Angular measurement

Introduction
• There are two methods for angular
measurement:
• 1) Triangulation Survey
• 2) Traverse Survey

Triangulation Survey
In the past it was difficult to accurately measure very long
distances, but it was possible to accurately measure the angles
between points many kilometres apart, limited only by being
able to see the distant beacome. This could be anywhere from
a few kilometres, to 50 kilometres or more. Triangulation is a
surveying method that measures the angles in a triangle
formed by three survey control points. Using trigonometry and
the measured length of just one side, the other distances in
the triangle are calculated.

Traverse Survey
DEFINITION:- Traversing is that type of survey in which a
number of connected survey lines form the framework and
the directions and lengths of the survey lines are measured
with the help of an angle measuring instrument and a tape or
chain respectively.
TYPES OF SURVEYING
There are two types of traverse surveying. They are:
• Closed traverse: When the lines form a circuit which ends
at the starting point, it is known as closed traverse.
• Open traverse : When the lines form a circuit ends
elsewhere except starting point, it is said to be an open
traverse.

Checks on traverse: Closed traverse
• Check on closed traverse:
– Sum of the measured interior angles (2n-4) x 90°
– Sum of the measured exterior angles (2n+4) x 90 °
– The algebric sum of the deflection angles should be equal
to 360°. Right hand deflection is considered +ve, left hand
deflection –ve
• Check on linear measurement
– The lines should be measured once each on two different
days (along opposite directions). Both measurement
should tally.
– Linear measurement should also be taken by the stadia
method. The measurement by chaining and stadia method
should tally.

Checks on traverse: Open traverse
• Taking cut-off lines: measured
the bearings and lengths of cut
off lines after plotting and tally
with actual values.
• Taking an auxiliary point: Take P
permanent point as auxiliary
point measured bearings and
lengths of P from each traverse
point. If survey is accurate,
while plotting all the measured
bearing of P should meet at P.

Compass
• A compass is a small instrument essentially
consisting of a graduated circle, and a line of
sight.
• The compass can not measures angle between
two lines directly but can measure angle of a
line with reference to magnetic meridian at
the instrument station point is called magnetic
bearing of a line.

Types of compass
• There are two types of magnetic compass they
are as follows:-
• The Prismatic Compass
• The Surveyor’s Compass
• The Transit Compass

Elements of prismatic compass
• Cylindrical metal box: Cylindrical metal box is having diameter of 8to 12 cm. It protects the
compass and forms entire casing or body of the compass. It protect compass from dust, rain etc.
• Pivot: pivot is provided at the center of the compass and supports freely suspended magnetic
needle over it.
• lifting pin and lifting lever: a lifting pin is provided just below the sight vane. When the sight vane
is folded, it presses the lifting pin. The lifting pin with the help of lifting lever then lifts the magnetic
needle out of pivot point to prevent damage to the pivot head.
• Magnetic needle: Magnetic needle is the heart of the instrument. This needle measures angle of a
line from magnetic meridian as the needle always remains pointed towards north south pole at two
ends of the needle when freely suspended on any support.
• Graduated circle or ring: This is an aluminum graduated ring marked with 0ᴼ to 360ᴼ to measures
all possible bearings of lines, and attached with the magnetic needle. The ring is graduated to half a
degree.
• Prism : prism is used to read graduations on ring and to take exact reading by compass. It is placed
exactly opposite to object vane. The prism hole is protected by prism cap to protect it from dust
and moisture.

• Object vane: object vane is diametrically opposite to the prism and eye
vane. The object vane is carrying a horse hair or black thin wire to sight
object in line with eye sight.
• Eye vane: Eye vane is a fine slit provided with the eye hole at bottom to
bisect the object from slit.
• Glass cover: its covers the instrument box from the top such that needle
and graduated ring is seen from the top.
• Sun glasses: These are used when some luminous objects are to be
bisected.
• Reflecting mirror: It is used to get image of an object located above or
below the instrument level while bisection. It is placed on the object vane.
• Spring brake or brake pin: to damp the oscillation of the needle before
taking a reading and to bring it to rest quickly, the light spring brake
attached to the box is brought in contact with the edge of the ring by
gently pressing inward the brake pin

Temporary adjustment of prismatic
compass
• The following procedure should be adopted after fixing the prismatic
compass on the tripod for measuring the bearing of a line.
• 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. If the pebble falls on the top of the peg then the centering is
correct, if not then the centering is corrected by adjusting the legs of the
tripod.
• 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. This can be checked by rolling round pencil on glass cover.
• 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. The position
of the prism will depend upon the vision of the observer.

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.
NORTH
OBJECT B
A
SOUTH
LINE OF
SIGHT
90
180
270
0

The Surveyor`s Compass
• 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
• 1) CENTERING
• 2) LEVELING
• 3) OBSERVING THE BEARING OF A LINE
• First two observation are same as prismatic
compass but third observation differs from that.
• 3) 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.

Meridian
• Bearing of a line is always measured clockwise wrt some reference line or
direction. This fixed line is known as meridian.
• There three types of meridian:
• 1) Magnetic meridian: The direction shown by a freely suspended needle which is
magnetized and balanced properly without influenced by any other factors is
known as magnetic meridian.
• 2) True meridian : True meridian is the line which passes through the true north
and south. The direction of true meridian at any point can be determined by either
observing the bearing of the sun at 12 noon or by sun’s shadow.
• 3) 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.

BEARINGS
• The bearing of a line is the horizontal angle which it makes with a
reference line(meridian).
• Depending upon the meridian , there are four type of bearings they are as
follows:
• 1) 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.
• 2) Magnetic Bearing: the magnetic bearing of a line is the horizontal angle
which the line makes with the magnetic north.
• 3) Grid Bearing: The grid bearing of a line is the horizontal angle which the
line makes with the grid meridian.
• 4) Arbitrary Bearing: The arbitrary baring of a line is the horizontal angle
which the line makes with the arbitrary meridian.

BEARINGS
TRUE
MERIDIAN
MAGNETIC
MERIDIAN
TRUE BEARING
MAGNETIC
BEARING
A
B
MN
TN

Designation of bearing
• The bearing are designated in the following
two system:-
• 1) Whole Circle Bearing System.(W.C.B)
• 2) Quadrantal Bearing System.(Q.B)

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.

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

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.

Quadrantal bearing system(Q.B.)

Reduced bearing (R.B)
• 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.

conversion of WCB to RB.
Line W.C.B Between Rule For R.B Quadrant
AB 0◦ and 90◦ R.B=W.C.B NE
AC 90◦ and 180◦ R.B=180◦-W.C.B SE
AD 180◦ and 270◦ R.B=W.C.B-180◦ SW
AF 270◦ and 360◦ R.B=360◦-W.C.B NW
conversion of RB to WCB .
Line R.B Rule For R.B Quadrant
AB Nq1E R.B=W.C.B 0◦ and 90◦
AC Sq2E W.C.B=180◦-R.B 90◦ and 180◦
AD Sq3E W.C.B=180◦+R.B 180◦ and 270◦
AF Nq4W W.C.B=360◦-R.B 270◦ and 360◦

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.

FB of line AB
BB of line AB
A
NORTH
NORTH
Θ1 Θ2
B
FB of AB = Θ1(from A to B)
BB of AB= Θ2(from B to A)
Remembering following points:
1) In the WCB system ,the differences
b/n the FB and BB should be exactly
180ᴼ. Remember the following
relation :
BB=FB+/-180ᴼ
+ is applied when FB is <180ᴼ
- is applied when BB is >180ᴼ
2) In the reduced bearing system the FB
and BB are numerically equal but the
quadrants are just opposite.

Computation of Angles
• Observing the bearing of the
lines of a closed traverse, it is
possible to calculate the
included angles, which can be
used for plotting the traverse.
• At the station where two
survey lines meet, two angles
are formed-an exterior angles
and an interior angles. The
interior angles or included
angle is generally the smaller
angles(<180ᴼ).
A
B
C
D

• Magnetic declination: The horizontal angle between the
magnetic meridian and true meridian is known as magnetic
declination.
• Dip of the magnetic needle: If the needle is perfectly
balanced before magnetisation, it does not remain in the
balanced position after it is magnetised. This is due to the
magnetic influence of the earth. The needle is found to be
inclined towards the pole. This inclination of the needle with
the horizontal is known as dip of the magnetic needle.
• Local Attraction
• Method of correction for traverse:
– First method: Sum of the interior angle should be equal to
(2n-4) x 90. if not than distribute the total error equally to
all interior angles of the traverse. Then starting from
unaffected line the bearings of all the lines are corrected
using corrected interior angles.
– Second method: Unaffected line is first detected. Then,
commencing from the unaffected line, the bearing of other
affected lines are corrected by finding the amount of
correction at each station.

Problems:
• Convert the following WCBs to QBs
– (a) WCB of AB = 45°30’
(Ans 45°30’)
– (b) WCB of BC = 125°45’
(Ans 180- 125°45’ = 54° 15’)
• Fore bearing of the following lines are given. Find back bearing
– AB=S 30°30’ E
– BC=N 40°30’ W
• The magnetic bearing of a line AB is 135°30’ what will be the true bearing, if the
declination is 5°15’ W.

Problems
Included angle at A= 280-180-40=60
=FB of DA-180-FB of AB
Included angle at B= 40+180-70= 150
=FB of AB+180-FB of BC
Included angle at C= 70+180-210
=FB of BC+180-FB of CD
Formula: FB of previous line+/-180-
FB of next line

CHAIN SURVEYING
• SUMMARY & ABSTRACT:
• Chain (Tape) surveying is the simplest form of
detail surveying. In this method the lengths of
lines marked on the field are measured, while the
details are measured by offsets and ties from
these lines. This field work will continue for 3
field hours. Every group is expected to submit a
detailed report besides the final plan of the area
surveyed.

OBJECTIVES:
• This field work aimed to train the student on the
following process:
• Selection of a frame work (chain or base lines)
and control points.
• Direct method of linear measurements
(horizontal distance measurement).
• Setting out right angles (offsets).
• Determining the direction of any line in the field
with respect to magnetic north "bearing".
• Booking Method.
• Plotting Method.

APPARATUS & INSTRUMENT
• 2 Tapes
• 3 Ranging Rods
• Arrows/Marker paints
• Prism Square
• Prismatic Compass
• Booking Board

PROCEDURE:
• Make a reconnaissance of the area and select a suitable framework
(chain lines) and stations based on the criterion given in Note 1.
• Mesure all the chain (based) lines once in each direction using the
direct measurement method. See Note 2.
• Measure the offsets/or ties from every necessary point on the
detail to the corresponding base line. Use the procedure explained
in Note 3.
• You may need some measurements on the details (on the building
sides…).
• Measure the bearing of one of the chain lines by using the prismatic
compass. See Note 4.
• Record all the information and measurements properly in the
booking papers as explained in Note 5.
• Make the necessary calculations and corrections.
• Draw the details in a suitable scale to produce a detailed map of the
area. See Note 6.

• Note 1: CHAIN LINES & STATIONS SELECTIONS
•
• To locate a suitable stations and chain lines, a reconnaissance of the
area should be undertaken by walking around the area required to
be surveyed. Any obstacles should be noticed. The selected stations
should produce a well formed linked triangles or braced
quadrilaterals.
• The principles to be considered are:
• Few long lines should be used.
• Avoid any obstacles to ranging or chaining.
• Angles should be > 30o & <120o.
• Make check lines when possible to detect errors when plotting.
• The lines should be closed to the details (Avoid long offsets (>10m)
and ties.
• After selection of the framework you should draw sketch of the
area and mark the stations by wooden pegs or marker paints, and
give a number for each station.

NOTE 2: DIRECT DISTANCE MEASUREMENT
• For measuring any distance between A and B, especially when it is
longer than the tape length, the following ranging is needed:
"ranging by eye".
• The ranging rode should be placed at the beginning point A and the
end point B. The first man should place the tape zero point at A.
• The second man holding the third raging rod and the tape should
move to the direction of B to a point of the end of the tape length.
Then he should hold the ranging rod vertically.
• The first man at point A lines up the ranging rod with that on point
B. "by sighting as low as possible".
• Then, the second man should straighten the tape and mark this
point.
• Both men move ahead repeat the whole steps beginning from the
first mark.
• As measurements processes, the second man should record the
length.

Note 3: SETTING THE OFFSET
• Any point on the detail can be related to the chain line by offset or
ties. This is accomplished by measuring all X's and Y's as shown in
the figure.
• To set out offsets, a prism square can be used. To locate the point at
which a 1 from any point on the feature would meet the chain line
(say AB) you can follow the following steps:
• One man should hold the ranging pole at the given point, while the
other pole is placed at any point on the chain line AB.
• The observer holds the instrument and walk along the line AB until
he see both poles coincide in each other. Then the distance to this
point along the chain line can be measured beside the length of the
perpendicular.
• Another method can be used by holding the zero point of the tape
at the given point and swinging tape over the chain line and mark
the point on the chain line at minimum reading.

NOTE 4: MEASURING THE BEARING OF A LINE
• To measure the angle that any line makes with the
magnetic direction, you can use a prismatic compass.
The procedure is as follow:
• Place the ranging pole vertically at point B.
• Place the prismatic compass over its tripod at point A
and level it using the bubble and screws.
• Rotate the compass until it is directed to the pole
and read the angle.
• Repeat the whole procedure for point B.

NOTE 5: BOOKING
• The field book should be neat and consistent:
• Each chain line is represented by double line
drawn through the corner of the page.
• Entries start at the bottom of the page.
• Detail that is on the right-hand side of the line
is booked on the right-hand side of the page
and voice versa.
• The lengths from the beginning of the line are
written inside the double lines while the offset
lengths outside.

NOTE 6: PLOTTING
• A. Plot the framework of chain lines by:
• Draw the longest line according to its bearing.
• Build up the other chain lines by using beam
compasses.
• Draw the check lines, and if there are any errors,
check the drawn lines in the incorrect triangles.
(You may need to measure them in the field).
•
• B. Draw the detail for each chain line based on
offsets and ties information. Then connect these
points to get the details.

Angular measurement

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