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Maps and Plans Background Basic Computations Geometrical Concepts Errors and Statistics Distances coordinates Angles Measurements heights Height differences Mid Semester examination New Technologies GPS Practical Surveying Setting Out Analysis Geographical Information Systems 1 Legalities involved Cadastral Surveying Computer assisted surveying The Department of Civil Engineering CE-209 Fundamentals of Surveying Lecture 2 Maps and Plans in Surveying/Basic Computations/Geometrical Concepts Dr.Orhan ERCAN 2 Maps and Plans in Surveying….. Surveys are carried out to make maps and plans. Maps and plans are used to carry out surveys. Survey Types * Detail * Control * Setting Out * Heighting 4 Surveying Terminology * Survey area * Coordinates * Control Points * Datums * North 5 Elements of a map eg * North - directions * Grid * Coordinates * Scale - distances * Heights 6 What is involved in conducting a survey? * What are the measurements made? * What do these measurements mean? * What further computations are required? * How good are our measurements? 7 What are the measurements made? * angles (degs,mins,secs, rads) * distances (m, km) * Height differences (m) 1000m = 1km 100cm = 1m 8 10mm = 1cm 1000mm = 1m What do these measurements mean? * Angles * angles between points (eg) * bearings 9 Basic Computation #1 Converting degrees, minutes, seconds to decimal degrees and radians Angle measured : 28o 31' 25" 1o = 60' 1' = 60" therefore 1o = 3600" To convert to decimal degrees = 28 + 31/60 + 25/3600 = 28.5236o p radians = 180o where p ~ 3.1416 10 To convert decimal degrees to radians = 28.5236 x p/180 = 0.497831rads Basic Computation #2 Converting radians to decimal degrees, and degrees, minutes and seconds To convert radians to decimal degrees = 0.497831 x 180/p = 28.5236o To convert decimal degrees to degs, mins, secs : degs = 28 mins = (28.5236 - 28 ) x 60 = 31.416 = 31 secs = (31.416 - 31) * 60 = 24.96 = 25 28o 31' 25" 11 North Directions and Whole Circle Bearings * True, magnetic, arbitrary, grid N N B D f C A 12 a Further Computations from the Measurements * Compute the distance and direction between two points given their coordinates. * Computing the coordinates of an unknown point given the coordinates of a known point and the direction and distance between them. 13 Basic Computation #3 Computing the distance between two points given their coordinates - Chart 3.xls distance E2 N2 14 Basic Computation #4 Computing the bearing between two points given their coordinates - Chart 2 .xls E tan N E tan 1 N 15 Basic Computation #5 Computing the coordinates of a point given the bearing and distance from a known point Chart 4.xls E distance x sin N distance x cos E B E A E N B N A N 16 Worked Example - Computation of Rectangular Coordinates The coordinates of a point A are 311.617m E, 447.245m N. Calculate the coordinates of point B where qAB = 37o 11’ 20” and sAB = 57.916m. EB E A s sin AB N B N A s cos AB 311.617 57.916 sin 37 11 20 o 447.245 57.916 cos 37 o11 20 311.617 35.007 447.245 46.139 346.624m 493.384m 16 Worked Example - Computation of bearing and distance The coordinates of point A are 469.72m E, 338.46 N and point B are 268.14m E and 116.19mN. Compute the bearing and distance between them. N 1 E AB AB tan N AB A E E A tan 1 B N B N A AB NAB 268.14 469.72 tan 1 sAB 116.19 338.46 201.58 tan 1 222.27 B tan 1 0.906915 18 EAB E + 180o 42o1219 Problem with quadrants! AB = 222o 12’ 19” Inverse Calculations 4 E -ve 1 E +ve N +ve N +ve +360o 270o 90o E -ve E +ve N -ve N -ve +180o +180o 19 3 180o 2 s AB E 2 N 2 N EB E A 2 N B N A 2 E AB N AB A sin AB cos AB 201.58 AB NAB sAB sin 222 o1219 300.06m B EAB E 20 Maps and Plans Background Basic Computations Geometrical Concepts Errors and Statistics Distances coordinates Angles Measurements heights Height differences Mid Semester examination New Technologies GPS Practical Surveying Setting Out Analysis Geographical Information Systems 21 Legalities involved Cadastral Surveying Computer assisted surveying How good are our measurements? * precision * accuracy 22 Precision refers to how good our observations are with respect to each other. Accuracy refers to how good our results are to the true value 23 When we talk about precision and accuracy we're talking about statistics and more specifically standard deviation. 24 Simple Statistics 30.615 Mean x x 306 .150 30.615 30.618 n 10 30.614 30.615 x x 2 30.616 S tan dard Deviation 0.002m 30.614 n 30.613 30.614 x x True 2 0.002m 30.616 n 25 30.618 The difference between x x is how we measure how good our observations are with respect to each other - precision. If we replace X with the true value we get a measure of accuracy. Chart1.xls 26 15 15 . . 10 .. . . 10 . 5 . . . 5 . . . . ... .. . . . 5 . 10 15 . . .. .... ... 5 .... 10 15 . . . . ... .... .. ... .. . . . . . . . . . . . . . . . (a) (b) Highly dispersed observations, therfore low precision Closely grouped observations indicating high precision 15 15 10 10 . ... .. . . . . .... ... .... . 5 .... .... . . . .. ... . 5 . . ... .. . . .. .... ... .... 5 10 15 5 10 15 . . ... .... .. ... .. . . . . (c) (d) Very precise observations, however poor Main distribution shows high precision, with several observations accuracy which are signiicantly different. These observations can be considered outliers and subsequently rejected 27 Errors in Survey Measurements * Gross - chart 5.xls * Systematic - chart 6.xls * Random 28 Errors in derived quantities We have measured two distances d1 and d2 in a straight line. What is the total distance (D) and its standard deviation? d1 = 154.26m and has a SD of 0.01m, d2 = 175.34m and has a SD of 0.05m D = d1 + d2 = 154.26 + 175.34 = 329.60m D = (d1 + e2) + (d2 + e2) = (154.26 +.01) +(175.34 +.05 ) = 154.27 + 175.39 = 329.66 difference = 0.06m 29 The coordinates of a point A are 311.617m E, 447.245m N. Calculate the coordinates of point B where qAB = 37o 11’ 20” and sAB = 57.916m. What are the coordinates of B. What effect would there be of an error in the bearing of 1o and in the distance of 0.5m. EB E A s sin AB N B N A s cos AB 311.617 57.916 sin 37 11 20 o 447.245 57.916 cos 37 o11 20 311.617 35.007 447.245 46.139 346.624m 493.384m 30 Maps and Plans Background Basic Computations Geometrical Concepts Errors and Statistics Distances coordinates Angles Measurements heights Height differences Mid Semester examination New Technologies GPS Practical Surveying Setting Out Analysis Geographical Information Systems 31 Legalities involved Cadastral Surveying Computer assisted surveying

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posted: | 3/29/2011 |

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