It is the art of determining the relative positions of natural and artificial features on the earth s surface, vertically and horizontally.

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1 SVG 105 Lectures Notes March 2011 BASIC INTRODUCTION TO SURVEYING DEFINITION OF SURVEYING It is the art of determining the relative positions of natural and artificial features on the earth s surface, vertically and horizontally. Land surveying has been defined as the art and science of determining the position of natural and artificial features on, above or below the earth s surface; and representing this information on paper plans, as figures in report tables or on computer based maps. This definition however would be seen as a very narrow view of what is encompassed by surveying today. The definition of surveying is changing, to reflect the applications of surveying techniques and the impact that the introduction of computer technology has had on the more traditional aspects of the discipline. Surveying may be defined as the science of determining the position, in three dimensions, of natural and man-made features on or beneath the surface of the Earth. These features may then be represented in analog form as a contoured map, plan or chart, or in digital form as a three-dimensional mathematical model stored in the computer. Surveying or land surveying is the technique and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them. These points are usually on the surface of the Earth, and they are often used to establish land maps and boundaries for ownership or governmental purposes. (Source: Wikipedia) CLASSES OF SURVEYING 1 (1) Plane Surveying In this class of survey the surface of the earth is considered to be a plane for all X and Y dimensions. Z dimensions are referred to the mean spherical surface of the earth (Mean Sea Level). The spherical shape of the earth is not considered. It is mostly applied in small scale surveys. (2) Geodetic Surveying This takes into account the true shape of the earth. That means curvature correction is applied to all measurements. Characteristics of this type of survey: - It covers large areas and is carried out at high precision. It is mainly used to establish Control points which are known in the vertical and horizontal dimensions. These control points are used in large scale mapping e.g. Trigonometrical Beacons. The above classes of survey can be divided into three main operations: (a) CONTROL SURVEY Establishing of permanent points whose planimetry positions and their elevations above mean sea level have been carefully determined.

2 (b) PRELIMINARY SURVEY The gathering of data to locate physical features, contouring spot heights so that the data can be plotted to scale on a map or plan. (c) LAYOUT SURVEY Marking on the ground features shown on a design plan or from an aerial photograph both horizontally and vertically. THE FUNDAMENTAL PRINCIPLES OF SURVEYING (1) No measurement is exact and that the true value of quantity being measured is never known (2) No measurement is acceptable or valid unless it has been followed by an independent check or by repeating the measurement a number of times. (3) Measurements should be precise and accurate. HISTORY OF SURVEYING The history of land surveying is very interesting and diverse and it is in fact one of the oldest professions in the world. The history of land surveying dates back thousands of years and forms of land surveying have been around since ancient man in all major civilizations across the globe. Surveying science has a very long and distinguished history, dating at least back to the rope stretchers of Babylonia and the Egyptian dynasties. The development of the principles of geometry, astronomy and time still forms the foundation on which current surveying knowledge is built. The first examples in the history of land surveying date back to the ancient Egyptians during the building of the Great Pyramid at Giza in 2700 BC. There is evidence of the Egyptians using basic geometry to redraw boundary lines when the Nile overflowed its banks. The Romans were the next civilization to advance on the initial land surveying techniques of the Egyptians. Historical evidence shows that the Roman Empire was the first civilization to employ an official land surveyor within their Empire. They used simple tools to create straight lines and angles. The land surveyors had a range of jobs in the Empire and some of their work is still evident today. Today surveyors use satellites to image the earth s environment, use different satellites for navigation and precise position fixing, use computer visualization techniques for mapping, micro-computer controlled equipment for measuring the earth s surface and information systems to present and analyse data about land and land usage. But, the underlying core of knowledge for all of this sophistication is the mathematics of geometry. TYPES OF SURVEYS [1] Control surveys. [2] Topographic. [3] Land, Boundary and Cadastral surveys. a. Original surveys. b. Retracement surveys. c. Subdivision surveys. 2

3 3 [4] Hydrographic surveys. [5] Route surveys. [6] Construction surveys. [7] As-build surveys. [8] Mine surveys.

4 IMPORTA CE OF SURVEYI G 4

5 U ITS OF MEASUREME T The system most commonly used in the measurement of distance and angle is the Systeme Internationale, abbreviated to SI. The basic units of prime interest are: Length in metres (m) from which we have: 1 m = 103 millimetres (mm) 1 m = 10 3 kilometres (km) ERRORS IN MEASUREMENT It should now be apparent that position fixing simply involves the measurement of angles and distance. However, all measurements, no matter how carefully executed, will contain error, and so the true value of a measurement is never known. It follows from this that if the true value is never known, the true error can never be known and the position of a point known only within certain error bounds. The sources of error fall into three broad categories, namely: (1) Natural errors caused by variation in or adverse weather conditions, refraction, gravity effects etc. (2) Instrumental errors caused by imperfect construction and adjustment of the surveying instruments used. (3) Personal errors caused by the inability of the individual to make exact observations due to the limitations of human sight, touch and hearing. CLASSIFICATION OF ERRORS MISTAKES are sometimes called gross errors, but should not be classified as errors at all. They are blunders, often resulting from fatigue or the inexperience of the surveyor. Typical examples are omitting a whole tape length when measuring distance, sighting the wrong target in a round of angles, reading 6 on a levelling staff as 9 and vice versa. Mistakes are the largest of the errors likely to arise, and therefore great care must be taken to obviate them. SYSTEMATIC ERRORS can be constant or variable throughout an operation and are generally attributable to known circumstances. The value of these errors can be calculated and applied as a correction to the measured quantity. They can be the result of natural conditions, examples of which are: refraction of light rays, variation in the speed of electromagnetic waves through the atmosphere, expansion or contraction of steel tapes due to temperature variations. In all these cases, corrections can be applied to reduce their effect. Such errors may also be produced by instruments, e.g. maladjustment of the theodolite or level, index error in spring balances, ageing of the crystals in EDM equipment. There is the personal error of the observer who may have a bias against setting a micrometer or in bisecting a target, etc. Such errors can frequently be selfcompensating; for instance, a person setting a micrometer too low when obtaining a direction will most likely set it too low when obtaining the second direction, and the resulting angle will be correct. Systematic errors, in the main, conform to mathematical and physical laws; thus it is argued that appropriate corrections can be computed and applied to reduce their effect. It is doubtful, however, whether the 5

6 effect of systematic errors is ever entirely eliminated, largely due to the inability to obtain an exact measurement of the quantities involved. Typical examples are: the difficulty of obtaining group refractive index throughout the measuring path of EDM distances; and the difficulty of obtaining the temperature of the steel tape, based on air temperaturee measurements with thermometers. Thus, systematic errors are the most difficult to deal with and therefore they require very careful consideration prior to, during, and after the survey. Careful calibration of all equipment is an essential part of controlling systematic error. RANDOM ERRORS are those variates (errors) which remain after all other errors have been removed. They are beyond the control of the observer and result from the human inability of the observer to make exact measurements, for reasons already indicated above. Random variates are assumed to have a continuous frequency distribution called normal distribution and obey the law of probability. A random variate x, which is normally distributed with a mean and standard deviation, is written in symbol form as N (µ, 2). It should be fully understood that it is random errors alone which are treated by statistical processes. ACCURACY A D PRECISIO In the fields of science, engineering, industry and statistics, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to its actual (true) value. The precision of a measurement system, also called reproducibility or repeatability, is the degree to which repeated measurements under unchanged conditions show the same results. Although the two words can be synonymous in colloquial use, they are deliberately contrasted in the context of the scientificc method. Accuracy indicates proximity of measurement results to the true value, precision to the repeatability or reproducibility of the measurement A measurement system can be accurate but not precise, precise but not accurate, neither, or both. For example, if an experiment contains a systematic error, then increasing the sample size generally increases precision but does not improve accuracy. Eliminating the systematic error improves accuracy but does not change precision. A measurement system is called valid if it is both accurate and precise. Related terms are bias (non-random or directed effects caused by a factor or factors unrelated by the independent variable) and error (random variability), respectively. The terminology is also applied to indirect measurements, that is, values obtained by a computational procedure from observed data. 6

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Chapter 2. Theory of Errors and Basic Adjustment Principles

Chapter 2. Theory of Errors and Basic Adjustment Principles Chapter 2 Theory of Errors and Basic Adjustment Principles 2.1. Introduction Measurement is an observation carried out to determine the values of quantities (distances, angles, directions, temperature