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Plane Surveying Traverse, Electronic Distance Measurement and Curves Civil Engineering Students Year (1) Second semester – Phase II Dr. Kamal M. Ahmed

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Introduction u Topics in Phase II: Angles and Directions, Traverse, EDM, Total Stations, Curves, and Introduction to Recent and supporting technologies u Introduction of the Instructor –Background, honors, research interests, teaching, etc. –Method of teaching: F what to expect and not to expect, what is allowed. F Language used. F Lecture slides: NO DISTRIBUTION WITHOUT PERMIT F Breaks

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u Lab sections u list u Textbook u Sheets u Exams Introduction

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Example Of Current Research Based on Laser Distance Measuerements LIDAR Terrain Mapping in Forests USGS DEM LIDAR DEM

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LIDAR Canopy Model (1 m resolution) WHOA!

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Canopy Height (m)

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Raw LIDAR point cloud, Capitol Forest, WA LIDAR points colored by orthophotograph FUSION visualization software developed for point cloud display & measurement

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Angles and Directions الزوايا و الاتجهات

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Angles and Directions 1- Angles: Horizontal and Vertical AnglesHorizontal and Vertical Angles Horizontal Angle: The angle between the projections of the line of sight on a horizontal plane.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.Vertical Angle: The angle between the line of sight and a horizontal plane. Kinds of Horizontal AnglesKinds 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).

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–Angles to the Left: counterclockwise, from the rear to the forward station. Polygons are labeled clockwise. –Right (clockwise) and Left (counterclockwise) Polygons

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2- Directions الاتجهات : Direction of a line is the horizontal angle between the line and an arbitrary chosen reference line called a meridian.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 ““مرجعWe will use north or south as a meridian ““مرجع Types of meridians:Types of meridians: Magnetic: defined by a magnetic needle “ ” ابرةMagnetic: defined by a magnetic needle “ ” ابرة Geodetic “ جيوديسى” meridian: connects the mean positions of the north and south poles “ اقطا ب”.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.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 meridianGrid شبكى : lines parallel to a central meridian Distinguish between angles, directions, and readings.Distinguish between angles, directions, and readings.

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Angles and Azimuth الزوايا والانحرافات Azimuth الانحراف : Azimuth الانحراف : –Horizontal angle measured clockwise from a meridian (north) to the line, at the beginning of the line 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.

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Azimuth and Bearing المختصر الانحراف 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“. 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 “ ? Azimuth and bearing: which quadrant “ اى ربع “ ?

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N N AZ = B AZ = BAZ = B AZ = B

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Departures and Latitudes المركبات السينية و الصادية

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Azimuth Equations 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 How to know which quadrant from the signs of departure and latitude?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) ? For example, what is the azimuth if the departure was (- 20 m) and the latitude was (+20 m) ?

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A B C N N N A B C N N Azimuth of a line such as BC = Azimuth of AB ± The angle B +180°

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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 P (E,N) E L α Easting and Northing

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Polar Coordinates +P ( r, ) N E r u u -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)

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Examples

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Example (1) Calculate the reduced azimuth of the lines AB and AC, then calculate the reduced azimuth (bearing) of the lines AD and AE LineAzimuth Reduced Azimuth (bearing) AB 120° 40’ AC 310° 30’ AD S 85 ° 10’ W A E N 85 ° 10’ W

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Example (1)-Answer LineAzimuth Reduced Azimuth (bearing) AB 120° 40’ S 59° 20’ E AC 310° 30’ N 49° 30’ W AD 256° 10’ S 85° 10’ W A E 274° 50’ N 85° 10’ W

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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 Example (2)

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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 ( α AB ), the bearing is B = tan -1 (ΔE/ Δ N) If we neglect the sign of B as given by the calculator, then, 1st Quadrant : α AB = B, 2nd Quadrant: α AB = 180 – B, 3rd Quadrant: α AB = B, 4th Quadrant: α AB = B

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- For the line (ab): calculate ΔE ab = E b – E a and ΔN ab = N b – N a - If both Δ E, Δ N are - ve, (3rd Quadrant) α ab = = If bearing from calculator is – 30 & Δ E is – ve& ΔN is +ve α ab = = 330 (4th Quadrant) - If bearing from calculator is – 30& ΔE is + ve& ΔN is – ve, α ab = = 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) α ab = 30 otherwise, if both ΔE, ΔN are –ve, (3 rd Quad.) α ab = = 210

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Example (2)-AnswerLineΔEΔEΔNΔNQuad. Calculated bearing tan-1( tan-1(ΔE/ ΔN)Azimuth AB st 32° 54’ 19” AC nd -59° 02’ 11” 120° 57’ 50” AD rd 38° 39’ 35” 218° 39’ 35” AE th -59° 02’ 11” 300° 57’ 50”

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Example (3) The coordinates of points A, B, and C in meters are (120.10, ), (214.12, ), and (144.42, 82.17) respectively. Calculate: a) The departure and the latitude of the lines AB and BC b) The azimuth of the lines AB and BC. c) The internal angle ABC d) 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.

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a) Dep AB = E AB = 94.02, Lat AB = N AB = 68.13m a) Dep AB = ΔE AB = 94.02, Lat AB = ΔN AB = 68.13m Dep BC = E BC = , Lat BC = N BC = m Dep BC = ΔE BC = , Lat BC = ΔN BC = m b) Az AB = ° b) Az AB = tan-1 (ΔE/ ΔN) = 54 ° 04’ 18” Az BC = ° Az BC = tan-1 (ΔE/ ΔN) = 215 ° 20’ 39” c) c) clockwise : Azimuth of BC = Azimuth of AB - The angle B +180° ABBC Angle ABC = AZ AB - AZ BC + 180° = °° = 54 ° 04’ 18” ° 20’ 39” +180 = 18° 43’ 22” Example (3) Answer A B C

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d) AZ AD : The line AD will have the same direction (AZIMUTH) as AB = 54° 04’ 18” L AD = (94.02) 2 + (68.13) 2 L AD = (94.02) 2 + (68.13) 2 = m E Calculate departure = ΔE = L sin (AZ) = 94.02m N latitude = ΔN = L cos (AZ)= 68.13m

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120 E C B A D Example (4) 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.

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Example (4) - Answer Bearing of DE = Bearing of CD + Angle D = = 320 Bearing of EA = Bearing of DE + Angle E = = 245 (subtracted from 360) Bearing of AB = Bearing of EA + Angle A = = 180 (subtracted from 360) Bearing of BC = Bearing of AB + Angle B = = 120 (subtracted from 360) CHECK : Bearing of CD = Bearing of BC + Angle C = = 30 (subtracted from 360), O. K. 120 E C B A D

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