Fundamentals of Surveying CE-FOS212 PDF

**INSTITUTE OF ENGINEERING** **FUNDAMENTALS OF SURVEYING** ***CE-FOS212*** **[MODULE 1]** **INTRODUCTION TO SURVEYING** **I. DEFINITION** ***"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; name...

**INSTITUTE OF ENGINEERING** **FUNDAMENTALS OF SURVEYING** ***CE-FOS212*** **[MODULE 1]** **INTRODUCTION TO SURVEYING** **I. DEFINITION** ***"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 & Schmidt*** **SURVEYING is the art and science determining the angular and linear measurements to establish the form, extent, and relative position of points, lines, and areas on or near the surface of the earth or on other extraterrestrial bodies through applied mathematics and the use of specialized equipment and techniques.** **PLAN VIEW -- same as Top View** **PROFILE -- same as Side View** **II. PLANE AND GEODETIC SURVEYING** **[GENERAL CLASSFICATION OF SURVEYING]** 1. **PLANE SURVEYING -- Is the type of surveying in which the earth is considered to be a flat surface, and where distances and areas involved are of a limited extent that the exact shape of the earth is disregarded.** 2. **GEODETIC SURVEYING -- are surveys of wide extent which take into account the spheroidal shape of the earth.**  **[TYPES OF SURVEYS]** **1. CADASTRAL SURVEYS - Are usually closed surveys which are undertaken in urban and rural location for the purpose of determining and defining property lines and boundaries, corners, and areas.** **2. CITY SURVEYS - Are surveys of the areas in and near a 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 forest lands.** **5. HYDROGRAPHIC SURVEYS - Refer to surveying streams, lakes, reservoirs, harbors, oceans, and other bodies of water. These surveys are made to map shorelines, 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.** **7. MINE SURVEYS - Are surveys which are performed to determine the position of all underground 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 survey which makes use of photographs taken with specially designed cameras either from airplanes or ground stations. Measurements are obtained from the photographs which are used in conjunction with limited ground surveys. (*Google earth, google maps, etc.)*** **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 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** **[SURVEYING INSTRUMENTS]** **1. ASTROLABE -- This instrument had a metal circle with a pointer hinged at its center and held by a ring at the top, and a cross staff, a wooden rod about 1.25 meters long with an adjustable crossarm at right angles to it. The known length of the arms of the cross staff allows distances and angles to be determined by proportion. It was originally designed for determining the altitude of the stars and for navigation.** **2. TELESCOPE -- The invention of the telescope in 1607 is generally accredited to Lippershey. It is used to form magnified images of distant objects. In 1609, Galileo constructed a refracting telescope for astronomical observations. However, it was only when cross hairs for fixing the line of sight were introduced, that the telescope was used in early surveying instruments.** **3. TRANSIT -- it is an optical instrument, or a telescope, complete with a built-in spirit level that is mounted on a tripod. Transit levels are used mainly for surveying and building, but they can be used to determine the relative position of lines and objects as well.** **4. SEMICIRCUMFERENTOR -- an early surveying instrument which was used to and lay-off angles and establish lines of sight by employing peep sights.** **5. PLANE TABLE -- one of the oldest types of surveying instruments used in field mapping. It is simple and cheaper than Theodolite survey, but it is mostly suitable for small scale survey.** **6. DIOPTRA -- a Theodolite and a choro bate from the past. It was and amazing geodetic instrument which was suitable for the precise measurement of horizontal, vertical and angular distances between two celestial or terrestrial points.** **7. ROMAN GROMA -- it is used for aligning or sighting points. It consisted basically of cross arms fixed at right angles and pivoted eccentrically upon a vertical staff.** **8. LIBELLA -- it is a type of leveling instrument used in ancient Roman construction, like a modern spirit level. It had an A-frame with a plumb line suspended from its apex and was used to determine the horizontal.** **9. VERNIER -- calipers that are used to measure the distance between objects. They can measure both internal and external dimensions accurately. They are used to measure exact linear measurements in various fields.** **10. DIOPTER -- it is also used for leveling, laying off right angles, and for measuring horizontal leveling.** **11. COMPASS -- used in navigation to find direction on the earth. The compass consists of a magnetized steel needle mounted on a pivot at the center of a graduated circle. The needle continues to point toward magnetic north and gives a reading which is dependent upon the position of the graduated circle.** **12. GUNTER'S CHAIN -- it is used for taping distances. It is 66 ft. long and contains 100 links, so that distances may be recorded in chains and in decimal parts of the chain. Each part, called a link, is 0.66 ft or 7.92 inches long.** **13. CHOROBATES -- This instrument was designed for leveling work. It consisted of a horizontal straight edge about 6 meters long with supporting legs, and a groove 2.5 cm deep and 1.5 m long on top. Water is poured into the groove and when the bar is leveled so that water stood evenly in the groove without spilling, a horizontal line is established.** **14. MERCHET -- it is a device for measuring time and meridian. By sighting through the slot and past the plumb bob string, a straight line could be projected.** **15. AUTOMATIC LEVEL -- a dumpy level, automatic level, leveling instrument is an optical instrument used to establish or verify points in the same horizontal plane. It is used in surveying and building with a vertical staff to measure height differences and to transfer, measure and set heights.** **16. THEODOLITE (MANUAL AND AUTOMATIC) -- a modern surveying instrument used for precision and measuring angles in the horizontal and vertical planes. Theodolites are used mainly for surveying applications and have been adapted for specialized purposes in fields like metrology and rocket launch technology.** **17. TOTAL STATION -- it is an electronic/optical instrument used for surveying and building construction.** **[SURVEYING FIELD NOTES]** **- constitute the only reliable and permanent record of actual work done in the field. If the notes are incorrect or incompletely done, or are obliterated, much or all of the time, money and effort in the gathering of survey data are wasted.** **- the notes should be recorded in the conventional and generally used format and not according to whims of the field surveyor.** **- it must contain all necessary information and the data recorded in such a manner that it will allow only the correct interpretation of gathered data.** **[TYPES OF NOTES]** **1. SKETCHES** **2. TABULATIONS** **3. EXPLANATORY NOTES** **4. COMPUTATIONS** **5. COMBINATION OF THE ABOVE** **[INFORMATION FOUND IN FIELD NOTEBOOK]** **1. TITLE OF THE FIELDWORK OR NAME OF PROJECT** **2. TIME OF THE DAY AND DATE** **3. WEATHER CONDITIONS** **4. NAMES OF GROUP MEMBERS AND THEIR DESIGNATIONS** **5. LIST OF EQUIPMENT** **[THE FIELD SURVEY PARTY]** **1. CHIEF OF PARTY -- the person who is responsible for the overall direction, supervision, and operational control of the survey party.** **2. ASSISTANT CHIEF OF PARTY -- his/her duty is to assist the chief of party in the accomplishment of the task assigned to the survey party. He takes over the duties of the chief of party during the absence of the chief.** **3. INSTRUMENTMAN -- the person whose duty is to set up, level, and operate surveying instruments such as the transit, engineer's level, theodolite, sextant, plane table and alidade, and etc.** **4. TECHNICIAN -- they are responsible for use and operation of all electronic instruments required in a field work operation. It is his duty to see to it that this equipment is functioning properly, are regularly calibrated, and are in proper adjustment.** **5. COMPUTER - the person whose duty is to perform all computations of survey data and works out necessary computational checks required in a field work operation.** **6. RECORDER -- their duty is to keep a record of all sketches, drawings, measurements and observations taken or needed for a field work operation.** **7. HEAD TAPEMAN -- they are responsible for the accuracy and speed of all linear measurements with tape. He determines and directs the marking of stations to be occupied by the surveying instruments and directs the clearing out of obstructions along the line of sight.** **8. REAR TAPEMAN -- the person whose duty is to assist the head tape man during taping operations and in other related work.** **9. FLAGMAN -- the person whose duty is to hold the flagpole or range pole at selected points as directed by the instrument man.** **10. RODMAN -- the person whose primary duty is to hold the stadia or leveling rod when sights are to be taken on it.** **11. PACER -- the person whose duty is to check all linear measurements made by the tape man.** **12. AXEMAN/LINEMAN -- the person whose duty is to clear the line of sight of trees, brush, and other obstructions in wooded country.** **13. AIDMAN -- their duty is to render first aid treatment to members of the survey party involving their health, safety, and well-being.** **14. UTILITY MEN -- whose duties are to render other forms of assistance needed by the survey party or as directed by the chief of party.** **III. THEORY OF ERRORS AND MEASUREMENTS** **[UNITS OF MEASUREMENTS ]** **Major measurements in Surveying:** - **Length** - **Area** - **Angle** - **Volume** **Measurements in Plane Surveying** **Angle AOB** **Line OB** **Angle AOC** **Line EO** **Line OC** **UNITS OF LENGTH** **1 foot = 12 inches** **1 yard = 3 feet** **1 inch = 2.54 centimeters** **1 meter = 39.37 inches** **1 rod = 16.5 feet** **1 Gunter's chain (ch) = 66 feet = 100 links (lk) = 4 rods** **1 mile = 5280 feet = 1.609 km** **1 nautical mile = 6076.10 feet = 1852.47 meters, using the assumption that Radius of the earth is 6,371 km** **1 fathom = 6 feet** **UNITS OF AREA** **1 acre = 43,560 sq.ft = 4047 sq.m** **1 hectare = 2.47 acres** **1 sq. mile = 2.59 sq. km** **UNITS OF ANGLE** ***-Sexagesimal System = degree, minute, seconds*** **1 circle = 360 degrees** **1 degree = 60 minutes** **1 minute = 60 seconds** ***-Centesimal system*** **1 circle = 400 grads = 400 gons = 400 centesimal degrees** **1 grad = 1 gon = 1 centesimal degree = 100 centesimal minutes** **1 centesimal minute = 60 centesimal seconds** ***-Circular system*** **1 circle = 6.28 radians** **Pi = 3.14 radians** ***(if you are using Pi, make sure you are in mode radian in calculator while computing for the angle)*** ***Military system*** **1 circle = 6400 mils** **A. PRECISION AND ACCURACY** ***Precision*** is the degree of closeness or conformity of repeated measurements of the same quantity to each other whereas ***accuracy*** is the degree of conformity of a measurement to its true value. **B. THEORY OF PROBABILITY** Probability is the number of times something will probably occur over the range of possible occurrences. Theory of probability is useful in indicating the precision of results only in so far as they are affected by accidental errors. It is based upon the following assumptions relative to the occurrences of error. **Laws of Probability** - Small errors occur more than large ones and they are more probable. - Large errors happen infrequently and are therefore less probable. - Positive and 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. **C.ERROR TYPES** ***Error --* Defined as the difference between the true value and the measure value of a quantity.** ***Mistakes --* are inaccuracies in measurements that occur because some aspect of a surveying operation is performed by the surveyor with carelessness, poor judgment, and improper execution.** **Types of Errors** **1. Systematic Errors -- are caused by the surveying equipment, observation methods, and certain environmental factors. Under the same measurement conditions, these errors will have the same magnitude and direction (positive or negative).** ***Ex. Instrument errors, calibration errors/defective instruments, errors in taping due to temperature, etc.*** **2. Accidental or Random errors -- are unpredictable and are often caused by factors beyond the control of the surveyor. Their occurrence, magnitude, and direction (positive or negative) cannot be predicted.** ***Ex. Instrument man accidentally read the upper stadia instead of the middle cross hair.*** **Sources of Errors** 1. **Instrumental Error -- are caused by imperfectly constructed, adjusted, or calibrated surveying equipment.** 2. **Natural Error -- are caused by environmental conditions or significant changes in environmental conditions.** 3. **Personal Error -- Human errors are caused by physical limitations and inconsistent setup and observation habits of the surveyor.** **Mistakes examples** - **Improperly leveling the surveying instrument.** - **Setting up the instrument or target over the wrong control point.** - **Incorrectly entering a control point number in the data collector** - **Transposing numbers or misplacing the decimal point.** **D.MOST PROBABLE VALUE** A fixed value of a quantity may be conceived as its *true value T.* *Since the true value of a measurement quantities is theoretically never known, we refer to the **Most Probable Value** as our "True Value".* Since the true value of a measured quantity cannot be determined, the exact value of *e* can never be found out. \ [\$\$\\overline{x} = \\frac{\\sum\_{}\^{}P}{n\_{T}}\$\$]{.math.display}\ Where: Σ *P* = sum of the individual measurements [*n*~*T*~]{.math.inline} = total number of observations **How to calculate the MPV** **1. For SINGLE QUANTITIES measured repeatedly** **a. Uniformly Weighted (Equally reliable)** **b. Weighted Measurements (Different reliabilities)** **2. For GROUP OF MEASUREMENTS forming a DEFINITE QUANTITY and needs CORRECTION.** **a. Uniformly Weighted (Equally reliable)** **b. Weighted Measurements (Different reliabilities)** **SITUATION NO. 1** A line is measured 5 times. The record shows the following measurements: 200.21 m, 200.48 m, 199.98 m, 200.05 m, 200.52 m. What is the most probable value? ***ANS: 200.248 m*** The **residuals**, which is sometimes referred to as the deviation, is defined as the difference between any measured value of a quantity and its most probable value. \ [\$\$v = x - \\overline{x}\$\$]{.math.display}\ Where: [*v*]{.math.inline} = residual in any measurements [*x*]{.math.inline} = measurement made of a particular quantity [\$\\overline{x}\$]{.math.inline} = most probable value of a quantity measured **E. STANDARD DEVIATION** *Standard deviation (Standard error)* is also called the *root-mean square* (R.M.S.) error; it is a measure of how dispersed the data is in relation to the mean. It tells you, on average, how far each score lies from the mean. \ [\$\$\\sigma\_{n - 1} = \\pm \\sqrt{\\frac{\\sum\_{}\^{}{(x - \\overline{x})}\^{2}}{n - 1}}\$\$]{.math.display}\ \ [\$\$\\sigma\_{n - 1} = \\pm \\sqrt{\\frac{{\\sum\_{}\^{}v}\^{2}}{n - 1}}\$\$]{.math.display}\ Where n = total number of observed values The standard deviation given by the above expression is also called the standard error. Simple [*σ*]{.math.inline} will mean [*σ*~*n* − 1~]{.math.inline} **F. VARIANCE** Variance (V) is used as a measure of dispersion or spread of a distribution. \ [\$\$V = \\frac{{\\sum\_{}\^{}v}\^{2}}{n - 1}\$\$]{.math.display}\ \ [*V* = *σ*^2^]{.math.display}\ **What's the difference between Standard Deviation and Variance?** Variance is the average squared deviations from the mean, while Standard Deviation is the square root of this number. Both measures reflect variability in a distribution, but their units differ: - Standard deviation is expressed in the same units as the original values (e.g., minutes or meters). - Variance is expressed in much larger units (e.g., meters squared). **G. STANDARD ERROR OF MEAN** **It is used as a measure of dispersion or spread of a distribution, indicates how different the population mean is likely to be from a sample mean. It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population.** The *standard error of mean*[ *σ*~*m*~]{.math.inline} is given by \ [\$\$\\sigma\_{m} = \\pm \\sqrt{\\frac{\\sum\_{}\^{}{(x - \\overline{x})}\^{2}}{n(n - 1)}}\$\$]{.math.display}\ \ [\$\$\\sigma\_{m} = \\pm \\frac{\\sigma}{\\sqrt{n}}\$\$]{.math.display}\ and hence the precision of the mean is enhanced with respect to that of a single observation. There are *n* deviations (or residuals) from the mean of the sample and their sum will be zero. Thus, knowing [(*n* − 1)]{.math.inline} deviations the surveyor could deduce the remaining deviation and it may be said that there are [(*n*−1)]{.math.inline} degrees of freedom. This number is used when estimating the population standard deviation. **H. PROBABLE ERROR** The *most probable error* is defined as the error for which there are equal chances of the true error being less and greater than probable error. Probable error of single measurement, [PE~*s*~]{.math.inline} \ [\$\$\\text{PE}\_{s} = \\pm 0.6745\\sqrt{\\frac{\\sum\_{}\^{}\\left( x - \\overline{x} \\right)\^{2}}{n - 1}}\$\$]{.math.display}\ Probable error of mean measurement, [PE~*m*~]{.math.inline} \ [\$\$\\text{PE}\_{m} = \\pm 0.6745\\sqrt{\\frac{\\sum\_{}\^{}\\left( x - \\overline{x} \\right)\^{2}}{n\\left( n - 1 \\right)}}\$\$]{.math.display}\ **I.WEIGHT** This quantity W is known as *weight* of the measurement indicates the reliability of a quantity. It is inversely proportional to the variance [*σ*^2^]{.math.inline} (or probable error, P.E) of the observation, and can be expressed as \ [\$\$W = \\frac{k}{\\sigma\^{2}}\$\$]{.math.display}\ \ [\$\$W = \\frac{k}{\\text{P.E}\^{2}}\$\$]{.math.display}\ where *k* is a constant of proportionality. If the weights and the standard errors for observations x₁, x₂, ,....., etc., are respectively W₁, W₂,......, etc., and σ₁, σ₂,....., etc., and [*σ*~*u*~]{.math.inline} is the standard error for the observation having unit weight then we have \ [*W*~1~*σ*~1~^2^ = *W*~2~*σ*~2~^2^ = .. = *σ*~*u*~^2^]{.math.display}\ Hence [\$W\_{1} = \\frac{\\sigma\_{u}\^{2}}{\\sigma\_{1}\^{2}}\$]{.math.inline}, [\$W\_{2} = \\ \\frac{\\sigma\_{u}\^{2}}{\\sigma\_{2}\^{2}}\$]{.math.inline}, etc., and [\$\\frac{W\_{1}}{W\_{2}} = \\frac{\\sigma\_{2}\^{2}}{\\sigma\_{1}\^{2}}\$]{.math.inline} etc. **WEIGHTED MEAN** The weights are applied to the individual measurements of unequal reliability to reduce them to one standard. The most probable value is then the **weighted mean** [\${\\overline{\\mathbf{x}}}\_{\\mathbf{m}}\$]{.math.inline} **of the measurements.** Thus \ [\$\$\\overline{x} = \\frac{\\sum\_{}\^{}\\text{Wx}}{\\sum\_{}\^{}W}\$\$]{.math.display}\ and **standard error of the weighted mean** \ [\$\$\\sigma\_{{\\overline{x}}\_{m}} = \\pm \\sqrt{\\frac{\\sum\_{}\^{}\\left\\lbrack w\\left( \\left( x - \\overline{x} \\right) \\right)\^{2} \\right\\rbrack}{\\sum\_{}\^{}{w\\left( n - 1 \\right)}}}\$\$]{.math.display}\ Where: w = [\$\\frac{W}{\\text{Wlargest}}\$]{.math.inline} The **standard deviation of an observation of unit weight** is given by \ [\$\$\\sigma\_{u} = \\pm \\sqrt{\\frac{\\sum\_{}\^{}\\left\\lbrack w\\left( x - \\overline{x} \\right)\^{2} \\right\\rbrack}{\\left( n - 1 \\right)}}\$\$]{.math.display}\ and the **standard deviation of an observation of weight** is given by \ [\$\$\\sigma\_{w} = \\pm \\sqrt{\\frac{\\sum\_{}\^{}\\left\\lbrack w\\left( x - \\overline{x} \\right)\^{2} \\right\\rbrack}{w\_{t}\\left( n - 1 \\right)}}\$\$]{.math.display}\ **SITUATION NO. 2** A line is measured 5 times. The record shows the following measurements: Measurement: Probable Error: 200.21 m [+] 0.20 200.48 m [+] 0.40 199.98 m [+] 0.20 200.05 m [+] 0.10 200.52 m [+] 0.50 What is the most probable value of the length of the line? ***ANS: 200.023 m*** **SITUATION NO. 3** A line is measured 5 times. The record shows the following measurements: Measurement: No. of Trials 200.21 m 2 200.48 m 3 199.98 m 1 200.05 m 5 200.52 m 1 What is the most probable value of the length of the line? ***ANS: 200.2175 m*** **J. RELATIVE PRECISION** Relative precision is commonly expressed as fraction with unity in the numerator. It is the relationship of the total error to the magnitude of the measured quantity. It is also used to define the degree of refinement obtained. \ [\$\$RP = \\frac{\\text{PE}\_{m}}{\\overline{x}}\$\$]{.math.display}\ **K. ADJUSTMENT OF WEIGHTED OBSERVATIONS** Two Cases 1. Various Measurements of the same quantity The most probable value of a quantity for which measurements of different reliability have been made is the weighted mean. 2. Measurement of related quantities When the sum of measured values having different weights most equal a known value either measure or exact, the most probable values are the observed values each corrected by an appropriate position of the discrepancy or of the total error. The corrections to be applied are inversely proportional to the weights. **Exercise Problem No. 1** Following is a series of 10 rod readings which were taken with a wye level under identical conditions. The day was calm or cloudy. The instrument was set-up, and the target rod was held on a point 600 ft. away. Rod readings are: 3.365, 3.366, 3.365, 3.363, 3.368, 3.366, 3.367, 3.364, 3.365, 3.364 Determine the following: a. Most probable value b. Variance c. Standard Deviation / Standard error d. Standard error of the mean measurement e. Probable error of single measurement f. Probable error of the mean measurement g. Relative precision **Exercise Problem No. 2** Lines of levels to establish the elevation of a point are run over four different routes. The observed elevations of the point with probable errors are given below. Line Observed Elev ± PE (m) ------ ------------------------ 1 252.07 ± 0.02 2 253.68 ± 0.04 3 252.88 ± 0.05 4 252.75 ± 0.08 Determine the following: a. Most Probable Value b. Standard Deviation c. Standard Error of the Weighted Mean Measurement d. Probable Error of Weighted Mean Measurement e. Relative Precision