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**ANGLE AND DIRECTION MEASUREMENT**

TOPIC 4 ANGLE AND DIRECTION MEASUREMENT MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING

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

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Types of Angles Vertical angles Zenith angles Nadir angles

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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

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**Three Reference Directions - Angles**

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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

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**Geographic and Grid Meridians**

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

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Closed Traverse

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Open Traverse

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**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).

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Azimuths

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Bearing

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**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

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**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

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**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

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**Counterclockwise Direction (1)**

Start Given

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**Counterclockwise Direction (2)**

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**Counterclockwise Direction (3)**

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**Counterclockwise Direction (4)**

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**Counterclockwise Direction (5)**

Finish Check

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**Sketch for Azimuth Computation**

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**Clockwise Direction (1)**

Start Given

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**Clockwise Direction (2)**

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**Clockwise Direction (3)**

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**Clockwise Direction (4)**

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**Clockwise Direction (5)**

Finish Check

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Finish Check Start Given

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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.

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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

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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

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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.

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

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**Sketch for bearing Computation**

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**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

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**Angle Measuring Equipment**

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

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**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

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**Determining Angles – Taping**

Measure distance AB Measure distance AC Measure distance BC Compute angle B A C Need to: measure angle at point A

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**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

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**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

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**Repeating Instruments**

Very commonly used Characterized by double vertical axis Three subassemblies

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**Directional Instruments**

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

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Total Stations Combined measurements Digital display

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**Measuring Angles Instrument handling and setup**

Discussed in lab Procedure with repeating instrument

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**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

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**Repetition and Centering**

Repetition provides advantages Centering process

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“Centering”

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**Measuring Angles Procedure with directional instruments**

Most total stations are directional instruments

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**Angle Measuring Errors and Mistakes**

Instrumental errors Natural errors Personal errors Mistakes

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THANK YOU

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