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Plane Surveying Traverse, Electronic Distance Measurement and Curves

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## Plane Surveying Traverse, Electronic Distance Measurement and Curves

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**Plane SurveyingTraverse, Electronic Distance Measurement and**Curves Civil Engineering Students Year (1) Second semester – Phase II Dr. Kamal M. Ahmed**Introduction**• Topics in Phase II: Angles and Directions, Traverse, EDM, Total Stations, Curves, and Introduction to Recent and supporting technologies • Introduction of the Instructor • Background, honors, research interests, teaching, etc. • Method of teaching: • what to expect and not to expect, what is allowed. • Language used. • Lecture slides: NO DISTRIBUTION WITHOUT PERMIT • Breaks**Introduction**• Lab sections • E-mail list • Textbook • Sheets • Exams**LIDAR DEM**USGS DEM Example Of Current Research Based on Laser Distance MeasuerementsLIDAR Terrain Mapping in Forests**LIDAR Canopy Model**(1 m resolution) WHOA!**Raw LIDAR point cloud, Capitol Forest, WA**LIDAR points colored by orthophotograph FUSION visualization software developed for point cloud display & measurement**Angles and Directions**1- Angles: • Horizontal and Vertical Angles • Horizontal Angle: The angle between the projections of the line of sight on a horizontal plane. • Vertical Angle: The angle between the line of sight and a horizontal plane. • Kinds of Horizontal Angles • Angles to the Right: clockwise, from the rear to the forward station, Polygons are labeled counterclockwise. • Interior (measured on the inside of a closed polygon), and Exterior Angles (outside of a closed polygon).**Angles to the Left: counterclockwise, from the rear to the**forward station. Polygons are labeled clockwise. • Right (clockwise) and Left (counterclockwise) Polygons**2- Directions الاتجهات :**• Direction of a line is the horizontal angle between the line and an arbitrary chosen reference line called a meridian. • We will use north or south as a meridian ““مرجع • Types of meridians: • Magnetic: defined by a magnetic needle “ ” ابرة • Geodetic “ جيوديسى” meridian: connects the mean positions of the north and south poles “ اقطا ب”. • Astronomic الفلكى : instantaneous لحظى , the line that connects the north and south poles “ اقطا ب” at that instant. Obtained by astronomical observations. • Grid شبكى : lines parallel to a central meridian • Distinguish between angles, directions, and readings.**Angles and Azimuthالزوايا والانحرافات**• Azimuth الانحراف: • Horizontal angle measured clockwise from a meridian (north) to the line, at the beginning of the line • The line AB starts at A, the line BA starts at B. • Back-azimuth “الانحراف الخلفى “ is measured at the end of the line.**Azimuth and Bearingالمختصرالانحراف و**الانحراف • Bearing (reduced azimuth): acute “حادة “ horizontal angle, less than 90°, measured from the north or the south direction to the line. Quadrant is shown by the letter N or S before and the letter E or W after the angle. For example: N30W is in the fourth quad “ الربع الرابع“. • Azimuth and bearing: which quadrant “ اى ربع “ ?**N**AZ = B AZ = 360 - B N AZ = 180 + B AZ = 180 - B**Departures and Latitudes**المركبات السينية و الصادية**Azimuth Equations**• How to know which quadrant from the signs of departure and latitude? • For example, what is the azimuth if the departure was (- 20 m) and the latitude was (+20 m) ? • The following are important equations to memorize and understand Azimuth of a line (BC)=Azimuth of the previous line AB+180°+angle B Assuming internal angles in a counterclockwise polygon**N**N N N N C B B A A C Azimuth of a line such as BC = Azimuth of AB ± The angle B +180°**P (E ,N)**α • L E N Easting and Northing • In many parts of the world, a slightly different form of notation is used. • instead of (x,y) we use E,N (Easting, Northing) . • In Egypt, the Easting comes first, for example: (100, 200) means that easting is 100 • In the US, Northing might be mentioned first. • It is a good practice to check internationally produced coordinate files before using them.**N**Polar Coordinates u +P ( ) r , r u E • The polar coordinate system describes a point by (angle, distance) instead of (X, Y) • We do not directly measure (X, Y in the field • In the field, we measure some form of polar coordinates: angle and distance to each point, then convert them to (X, Y)**Example (1)**Calculate the reduced azimuth of the lines AB and AC, then calculate the reduced azimuth (bearing) of the lines AD and AE**Example (2)**Compute the azimuth of the line : - AB if Ea = 520m, Na = 250m, Eb = 630m, and Nb = 420m - AC if Ec = 720m, Nc = 130m - AD if Ed = 400m, Nd = 100m - AE if Ee = 320m, Ne = 370m**Note: The angle computed using a calculator is the reduced**azimuth (bearing), from 0 to 90, from north or south, clock or anti-clockwise directions. You Must convert it to the azimuth α , from 0 to 360, measured clockwise from North. • Assume that the azimuth of the line AB is (αAB ), • the bearing is B = tan-1 (ΔE/ ΔN) • If we neglect the sign of B as given by the calculator, then, • 1st Quadrant : αAB = B , • 2nd Quadrant:αAB = 180 – B, • 3rd Quadrant: αAB = 180 + B, • 4th Quadrant: αAB = 360 - B**- For the line (ab): calculate**ΔEab = Eb – Ea and ΔNab = Nb – Na - If both Δ E, Δ N are - ve, (3rd Quadrant) αab = 180 + 30= 210 - If bearing from calculator is – 30 & Δ E is – ve& ΔN is +ve αab = 360 -30 = 330 (4th Quadrant) - If bearing from calculator is – 30& ΔE is + ve& ΔN is – ve, αab = 180 -30 = 150 (2nd Quadrant) - If bearing from calculator is 30 , you have to notice if both ΔE, ΔN are + ve or – ve, If both ΔE, ΔN are + ve, (1st Quadrant) αab = 30 otherwise, if both ΔE, ΔN are –ve, (3rd Quad.) αab = 180 + 30 = 210**Example (3)**The coordinates of points A, B, and C in meters are (120.10, 112.32), (214.12, 180.45), and (144.42, 82.17) respectively. Calculate: • The departure and the latitude of the lines AB and BC • The azimuth of the lines AB and BC. • The internal angle ABC • The line AD is in the same direction as the line AB, but 20m longer. Use the azimuth equations to compute the departure and latitude of the line AD.**B**A C Example (3) Answer • DepAB = ΔEAB = 94.02, LatAB = ΔNAB = 68.13m DepBC = ΔEBC = -69.70, LatBC = ΔNBC = -98.28m b) AzAB = tan-1 (ΔE/ ΔN) = 54 ° 04’ 18” AzBC = tan-1 (ΔE/ ΔN) = 215 ° 20’ 39” • clockwise : Azimuth of BC = Azimuth of AB - The angle B +180° Angle ABC = AZAB- AZBC + 180° = = 54 ° 04’ 18” - 215 ° 20’ 39” +180 = 18° 43’ 22”**d) AZAD:**The line AD will have the same direction (AZIMUTH) as AB = 54° 04’ 18” LAD = (94.02)2 + (68.13)2 = 116.11m Calculate departure = ΔE= L sin (AZ) = 94.02m latitude = ΔN= L cos (AZ)= 68.13m**Example (4)**E A 105 115 110 D 30 120 B 90 C In the right polygon ABCDEA, if the azimuth of the side CD = 30° and the internal angles are as shown in the figure, compute the azimuth of all the sides and check your answer.**Example (4) - Answer**E A 105 115 110 D 30 120 B 90 C CHECK : Bearing of CD = Bearing of BC + Angle C + 180 = 120 + 90 + 180 = 30 (subtracted from 360), O. K. Bearing of DE = Bearing of CD + Angle D + 180 = 30 + 110 + 180 = 320 Bearing of EA = Bearing of DE + Angle E + 180 = 320 + 105 + 180 = 245 (subtracted from 360) Bearing of AB = Bearing of EA + Angle A + 180 = 245 + 115 + 180 = 180 (subtracted from 360) Bearing of BC = Bearing of AB + Angle B + 180 =180 + 120 + 180 = 120 (subtracted from 360)