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CEE 317 GeoSurveying

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Required Readings:Chapter 1 Sections: 7-1 through 7-10 Figures: 7-2 Recommended solved examples: 7-1 and 7-2Recommended solved examples: 7-1 and 7-2 The packetThe packet

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Lecture Outline Contents:Contents: Introduction: instructor, syllabus, exams, extra work, labs, homework.Introduction: instructor, syllabus, exams, extra work, labs, homework. Definition of surveying and GeoSurveuing.Definition of surveying and GeoSurveuing. Geodetic and plane surveying.Geodetic and plane surveying. Horizontal and vertical angles.Horizontal and vertical angles. Azimuth and bearing.Azimuth and bearing. Total stations.Total stations.

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Introduction Instructor:Instructor: Kamal Ahmed. Room 121c.Kamal Ahmed. Room 121c. Office hours: see syllabus. Office hours: see syllabus. Email: kamal@u.Washington.eduEmail: kamal@u.Washington.edu Class website: http ://courses.Washington.edu/cive316.Class website: http ://courses.Washington.edu/cive316.http ://courses.Washington.edu/cive316http ://courses.Washington.edu/cive316 Facebook/Facebook/ The rest of the team.The rest of the team.

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Past President of the ASPRS - PSR

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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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Syllabus, Exams, and Extra Work The packet Syllabus: course structure and paceSyllabus Three Exams. Extra Work: Purpose, weight Ideas: C++, New Subject See the page on extra work for more details. Labs: First few labs: keep good notes for the rest of the quarter Resection: no report, you will need data from the lab to solve Homework. Leveling: Group work and report. Two Projects: group work and report. Homework due dates, where to drop papers, honor systemHomework In hw1 you will use Wolfpack to solve the resection problem and find the coordinates of the point on the roof. Other Problems (see handouts)

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Surveying Definition : surveying is the science art and technology of determining the relative positions of points above, on, or beneath the earths surface.Definition : surveying is the science art and technology of determining the relative positions of points above, on, or beneath the earths surface. Geo SurveyingGeo Surveying History of surveying : earliest recorded documents suggest that surveying began in Egypt thousands of years History of surveying : earliest recorded documents suggest that surveying began in Egypt thousands of years ago the era of Sesostrs ago the era of Sesostrs about 1400 BC about 1400 BC for taxation purposes. for taxation purposes.

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Aswan Eratosthenes, 220 BC, measured the distance S knowing the speed of camel caravans and measuring the time. He then estimated the angle (α) from the length of the shadow of a vertical mast at the same time when the sun illuminated the bottom of a deep well in Aswan, same time in two summers. The extension of the vertical mast will pass by the center of the earth. Determining the Dimensions of the Earth

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Why Surveying and what do surveyors do? {paper to ground and ground to paper}Why Surveying and what do surveyors do? {paper to ground and ground to paper} Present and future: technological advances and application: GPS, LIDAR, softcopy Phtogrammetry, remote sensing and high.Present and future: technological advances and application: GPS, LIDAR, softcopy Phtogrammetry, remote sensing and high. Resolution satellite images, Resolution satellite images, And GIS. Geodetic & plane:Geodetic & plane: 0.02 ft in 5 miles difference.0.02 ft in 5 miles difference. Accuracy considerations.Accuracy considerations.

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Surveying Measurements Surveyors, regardless of how complicated the technology, measure two quantities: angle and distances. Surveyors, regardless of how complicated the technology, measure two quantities: angle and distances. They do two things: map or set-out They do two things: map or set-out Angles are measured in horizontal or vertical planes only to produce horizontal angles and vertical angles. Angles are measured in horizontal or vertical planes only to produce horizontal angles and vertical angles. Distances are measured in the horizontal, the vertical, or sloped directions. Distances are measured in the horizontal, the vertical, or sloped directions. Our calculations are usually in a horizontal or a vertical plane for simplicity. Then, sloped values can be calculated if needed. Our calculations are usually in a horizontal or a vertical plane for simplicity. Then, sloped values can be calculated if needed.

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For example: maps are horizontal projections of data, distances are horizontal on a map and so are the angles. For example: maps are horizontal projections of data, distances are horizontal on a map and so are the angles. Assume that you are given the horizontal coordinates X (E), and Y (N) of two points A and B: (20,20) and (30, 40). If you measure the horizontal angle CBA and the horizontal distance AC, found them to be: 110 and 15m, then the coordinates of C can easily be computed, here is one way : Assume that you are given the horizontal coordinates X (E), and Y (N) of two points A and B: (20,20) and (30, 40). If you measure the horizontal angle CBA and the horizontal distance AC, found them to be: 110 and 15m, then the coordinates of C can easily be computed, here is one way : Calculate the azimuth of AB, then BCCalculate the azimuth of AB, then BC Calculate ( X, Y) for BCCalculate ( X, Y) for BC Calculate (X, Y) for CCalculate (X, Y) for C A B C

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But, if you were given a slope distance or a slope angle, you wont be able to compute the location (Coordinates) of C. But, if you were given a slope distance or a slope angle, you wont be able to compute the location (Coordinates) of C. What we did was to map point C, we found out its coordinates, now you plot it on a piece of paper, a map is a large number of points such as C, a building is four points, and so on. What we did was to map point C, we found out its coordinates, now you plot it on a piece of paper, a map is a large number of points such as C, a building is four points, and so on. Now, if point C was a column of a structure and we wanted to set it out, then we know the coordinates of C from the map: Now, if point C was a column of a structure and we wanted to set it out, then we know the coordinates of C from the map:

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Calculate the angle ABC and the length of BCCalculate the angle ABC and the length of BC Setup the instrument, such as a theodolite, on B, aim at ASetup the instrument, such as a theodolite, on B, aim at A Rotate the instrument the angle ABC, measure a distance BC, mark the point.Rotate the instrument the angle ABC, measure a distance BC, mark the point. You set out a point, then you can set out a project. You set out a point, then you can set out a project. In both cases, you need two known points such as A and B to map or set out point C In both cases, you need two known points such as A and B to map or set out point C We call precisely known points such as A and B control points We call precisely known points such as A and B control points In horizontal, we do a traverse to construct new control points based on given points. In horizontal, we do a traverse to construct new control points based on given points. You need at least two points given in horizontal ( or one and direction) and one in vertical to begin your project You need at least two points given in horizontal ( or one and direction) and one in vertical to begin your project

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Angles and Directions

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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 –Interior (measured on the inside of a closed polygon), and Exterior Angles (outside of a closed polygon). –Angles to the Right: clockwise, from the rear to the forward station, Polygons are labeled counterclockwise. Figure 7-2. –Angles to the Left: counterclockwise, from the rear to the forward station. Polygons are labeled clockwise. Figure 7-2 –Right (clockwise angles) and Left (counterclockwise angles) Polygons

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Figure (a) Figure (a) Figure (b) angles to the rightangles to the left right anglesLeft angles rightleft Clockwise anglesCounterclockwise angles Counterclockwiseclockwise Labeled in a Counterclockwise fashion Labeled in a clockwise fashion In this class, I will refer to the polygons as follows Polygon

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2- Directions: 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 meridianWe will use north or south as a meridian Types of meridians:Types of meridians: Magnetic: defined by a magnetic needle.Magnetic: defined by a magnetic needle. Geodetic meridian: connects the mean positions of the north and south poles.Geodetic meridian: connects the mean positions of the north and south poles. Astronomic: instantaneous, the line that connects the north and south poles at that instant. Obtained by astronomical observations.Astronomic: instantaneous, the line that connects the north and south poles at that instant. Obtained by astronomical observations. Grid: lines parallel to a central meridianGrid: 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 Azimuth: Azimuth: –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 -Back-azimuth is measured at the end of the line, such as BA instead of AB. -The line AB starts at A, the line BA starts at B.

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Azimuth and Bearing Bearing: acute 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. Bearing: acute 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. Azimuth and bearing: which quadrant? Azimuth and bearing: which quadrant?

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N E AZ = B AZ = 180 - BAZ = 180 + B AZ = 360 - B 1 ST QUAD. 2 nd QUAD. 3 rd QUAD. 4 th QUAD. Bearing Azimuth

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Example (1) Calculate the reduced azimuth (bearing) of the lines AB and AC, then calculate azimuth 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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How to know which quadrant from the signs of departure and latitude For example, what is the azimuth if the departure was (- 20 ft) and the latitude was (+20 ft) ?

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Azimuth Equations Important to remember and understand: Azimuth of a line (BC)=Azimuth of the previous line AB+180°+angle B Assuming internal angles in a counterclockwise polygon

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Azimuth of a line BC = Azimuth of AB - The angle B +180° AZ ab +180 -int angle = AZ bc N N A B C

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A B C N N N A B C N N Azimuth of a line BC = Azimuth of AB ± The angle B +180° Homework 1

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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 = 180 + B, 4th Quadrant: α AB = 360 - 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 = 180 + 30= 210 - If bearing from calculator is – 30 & Δ E is – ve& ΔN is +ve α ab = 360 -30 = 330 (4th Quadrant) - If bearing from calculator is – 30& ΔE is + ve& ΔN is – ve, α ab = 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) α ab = 30 otherwise, if both ΔE, ΔN are –ve, (3 rd Quad.) α ab = 180 + 30 = 210

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Example (2)-AnswerLineΔEΔEΔNΔNQuad. Calculated bearing tan-1( tan-1(ΔE/ ΔN)Azimuth AB1101701st 32° 54 19 AC200-1202nd -59° 02 11 120° 57 50 AD-120-1503rd 38° 39 35 218° 39 35 AE-2001204th -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, 112.32), (214.12, 180.45), 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 = -69.70, Lat BC = N BC = -98.28m Dep BC = ΔE BC = -69.70, Lat BC = ΔN BC = -98.28m 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 - 215 ° 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 = 116.11m 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 115 90 110 105 30 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 Azimuth of DE = Bearing of CD + Angle D + 180 = 30 + 110 + 180 = 320 Azimuth of EA = Bearing of DE + Angle E + 180 = 320 + 105 + 180 = 245 (subtracted from 360) Azimuth of AB = Bearing of EA + Angle A + 180 = 245 + 115 + 180 = 180 (subtracted from 360) Azimuth of BC = Bearing of AB + Angle B + 180 =180 + 120 + 180 = 120 (subtracted from 360) CHECK : Bearing of CD = Bearing of BC + Angle C + 180 = 120 + 90 + 180 = 30 (subtracted from 360), O. K. 120 E C B A 115 90 110 105 30 D

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Homework 1 Problem 3? compute Azimuth of AB compute Azimuth of AB compute Azimuth of BC (-VE internal angle) compute Azimuth of BC (-VE internal angle) compute dep and lat of BC compute dep and lat of BC compute coordinates of C compute coordinates of CQuestions?

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SOLVING THE RESECTION PROBLEM WITH WOLFPACK

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Solving Triangle Problems with WolfPack

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