CE 371 Surveying

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ANGLE MEASURING

Dr. Ragab Khalil

Department of Landscape Architecture Faculty of Environmental Design

King AbdulAziz University Room LIE15

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Dr. Ragab Khalil KAU – FED – CE371 - Surveying

Overview

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• Introduction

• Kinds of Horizontal Angles

• Reference Meridian

• Bearing and Azimuth Angle

• Angle Measuring Instruments

• Theodolites

• Measuring angle methods

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Introduction

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•

An angle is determined by three elements:

1. reference line,

2. direction of turning; clockwise (cw)or counterclockwise (ccw), and

3. angle magnitude.

•

Units of angle measurement are three:

1. sexagesimal units of degrees, minutes, and seconds, 2. centesimal units of grads (gons),and

3. radians.

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Kinds of Horizontal Angles

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• Angles to the right: Measured clockwise from the rear station to the forward station with magnitudes from 0

^o

to 360

^o

.

• Angles to the left: measured counterclockwise

with similar magnitudes.

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Kinds of Horizontal Angles

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•

Interior angles: on the inside of a closed polygon, they can be angles to the right or to the left.

S (interior angles)= (n-2)x180^o

•

Exterior angles are on the outside of a closed polygon, they can be angles to the right or to the left.

S (exterior angles)= (n+2)x180^o

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Kinds of Horizontal Angles

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•

Deflection angles: Measured clockwise (R), or counterclockwise (L) from an extension of the back line to the forward station. Magnitudes are from 0^o to 180^o preceded by R or L letters

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Reference Meridian

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• It is the north-south reference line to which directions of lines are referred.

• Four kinds of meridians are used:

1. True (astronomic) meridian: it defines the direction of earth's geographic poles.

2. Magnetic meridian: it is defined by a freely suspended magnetic needle.

3. Grid meridian: it is the direction of true north for a selected central meridian of any coordinate system.

4. Assumed meridian: it is defined by the user in an arbitrary manner

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Bearing Angle

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•

It is the acute horizontal angle measured from either the north or south. Bearing is written as a number ≤ 90º with letter N or S preceding it, and with letter E or W following it.

N---W N---E

S---W S---E

N70E

S35E

S55W N30W

I

II III

IV

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Azimuth Angle

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• It is the clockwise angle measured from the north direction of the reference meridian.

Azimuth angle can take values from 0

^o

to 360

^o

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Relation Between Bearing And Azimuth

• example

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Back Bearing

• back bearing of a line is equal in magnitude but opposite in direction.

• If bearing of line AB is N70

^o

E, then back bearing of line AB will be S70

^o

W

• Back bearing of AB = Bearing of BA

B

A

N

E

S W

70

N

E

S W

70

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Back Azimuth

• If azimuth of line AB is ≤ 180º,

 the back azimuth = azimuth + 180o

• If azimuth of line AC is > 180o, then

 its back azimuth = azimuth - 180o

• Back azimuth of AB = Azimuth of BA

B

A

N

E

S W

70

N

E

S W

70+180=250

280 N

E

S W

280-180=100

C

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Calculation of Azimuths

• Azimuth of BC = Back Azimuth of AB + angle B (to the right)

• Example

• Compute azimuths of BC, CD and DE.

• ^Solution:

• Azimuth of AB=40^o

• Back azimuth of AB=180+40= 220^o

• Azimuth of BC=220+130=350^o

• Back azimuth of BC=350-180= 170^o

• Azimuth of CD=170+80=250^o

• Back azimuth of CD= 250-180= 70^o

• Azimuth of DE=70+320=390ô> 360ô (subtract 360ô) = 30ô

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Calculation of Bearings

• Example

• In the figure, angles to the right are measured at B, C, & D, if bearing of AB is 40^o, compute bearings of BC, CD & DE.

• Solution:

• Bearing of BC= N10^oW

• because 10 =180 - (40+130)

• Bearing of CD= S70^oW

• because 70 = 80-10

• Bearing of DE= N30^oE

• because 30 = 70+320-360

40 1010

We can compute Azimuth first then compute bearing

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Angle Measuring Instruments

• Compass

• Sextant

• Theodolite

• Total station

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Compass

• It consists of a magnetised pointer free to

align itself accurately with Earth's magnetic

field, which is of great assistance in navigation

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Sextant

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Sextant

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Theodolite

Theodolites are perhaps the most universal

surveying instruments, their primary use is for

accurate measurement or layout of horizontal

and vertical angles. A similar instrument

common in the U.S.A. is called "Transit".

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Circular vial

Vertical axis

Internal Focus

(For sighting object)

Slow motion tangent screw (up / down)

Horizontal circle

Vertical circle

Optical Plummet

Theodolite parts

Tubular vial

Leveling screw Slow motion tangent screw (left / right) Horizontal axis

Collimation axis

Alidade

Tribrach

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Theodolite axes

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Theodolite types

1. Optical mechanical theodolite

2. Electronic digital theodolite

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Theodolite types

Vernier Theodolite

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Theodolite types

Micrometer Theodolite

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Theodolite types

Digital Theodolite

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Total station

Theodolite types

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Double Centering

•

To eliminate many instrumental errors, an angle is measured first with face left, then the telescope is plunged (or inverted) and a second reading with face right is made, then the average is taken.

•

Double centering eliminates the following instrumental errors:

1. theodolite vertical axis is not perpendicular to the transverse axis,

2. telescope line of sight is not perpendicular to the transverse axis,

3. level vial axis is not parallel to the transverse axis.

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Measuring angles

• Repetition method

• Directional method

•

Closing the horizon method (Reiteration method)

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Repetition method

•

This method is used for very accurate work. In this method ,the same angle is added several times mechanically and the correct value of the angle is obtained by dividing the accumulated reading by the no. of repetitions.

•

The No. of repetitions made usually in this method is six, three with the face left and

three with the face right . o

A B

θ₁θ₂ θ₃

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Directional method

•

This method is another precise and comparatively less tedious method of measuring the horizontal angles.

•

It is generally preferred when several angles with multiple repetitions are to be measured at a particular station.

•

The needed angles are measured on face left (from left to right), then measured on face right (from right to left)

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Reiteration method

•

The same as directional method but including all angles around a point

•

This method consists in measuring several angles successively and finally closing the horizon at the starting point. The final reading of horizontal circle should be same as its initial reading.

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Summary

• Introduction

• Kinds of Horizontal Angles

• Reference Meridian

• Bearing and Azimuth Angle

• Angle Measuring Instruments

• Theodolites

• Measuring angle methods