CE 311. Elementary & Higher Surveying

Transcription

1 CE 311 Elementary & Higher Surveying

2 Surveying Concept What do surveyors do? What do surveyors measure? What distances do surveyors measure? What angles do surveyors measure? What positions do surveyors measure?

3 SURVEYING is the art and science of measuring distances, angles, and positions of points, lines, areas on or near the surface of the earth or on other extra-terrestrial bodies through applied mathematics and the use of specialized equipment and techniques.

4 Two General Classifications of Surveying: 1. PLANE SURVEYING type of surveying in which the earth is considered to be a flat surface, and distances and areas involved are of 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.

5 Types of Surveys: 1. Cadastral Surveys In urban and rural locations (municipalities, towns) Purpose: determining and defining property lines and boundaries, corners, and areas 2. City Surveys Areas in and near a city Purpose: planning expansions or improvements, locating property lines, fixing reference monuments 3. Construction Surveys In construction sites Purpose: grades, reference lines, dimensions, ground configuration, location and elevation of structure 4. Forestry Surveys Forest management (production and conservation of forest land) 5. Hydrographic Surveys Bodies of water Purpose: to map shorelines, chart the shape of areas underlying water surfaces, and measure the flow of streams Water Supply, irrigations, flood control

6 Types of Surveys: 6. Industrial Surveys Ship building, aircrafts, machineries 7. Mine Surveys Determine the position of all underground excavations and surface mine structures, surface boundaries, excavated volumes, and establish lines and grades 8. Photogrammetric Surveys (Aerial Survey) Photographs taken from airplanes 9. Topographic Surveys Determine the shape of the ground, location and elevations 10. Route Surveys Construction of highways, railroads, pipelines, canals, transmission lines, and other linear projects Determines the alignment, grades, earthwork quantities

7 SURVEYING INSTRUMENTS TRANSIT DUMPY LEVEL TOTAL STATION TRIPOD

8 STEEL TAPE METER STAFF THEODOLITE

9 Surveying Measurements Measurement is the process of determining the extent, size or dimensions of a particular quantity in comparison to a given standard. Two Kinds of Measurements 1. DIRECT MEASUREMENT Comparison of measured quantity with a standard measuring unit employed for measuring a quantity of that kind 2. INDIRECT MEASUREMENT Combination of many measurements

10 UNITS OF MEASUREMENT Mega- = Centi- = 0.01 Kilo- = Milli- = Hecto- = 100 Micro- = Deca- = 10 Nano- = Deci- = Linear, Area, and Volume Measurements 1 km = m 1 m = mm 1 mm= um 1 m = 10 dm 1 dm = 10 cm 1 cm = 10 mm 1 ha = sq m 1 L = cc 1 m 3 = cc 2. Angular Measurements 2π rad Sexagesimal Units Centesimal Units = 360 deg 1 deg = 60 mins 1 min = 60 sec 1 rev = 400 grads 1 grad = 100 centesimal mins 1 c.mins = 100 centesimal sec

11 Conversion 1 mile = 5280 ft = 1.61 km 1 foot = 12 inches 1 yard = 3 ft 1 meter = 3.28 ft 1 km 2 = acres 1 inch = 25.4 mm

12 Significant Figures General Rules: Rule 1 : Zeroes between other significant figures are significant. ex. 4 SF: Rule 2 :For any value less than one, zeroes immediately to the right of the decimal are not significant. ex. 3 SF: Rule 3 : Zeroes placed at the end of the decimal numbers are significant. ex. 5 SF: Rounding Off Numbers Procedures: 1.Digits less than 5. When the digit to be dropped is less than 5, the number is written without the digit. 2. Digit is equal to 5. When the digit to be dropped is exactly 5, the nearest even number is used for the 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.

13 Errors vs. Mistakes Error is the difference between the true value and the measured value of the quantity. Mistakes 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. Types of Errors 1.Systematic Errors can be computed and corrected 2.Accidental Errors neglected Sources of Errors 1.Instrumental Errors 2. Natural Errors 3. Personal Errors

14 Accuracy and Precision Accuracy indicates how close a given measurement is to the absolute or true value of the quantity measured. Precision Refers to the degree of refinement and consistency with which any physical measurement is made.

15 Theory of Probability Probability The number of times something will probably occur over the range of possible occurrences. Most Probable Value (mpv) The most probable value of a group of repeated measurements made under similar conditions is the arithmetic mean or average. mpv x x1 x2... x n n x n Residual The difference between any measured value of a quantity and its mpv v x x

16 Illustrative Problem: The angles about a point Q have the following observed values: , , and Determine the most probable value of each angle.

17 Probable Error 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 PE s v 2 n 1 PE m v 2 n( n 1) PE s = Probable error of a single measurement PE m = Probable error of the mean n = number of observations

18 Relative Precision * Usually expressed in fraction having 1 as numerator RP magnitudeoferror magnitudeofrmeasuredquantity Weighted Observation W 1 E 2 W = weight being assigned E = probable error

19 Interrelationship of Errors 1. Summation of Errors (Perimeter) PE S PE1 PE2... PEn PE S = Probable error of the sum PE 1, PE 2, PE n = Probable error of each measurement 2. Product of Errors (Area) PE P ( Q PE PE2 ) ( Q2 1 ) PE P = Probable error of the product Q 1, Q 2 = Measured quantity PE 1, PE 2 = Probable error corresponding to each Q

20 Illustrative Problem 1. The ff values were determined in a series of tape measurements of a line: , , , , and Determine the ff: A. MPV of the measured length B. PE of single measurement and mean C. Final expression of the most probable length (MPL) D. Relative precision of the measurement

21 Illustrative Problem 2. The three sides of a triangular shaped tract of land is given by the following measurements and corresponding probable error: a = ± 0.05m b = ± 0.02m c = ± 0.04m

22 Illustrative Problem 3. The two sides of a rectangular lot were measured with certain estimated probable error as follows: W = ± 0.1m L = ± 0.08m Determine the area of the lot and the probable error in the resulting calculation.