: General I INTRODUCTION TO SURVEYING Lecture No. Caraga State University College of Engineering and Information Technology
SURVEYING It is the art and science of determining 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. Elementary
CLASSIFICATION OF SURVEYS 1. Plane It is a type of surveying in which the earth is considered to be a flat surface, and where distances and areas involved are of limited extent that the exact shape of the earth is disregarded.. Geodetic They are surveys of wide extent which take into account the spheroidal shape of the earth. Elementary
TYPES OF SURVEYS 1. Cadastral Survey They 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.. City Surveys They 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 land and preparing maps. Elementary
3. Construction Surveys They 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 This type of survey executed in connection with forest management and mensuration, and the production and conservation of forest land. Elementary
5. Hydrographic Surveys It refers to surveying streams, lakes, reservoirs, harbors, oceans, and other bodies of water. 6. Industrial Surveys It is sometimes known as optical tooling. It refers to the use of surveying techniques in ship building, construction and assembly or aircrafts, lay out and installation of heavy and complex machinery, and other industries where very accurate dimensional layouts are required. Elementary
7. Mines Surveys They 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 It is a type of surveys which makes use of photographs taken with specially designed cameras either from airplanes or ground stations. Elementary
9. Route Surveys It involves the determination of alignment, grade, 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 They are surveys made for determining the shape of the ground, and the location and elevation of natural and artificial features. Elementary
Development of Instruments 1. Astrolabe. Telescope 3. Transit 4. Semicircumferentor 5. Plane Table 6. Dioptra 7. Roman Groma 8. Libella 9. Vernier 10. Diopter 11. Compass 1. Gunter s Chain 13. Chorobates 14. Merchet Elementary
Measurements Measurement It is the process of determining the extent, size or dimensions of a particular quantity in comparison to a given standard. It was concentrated on angles, elevations, times, lines, areas, and volumes. Note: Measurements are never exact and they will always imperfect no matter how carefully made. The physical measurements acquired are correct only within certain limits because errors cannot be totally eliminated. Elementary
Types of Measurements 1. Direct Measurement It is a comparison of measured quantity with a standard measuring unit or units employed for measuring a quantity of that kind.. Indirect Measurement The observed value is determined by the relationship to some other known values. Elementary
The Meter The international unit of linear measure It was defined as 1/10,000,000 of the earth s meridional quadrant. The International System of Units ( SI ) It was promulgated by the International Bureau of Weights and Measures in 1960. Units in SI of major concern to 1.Meter (m) linear measure.square Meter (m ) areas 3.Cubic Meter (m 3 ) volume 4.Radian (rad) plane angles Elementary
Units of Measurement Prefixes Giga - 1x10 9 Mega - 1x10 6-1 000 000 Kilo - 1x10 3-1 000 Hecto - 1x10-100 Deca - 1x10 1-10 Deci - 1x10-1 - 0.1 Centi - 1x10 - - 0.01 Milli - 1x10-3 - 0.001 Micro - 1x10-6 - 0.000 001 Nano - 1x10-9 - 0.000 000 001 Elementary
1. Linear, Area, and Volume Measurements Linear units: 1 kilometer (km) = 1 000 meters 1 meter (m) = 1 000 millimeters 1 millimeter (mm) = 1 000 micrometers 1 micrometer (um) = 1 000 millimicrometers 1 millimicrometer (mu) = 1000 million micrometers 1 meter (m) = 10 decimeters 1 decimeter (dm) = 10 centimeters 1 centimeter (cm) = 1 0 millimeters The common units for length are: 1. kilometer. meter 3. centimeter 4. millimeter Length may also refer to other linear dimensions such as width, depth, thickness, height, or distance. Elementary
. Angular Measurements Radian The SI unit for plane angles. It is defined as an angle subtended by an arc of a circle having a length equal to the radius of the circle. ᴫ rad = 36 deg, 1 rad = 57 deg 17 min 44.8 sec or 57.958 deg 0.01745 rad = 1 deg Steradian It is the supplementary unit of a solid angle. a. Sexagesimal Units (degree,minute, and second ) b. Centisimal Units ( grad ) Elementary
Significant Figures It is the number of significant figures in any value includes the number of certain digits plus one digit that is estimated, and therefore, questionable or uncertian. Elementary
Some general rules regarding Significant Figures Rule 1: Rule : Rule 3: Zeroes between other significant figures are significant. For values less than one, zeroes immediately to the right of the decimal are not significant. Zeroes placed at the end of decimal numbers are significant. Elementary
Rounding off Numbers It is the process of dropping one or more of the final digit so that the values contains only the significant figure required. Procedure of Rounding Off Numbers 1. Digit is less than 5. When the digit to be dropped is less than 5, the number is written without the digit.. Digit is equal to 5. When the digit to be dropped is exactly 5, the nearest even number is used for preceding digit. 3. Digit is greater than 5. When the digit to be dropped is greater than 5, the number is written with the preceding digit increased by one. Elementary
Errors Errors and Mistakes It is defined as the difference between the true value and the measured value of a quantity. Mistakes They are inaccuracies in measurements which occur because some aspect of a surveying operation is performed by the surveyor with carelessness, inattention, poor judgment, and improper execution. Elementary
Types of Errors 1. Systematic Errors It is one which will always have the same sign and magnitude as long as field conditions remain constant and unchanged.. Accidental Errors They are caused by factors beyond the control of the surveyor and are present in all surveying measurements. The occurrence of such errors are matter of chance as they are likely to be positive or negative. Elementary
Sources of Errors 1. Instrumental Errors These errors are due to imperfections in the instruments used either from faults in their construction or from improper adjustments between the different parts prior to their use.. 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. They are beyond the control of man. Elementary
3. Personal Errors These errors arise principally from limitations of the senses of sight, touch, and hearing of the human observer which are likely to be erroneous or inaccurate. Elementary
Accuracy and Precision Accuracy It 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. Elementary
Accuracy and Precision Precision It 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. Elementary
Good Precision but Poor Accuracy Good Accuracy but Poor Precision Elementary
Good Precision and Good Accuracy Poor Accuracy and Poor Precision Elementary
Good Precision and Good Accuracy Poor Accuracy and Poor Precision Elementary
Probability Theory of Probability it is defined as the number of times something will probably occur over the range of possible occurences. Most Probable Value (MPV) it is the arithmetic mean or the average. it refers to a quantity which based on available data has more chances of being correct than has any other. MPV X X/ n ( X1 X X3. Xn)/ n Elementary
Sample Problem 1 A surveying instructor sent out six groups of students to measure a distance between two points marked on the ground. The students came up with the following six different values: 50.5, 50.15, 49.90, 51.04, 50.50, and 51. meters. Assuming these values are equally reliable and that variations result from accidental errors, determine the most probable value of the distance measured.
Sample Problem The angles at point Q have the following observed values. 130 0 15 0, 14 0 37 30, and 87 0 07 40. Determine the most probable value of each angle.
Quiz (10 pts each) 1. The observed interior angles of a triangle are A= 35 0 14 37, B= 96 0 30 09, and C= 48 0 15 05. Determine the discrepancy for the given observation and the most probable value of each angle.. Measurement of three horizontal angles about point P are: APB= 1 0 31 50, BPC= 37 0 9 0, and CPD= 47 0 36 30. If the measurement of the single angle APD is 97 0 37 00, determine the most probable values of the angles. D C B A P
Residual It is sometimes referred to as the deviation and defined as the difference between any measured value of a quantity and its most probable value. v x x where: v is the residual in any measurement. X is the measurement made of a particular quantity. is the most probable value of the quantity x measured. Elementary
Probable Error It is a quantity which, when added to and subtracted from the most probable value, defines a range within which there is a 50 percent chance that the true value of the measured quantity lies inside ( or outside ) the limits thus set. PEs 0.6745 v n 1 Elementary
Probable Error PEs 0.6745 v n 1 where: PEs is the probable error of any single measurement of a series. PEm is the probable error of the mean. summation of the squares of the residual v PEm n is the number of observation. 0.6745 n( n v 1) Elementary
Relative Precision It is expressed by a fraction having the magnitude of the error in the numerator and the magnitude of a measured quantity in the denominator. RP PE MPV where: RP is the relative precision. PE is the probable error. MPV is the most probable value. Elementary
Sample Problem The following values were determined in a series of tape measurements of a line : 1000.58, 1000.40, 1000.38, 1000.48, 1000.40, and 1000.46 meters. Determine the following: a. most probable value of the measured length. b. probable error of a single measurement and probable error of the mean. c. final expression for the most probable length. d. relative precision of the measurement. Elementary
Weighted Observation 1. The weight is directly proportional to the number of observation. W kn W 1 kn 1 W kn k W n W n 1 1 W n Elementary
Weighted Observation. The weight is inversely proportional to the square of the error. W k E k WE W 1 W E 1 1 k E 1 W E W E k Elementary
Interrelationship of Errors 1. Summation of Errors PEs PE 3 PE PE.. 1. PEn where: PEs is the probable error of the sum. PE 1, PE, etc are the probable error of each measurement. n is the number of values added. Elementary
. Product of Errors PEp PE ) ( ) 1 1 ( Q Q PE where: PEp is the probable error of the product. Q 1 and Q are measured quantities. PE 1 and PE are the probable error corresponding to each quantity measured. Elementary
EXAMPLE PROBLEM Elementary
Example (Weighted): Four measurements of a distance were recorded as 84.18, 84.19, 84., and 84.0 meters and given weights of 1, 3,, and 4 respectively. Determine the weighted mean. Elementary
Example # 3: 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. Determine the most probable value of the elevation of the point. Line Observed Elevation Probable Error 1 19.83 m. ±0.006 m. 19.930 m. ±0.01 m. 3 19.701 m. ±0.018 m. 4 0.01 m. ± 0.04 m. Elementary