TOPIC 4ANGLE AND DIRECTION

MEASUREMENT

MS SITI KAMARIAH MD SA’ATLECTURER

SCHOOL OF BIOPROCESS ENGINEERINGsitikamariah@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.

Relationship between “true” meridian and grid meridians

Figure 4.2

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 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

Figure 4.7

Reverse DirectionsFigure 4.8

Reverse Bearings

Line Bearing

AB N 62o 30’ E

BA S 62o 30’ W

Line Bearing

AB N 62o 30’ E

BA S 62o 30’ W

Reverse Direction

CD has an azimuths of 128o 20’ DC has an azimuths of 308o 20’

To reverse azimuths: add 180o

Figure 4.8

Reverse Bearings

Line Azimuths

CD 128o 20’

DC 308o 20’

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

Start

Given

Finish

Check

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

Need to: measure 90° angle at point X

d d

Lay off distance d either side of X

X

l l

Swing equal lengths (l)

Connect point of intersection and X

Determining Angles – Taping

A

B

C

Need to: measure angle at point A

Measure distance ABMeasure distance ACMeasure distance BC

Compute angle

)AB)(AC2(

BCABACcos

222

1α

Determining Angles – Taping

A

B

C

Need to: measure angle at point A

AP

PQtan 1α

Q

Lay off distance APEstablish QP AP

Measure distance QP

Compute angle

P

Determining Angles – Taping

A

B

C

Need to: measure angle at point A

)AD2(

DE)sin(0.5 α

D

Lay off distance ADLay off distance AE = AD

Measure distance DE

Compute angle E

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

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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