Geodesy, GPS & GIS WEEK – 08 ITU DEPARTMENT OF GEOMATICS ENGINEERING1 DEPARTMENT OF GEOMATICS ENGINEERING

AZıMUTH The azimuth of a line on the ground is its horizontal angle measured clockwise from the meridian to the line. Azimuth gives the direction of the line with respect to the meridian. In plan surveying azimuths are generally measured from the north. Azimuths may have values between 0 g and 400 g ( 0 – 360 degrees). ITU DEPARTMENT OF GEOMATICS ENGINEERING 2

The Azimuths from North for Each Lines Figure:1 ITU DEPARTMENT OF GEOMATICS ENGINEERING 3 Line Azimuth O – A 54 g O – B 133 g O – C 211 g O - D 334 g

ITU DEPARTMENT OF GEOMATICS ENGINEERING4 Figure:2 t AB = forward azimuth of AB line t BA = back azimuth of AB line AZIMUTH

ITU DEPARTMENT OF GEOMATICS ENGINEERING5 Figure:3 Figure:4 In plane surveying, forward azimuths are converted to back azimuths, and vice versa, by adding or subtracting 200 g. t AB t BA = t AB g t AB > 200 g —> t BA = t AB g AZIMUTH

ITU DEPARTMENT OF GEOMATICS ENGINEERING6 Figure:5 In plane surveys it is convenient to perform the work in a rectangular XY coordinate system. Direction of +X refers to north, Direction of +Y refers to east, Rectangular Coordinate System

ITU DEPARTMENT OF GEOMATICS ENGINEERING7 The x and y axes divide the plane into four parts. The quadrants are numbered clockwise starting with the upper right quadrant. QUADRANT ΔX ΔY I. QUADRANT + + II.QUADRANT - + III.QUADRANT - - IV.QUADRANT + - Rectangular Coordinate System

ITU DEPARTMENT OF GEOMATICS ENGINEERING8 Azimuth Calculation

ITU DEPARTMENT OF GEOMATICS ENGINEERING9 Fundamental Computation -1 Known: Unknown: Figure:8 Computation of Coordinates

ITU DEPARTMENT OF GEOMATICS ENGINEERING10 Fundamental Computation -1 Formula: ΔY = S AB. sin t AB ΔX = S AB. cos t AB Y B = Y A + ΔY = Y A + S AB sin t AB X B = X A + ΔX = X A + S AB cos t AB Figure:9 Computation of Coordinates

ITU DEPARTMENT OF GEOMATICS ENGINEERING11 Fundamental Computation -1 Question1: Known: A (Y A = m ; X A = m) S AB = m, t AB = 347 g.3540 Unknown: B (Y B ; X B ) Solution: Y B = (94.17 * sin( )) = = m X B = (94.17 * cos( )) = = m Computation of Coordinates

ITU DEPARTMENT OF GEOMATICS ENGINEERING12 Fundamental Computation -2 Known: Unknown: Figure: 10 Computation of Coordinates

ITU DEPARTMENT OF GEOMATICS ENGINEERING13 Fundamental Computation -2 Formula: ΔY = Y B – Y A ΔX = X B – X A Figure: 11 Computation of Coordinates

ITU DEPARTMENT OF GEOMATICS ENGINEERING14 Fundamental Computation -2 Formula: This equation is used for calculating the azimuth in first quadrant. Computation of Coordinates & Distaces

ITU DEPARTMENT OF GEOMATICS ENGINEERING15 Fundamental Computation -2 Formula: QUADRANT Δy / Δx Azimuth FIRST QUADRANT + / +t = t’ SECOND QUADRANT + / -t = 200 g – t’ THIRD QUADRANT - / -t = 200 g +t’ FOURTH QUADRANT - / +t = 400 g – t’ Computation of Coordinates & Distaces

ITU DEPARTMENT OF GEOMATICS ENGINEERING16 Fundamental Computation -2 Formula: Figure:12 Computation of Coordinates & Distaces

ITU DEPARTMENT OF GEOMATICS ENGINEERING17 Fundamental Computation -2 Ouestion2: Known: A (Y A = m ; X A = m) B(Y B = m ; X B = m) Unknown: S AB, t AB Solution: ΔY = Y B – Y A S AB = ΔX = X B – X A S AB = m Computation of Coordinates & Distaces

ITU DEPARTMENT OF GEOMATICS ENGINEERING18 Fundamental Computation -2 Solution: QUADRANT Δy / Δx Azimuth FIRST QUAD + / +t = t’ Computation of Coordinates & Distaces

ITU DEPARTMENT OF GEOMATICS ENGINEERING19 Fundamental Computation -3 Known: A(Y,X), B(Y,X), C(Y,X) Unknown: ß B Relationship Between Azimuths & Traverse Angles

ITU DEPARTMENT OF GEOMATICS ENGINEERING20 Fundamental Computation -3 Question3: Known: A(Y A =760.42m, X A = m) B(Y B =840.75m, X B = m) C(Y C = m, X C =272.41m) Unknown: α Figure:14 Formula: α = t AC - t AB Relationship Between Azimuths & Traverse Angles

ITU DEPARTMENT OF GEOMATICS ENGINEERING21 Fundamental Computation -3 Solution: Relationship Between Azimuths & Traverse Angles

ITU DEPARTMENT OF GEOMATICS ENGINEERING22 Fundamental Computation -4 Known: t AB, β B Unknown: t BC Figure:15 Relationship Between Azimuths & Traverse Angles

ITU DEPARTMENT OF GEOMATICS ENGINEERING23 Fundamental Computation (a) 16. (b) 16. (c) Relationship Between Azimuths & Traverse Angles

ITU DEPARTMENT OF GEOMATICS ENGINEERING24 Fundamental Computation -4 Formula: (16.a) K < 200 g ; K+ 200 g (n=1); t BC = t AB + β B g (16.b) 200 g < K < 600 g ; K g (n=-1); t BC = t AB + β B g (16.c) K > 600 g ; K g (n=-3); t BC = t AB + β B g _- Relationship Between Azimuths & Traverse Angles

ITU DEPARTMENT OF GEOMATICS ENGINEERING25 Fundamental Computation -4 Question4: Known: t AB = 115 g.1420 Unknown: t BC, t CD β B = 165 g.3140 β C = 235 g.2570 Relationship Between Azimuths & Traverse Angles

ITU DEPARTMENT OF GEOMATICS ENGINEERING26 Fundamental Computation -4 Solution: t’ BC = t AB + β B = 115 g g.3140 = 280 g.4560 *200 g < K < 600 g ; K g ; t BC = t AB + β B g t BC = t’ BC g = 80 g.4560 t’ CD = t BC + β C = 80 g g.2570 = 315 g.7130 *200 g < K < 600 g ; K g ; t CD = t BC + β C g t CD = t’ BC g = 115 g.7130 Relationship Between Azimuths & Traverse Angles

ITU DEPARTMENT OF GEOMATICS ENGINEERING27 Basic Surveying -The Theory and Practice, Oregon Department of Transportation, Geometronics Unit, Ninth Annual Seminar, February 2000, C.D. Ghilani, P.R. Wolf; Elementary Surveying, Pearson Education International Edition, Twelfth Edition, Ü.Öğün, Topografya Ders Notları, E.Tarı, M.Sahin, Surveying II Lecture Notes - Slides, U.Özerman, Topografya Ders Notları, Bahar 2010, References