calculated.Further, solving the right-angled triangle OC1, one obtains:

Office processing of measurement results and

Creating a longitudinal profile of the route

I. Processing the results of the log of technical leveling.

The condition must be strictly met: ΣЗ - ΣП \u003d Σhcalc. The following condition must also be met: 2Σhsr \u003d Σhcalc, Violation of 1–2 mm.

II. Creation of a longitudinal profile along the route axis

Fill in the "Distances" column. To do this, on the horizontal scale of the profile, the distances between the pickets are laid and vertical lines are drawn through ... In the column "Pickets", using conventional signs, they depict pickets and sign them ... In the column "Actual marks" from the leveling log write out the marks of the pickets and "plus" points, rounding up to 0.01 ...

Drawing up a site plan based on the results

Leveling the area.

Depending on the size and shape of the sections of the leveling area, it can be performed in different ways: laying the main line with cross-sections or ... The main line with cross-laid in stretched sections, ... The points ...

Drawing up a site plan

A grid of squares is drawn on a sheet of paper in the selected scale, marks are drawn, the horizontal lines are drawn by interpolation, the contours of the terrain are transferred from the outlines and the inscriptions are drawn up.

Vertical layout of the site

Performed at the construction site before and sometimes after the construction of structures. Vertical leveling is performed by moving the masses of soil on the site ... Calculate the distance from the working marks to the zero points of work by the formulas:

Alignment work methods

2. Method of polar coordinates.

Geodetic works at a construction site

The work is reduced to the following stages: 1. Work on the creation of a master plan for the site: this stage consists of ... The master plan is a plan on a scale of 1: 500-1: 2000, which indicates all the projected buildings, structures, driveways ...

Geodetic services for the construction of structures.

Backbone creation works

Core networks can also be created using satellite systems. The points of the GGS (reference and networks ... The density of the high-altitude network is not less than one benchmark per 10-15 km2 for surveys at a scale of 1: 5000 and at least one benchmark per ...

Construction site survey

The survey is carried out in various ways: theodolite, tacheometric, phototopographic, stereophototopographic. The plans reflect all the objects of the area - relief and objects associated with ... The boundaries of mountain and land allotments are applied to the plans.

Creation of construction mesh

For the construction grid, a conditional system of rectangular coordinates is used, which is chosen so that the value of the abscissa of the coordinates x and y for points ... The requirement for accuracy is determined from the purpose of the grid. In most cases ... Removal of points is carried out in several stages.

Elements of geodetic alignment works

Building on the ground the design horizontal angle

1.with an accuracy equal to that of theodolite; 2. with an accuracy exceeding the accuracy of the theodolite (method of increased ... 1st method. The design angle B is laid off twice from the original direction using the theodolite at CL and CP, marking on ...

The subject and tasks of geodesy, its relationship with other sciences. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
The shapes and sizes of the Earth. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Coordinate systems. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Planned coordinate systems. Geographical coordinates. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Gauss-Kruger coordinate system (zonal coordinate system). ... ... ... ... ... ... ... ... ...
Line orientation. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Basic geodetic tasks. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Direct geodetic problem. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Inverse geodesic problem. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Basic geodetic drawings. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
The scale. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Relief. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	The main forms of relief. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Tasks to be solved according to topographic plans. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Determination of distance using scale. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Determination of rectangular coordinates of Gauss-Kruger. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Determination of elevations of points lying on the horizontal and between the horizontals. ...
	Determination of the slope steepness according to the laying schedule on the plan ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Drawing lines of the design or specified slope. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Determination of the catchment area. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Constructing a profile horizontally. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Measurement of the directional angle and true azimuth. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Nomenclature of topographic maps and plans. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
The main parts of geodetic instruments. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	The telescope. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Horizontal and vertical circles of theodolite. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Readout devices. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Angle measurements. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Classification of theodolites. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Theodolite checks. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Methods for measuring horizontal angles. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Method of receptions. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	The method of circular techniques. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Repetition method. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Measurement of vertical angles. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Methods for measuring vertical angles. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	The zero point of the vertical circle. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Measuring the angle of inclination of the terrain. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Measuring line lengths. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Measurement of line lengths with a mechanical device. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Line measurement order. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Corrections to be introduced to the line lengths measured by mechanical devices. ...
	Measurement of distances using physical and optical measuring devices. ... ... ... ...
Leveling. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Hydrostatic leveling. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Barometric leveling. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Trigonometric leveling. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Geometric leveling. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Forward leveling. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Leveling from the middle. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Simple and difficult leveling. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Classification and device of levels. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Leveling device with a cylindrical level. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Leveling battens. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Level checks with level. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Geodetic networks. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Planned networks. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Geodetic planned networks. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	High-rise geodetic network. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Planned filming networks. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	High-altitude survey networks. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Shooting. Types of filming. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Procedure for theodolite survey. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Terrain survey methods. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Office processing of the measurement results of the theodolite line. ... ... ... ... ... ... ... ... ... ...
Tacheometric survey. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Instruments used in tacheometric surveying. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	The order of work at the station during tacheometric survey. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Office processing of the measurement results of the tacheometric survey. ... ... ... ...
Menzular shooting. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Verifications of the kipregel. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Checking the beaker. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Shooting situations and relief. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Direct serif. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Resection. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Side serif. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Photographic shooting. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Engineering and technical work. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Field tracing. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Circular curve scheme. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Methods for detailed breakdown of roundings. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Method of rectangular coordinates. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Polar way. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Continued chord method. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Cameral processing of measurement results and construction of a longitudinal profile of the track. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Drawing up a site plan based on the results of leveling the area. Vertical layout. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Drawing up a site plan. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Vertical layout. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Center work. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Center work methods. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Geodetic works at a construction site. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Work on the creation of the backbone. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Filming of a construction site. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Creation of a construction grid. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Elements of geodetic alignment works. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Construction of the design horizontal angle on the ground. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Draws a line to the design length. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Setting out a point with a design elevation on the terrain. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
	Draws a line with a design slope. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

Geodesy is the science of determining the shape, size and gravitational field of the Earth and measurements on the earth's surface for displaying it on plans and maps, as well as for carrying out various engineering and national economic activities. In practice, measurements have to be taken both on the surface of the earth and under its surface (metro tunnels, mines), and above the ground (for example, when building high-rise buildings or such unique structures as the Ostankino TV tower). Geodetic work is needed for a wide variety of purposes, and above all for drawing up plans and maps.

Geodesy tasks are subdivided into scientific and scientific and technical.

The main scientific task of geodesy is to determine the shape and size of the Earth and its external gravitational field. Along with this, geodesy plays an important role in solving many other scientific problems related to the study of the Earth. Such tasks, for example, include: studies of the structure and internal structure of the Earth, horizontal and vertical deformations of the earth's crust; movements of coastlines of seas and oceans; determination of differences in heights of sea levels, movements of the earth's poles, etc.

The scientific, technical and practical tasks of geodesy are extremely diverse; with essential generalizations, they are as follows:

- field research - field geodesy provides the preparation of projects of structures by performing field geodetic measurements and computational graphic works;

- layout work - transfer of the designed structures to the terrain;

- executive shooting - in order to find out how much the results of the completed stage differ from the project;

- observation of deformations.

All geodesy tasks are solved based on the results of special measurements, called geodetic measurements, performed using special geodetic instruments. Therefore, the development of programs and measurement methods, the creation of the most expedient types of geodetic instruments are important scientific and technical problems of geodesy.

The multitude of scientific and practical problems solved by geodesy led to the allocation of a number of independent sections in it: topography, higher geodesy, cartography, applied (engineering) geodesy, aerial photogeodesy and space geodesy (remote sensing methods):

Higher Geodesy - studies the shape, size and gravitational field of the Earth and the planets of the Solar System, as well as the theory and methods of constructing a geodetic network in a single coordinate system. Higher geodesy is closely related to astronomy, gravimetry, geophysics and space geodesy.

Geodesy (topography) - deals with the survey of relatively small areas of land and develops ways to depict them on plans and maps.

Cartography - studies the methods, processes, and processes for creating and using maps, plans, atlases, and other cartographic products.

Photogrammetry - studies how to determine the shape, size and position of objects in space from their photographic images.

Space Geodesy - studies methods of processing data obtained from outer space using artificial satellites, interplanetary ships and orbital stations, which are used for measurements on the earth and planets of the solar system.

Engineering (applied) geodesy - studies the methods and means of conducting geodetic work in the survey, design, construction and operation of various and engineering structures, in the exploration, use and exploitation of natural resources.

Mine survey (underground geodesy) studies methods of conducting geodetic works in underground mine workings.

There are no clearly defined boundaries between the listed disciplines. So, topography includes elements of higher geodesy and cartography, engineering geodesy uses sections of almost all other geodetic disciplines, etc.

Already from this incomplete list of geodetic disciplines, it is clear what a variety of tasks - both theoretical and practical - surveyors have to solve in order to meet the requirements of public and private institutions, companies and firms. For state planning and the development of the country's productive forces, it is necessary to study its territory in a topographic respect. Topographic maps and plans created by surveyors are needed by everyone who works or moves around the Earth: geologists, sailors, pilots, designers, builders, farmers, foresters, tourists, schoolchildren, etc. Army maps are especially needed: building defensive structures, shooting at invisible targets, using rocketry, planning military operations - all this is simply impossible without maps and other geodetic materials.

Geodesy constantly absorbs the achievements of mathematics, physics, astronomy, radio electronics, automation and other fundamental and applied sciences. The invention of the laser led to the appearance of laser geodetic devices - laser levels and optical range finders; code measuring devices with automatic fixation of readings could appear only at a certain level of development of microelectronics and automation. And the achievements of informatics have caused a real revolution in geodesy, in recent years the construction of so-called unique engineering structures has demanded a sharp increase in the accuracy of measurements from geodesy, and take into account tenths and even hundredths of a millimeter. Based on the results of geodetic measurements, deformations and settlements of operating industrial equipment are studied, the movement of the earth's crust in seismically active zones is detected, water levels in rivers, seas and oceans and the level of ground waters are monitored. The possibility of using artificial earth satellites for solving geodetic problems led to the emergence of new sections of geodesy - space geodesy and geodesy of planets.

 Introduction

Discipline "Fundamentals of Geodesy and Cartography" its tasks, content, connection with other sciences and role in the training of specialists in land surveyors.

Geodesy (Greek γεωδαισία - division of the earth, from γῆ - Earth and δαΐζω - delyu,, or "land allocation") is the science of methods of making measurements on the earth's surface, carried out in order to study the size and shape of the Earth, the image of the entire earth and its parts on maps and plans, as well as the methods of special measurements required to solve various engineering and economic problems.

Geodesy is widely used in various fields of science, industry and military affairs. Topographic maps are used in planning and locating the productive forces of the state, in the exploration and exploitation of natural resources, in architecture and urban planning, in land reclamation, land management, forest management, land and city cadastre. Geodesy is used in the construction of buildings, bridges, tunnels, subways, mines, hydraulic structures, railways and highways, pipelines, airfields, power lines, in determining the deformations of buildings and engineering structures, in the construction of dams, in solving defense problems.

In the scientific setting of work, any more or less significant economic construction begins with the preparation of a project, that is, with the establishment of the type, shape, size and location of the necessary structures and the identification of all types of work required for their implementation. Drawing up a project is impossible without a plan of the area on which the structure is supposed to be erected. Therefore, in the absence of a plan or map, the construction of engineering structures begins with geodetic works. In this order, for example, they carry out canals, carry out work related to drainage of swamps and irrigation of desert lands, build railways and highways, build large factories and factories, high-rise buildings, the subway, etc.

In the process of farming, it is often required to perform some geodetic operations. The agronomist needs to be able to use the plan of the territory of the economy, the ability, as they say, to read the plan, that is, to distinguish all the soils and lands depicted on it, to see the relief, etc. , and in nature and perform the simplest shooting and making plans.

The image of the earth's surface is extremely important for the defense of the country. Only with a visual image of the terrain in front of your eyes, you can choose the most convenient places for the location of individual units of troops, arrange the most convenient crossings over rivers and mountains, find cover from enemy fire, etc. Therefore, in each country, so-called topographic maps are drawn up in advance. on which the terrain is depicted with all the details that may have one or another meaning in military operations.

The objective of the course "Fundamentals of Geodesy and Cartography" is to study the theoretical foundations and practical techniques for training land surveyors to independently perform the following simple geodetic works:

As a result of mastering the academic discipline "Fundamentals of Geodesy and Cartography", students:

should be able to:

Use the scale when measuring and plotting segments on topographic maps and plans;

Determine orienting angles on the map (plan);

Solve problems on the relationship between the orienting angles;

Determine the nomenclature of sheets of topographic maps of a given scale;

Determine geographic and rectangular coordinates of points on the map and plot points on the map at specified coordinates;

Determine relief shapes on the map, solve problems with contours;

Make a profile of the terrain in any direction;

Use basic geodetic instruments;

Perform linear measurements;

Carry out basic instrument checks and adjustments;

Measure horizontal and vertical angles;

Determine the elevations and heights of points;

must know:

Coordinate and elevation systems used in geodesy;

Types of scales;

Orientation angles, lengths of terrain lines and the relationship between them;

Scale series, layout and nomenclature of topographic maps and plans;

Features of the content of agricultural maps;

Methods for depicting the terrain on topographic maps and plans;

Basic geodetic instruments, their device, verification and adjustment procedure;

Basic methods for measuring horizontal angles;

Measuring instruments and methods for measuring terrain lines;

Methods and methods for determining the excess.

Geodesy is one of the most ancient earth sciences, has a long history. In the course of its development, the content of the subject has been enriched, expanded and in this regard, several scientific and scientific-technical disciplines have arisen.

Higher geodesy, using the results of high-precision geodetic, astronomical, gravimetric and satellite measurements, studies the shape, size and gravitational field of the Earth and the planets of the solar system, is engaged in the creation of state geodetic reference networks, the study of geodynamic phenomena, the solution of various geodetic problems on the surface of the ellipsoid and in space.

Space geodesy is a science that studies the use of the results of observations of artificial and natural satellites of the Earth for solving scientific and scientific-technical problems of geodesy. Observations are carried out both from the surface of the planet and directly on the satellites.

Topography refers to the measurements taken to create plans and maps of relatively small areas of the earth's surface.

Cartography is the science that studies the issues of cartographic representation and develops methods for creating maps and their use. Cartography is closely related to geodesy, topography and geography. The results of geodetic determinations of the size and shape of the Earth and the coordinates of points of geodetic networks, as well as the results of topographic surveys, are used in cartography as an initial basis for compiling maps.

Photogrammetry studies the shapes, sizes, positions, dynamics and other qualitative and quantitative characteristics of objects from their photographic images. Photogrammetric methods are used in various fields of science and technology; in topography and geodesy, astronomy, architecture, construction, geography, oceanology, medicine, forensics, space research, etc.

Engineering geodesy studies geodetic work during surveys, design, construction, reconstruction, installation and operation of various engineering structures and technological equipment, in the exploration and extraction of natural resources of the country and its subsoil, in the creation of unique objects, etc.

The following types of work are performed by geodetic methods and instruments:

1. Survey (contour and topographic surveys).

2. Breakout (transferring the project to the area).

3.Control (carried out during the delivery of objects and during their operation)

Geodesy and applied geodesy, in their development, are based on the achievements of other sciences and especially mathematics, astronomy, physics, geography, engineering, etc.

Mathematics equips geodesy with methods of analysis and processing of the results obtained during measurements. On the example of geodesy and mathematics, there is an extremely close connection between related disciplines, which is now characteristic of various technical and mathematical sciences.

Surveyors use astronomical observation data to orientate and determine the coordinates of the original or control points.

The advances in physics for the benefit of geodesy are invaluable. The discovery of the law of gravitation was the theoretical basis for determining the shape of the Earth. The development of optics and electronics made it possible to design a telescope, develop rangefinder devices and other optical and electronic measuring devices. A number of laws related to the physics of liquid and gaseous bodies are used in geodetic measurements.

Geographic data helps to correctly understand and depict the terrain on the plans and maps. Geomorphology, a branch of geography that studies the structure of the earth's surface relief, is of particular importance for geodesists, hydraulic engineers and land reclamators.

Geodesy plays an important role in land management, the task of which is to organize the territory for successful agriculture. In the initial, so-called preparatory stage of land management, geodesy is tasked with providing it with accurate planning and cartographic material. At the stage of drawing up a project according to the rules of geodesy, the technical part of the design is carried out. Purely geodetic work is the transfer of the project to nature.

In land management using geodetic methods and instruments, the following types of work are performed:

1. Survey (for drawing up a plan for on-farm land management)

2.Display (transferring the project to nature)

3. Correcting (applying changes in the contours to the plan of on-farm land management).