Surveying Engineering CEE 316 Surveying Engineering 1 1

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

Lecture Outline Contents: Introduction: instructor, syllabus, exams, extra work, labs, homework. Definition of surveying. Geodetic and plane surveying. Horizontal and vertical angles. Azimuth and bearing. Total stations. 2 2

Introduction Instructor: Kamal Ahmed. Room 121c. Office hours: see syllabus. Email: kamal@u.Washington.edu Class website: http://courses.Washington.edu/cive316. The rest of the team. 3 3

Past President of the ASPRS - PSR

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

WHOA! LIDAR Canopy Model (1 m resolution)

Canopy Height (m)

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

Syllabus, Exams, and Extra Work Syllabus: course structure and pace Two Exams. Extra Work: Purpose, weight Ideas: AoutCAD, C++, New Subject See the page on “ extra work” for more details. Labs: First two 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 (1) and homework (2) due as in syllabus: use Wolfpack to solve the resection problem and find the coordinates of the point on the roof. Other Problems (see handouts) 4 4

Surveying Definition: surveying is the science art and technology of determining the relative positions of points above, on, or beneath the earth’s surface. History of surveying: began in Egypt thousands of years ago for taxation purposes. Sesostrs about 1400 BC 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. Resolution satellite images, And GIS. Geodetic & plane: 0.02 ft in 5 miles difference. Accuracy considerations. 5 5

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

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 : Calculate the azimuth of AB, then BC Calculate (X, Y) for BC Calculate (X, Y) for C C B A

But, if you were given a slope distance or a slope angle, you won’t 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. 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:

You set out a point, then you can set out a project. Calculate the angle ABC and the length of BC Setup the instrument, such as a theodolite, on B, aim at A 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. 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” 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

Angles and Directions

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 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) and Left (counterclockwise) Polygons

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

Distinguish between angles, directions, and readings. 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 Types of meridians: Magnetic: defined by a magnetic needle. 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. Grid: lines parallel to a central meridian Distinguish between angles, directions, and readings.

Angles and Azimuth Azimuth: Horizontal angle measured 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. 8 8

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. Azimuth and bearing: which quadrant? 9 9

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

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

Example (1)-Answer Line Azimuth 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

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) ?

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 10 10

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

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 (2)-Answer Line ΔE ΔN Quad. Calculated bearing tan-1(ΔE/ ΔN) Azimuth AB 110 170 1st 32° 54’ 19” AC 200 -120 2nd -59° 02’ 11” 120° 57’ 50” AD -150 3rd 38° 39’ 35” 218° 39’ 35” AE -200 120 4th 300° 57’ 50”

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.

Example (3) Answer DepAB = ΔEAB = 94.02, LatAB = ΔNAB = 68.13m C 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) 120 E C B A 115 90 110 105 30 D 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 Azimuth of DE = Bearing of CD + Angle D + 180 120 E C B A 115 90 110 105 30 D 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.

SOLVING THE RESECTION PROBLEM WITH WOLFPACK

Solving Triangle Problems with WolfPack