It is known that triangulation as a geodetic term means a way of creating geodetic networks. Yes it is. But we should start with something else.
Initially, with the emergence of a person’s need for knowledge, ordinary thinking leads him to the accumulation of a certain amount of knowledge. With the development of scientific thinking, all this knowledge is systematized, including explanations based on facts, phenomena and evidence. By applying theoretical assumptions in practice, a kind of criteria of truth arise. That is, are all those assumptions that, using certain methods, give a specific result confirmed in a practical way? Perhaps one of these scientific methods that solves the problem of high-precision measurement of large distances between points on earth's surface with the construction of triangles adjacent to each other and measurements within them, a method of triangulation became available.
The first to invent and apply the triangulation method (1614-1616) was the great Dutch scientist Willebrord Snell (Snellius). In those years, there were already assumptions that the Earth is a planet in outer space and has the shape of a sphere (from the cosmology of Giordano Bruno 1548-1600). Establishment exact dimensions planet was of great practical importance for its development in the future. For this purpose, in the Netherlands, through the construction of a series of triangles, degree measurements of the meridian arc were made for the first time using the triangulation method. What is meant. Having carried out measurements between rigid geodetic points with a difference in latitude between them of one degree (for Snell 1º11´30") using the triangulation method and obtaining a specific distance of the arc, the Dutch mathematician could, by ordinary calculation, obtain the length of the entire meridian circle. Obviously, calculate the radius of the Earth, taking it figure for the shape of a ball (ellipse), remained a matter of technology.
At the end of the historical excursion, we can highlight the interconnectedness and electivity scientific knowledge for the future practical application person. And it is not surprising that the invention of the triangulation method occurred precisely in the Netherlands, which at that time was considered a leading maritime power with the need for new knowledge in navigation, geography, astronomy and, of course, geodesy.
Essence of the method
Triangulation consists of determining the spatial location of geodetic points specially fixed on the ground at the vertices of a number of triangles. Initially, the azimuths of the original directions are determined with a high degree of accuracy (up to fractions of seconds) ab, ba, mn, nm(Fig. 1. Triangulation series of triangles along the meridian). The next step there will be a determination of astronomical coordinates (latitude and longitude) at measurement points of the azimuths of two initial bases. In each pair of hard sides ( ab, mn) coordinates are measured at only one point, for example a, m(Fig. 1). In this case, you should pay attention Special attention to determine astronomical latitudes in a series of triangles located in the direction of the meridians. When taking measurements in triangles formed along parallels, due attention must be paid to determining astronomical longitudes. Next, measure the lengths of the two base sides ( ab, mn). These sides are relatively short in length (about 8-10 km). Therefore, their measurements are more economical and accurate relative to the sides CD, tq, making up distances from 30 to 40 km. The next step is to move from the bases ab, mn through angular measurements in rhombuses abcd And mntq to the sides CD, tq. And then sequentially at almost every vertex of the triangles cde, def, efg and others, horizontal angles are measured before adjoining the next main side tq whole series of triangles. Using the measured angles of a triangle with the measured base or calculated base side, all other sides, their azimuths and coordinates of the vertices of the triangles are sequentially calculated.
Fig.1. Triangulation series of triangles along the meridian.
Triangulation networks
After the first use of the degree measurement of an arc by Snell, the triangulation method became the main method in geodetic high-precision measurements. Since the 19th century, when triangulation work became more advanced, entire geodetic networks began to be formed with its help, built along parallels and meridians. The most famous of all is known under the name of the geodetic meridian arc of Struve and Tenner (1816-1852) and was subsequently included in the world heritage by UNESCO. Its triangulation series stretched across Norway, Sweden, Finland and Russia from the Arctic Ocean to the Black Sea at the mouth of the Danube and formed an arc of 25º20´ (Fig. 2).
Fig.2.
The scheme of Professor F.N. Krasovsky (Fig. 3) was adopted as the basis for geodetic triangulation networks in our country. Its essence lies in the application of the principle of construction from the general to the specific. Initially, points are laid along the meridians and parallels, forming rows of triangles with a length of 200-240 km. The lengths of the sides in the triangles themselves are 25-40 km. All astronomical measurements of azimuths, coordinates (latitudes and longitudes) of output points at Laplace points (1) and intermediate astronomical points (2), high-precision basic (3) geodetic measurements and at each point of this chain must meet the established requirements of class I accuracy (Fig. 3). A closed polygon of four triangulation rows is a figure resembling a square with a perimeter of approximately 800 km. Through the central parts of the first-class triangulation rows, the main rows of the class II triangulation network (Fig. 3) of appropriate accuracy are arranged towards each other. The base lengths of the sides in these rows are not measured, but the bases from the sides of class I triangulation are accepted. Likewise, there are no astronomical points. The resulting four spaces are filled with continuous triangulation networks of both classes II and III.
Fig. 3. State triangulation networks.
Of course, the described scheme for the development of triangulation networks according to Krasovsky cannot cover the entire territory of the country due to obvious reasons for the large forested and uninhabited areas of the country. Therefore, from west to east, separate rows of first-class triangulation and polygonometry were laid along the parallels, rather than a continuous triangulation network.
Advantages of triangulation
In the development of geodetic science and its practical application, the advantages of the triangulation method of measurements are obvious. With the help of this universal method Maybe:
- determining the position of geodetic points at significantly distant distances;
- performing basic work on the construction of geodetic networks throughout the country;
- providing the basis for all topographic surveys;
- alignment of various coordinate systems through basic geodetic work;
- production of engineering and survey work;
- periodic determination of the size of the Earth;
- study of movements of the earth's surface.
The main methods for creating a state geodetic network are triangulation, trilateration, polygonometry and satellite coordinate determinations.
Triangulation(Fig. 68, a) is a chain of triangles adjacent to each other, in each of which all angles are measured with high-precision theodolites. In addition, I measure the lengths of the sides at the beginning and end of the chain.
Rice. 68. Scheme of triangulation (a) and polygonometry (b).
In a triangulation network, the basis L and the coordinates of points A and B are known. To determine the coordinates of the remaining points of the network, horizontal angles are measured in triangles.
Triangulation is divided into classes 1, 2, 3, 4. Triangles of different classes differ in the lengths of the sides and the accuracy of measuring angles and bases.
The development of triangulation networks is carried out in compliance with the basic principle “from general to specific”, i.e. First, a triangulation of class 1 is built, and then classes 2, 3 and 4 are successively constructed.
Points of the state geodetic network are fixed on the ground by centers. To ensure mutual visibility between points, wooden or metal geodetic signs are installed above the centers. They have a device for installing the device, a platform for the observer and a sighting device.
Depending on the design, ground geodetic signs are divided into pyramids and simple and complex signals.
The types of underground centers are established depending on the physical and geographical conditions of the region, the composition of the soil and the depth of seasonal freezing of the soil. For example, the center of a point of the state geodetic network of classes 1-4 of type 1 according to the instructions “Centers and Benchmarks of the State Geodetic Network” (M., Nedra, 1973) is intended for the southern zone of seasonal soil freezing. It consists of a reinforced concrete pylon with a cross section of 16X16 cm (or an asbestos-cement pipe 14-16 cm filled with concrete) and a concrete anchor. The pylon is cemented into the anchor. The base of the center must be located below the depth of seasonal soil freezing of at least 0.5 m and at least 1.3 m from the surface of the earth. A cast iron mark is concreted in the upper part of the sign at ground level. A layer of 10-15 cm of soil is poured over the mark within a radius of 0.5 m. An identification pole with a security plate is installed 1.5 m from the center.
Currently, radio engineering means are widely used to determine distances between network points with relative errors of 1:100,000 - 1:1,000,000. This makes it possible to build geodetic networks using the trilateration, in which only the sides are measured in triangle networks. The angles are calculated using the trigonometric method.
Method polygonometry(Fig. 68, b) consists in the fact that geodetic reference points are connected with each other by passages called polygonometric ones. They measure distances and angles on the right.
Satellite methods for creating geodetic networks are divided into geometric and dynamic. In the geometric method, an artificial Earth satellite is used as a high sighting target; in the dynamic method, the satellite is a carrier of coordinates.
Triangulation(from Latin triangulum - triangle) - one of the methods for creating a geodetic reference network.
Triangulation- a method of constructing horizontal structures on the ground in the form of triangles, in which all angles and basic output sides are measured (Fig. 14.1). The lengths of the remaining sides are calculated using trigonometric formulas(for example, a=c . sinA/sinC, b=c . sinA/sinB), then find the directional angles (azimuths) of the sides and determine the coordinates.
It is generally accepted that the triangulation method was invented and first used by W. Snell in 1615–17. when laying out a series of triangles in the Netherlands for degree measurements. Work on the use of the triangulation method for topographic surveys in pre-revolutionary Russia began at the turn of the 18th–19th centuries. By the beginning of the 20th century. The triangulation method has become widespread.
Triangulation is of great scientific and practical importance. It serves to: determine the shape and size of the Earth using the method of degree measurements; studying horizontal movements of the earth's crust; justification of topographic surveys at various scales and purposes; justification of various geodetic works in the survey, design and construction of large engineering structures, in the planning and construction of cities, etc.
In practice, it is allowed to use the polygonometry method instead of triangulation. In this case, the condition is set that when constructing a reference geodetic network using this and other methods, the same accuracy in determining the position of points on the earth’s surface is achieved.
The vertices of the triangulation triangles are marked on the ground by wooden or metal towers with a height of 6 to 55 m, depending on terrain conditions (see Geodetic signal). For the purpose of their long-term preservation on the ground, triangulation points are secured by placing special devices in the ground in the form metal pipes or concrete monoliths with metal marks embedded in them (see Geodetic center), fixing the position of points for which coordinates are given in the corresponding catalogs.
3) Satellite topographic survey
Satellite photography is used to compile topographic maps of an overview or small scale. Satellite GPS measurements are very accurate. But in order to avoid the use of this system for military needs, the accuracy was reduced from
Topographic surveys using global navigation satellite systems make it possible to depict the following objects on topographic plans at scales of 1:5000, 1:2000, 1:1000 and 1:500 with the necessary reliability and accuracy:
1) points of triangulation, polygonometry, trilateration, ground benchmarks and survey justification points fixed on the ground (plotted according to coordinates);
2) industrial facilities - drilling and production wells, oil and gas rigs, above-ground pipelines, wells and underground communication networks (during as-built survey);
3) railways, highways and dirt roads of all types and some structures attached to them - crossings, crossings, etc.;
4) hydrography - rivers, lakes, reservoirs, spill areas, tidal strips, etc. Coastlines are drawn according to the actual state at the time of surveying or at low water;
5) hydraulic engineering and water transport facilities - canals, ditches, water conduits and water distribution devices, dams, piers, moorings, piers, locks, etc.;
6) water supply facilities - wells, standpipes, reservoirs, settling tanks, natural springs, etc.;
7) terrain using contours, elevation marks and symbols of cliffs, craters, screes, ravines, landslides, glaciers, etc. Microrelief forms are depicted by semi-horizontals or auxiliary contours with terrain elevation marks;
8) shrubby, herbaceous, cultivated vegetation (plantations, meadows, etc.), free-standing bushes;
9) soils and microforms of the earth’s surface: sands, pebbles, takyrs, clayey, crushed stone, monolithic, polygonal and other surfaces, swamps and salt marshes;
10) boundaries - political and administrative, land use and nature reserves, various fences.
Many GPS devices on the market today allow specialists to take careful measurements during road laying and construction. various structures, measuring land area, creating terrain maps for oil production, etc.
The use of computer modeling methods and the perfection of calculations perfectly complement topographic survey.
Triangulation method. It is generally accepted that the triangulation method was first proposed by the Dutch scientist Snellius in 1614. This method is widely used in all countries. The essence of the method: at commanding heights of the area, a system of geodetic points is fixed, forming a network of triangles. IN Triangulation network this network determines the coordinates of the starting point A, measure the horizontal angles in each triangle, as well as the lengths b and azimuths a of the base sides, which specify the scale and azimuth orientation of the network.
The triangulation network can be built in the form of a separate row of triangles, a system of rows of triangles, and also in the form of a continuous network of triangles. Elements of a triangulation network can be not only triangles, but also more complex figures: geodesic quadrangles and central systems.
The main advantages of the triangulation method are its efficiency and the ability to use in a variety of physical and geographical conditions; big number redundant measurements in the network, allowing reliable control of all measured values directly in the field; high accuracy in determining the relative position of adjacent points in a network, especially a continuous one. The triangulation method has become most widespread in the construction of state geodetic networks.
Polygonometry method. Polygonometry is a method of constructing a geodetic network in the form of a system of closed or open broken lines, in which all elements are directly measured: angles of rotation and lengths of sides d
The essence of this method is as follows. A system of geodetic points is fixed on the ground, forming an elongated single passage or a system of intersecting passages, forming a continuous network. Between adjacent traverse points, the lengths of the sides s,- are measured, and at the points - the angles of rotation p. Azimuthal orientation of a polygonometric traverse is carried out using azimuths determined or specified, as a rule, at its end points, while measuring adjacent angles y. Sometimes polygonometric passages are laid between points with given coordinates of a geodetic network of a higher accuracy class.
Angles in polygonometry are measured with precise theodolites, and sides - with measuring wires or light-distance numbers. Moves in which the sides are measured with steel h measuring tapes, and the corners - theodolites of technical accuracy 30" or G, are called theodolite passages. Theodolite passages are used in the creation of survey geodetic networks, as well as in engineering, geodetic and survey work. In the polytonometry method, all construction elements are measured directly, and the directional angles a and the coordinates of the vertices of the rotation angles are determined in the same way as in the triangulation method.
The order of constructing network plans: according to the principle from general to specific, from large to small, from precise to less precise.
Trilateration method. This method, like the triangulation method, involves the creation of geodetic networks on the ground, either in the form of a chain of triangles, geodetic quadrangles and central systems, or in the form of continuous networks of triangles, in which not angles are measured, but the lengths of the sides. In trilateration, as in triangulation, in order to orient networks on the ground, the azimuths of a number of sides must be determined.
With the development and increase in the accuracy of light and radio ranging technology for measuring distances, the trilateration method is gradually gaining more and more importance, especially in the practice of engineering and geodetic work.
Satellite methods for constructing a geodetic network.
Methods using satellite technologies, in which the coordinates of points are determined using satellite systems - the Russian Glonass and the American GPS. These methods have revolutionary scientific and technical significance in terms of the results achieved in accuracy, efficiency in obtaining results, all-weather capability and relatively low cost of work compared to traditional methods restoration and maintenance of the state geodetic basis at the proper level.
Satellite methods for creating geodetic networks consist of geometric And dynamic. In the geometric method, the satellite is used as a high sighting target; in the dynamic method, the satellite (artificial earth satellite) is the carrier of coordinates. In the geometric method, satellites are photographed against the background of reference stars, which makes it possible to determine the directions from the tracking station to the satellites. Photographing several satellite positions from two or more initial and several determined points allows one to obtain the coordinates of the determined points. The same problem is solved by measuring the distance to satellites. The creation of navigation systems (in Russia - Glonass and in the USA - Navstar), consisting of at least 18 satellites, makes it possible to determine geocentric coordinates at any time in any part of the Earth X, Y, Z, with higher accuracy than the previously used American Transit navigation system, which allows you to determine coordinates X, Y, Z, with an error of 3-5 m.
No. 16 Planned justification for topographic surveys. Field work.
Points of state geodetic networks and condensation networks do not have sufficient density for topographic surveys. Therefore, a survey justification is created on the territory of the proposed construction. The points of this justification are located in such a way that all measurements when photographing the situation and relief are made directly from its points. The survey justification is created on the basis of the general principle of constructing geodetic networks - from the general to the specific. It is based on points of the state network and condensation networks, the errors of which are negligibly small compared to the errors of the survey justification.
The accuracy of creating a justification ensures that topographic surveys are carried out with errors within the limits of the graphical accuracy of constructions on a plan of a given scale. In accordance with these requirements, the instructions for topographic surveys regulate the accuracy of measurements and the maximum values of stroke lengths.
Theodolite traverses are most often used as a planning justification. In open areas, theodolite passages are sometimes replaced by rows or a microtriangulation network, and in built-up or forested areas - by networks of quadrangles without diagonals.
Planned high-altitude surveys. In which both the horizontal and altitude positions of the points being surveyed are determined. The result is a plan or map depicting both the situation and the relief. Field geodetic work are carried out directly on the ground and, depending on the purpose, they include:
picket breakdown;
creation of a planning framework;
documentation
№17Office processing of theodolite traverse materials.
Chamber work is work that is carried out in the winter in an office (chamber in Latin means room) for the purpose of final processing in summer time obtained field work material. Calculations are made, maps, reports, articles, books are compiled for printing, which are the result of geological, geophysical, exploration, etc., carried out on the spot. works
Purpose: automation of processing of engineering and geodetic surveys obtained from field measurement logs.
Software features:
calculation and adjustment of theodolite traverses of various configurations;
processing the results of tacheometric survey of the area;
processing of leveling results;
solving geodetic referencing problems (coordinate offset, triangle, etc.);
calculating the area of a closed polygon from the coordinates of its boundary points;
plotting calculation and adjustment results on a map;
generation and printing of statements for solving geodetic problems.
Application Description:
To perform office processing of engineering and geodetic surveys, the GIS “Map 2008” provides the “Geodetic Computations” software package. The procedures included in the software package allow you to process field measurement data, plot the calculation results on a map and draw up reporting documentation in the form of payroll statements using data during the calculations.
The procedures included in the complex allow you to perform calculations and equalize geodetic measurements for subsequent use of the results for the purpose of drawing up topographic plans, generating land management documentation, designing and monitoring linear structures, constructing relief models, etc. All modes are designed for processing “raw” measurements and provide a tabular form for data entry. Appearance and the entry procedure are as close as possible to traditional forms of filling out field journals. Required fields for entering information are highlighted in color.
No. 18 High-altitude justification of topographic surveys. Field work
High-rise justification points, as a rule, are combined with planning justification points. The height justification is created using geometric or trigonometric leveling methods. The distance between the level and the slats should exceed 150m. The difference in shoulders should not exceed 20m. Level on both sides of the slats. The difference between the elevations should not exceed ±4mm.
High-altitude survey justification is usually created in the form of class IV leveling networks or technical leveling. On large areas, when creating a high-altitude justification using the geometric leveling method, a sparse network of points is obtained, which is subsequently condensed by high-altitude passages. In these moves, the excesses are determined trigonometrically. To obtain the required accuracy, the instructions for topographic surveys regulate the accuracy of measurements of elevations, the methodology for their determination and the maximum lengths of high-altitude passages.
According to the purpose, composition and methods of performing field and office work, two types of phototheodolite survey are distinguished - topographic and special.
For topographic phototheodolite surveying, carried out to obtain topographic maps and plans at scales of 1:500, 1:1000, 1:2000, 1:5000, 1:10,000, the work includes:
1) drawing up a work project (choosing a survey scale, drawing up a work program and estimates for them, calendar plan)
2) reconnaissance of the shooting area (inspection of the situation and terrain, selection of the type of geodetic support network for survey justification, locations of photographing bases and control points);
3) creation of a geodetic reference network (installation of network signs, measurements in the network, preliminary calculation of coordinates and elevations of network points);
4) creation of a survey working justification and plan-altitude reference of base points and control points;
5) photographing the area;
6) measuring the lengths of photographing bases;
7) laboratory and office work.
Planned high-altitude surveys. In which both the horizontal and altitude positions of the points being surveyed are determined. The result is a plan or map depicting both the situation and the relief. Field geodetic work is carried out directly on the ground and, depending on the purpose, includes:
picket breakdown;
creation of a planning framework;
linking the geodetic basis of survey areas to points of the state basis or departmental surveys;
shooting details of the situation, relief, profiles and individual objects;
breakdown of the transfer of the project to the area with capital works and with the current content of the path;
monitoring the regime of rivers and reservoirs and a number of other types of geodetic work.
By doing field work is underway documentation: picketing, leveling, tacheometric logs, rotation angle logs, outlines, etc.
No. 19 Office processing of leveling materials.
Office processing of leveling materials is divided into preliminary (processing of field journals) and final calculations. During the final calculations, the accuracy of the leveling results is assessed, the results are equalized and the point marks are calculated.
Preliminary calculations begin with a thorough check of all journal entries and calculations. Then on each page the sums of the back (∑ Z) and front (∑ P) samples and find their half-difference. After this, calculate the sum of average excesses (∑ h avg). The page-by-page calculation control is equality
The discrepancy is explained by possible deviations due to rounding when deriving the average.
In the case of a leveling move based on two fixed points, a known excess h 0 is calculated as the difference between the known marks of the final H to and primary H n move points, and then
h 0 = H to - H n .
If leveling is carried out over a closed area, then the known excess h 0 will be equal to zero.
Hanging leveling passages are leveled twice and then the excess h 0 is calculated as half the sum of the excesses of two leveling moves
No. 20 Methods of topographic surveys.
Topographic survey is a complex of geodetic works, the result of which is topographic map or site plan. Topographic surveys are carried out using aerial phototopographic and ground methods. Ground-based methods are divided into tacheometric, theodolite, phototheodolite and scale surveys. The choice of shooting method is determined technical feasibility and economic feasibility, the following main factors are taken into account: - size of the territory, complexity of the terrain, degree of development, etc. When surveying large areas, it is most effective to use aerial phototopographic survey; in small areas, tacheometric and theodolite surveys are usually used. Periodic photography is currently used quite rarely, as a technologically outdated type of shooting. The most common type of ground topographic survey is tacheometric survey. It is mainly carried out using an electronic total station, but it is also possible to survey using a theodolite. When tacheometric surveying in the field, all the necessary measurements are carried out, which are entered into the memory of the device or in a journal, and the plan is drawn up in office conditions. Theodolite survey is carried out in two stages: building a survey network and surveying contours. The survey network is built using theodolite traverses. Filming work is carried out from points of the filming network in the following ways: rectangular coordinates, linear serifs, angular serifs, polar coordinates. Theodolite survey results are reflected in the outline. All sketches in outlines must be carried out clearly and accurately, arranging objects in such a way that it remains free place for recording measurement results. During time-lapse surveying, the area plan is drawn directly at the survey site on a pre-prepared tablet, in the field.
Mensula survey is a topographical survey carried out directly in the field using mensula and kipregel. Horizontal angles are not measured, but plotted graphically, which is why linear surveys are called angle surveys. When photographing a situation and relief, distances are usually measured with a rangefinder, and excesses are determined by trigonometric leveling. Constructing a plan directly in the field makes it possible to eliminate gross errors during surveying and achieve the most complete correspondence between the topographic plan and the terrain.
No. 21 Theodolite-altitude survey
Theodolite-high-altitude move is a theodolite traverse, in which, in addition to determining the coordinates of the traverse points, their heights are determined by trigonometric leveling. Measurements and calculations performed to determine plan coordinates X, at. Let's consider the definition of heights.
On each side of the move, the angles of inclination are measured with a technical precision theodolite. Angle measurement is performed in one step. The excess is calculated using the formula. To control and improve accuracy, each excess is determined twice - in the forward and reverse directions. Direct and reverse excess, having different sign, should not differ in absolute value more than 4 cm for every 100 m of line length. The final value of the excess is taken as the average, with a direct sign.
Theodolite-altitude passages begin and end at starting points, the heights of which are known. The shape of the move can be closed (with one starting point) or open (with two starting points).
No. 22 Tacheometric survey
Tacheometric survey is a combined survey, during which the horizontal and elevation positions of points are simultaneously determined, which allows you to immediately obtain a topographic plan of the area. Tacheometry literally means quick measurement.
The position of the points is determined relative to the survey justification points: horizontal - by polar method, high-altitude - by trigonometric leveling. The lengths of polar distances and the density of picket (batten) points (maximum distance between them) are regulated in the instructions for topographic and geodetic work. When performing tacheometric surveys, a geodetic tacheometer is used, designed to measure horizontal and vertical angles, line lengths and elevations. A theodolite, which has a vertical circle, a device for measuring distances and a compass for orienting the limb, belongs to theodolites-tacheometers. Theodolites-tacheometers are the majority of technical precision theodolites, for example T30. The most convenient for performing tacheometric surveys are tacheometers with a nomogram determination of elevations and horizontal alignments of lines. Currently, electronic total stations are widely used.
No. 23 Surface leveling methods.
Leveling is a type of geodetic work, as a result of which the differences in heights (elevations) of points on the earth's surface are determined, as well as the heights of these points above the accepted reference surface.
According to the methods, leveling is divided into geometric, trigonometric, physical, automatic, stereophotogrammetric.
1. Geometric leveling - determining the excess of one point over another using a horizontal sighting beam. It is usually carried out using levels, but you can also use other devices that allow you to obtain a horizontal beam. 2. Trigonometric leveling - determination of excesses using an inclined sighting beam. The excess is determined as a function of the measured distance and inclination angle, for the measurement of which appropriate geodetic instruments (tacheometer, cypregel) are used.
3. Barometric leveling - it is based on the relationship between atmospheric pressure and the height of points on the ground. h=16000*(1+0.004*T)P0/P1
4. Hydrostatic leveling - determination of excesses is based on the property of liquid in communicating vessels to always be at the same level, regardless of the height of the points at which the vessels are installed.
5. Aeroradio leveling - excesses are determined by measuring flight altitudes aircraft radio altimeter. 6. Mechanical leveling - is carried out using instruments installed in track-measuring cars, trolleys, cars, which, while moving, draw the profile of the traversed path. Such devices are called profilographs. 7. Stereophotogrammetric leveling is based on determining the elevation from a pair of photographs of the same area, obtained from two photographic reference points. 8. Determination of excesses based on the results of satellite measurements. Using the GLONASS satellite system - Global Navigation Satellite System allows you to determine the spatial coordinates of points.
What is triangulation? It should be noted that this word has several meanings. Thus, it is used in geometry, geodesy and information technology. Within the framework of the article, attention will be paid to all topics, but the most popular area will receive the most attention - use in technical equipment.
In geometry
So, let's begin to understand what triangulation is. What is this in geometry? Let's say we have a non-developable surface. But at the same time it is necessary to have an idea of its structure. And to do this you need to expand it. Sounds impossible? But no! And the triangulation method will help us with this. It should be noted that its use provides the opportunity to construct only an approximate scan. The triangulation method involves the use of triangles adjacent to one another, where all three angles can be measured. In this case, the coordinates of at least two points must be known. The rest are to be determined. In this case, either a continuous network or a chain of triangles is created.
To obtain more accurate data, electronic computers are used. Separately, mention should be made of such a point as Delaunay triangulation. Its essence is that given the set of points, with the exception of the vertices, they all lie outside the circle that is described around the triangle. This was first described by the Soviet mathematician Boris Delaunay in 1934. His developments are used in the Euclidean traveling salesman problem, bilinear interpolation and This is what Delaunay triangulation is.
In geodesy
IN in this case It is envisaged that a triangulation point is created, which is subsequently included in the network. Moreover, the latter is built in such a way that it resembles a group of triangles on the ground. All angles of the resulting figures are measured, as well as some basic sides. How surface triangulation will be carried out depends on the geometry of the object, the qualifications of the performer, the available fleet of instruments and technical and economic conditions. All this decides the level of complexity of the work that can be carried out, as well as the quality of its implementation.
In information networks
And gradually we come to the very interesting interpretation the words "triangulation". What is this in information networks? It should be noted that there is a large number of various options interpretation and use. But within the framework of the article, due to the limitation of its size, only GPS (global positioning system) will receive attention. Despite certain similarities, they are quite different. And now we will find out what exactly it is.
Global Positioning System
More than a decade has passed since GPS was launched and is functioning successfully. The Global Positioning System consists of a central control station located in Colorado and observation posts around the world. During its work, several generations of satellites have already changed.
GPS is now a worldwide radio navigation system that is based on a number of satellites and earth stations. Its advantage is the ability to calculate the coordinates of an object with an accuracy of a few meters. How can triangulation be represented? What is it and how does it work? Imagine that every meter on the planet has its own unique address. And if there is a user receiver, then you can request the coordinates of your location.
How does this work in practice?
Conventionally, four main stages can be distinguished here. Initially, triangulation of the satellites is carried out. Then the distance from them is measured. Held absolute measurement time and identification of satellites in space. And finally, differential correction is carried out. That's it in short. But it is not entirely clear how triangulation works in this case. It is clear that this is not good. Let's get into detail.
So, initially to the satellite. It was found that it is 17 thousand kilometers. And the search for our location is significantly narrowed. It is known for sure that we are at a specific distance, and we must be looked for in that part of the earth’s sphere that is located 17 thousand kilometers from the detected satellite. But that is not all. We measure the distance to the second satellite. And it turns out that we are 18 thousand kilometers away from him. So, we should be looked for at the place where the spheres of these satellites intersect at a set distance.
Contacting a third satellite will further reduce the search area. And so on. The location is determined by at least three satellites. The exact parameters are determined according to the provided data. Let's assume that the radio signal moves at a speed close to light (that is, a little less than 300 thousand kilometers per second). The time it takes for it to travel from the satellite to the receiver is determined. If the object is at an altitude of 17 thousand kilometers, then it will be about 0.06 seconds. Then the position in the space-time coordinate system is established. Thus, each satellite has a clearly defined rotation orbit. And knowing all this data, the technology calculates the person’s location.
Specifics of the global positioning system
According to the documentation, its accuracy ranges from 30 to 100 meters. In practice, the use of differential correction makes it possible to obtain data detail down to centimeters. Therefore, the scope of application of the global positioning system is simply enormous. It is used to track the transportation of expensive cargo, helps to accurately land planes, and navigate ships in foggy weather. Well, the most famous is its use in automobile
Triangulation algorithms, due to their versatility and coverage of the entire planet, allow you to freely travel even to unfamiliar places. At the same time, the system itself paves the way, indicates where it is necessary to turn in order to get to the established final goal. Thanks to the gradual reduction in the cost of GPS, there are even car alarms based on this technology, and now if a car is stolen, it will not be difficult to find and return it.
What about mobile communications?
Here, alas, not everything is so smooth. While GPS can determine coordinates with an accuracy of up to a meter, triangulation in cellular communications cannot provide such quality. Why? The fact is that in this case the base station acts as a reference point. It is believed that if there are two BSs, then you can get one of the phone coordinates. And if there are three of them, then the exact location is not a problem. This is partly true. But triangulation mobile phone has its own characteristics. But here the question of accuracy arises. Before this, we looked at a global positioning system that can achieve phenomenal accuracy. But, despite the fact that mobile communications have significantly more equipment, there is no need to talk about any kind of qualitative correspondence. But first things first.
Looking for answers
But first, let's formulate questions. Is it possible to determine the distance from the base station to the phone using standard means? Yes. But will this be the shortest distance? Who does the measurements - the phone or the base station? What is the accuracy of the data obtained? While servicing a conversation, the base station measures the time it takes for the signal to travel from it to the phone. Only in this case it can be reflected, say, from buildings. It should be understood that the distance is calculated in a straight line. And remember - only during the call service process.
Another significant disadvantage is the rather significant level of error. So, it can reach a value of five hundred meters. Mobile phone triangulation is further complicated by the fact that base stations do not know what devices are in the territory under their control. The device catches their signals, but does not inform itself. In addition, the phone is able to measure the base station signal (which, however, it constantly does), but the amount of attenuation is unknown to it. And here comes an idea!
Base stations know their coordinates and transmitter power. The phone can determine how well it can hear them. In this case, it is necessary to detect all stations that are operating, exchange data (for this you will need a special program that sends out test packets), collect coordinates and, if necessary, transfer them to other systems. It would seem that everything is in the bag. But, alas, for this it is necessary to make a number of modifications, including the SIM card, access to which is not at all guaranteed. And in order to turn a theoretical opportunity into a practical one, it is necessary to work significantly.
Conclusion
Despite the fact that almost all people have phones, one should not say that a person can be easily tracked. After all, this is not as easy as it might seem at first glance. You can more or less confidently talk about luck only when using a global positioning system, but it requires a special transmitter. In general, after reading this article, we hope that the reader no longer has any questions regarding what triangulation is.