Sec. 1-1. The Subject of Surveying. Representation

of the Earth's Surface on a Plane

Surveying is a science studying the shape and size of the Earth, its physical surface and methods of representation of this latter on a plane in the form of plans and maps.

Surveying may be concerned with different problems owing to which fact it is currently divided into several disciplines each of which undertakes to solve specific tasks. For instance, geodetic sur­veying is concerned with the determination of the exact shape and size of the Earth by using methods of precise measurements and processing the observed results to locate points on the earth's surface. It is the object of surveying or topography to study the methods of delineation of relatively small portions of the earth's surface on a plane and of field measurements needed for that which require less accuracy compared with ones involved in geodetic surveying. Problems related to the theory and techniques of the representation on a plane of substantial portions of the globe, e.g., individual states, continents or the entire globe, are the domain of mapping or cartography. The purpose of engineering surveying is to consider various measurement techniques necessary for preliminary site investigations to design and build structures, transfer the design into the ground and monitor deformations and settlements of the structures.

We make various measurements on the earth's physical surface, determining line lengths, angles, height differences, time, etc. However, these measurements do not provide data that can be used for practical purposes. This requires the computation of coordinates and heights of points on the earth's surface by referring to the measured results.

The earth's physical surface is rather complex and the mathematical treatment of survey determinations made on such a surface poses major difficulties which are hard to cope with.

Let us imagine a surface that agrees with the mean level of water (MSL) in the oceans and seas when they are quiet on an assumption that there are no tides, storms or currents and continue mentally this surface under continents and islands. The surface could be taken as one forming the figure of the earth, and the land and seabed surface could be studied by referring to this hypothetical surface. However, we can handle the

Fig. 1

Ellipsoid of revolution

observed results (to determine the coordinates and heights of points on the earth's surface) only by referring to a surface that is known in mathematical terms. The aforementioned level surface fails to satisfy this condi­tion.

Investigations show that the surface of an ellipsoid of revolution PEP₁E₁ (Fig. 1) about the minor polar axis PP₁ most close­ly approaches the surface of the earth and represents one that has been studied in terms of mathematics. By referring to the results of geodetic measurements made on the earth’s surface scien­tists from different countries have repeatedly determined the size of the terrestrial ellipsoid. In 1942 A.A. Izotov led by Prof. F.N. Krasovskii determined the most accurately the size of the terrestrial ellipsoid of revolution. A decree of the USSR Council of Ministers in 1946 adopted this ellipsoid as reference for survey operations and termed it Krasovskii's ellipsoid of revolution.

The earth's surface may be approximated by a sphere. The radius of the sphere has been determined to be 6 371 110 m, and the length of the circumference to be 40 010 570 m. The lengths of arcs of meri­dian are

In degrees In linear units

1° 111 140 m

1' 1 852 m

1'' 31 m

The lengths of the arcs of the parallels decrease with increasing the distance north and south from the equator.

It is usual to represent portions of the earth's surface on a plane (paper) reduced to a definite scale (cf. Sec. 2-1). However, there is no way of developing the surface of an ellipsoid or a sphere onto a plane without rupturing it. That is why representations of the earth's surface on a plane (paper) are liable to be distorted. Both line lengths and angles between them will as a rule be distorted. Only mi­nor portions of the earth's surface (up to 20 km in length and width) may be considered as being plane, and distortions involved in the delineation of such portions will be within the accuracy of measure­ments and graphical work to prepare a map or plane.

A plan is a reduced and congruent representation of a small part of the terrain in which the spherical surface of the earth may be taken to be plane. A map is a diminished and distorted, owing to the curvature of the earth's surface, representation on a plane of a major portion of or the entire globe obeying definite mathematical principles or projections.

Features of the landscape, contours and their content (detail) are delineated on topographic maps and plans by using conventional symbols that, whenever necessary, are accompanied by explanations, figures and names (populated areas, rivers, lakes, land uses, etc.).

If we cut the earth's surface by a vertical plane in a desired direc­tion, we obtain a profile of the terrain along this direction. Its reduced drawing is also called a profile.

Surveying most commonly uses an orthogonal projection. Sup­pose P (Fig. 2) is a horizontal plane. Drop perpendiculars on the plane P from points A, B, C, E, F of a spatial

Fig. 2

Projection of a portion of terrain

polygon located on the physical surface of the earth. The feet of these perpendiculars a, b, c, e, f are orthogonal projections of the similar points on the terrain, and lines ab, bc, . . ., fa are orthogonal projections of lines AB, BC, . . ., FA.

In like manner we can obtain projections of all characteristic points on the ground and, consequently, an orthogonal projection of the entire portion of the terrain of interest to us. In order to obtain a projection of a curved feature of the terrain, e.g. a road, stream etc., we must evidently project its characteristic points, such that parts of a contour between two adjacent points may be considered to be straight.

We can easily plot horizontal projection on paper. To do this, we must know the horizontal projections ab, bc, . . ., fa (sides) and horizontal angles p_1, p_2, . . ., p₅ between them.

Sec. 1. The Topic of Geodesy

Geodesy is the science concerned with the measurement of the earth's surface and how to represent it. It is the purpose of geodesy to develop methods and measurement procedures for determining the size and shape of the earth, and to prepare maps, plans, mathe­matical, geometrical and stereoscopic terrain models. It also under­takes to plot vertical cross sections (profiles) of the earth's surface along the specified directions and to deal with a variety of economic problems that occur both directly on the terrain and on miscella­neous geodetic materials and terrain models.

In terms of operation conditions, geodesy falls into the topic areas of: terrestrial surveying, where measurements are made on the earth's surface; aerial surveying (aerial photogrammetry), which is concerned with the transformation and measurement of terrain representa­tions that have been obtained from the air; and space surveying, which considers, transforms and measures representations of the earth, or parts of it, that have been obtained during space missions*(* In addition, the purpose of space geodesy is to measure and transform images of the planets of the solar system and their satellites as obtained from space probes.) Special types of surveying done under the earth's surface or in its surface layers are referred to as mining geodesy (mining surveying}. In the last few years, the sea floor, and the bottoms of water reser­voirs and rivers have been surveyed. These activities may be described as underwater surveying.

The diversity of economic activities to which surveying is applied has meant that the subject area has been divided into individual disciplines, that each have their own scientific and technological domains and industrial applications. Currently the principal branches of geodesy may be said to be advanced geodesy, cartography (mapping), topography, and engineering geodesy (geodetic engineer­ing) and applied geodesy.

Engineering surveying deals with the geodetic methods, processes and solutions involved in the reconnaissance, design, construction and erection of new buildings, or in the reconstruction or operation of existing engineering structures. It is also used for: land management; the reconnaissance, surveying and development of mineral resources; and the design, erection, installation and operation of complex industrial equipment, experimental devices and structures for scientific purposes.

The problems representing comparatively small areas of the earth's surface, such as plans, aerial plans, or mathematical, geometrical and stereoscopic models, are the domain of topography. Cartography is the study of the methods and procedures for dealing with large areas of the earth's surface using maps or special terrain models. The problems involved in the topography and cartography using photographs taken on the ground belong to terrestrial phototopography (terrestrial photogrammetry), while those that involve aerial photography belong to aerial phototopography (aerial photogrammetry).

Advanced geodesy undertakes to determine the shape and size of the earth and of its external gravitational field, and also to estab­lish very precise geodetic control networks.

Geodesy and its principal branches are extensively used by many state agencies being of crucial importance for national defense.

Geodesy's development is closely associated with that of other scientific disciplines and advances, in this science are largely due to the advances in mathematics, astronomy and physics. Mathematics provides geodesy with the means for analyzing and techniques for processing measured results. Astronomy furnishes geodesy with all the relevant initial data, the laws of physics make it possible to design surveying optical instruments. Mechanics, automation and electronics are widely used to manufacture sophisticated surveying apparatus.

Moreover, geodesy is intimately linked to geography, geology and geomorphology. A knowledge of geography allows, one to cor­rectly estimate the elements of the terrain that make up the relief features of the earth's surface (vegetation, soils and others), and the results of man's activities (occupied points, roads, communication means, industrial enterprises and so on). The forms of the relief and laws that govern the way they change are the domain of geology and geomorphology.

In order that aerial photos can be used for geodesy calls for knowl­edge about photography, while plan and map preparation requires topographical drawing.

Sec. 2. Engineering Surveying

Engineering surveying is a branch of geodesy that is the most closely associated with the various aspects of economic activity. It is essen­tial for many industrial processes and significantly contributes to progress in them.

Engineering surveying is important for every kind of engineering venture, such as the construction of highways, railroads, canals, dams, bridges, air fields, pipelines, and power and communication lines. It is also used when designing and erecting industrial and office buildings, when surveying, reconnoitering and developing mineral resources; and for monitoring deformations or shifts in structures and their components during construction, testing and operation.

Currently an impressive quantity of raw data about terrain, its topographic, geological and hydrological features, is being gathered using a range of special engineering surveying activities and aerial photogrammetry. These activities depend in part on topographic surveying which requires many interrelated activities to prepare a topographical map or plan or to obtain other topographic informa­tion. This may take the form of a mathematical, stereoscopic or geometric terrain model, or alternatively longitudinal and transverse cross sections (profiles of terrain lines). Not only do these materials identify characteristic natural features of the ground but they also help in the decision as to where to site the planned structures and to take into account economic and performance consequences of the construction.

Engineering surveying and photogrammetry are indispensable for all kinds of design decision making when designing engineering structures.

During construction the purpose of overall engineering geodetic operations is to have the structure built according to the design and also to fulfill the relevant estimates. Not only does modern engineering geodesy make it possible to transfer projects onto the ground, staking them out, it ensures proper siting, showing the location and mutual position of individual elements on the terrain. What is more, it provides continuous geodetic control of all the important machinery on the construction site.

When engineering structures are in operation it is the purpose of surveying to control and monitor the permanence, durability and safety of each structure, to discover deformations in component parts and elements, and to trace the vibration and subsidence of individual elements of structure at the time and under the effect of various loads. This helps to restore the strength and stability of structures and their elements as well as rebuild different parts and elements of existing structures.

The automation of engineering geodesy and aerial geodesy has radically changed surveying techniques and procedures, and the working conditions and activities of its practitioners. In such conditions the surveying engineers, designers and civil engineers carry­ing out geodetic and aerial surveys necessarily participate in the development of the new technology.

Sec. 3. Some Facts from the History of Geodesy and Engineering Surveying

Geodesy*(* Greek for "land division") dates back to ancient times. Relics that have survived show that hundreds of years B.C. mankind knew how to measure plots of land and lay out specific angles and distances when erecting structures.

Methods of land measurement were known in ancient Greece as well. These were theoretically substantiated and gave birth to geometry**(** Greek for "land measurement"). Geodesy and geometry developed side by side for a long time supporting each other. It took several millennia for geodesy to emerge as a scientific discipline.

The need to measure land arose in Russia in remote times. The first evidence of geodetic measurement dates from the tenth century.

From the eighteenth century onwards, apart from surveying for maps, special-purpose surveys began to be performed. These included boundary, forestry, hydrographic, and road surveys. As the water­ways expanded, land and hydrographic surveys were undertaken, in this country to explore the coasts of the Asov, Black, Baltic, Caspian and White Seas. Work was started on the construction of water communication system and for river-flow control. Before the eighteenth century the principal communication routes in Russia had been the rivers with dirt roads for horse-drawn traffic. The eighteenth century saw the beginning of highway construction, and the next century saw railways followed by construction and reconstruction of ports. All these activities promoted the progress of engineering surveying. Still the scope of surveying in Tsarist Russia was insignificant.

The development of geodesy and cartography in this country followed a new path after the Great October Socialist Revolution. A decree of the Council of People's Commissars signed by Lenin on March 15, 1919 unequivocally set the aims and purposes of Soviet geodesy and cartography. Central and local surveying agencies were established and charged with the task of carrying out principal sur­veying operations, complete topographic coverage and higher-order levelling. The main objective of Soviet geodesy became to promote may be used individually, such as the Д-2, ДВ-20 and other instru­ments. All these are double-image, constant-base and variable angle or constant angle-of-parallax and variable-base instruments. Distances to be measured do not generally exceed 400 m and the accuracy of measurement varies from type to type from 1/1 000 to 1/6 000.

6. Radio- and optical range finders relying for their operation on the speed of the propagation of radio and optical waves. Optical range finders (e.g. "Kwarts") can determine distances within an error 1/400 000; and radio range finders ("Luch"), accurate to 1/200 000.

Angle-measuring devices. These include theodolites and telescopic alidades. In conformity with the USSR St. St. COST 10 529-79 "Theodolites. Types, principal parameters and technical require­ments", the following theodolite types are manufactured in this country: high-precision T05 and T1, precision T2 and T5 and engi­neering instruments T15 and T30.

Telescopic alidades permit horizontal directions to be plotted by graphical means accurate to 5-6'.

Surveyor's levels. High-precision H-05, precision H-3 and engi­neers' H-10 levels are used to determine height differences by a hori­zontal ray of light.