Fundamentals of Surveying PDF

FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV INTRODUCTION TO SURVEYING SURVEYING One of the oldest arts practiced by man is surveying. From the earliest times it has always been necessary to mark boundaries and divide tra...

FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV INTRODUCTION TO SURVEYING SURVEYING One of the oldest arts practiced by man is surveying. From the earliest times it has always been necessary to mark boundaries and divide tracts of land. Through the centuries, the uses of surveying have expanded such that today it is difficult to undertake any type of engineering construction that does not involve some type of surveying. Surveys cover a wide range in scope and complexity from the staking out of simple structures or the surveying of small parcels of land to the extensive and difficult surveys required in the different constructions. Surveying is also required for the laying out of industrial equipment, preparing forestry and geological maps, positioning massive and complex machinery, in the construction of ships and airplanes, as well as in the survey and exploration of extraterrestrial bodies such as the moon and the planets. DEFINITION OF SURVEYING All surveying operations have the same characteristics – that of delineating a portion of the earth’s surface or substance or of establishing the position or boundaries of some object upon it. A host of definitions have been made by different authors, and the following are listed:  1. “Surveying is the art of determining the positions of points on or near the earth’s surface by means of measurements in the three elements of space; namely, distance, direction and elevation.” – Rayner and Schmidt. FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV  2. “Surveying is the art of measuring horizontal; and vertical distances between objects, of measuring angles between lines, and of establishing points by predetermined angular and linear measurements.” – Davis, Foote, Anderson and Mikhail.  3. “Surveying is the art of making such measurements of the relative positions of points on the surface of the earth that, on drawing them to scale, natural and artificial features may be exhibited in their correct horizontal or vertical relationships.” – Clarke.  4. “Surveying is that branch of applied mathematics which teaches the art of determining the area of any portion of the earth’s surface, the length and direction of the boundary lines, the contour of the surface, and on accurately delineating the whole on the paper.” – Webster.  5. “Surveying is the science of art of making such measurements as are necessary to determine the relative positions of points above, on or beneath the surface of the earth, or to establish such pints.” – Breed, Hosmer and Bone.  6. “Surveying is the science and art of determining relative positions of points above, on or beneath the surface of the earth, or establishing such points.” – Brinker and Wolf. FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV From the different definitions given above, it is obvious that surveying activities during the earlier part of the decade has only been limited to surveys on or near the surface of the earth. Times, however, have changed and modern surveying techniques are now applied to space exploration and in the mapping of extraterrestrial bodies such as the moon, mars, and in the near future the other planets, stars, and other heavenly bodies in the universe. PLANE AND GEODETIC SURVEYING Surveys are divided into two general classifications, plane and geodetic.  1. Plane Surveying – is that type of surveying on which the earth is considered to be a flat surface and when distances and areas are involved are of limited extent that exact shape of the earth is disregarded. With regards to horizontal distances and directions, a level line is considered as mathematically straight, the direction of the plumb line is assumed to be same at all points within the limits of the survey, and all angles are considered to be plane angles.  2. Geodetic Surveying - are surveys of wide extent which take into account the spheroidal shape of the earth. These surveys employ principles of geodesy, are of high precision and the related calculations involve the solving of equations derived from advance mathematics particularly spherical trigonometry, calculus, and some applications of the theory of least squares. TYPES OF SURVEYS FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV Of the different types of surveys, the following are the more commonly used:  1. Cadastral Surveys – are usually closed surveys which are undertaken in urban and rural locations for the purpose of determining and defining property lines and boundaries, corners, and areas. These surveys are also made to fix the boundaries of municipalities, towns, and provincial jurisdictions.  2. City Surveys – are surveys of the areas in and near the city for the purpose of planning expansions or improvements, locating property lines, fixing reference monuments, determining the physical features and configuration of the land, and preparing maps.  3. Construction Surveys - these are surveys which are undertaken at a construction site to provide data regarding grades, reference lines, dimensions, ground configuration, and the location and elevation of structures which are of concern to engineers, architects and builders.  4. Forestry Surveys – a type of survey executed in connection with forest management and mensuration, and the production and conservation of forests lands.  5. Hydrographic Surveys – refers to surveying streams, lakes, reservoirs, harbors, oceans, and other bodies of water. These surveys are made to map shore lines, chart the shape of areas underlying water surfaces, and measure the flow of streams.  6. Industrial Surveys – sometimes known as optical tooling. It refers to the use of surveying techniques in ship building, construction and assembly of aircraft, layout and installation of heavy and complex machinery, and in other industries where very accurate dimensional layouts are required. FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV  7. Mine Surveys – are surveys which are performed to determine the position of all ground excavations and surface mine structures, to fix surface boundaries of mining claims, determine geological formations, to calculate excavated volumes, and establish lines and grades for other related mining work.  8. Photogrammetric Surveys – a type of surveys which makes use of photographs taken with specially designed cameras either from airplanes or ground stations. 9. Route Surveys – involves the determination of alignment grades, earthwork quantities, location of natural and artificial objects in connection with the planning, design and construction of highways, railroads, pipelines, canals, transmission lines, and other linear projects. 10. Topographic Surveys – are those surveys made for determining the shape of the ground, and the location and elevation of the natural and artificial features upon it. The features shown include such natural objects as hills, mountains, rivers, lakes, relief of the ground surface, etc; and works of man, such as roads, buildings, ports, towns, municipalities and bridges. FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV ERRORS AND MISTAKES  ERRORS  An error is defined as the difference between the true value and the measured value and the measured value of the quantity. It is a deviation of an observation or a calculation from the true value and is often beyond the control of the one performing the operation.  MISTAKES  Mistakes are inaccurate in measurements which occur because some aspect of a surveying operation is performed by the surveyor with carelessness, inattention, poor judgment, and improper execution. Mistakes and blunders are not classified as errors because they usually are so large in magnitude when compared to errors. TYPES OF ERRORS Systematic Errors – This type of error is one which will always have the same sign and magnitude as long as field conditions remain constant and unchanged. It is also known as cumulative error. For instance, in making a measurement with a 30-m tape which is 5-cm too short, the same error is made each time the tape is used. If a full FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV length tape is used 6 times, the error accumulates and totals six times the error (or 30-cm) for the total measurement. Accidental Errors – These errors are purely accidental in character. Accidental errors are caused by factors beyond the control of the surveyor and are present in all surveying measurements. They remain after mistakes and systematic errors have been eliminated. An example of such an error is the failure of the tapeman to exert the correct amount of pull on the ends of a tape during measurement. SOURCES OF ERRORS Instrumental Errors  Instrumental errors. These errors are due to the imperfections in the instruments used.  Examples of instrumental errors are: ​ Measuring with a steel tape of incorrect length. ​ Using a leveling rod with painted graduations not perfectly shaped. ​ Determining the differences in elevation between two points with an instrument whose line of sight is not in adjustment. ​ Sighting on a rod which is warped. ​ Improper adjustment of the plate bubbles of a transit or level. Natural Errors  Natural Errors. These errors are caused by variations in the phenomena of nature such as changes in magnetic declination, temperature, humidity, wind, refraction, gravity, and curvature of the earth. FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV  The surveyor may not be able to totally remove the cause of such errors but he can minimize their effects by making proper corrections of the results and using good judgment. Common examples are: ​ The effect of temperature variation on the length of the steel tape. ​ Errors in the readings of the magnetic needle due to variations in magnetic declination. ​ Deflection to the line of sight due to the effect of the earth’s curvature and atmospheric refraction. ​ Error in the measurement of a line with a tape being blown sidewise by a strong wind. ​ Error in the measurement of a horizontal distance due to slope or uneven ground. Personal Errors Personal Errors. These errors arise principally from limitations of the senses of sight, touch or inaccurate. Typical of these errors are: ​ Error in determining a reading on a rod which is out of plumb during sight. ​ Error in the measurement of a vertical angle when the cross hairs of the telescope are not positioned correctly on the target. ​ Making an erroneous estimate of the required pull to be applied on a steel tape during measurement. FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV ACCURACY AND PRECISION Accuracy and precision are two terms which are constantly used in surveying, however, their correct meanings are often misunderstood. While accuracy may be synonymous with precision, the two should not be used interchangeably. The surveyor should always attempt to obtain measurements which are not only accurate but also precise. Accuracy indicates how close a given measurement is to the absolute or true value of the quantity measured. It implies the closeness between related measurements and their expectations. Precision refers to the degree of refinement and consistency with which any physical measurement is made. It is portrayed by the closeness to one another of a set of repeated measurements of a quantity.  Positive or negative errors of the same size happen with equal frequency; that is, they are equally probable.  The mean of an infinite number of observations is the most probable value. FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV MOST PRABABLE VALUE, X  From the theory of probability a basic assumption is the most probable value (mpv) of a group of repeated measurements made under similar conditions is the arithmetic mean or the average. Most probable value refers to a quantity which, based on available data, has more chances being correct than has any other.  There is only one correct value that should be considered and it is determined by using the following equation: mpv = X = ΣX/n = (X1 + X2 + X3 +.... + Xn) /n  in the case of related measurements taken under identical conditions where the sum should equal a mathematically exact quantity, the most probable values are the observed values corrected by an equal part of the total error. FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV RESIDUAL The residual, which is sometimes referred to as the deviation, is defined as the difference between any measured value of a quantity and its mpv or v = x - x... eq. (1) Where v is the residual, x is a measurement made of a particular quantity, and x is the mpv of the quantity measured. PROBABLE ERROR The PE is a quantity which, when added to and subtracted from the mpv, defines a range within which there is a 50% chance that the true value of the measured quantity lies inside (or outside) the limits thus set. Pes = ± 0.6745 √Σv2 / n-1.... Eq. (2) Pem = ± 0.6745 √Σv2 / n(n-1).... Eq. (3) Where: PEs = probable error of any single measurement of a series PEm = probable error of the mean Σv2 = summation of the squares of the residuals n = number of observations RELATIVE (ERROR) PRECISION Relative error, sometimes called relative precision is expressed by a fraction having the magnitude of the error in the numerator and the magnitude of a measured quantity in the denominator. For example, if for a particular measurement the probable error of the FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV mean is 0.10m and the mpv of the measurement is 235.50m, the relative precision (RP) would be expressed as 0.10/235.50 or 1/2355, also written as 1:2355. FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV FUNDAMENTALS OF SURVEYING​ ​ #DrBantayanBryanV