Presentation on theme: "ANGLE AND DIRECTION MEASUREMENT"— Presentation transcript:
1 ANGLE AND DIRECTION MEASUREMENT TOPIC 4ANGLE AND DIRECTION MEASUREMENTMS SITI KAMARIAH MD SA’ATLECTURERSCHOOL OF BIOPROCESS ENGINEERING
2 IntroductionAn angle is defined as the difference in direction between two convergent lines.
3 Types of AnglesVertical anglesZenith anglesNadir angles
4 DefinitionA vertical angle is formed by two intersecting lines in a vertical plane, one of these lines horizontal.A zenith angle is the complementary angle to the vertical angle and is directly above the obeserverA Nadir angle is below the observer
6 MeridiansA line on the mean surface of the earth joining north and south poles is calledmeridian.Note:Geographic meridians are fixed, magnetic meridians vary with time and location.Figure 4.2Relationship between “true” meridian and grid meridians
11 Directions Azimuth Bearing An Azimuth is the direction of a line as given by an angle measured clockwise (usually) from the north.Azimuth range in magnitude from 0° to 360°.BearingBearing is the direction of a line as given by the acute angle between the line and a meridian.The bearing angle is always accompanied by letters that locate the quadrant in which line falls (NE, NW, SE or SW).
14 Relationships Between Bearings and Azimuths To convert from azimuths to bearing,a = azimuthsb = bearingQuadrantAnglesConversionNE0o 90oa = bSE90o 180oa = 180o – bSW180o 270oa = b +180oNW270o 360oa = 360o – b
15 Reverse Direction In figure 4.8 , the line AB has a bearing of N 62o 30’ EBA has a bearing of S 62o 30’ WTo reverse bearing: reverse the directionLineBearingABN 62o 30’ EBAS 62o 30’ WLineBearingABN 62o 30’ EBAS 62o 30’ WFigure 4.7Figure 4.8Reverse DirectionsReverse Bearings
30 Azimuth ComputationWhen computations are to proceed around the traverse in a clockwise direction,subtract the interior angle from the back azimuth of the previous course.When computations are to proceed around the traverse in a counter-clockwise direction, add the interior angle to the back azimuth of the previous course.
31 Azimuths ComputationCounterclockwise direction: add the interior angle to the back azimuth of the previous courseCourseAzimuthsBearingBC270o 28’N 89o 32’ WCD209o 05’S 29o 05’ WDE134o 27’S 45o 33’ EEA62o 55’N 62o 55’ EAB330o 00’N 30o 00’ W
32 Azimuths ComputationClockwise direction: subtract the interior angle from the back azimuth of the previous courseCourseAzimuthsBearingAE242o 55’S 62o 55’ WED314o 27’N 45o 33’ WDC29o 25’N 29o 05’ ECB90o 28’S 89o 32’ EBA150o 00’S 30o 00’ E
33 Bearing ComputationPrepare a sketch showing the two traverse lines involved, with the meridian drawn through the angle station.On the sketch, show the interior angle, the bearing angle and the required angle.
34 Bearing ComputationComputation can proceed in a Clockwise or counterclockwiseFigure 4.11Sketch for Bearings Computations
36 Comments on Bearing and Azimuths Advantage of computing bearings directly from the given data in a closed traverse, is that the final computation provides a check on all the problem, ensuring the correctness of all the computed bearings
37 Angle Measuring Equipment Plane tables (graphical methods)SextantsCompassTapes (or other distance measurement)Repeating instrumentsDirectional instrumentsDigital theodolites and total stations
38 Determining Angles – Taping Lay off distance d either side of XlSwing equal lengths (l)Connect point of intersection and XXNeed to: measure 90° angle at point X
39 Determining Angles – Taping Measure distance AB Measure distance AC Measure distance BCCompute angle BACNeed to: measure angle at point A
40 Determining Angles – Taping ABCLay off distance AP Establish QP AP Measure distance QPCompute angle PQNeed to: measure angle at point A
41 Determining Angles – Taping ABCDLay off distance AD Lay off distance AE = AD Measure distance DECompute angle ENeed to: measure angle at point A
42 Repeating Instruments Very commonly usedCharacterized by double vertical axisThree subassemblies
43 Directional Instruments Has single vertical axisZero cannot be setMore accurate but less functional
44 Total StationsCombined measurementsDigital display
45 Measuring Angles Instrument handling and setup Discussed in labProcedure with repeating instrument
46 Angles Backsight: The baseline or point used as zero angle. All angles have three partsBacksight: The baseline or point used as zero angle.Vertex: Point where the two lines meet.Foresight: The second line or point
47 Repetition and Centering Repetition provides advantagesCentering process