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Chapter-3:�Angular Measurements

Dept. of Civil Engineering

Indus Institute of Tech. & Engg.

Subject: Elements of Civil & Environment Engineering

Subject Code:FY410021

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Topics to be covered (Teaching hours: 05)

Instruments used for angular measurement
Traversing
Principles of Compass Surveying
Types of compass : Overview
Types of bearings
Measurement of bearings

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Introduction

Points on the ground or on a map are related to each other through a horizontal distance and a horizontal angle (or direction).
Horizontal angular measurements are made between survey lines to determine angle between the lines.
A horizontal angle is the difference between two measured dirctions.

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Instruments used for Angular Measurement

When area is large , undulating and crowded with many details, triangulaion is not possible.
Thus it becomes essential to use some sort of instrument which enables us to measure horizontalangles or directions.
The instruments used for this purpose are:

Compass
Box-Sextant
Theodolite
Total station

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Traversing

Traversing is generally adopted when the area is large and undulating or where triangulation is not possible.
In traversing, the frame work consists of number of connected lines.

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Principle of Compass Surveying

The Principle of compass surveying is traversing; which involves a series of connected lines.
The magnetic bearings of the lines are measured by prismatic compass and the distances are measured by chain
Recommended when area I large , undulating and crowded with many details.
Not recommended where local attraction is suspected.

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Types of Compass

A compass is a small instrument essentially consisting of magnetic needle, a graduated needle, and a line of sight.
The compass cannot measure angle between two lines but directly measure angle of a line with reference to magnetic meridian .
There are two types of compass:

Prismatic compass
Surveyor’s compass

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Prismatic compass

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Temporary adjustments of a prismatic compass are :

Centering : Centering is the operation in which compass is kept exactly over the station from where the bearing is to be determined. The centering is checked by dropping a small pebble from the underside of the compass.
Leveling : Leveling of the compass is done with the aim to freely swing the graduated circular ring of the prismatic compass. The ball and socket arrangement on the tripod will help to achieve a proper level of the compass.
Focusing : The prism is moved up or down in its slide till the graduations on the aluminum ring are seen clear, sharp and perfect focus.

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Observing Bearing of Line:

Consider a line AB of which the magnetic bearing is to be taken.
By fixing the ranging rod at station B we get the magnetic bearing of needle wrt north pole.
The enlarged portion gives actual pattern of graduations marked on ring.

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Surveyor’s Compass

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It is similar to a prismatic compass except that it has a only plain eye slit instead of eye slit with prism and eye hole.
This compass is having pointed needle in place of broad form needle as in case of prismatic compass.
Working of Surveyor`s Compass:

Centering
Leveling
Observing the bearing of a line : In this compass ,the reading is taken from the top of glass and under the tip of north end of the magnetic needle directly. No prism is provided here.

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Difference between Prismatic Compass � and Surveyor

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Types of Meridian

Bearing of a line is always measured clockwise wrt to some reference line or direction. This fixed reference line is known as meridian. There three types of meridian:

Magnetic meridian: The direction shown by a freely suspended needle which is magnetized and balanced properly without any influence by other factors is known as magnetic meridian.
True meridian : True meridian is the line which passes through the true north and south.
Arbitrary meridian: In case of small works or in places where true meridian or magnetic meridian cannot be determined, then ,any direction of a prominent object is taken as a reference direction called as arbitrary meridian.

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Types of Bearings

The bearing of a line is the horizontal angle which it makes with a reference line(meridian).
There are four type of bearings they are as follows:

True Bearing: The true bearing of a line is the horizontal angle between the true meridian and the survey line. The true bearing is measured from the true north in the clockwise direction.
Magnetic Bearing: the magnetic bearing of a line is the horizontal angle which the line makes with the magnetic north.
Grid Bearing: The grid bearing of a line is the horizontal angle which the line makes with the grid meridian.
Arbitrary Bearing: The arbitrary baring of a line is the horizontal angle which the line makes with the arbitrary meridian.

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Measurement of Bearings

Can be measured in following systems:

Whole Circle Bearing System(WCB).
Quadrantal Bearing System(QB)

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Whole circle bearing system(W.C.B.)

The bearing of a line measured with respect to magnetic meridian in clockwise direction is called magnetic bearing and its value varies between 0ᴼ to 360ᴼ.
The quadrant start from north an progress in a clockwise direction as the first quadrant is 0ᴼ to 90ᴼ in clockwise direction , 2nd 90ᴼ to 180ᴼ , 3rd 180ᴼ to 270ᴼ, and up to 360ᴼ is 4th one.

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Quadrantal bearing system(Q.B.)

In this system, the bearing of survey lines are measured wrt to north line or south line which ever is the nearest to the given survey line and either in clockwise direction or in anti clockwise direction.

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Reduced Bearing

When the whole circle bearing is converted into Quadrantal bearing , it is termed as “REDUCED BEARING”.
Thus , the reduced bearing is similar to the Quadrantal bearing.
Its values lies between 0ᴼ to 90ᴼ, but the quadrant should be mentioned for proper designation.

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The following table should be remembered for conversion of WCB to RB.

W.C.B OF ANY LINE	QUADRANT IN WHICH IT LIES	RULES FOR CONVERSION	QUADRANT
0º TO 90º	I	RB=WCB	N-E
90º TO 180º	II	RB=180º-WCB	S-E
180º TO 270º	III	RB =WCB-180ᴼ	S-W
270º TO 360º	IV	RB=360ᴼ - WCB	N-W

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Fore bearing and Back bearing

The bearing of a line measured in the forward direction of the survey lines is called the ‘fore bearing’(F.B.) of that line.
The bearing of a line measured in direction backward to the direction of the progress of survey is called the ‘back bearing’(B.B.) of the line.