ANGLE AND DIRECTION MEASUREMENT TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my

Introduction An angle is defined as the difference in direction between two convergent lines.

Types of Angles Vertical angles Zenith angles Nadir angles

Definition A 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 obeserver A Nadir angle is below the observer

Three Reference Directions - Angles

Meridians A line on the mean surface of the earth joining north and south poles is called meridian. Note: Geographic meridians are fixed, magnetic meridians vary with time and location. Figure 4.2 Relationship between “true” meridian and grid meridians

Geographic and Grid Meridians

Horizontal Angles A horizontal angle is formed by the directions to two objects in a horizontal plane. Interior angles Exterior angles Deflection angles

Closed Traverse

Open Traverse

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°. Bearing Bearing 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).

Azimuths

Bearing

Relationships Between Bearings and Azimuths To convert from azimuths to bearing, a = azimuths b = bearing Quadrant Angles Conversion NE 0o  90o a = b SE 90o  180o a = 180o – b SW 180o  270o a = b +180o NW 270o  360o a = 360o – b

Reverse Direction In figure 4.8 , the line AB has a bearing of N 62o 30’ E BA has a bearing of S 62o 30’ W To reverse bearing: reverse the direction Line Bearing AB N 62o 30’ E BA S 62o 30’ W Line Bearing AB N 62o 30’ E BA S 62o 30’ W Figure 4.7 Figure 4.8 Reverse Directions Reverse Bearings

Reverse Direction Line Azimuths CD has an azimuths of 128o 20’ DC has an azimuths of 308o 20’ To reverse azimuths: add 180o Line Azimuths CD 128o 20’ DC 308o 20’ Figure 4.8 Reverse Bearings

Counterclockwise Direction (1) Start Given

Counterclockwise Direction (2)

Counterclockwise Direction (3)

Counterclockwise Direction (4)

Counterclockwise Direction (5) Finish Check

Sketch for Azimuth Computation

Clockwise Direction (1) Start Given

Clockwise Direction (2)

Clockwise Direction (3)

Clockwise Direction (4)

Clockwise Direction (5) Finish Check

Finish Check Start Given

Azimuth Computation When 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.

Azimuths Computation Counterclockwise direction: add the interior angle to the back azimuth of the previous course Course Azimuths Bearing BC 270o 28’ N 89o 32’ W CD 209o 05’ S 29o 05’ W DE 134o 27’ S 45o 33’ E EA 62o 55’ N 62o 55’ E AB 330o 00’ N 30o 00’ W

Azimuths Computation Clockwise direction: subtract the interior angle from the back azimuth of the previous course Course Azimuths Bearing AE 242o 55’ S 62o 55’ W ED 314o 27’ N 45o 33’ W DC 29o 25’ N 29o 05’ E CB 90o 28’ S 89o 32’ E BA 150o 00’ S 30o 00’ E

Bearing Computation Prepare 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.

Bearing Computation Computation can proceed in a Clockwise or counterclockwise Figure 4.11 Sketch for Bearings Computations

Sketch for bearing Computation

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

Angle Measuring Equipment Plane tables (graphical methods) Sextants Compass Tapes (or other distance measurement) Repeating instruments Directional instruments Digital theodolites and total stations

Determining Angles – Taping Lay off distance d either side of X l Swing equal lengths (l) Connect point of intersection and X X Need to: measure 90° angle at point X

Determining Angles – Taping Measure distance AB Measure distance AC Measure distance BC Compute angle  B  A C Need to: measure angle  at point A

Determining Angles – Taping  A B C Lay off distance AP Establish QP AP Measure distance QP Compute angle  P Q Need to: measure angle  at point A

Determining Angles – Taping  A B C D Lay off distance AD Lay off distance AE = AD Measure distance DE Compute angle  E Need to: measure angle  at point A

Repeating Instruments Very commonly used Characterized by double vertical axis Three subassemblies

Directional Instruments Has single vertical axis Zero cannot be set More accurate but less functional

Total Stations Combined measurements Digital display

Measuring Angles Instrument handling and setup Discussed in lab Procedure with repeating instrument

Angles Backsight: The baseline or point used as zero angle. All angles have three parts Backsight: The baseline or point used as zero angle. Vertex: Point where the two lines meet. Foresight: The second line or point

Repetition and Centering Repetition provides advantages Centering process

“Centering”

Measuring Angles Procedure with directional instruments Most total stations are directional instruments

Angle Measuring Errors and Mistakes Instrumental errors Natural errors Personal errors Mistakes

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