Angles and Directions الزوایا و الاتجھات

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1 Section I Surveying Measurements Leveling, horizontal and slope distance, angles and directions 2. Angles and Directions Angles and Directions الزوایا و الاتجھات

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.

2 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. 2- Directions: 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 Distinguish between angles, directions, and readings. الانحراف Angles and Azimuth Azimuth: Horizontal angle measured clockwise from a meridian (north) to the line, at the beginning of the line -The line A starts at A, the line A starts at.

3 Azimuth and earing الانحراف و الانحراف المختصر earing (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 or S before and the letter E or W after the angle. For example: 30W is in the fourth quad الرابع. الربع Azimuth and bearing: which quadrant ربع اى? 4 th QUAD. AZ = AZ = 1 ST QUAD. E 3 rd QUAD. AZ = AZ = nd QUAD.

4 Departures and Latitudes المركبات السینیة و الصادیة ΔΧ ΔΥ ΔE Δ L* L* sin(az) cos(az 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 tan(az A) = E E E A A Departure Latitude E L * sin( L * cos( AZ ) AZ ) E = E A + E A = A + A Azimuth C = Azimuth A +?

5 AZ C = AZ A C AZ A 180 AZ A AZ C A AZ C = AZ A AZ C AZ A 180 AZ A A C

6 C انحراف خط = انحراف الخط قبلھ ± الزاویھ الداخلھ A A C Azimuth of a line such as C = Azimuth of A ± The angle +180 Sign is + if the polygon is to the right clockwise : angles measured clockwise, letters are in a counterclockwise sequence. Easting and orthing P (E,) α L In many parts of the world, a slightly different form of notation is used. instead of (x,y) we use E, (Easting, orthing). In Egypt, the Easting comes first, for example: (100, 200) means that easting is 100 In the US, orthing might be mentioned first. It is a good practice to check internationally produced coordinate files before using them. E

7 Polar Coordinates +P (r, u ) 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) Examples

8 Example (1) Calculate the reduced azimuth of the lines A and AC, then calculate the reduced azimuth (bearing) of the lines AD and AE Line Azimuth A AC AD S W A E W Reduced Azimuth (bearing) Example (1)-Answer Line Azimuth Reduced Azimuth (bearing) A S E AC W AD S W A E W

9 Example (2) Compute the azimuth of the line : - A if Ea = 520m, a = 250m, Eb = 630m, and b = 420m - AC if Ec = 720m, c = 130m - AD if Ed = 400m, d = 100m - AE if Ee = 320m, e = 370m ote: 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 orth. Assume that the azimuth of the line A is (α A ), the bearing is = tan -1 (ΔE/ Δ) If we neglect the sign of as given by the calculator, then, 1st Quadrant : α A =, 2nd Quadrant: α A = 180, 3rd Quadrant: α A = 180 +, 4th Quadrant: α A = 360 -

10 - For the line (ab): calculate ΔE ab = E b E a and Δ ab = b a - If both Δ E, Δ are - ve, (3rd Quadrant) α ab = = If bearing from calculator is 30 & Δ E is ve& Δ is +ve α ab = = 330 (4th Quadrant) - If bearing from calculator is 30& ΔE is + ve& Δ is ve, α ab = = 150 (2nd Quadrant) - If bearing from calculator is 30, you have to notice if both ΔE, Δ are + ve or ve, If both ΔE, Δ are + ve, (1st Quadrant) α ab = 30 otherwise, if both ΔE, Δ are ve, (3 rd Quad.) α ab = = 210 Example (2)-Answer Line ΔE Δ Quad. Calculated bearing tan-1( 1(ΔE/ Δ) Azimuth A st AC nd AD rd AE th

11 Example (3) The coordinates of points A,, 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 A and C b) The azimuth of the lines A and C. c) The internal angle AC d) The line AD is in the same direction as the line A, but 20m longer. Use the azimuth equations to compute the departure and latitude of the line AD. Example (3) Answer a) Dep A = ΔE A = 94.02, Lat A = Δ A = 68.13m Dep C = ΔE C = , Lat C = Δ C = m b) Az A = tan-1 (ΔE/ Δ) = Az C = tan-1 (ΔE/ Δ) = c) clockwise : Azimuth of C = Azimuth of A - The angle +180 Angle AC = AZ A - AZ C = = = A C

12 d) AZ AD : The line AD will have the same direction (AZIMUTH) as A = LAD = (94.02)2 + (68.13)2 = m Calculate departure = ΔE = L sin (AZ) = 94.02m latitude = Δ= L cos (AZ)= 68.13m Example (4) E A D In the right polygon ACDEA, 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. C

13 Example (4) - Answer E A CHECK : earing of CD = earing of C + Angle C D 30 = = (subtracted from 360), O. K earing of DE = earing of CD + Angle D = = 320 earing of EA = earing of DE + Angle E = = 245 (subtracted from 360) earing of A = earing of EA + Angle A = = 180 (subtracted from 360) earing of C = earing of A + Angle = = 120 (subtracted from 360) C Instruments Regular and Digital Theodolites Regular Theodolites: theologies measure the horizontal and vertical angles by measuring the amount of rotation around a horizontal and a vertical axes on graded circles

14 Gurley Antique Thodolite Digital Theodolites Can read and record horizontal and vertical angles in digital format

15 Total Stations Measure angles and distances and performs computations A total station includes a digital thodolite for angles, an EDM for distances, and a processor for computations.

16 Prism and sighting target Pole and tripod Aiming at a prism through the telescope of a total station in a zoo!

17 Multi Prisms, or group for a longer distance

18 Total station Vs EDM. Data collectors. Prismless total stations Robotic and Prismless Total Stations Methodology Advantages

Plane Surveying Traverse, Electronic Distance Measurement and Curves. Introduction

Plane Surveying Traverse, Electronic Distance Measurement and Curves Civil Engineering Students Year (1) Second semester Phase II Dr. Kamal M. hmed Raw LIDR point cloud, Capitol Forest, W LIDR points colored