Code No: LM for practice

FUNDAMENTALS OF
SURVEYING

CTEVT, NLPI, KOICA, TU of Korea consortium

This learning materials was developed by the

collaboration between KOICA and CTEVT through

project for establishment of polytechnic institute for

construction workforce development in Province 2

in Nepal in 2025 with the fund of the republic of

Korea.
 Table of Contents
No. Job name Page Hours
1-1 Revision of Secondary level mathematics and
1 Science. Apply simple Algebraic formulae. Acquire 4 20
skill in Graphical plotting. Define Number System.

2 1-2 State different types of Measurement Units,

2 12
Define meter. Make conversions of Units
1-3 Be familiar with the concepts of lines and angles
and Geometry of Plane figures –Intersecting lines,
3 Parallel lines Triangles, Parallelograms, Quadrilaterals, 1 2
Polygons, Elements of simple circular Curves use
property of regular plane Geometric Figures

4 1-4 Define area, Determine area of regular and

2 4
irregular plane figures

5 1-5 Define volume, Define liter, Determine volumes of

solids bounded by plane surfaces 4 8

6 Generalize the boundary of given District/

Municipality Polygon
2 4

7 Observation for Colour Separation Sheets (2' 30" X 2'

30" Topographic Map; Four Colours) for Plate Making 1 2

8 Map Reproduction and Printing Process: Observation 1 2

of Map Printing Press

Total 15 30
 Hours
Job Name 1.a Perform Road survey

1. Understand the road alignment

2. Identify and establish control points
3. Understand the concept of curve setting.
Objectives 4. Perform detailing of route.
5. Perform L-section and x- section survey
6. Compute survey data
7. Prepare plans and profiles
Instruments Safety and
Materials Specification Quantity
1.Set up following
and Tools Caution
-Level - Sheet -Auto Level Level machine-1

2. Hold staff
Machine paper -3 or 5m staff Tripod-1 temporary adjustment.
-Tripod - Pencil -Peg: rigid suitable, Theodolite -1
-Theodolite - Eraser pointed and rigid Staff-2 perfectly vertical.
-Staff - Ink pen type Pegs-2 3.Prevent instruments
-Pegs -Tape:20m or 30m Tape-1 from rainfall or high
-Tape tape Hammer-1 heat.
-Hammer 4. Avoid working
on extreme
weather
conditions.

< Related Knowledge>

Road alignment survey
A road is an identifiable route, way or path
between two or more places.
Road alignment is the preliminary stage of road
construction. It is the survey which is used
select route for the construction of road or
highway
It allows to select short, easy, safe and
economic route for the construction of road.
Curve
Curve is arc of finite radius introduced between
to straights used to change the direction of path
gradually. It allows vehicle to pass easily from Figure 1.a- 1 Road alignment
one direction to another. It can be classified into
different categories as shown in figure below.
But we only study about simple circular curve
in details.

Figure 1.a- 2 Curve in road

Simple circular curve
A curve which consists of a single arc of a circle connecting two straights is called simple circular
curve. It is tangential to both the straight lines. It is commonly used to create curves with a constant
radius, such as in highways and railways, to provide a smooth and comfortable ride for vehicles and
trains. The curve is defined by its radius (R) and Deflection angle ( ∆ ), which determines the length
and geometry of the curve.
Elements of simple circular curve
a.) Point of curve or commencement or beginning of Curve (B.C): - The point from
where the curve Starts, is called point of curve. Also, it is the point where the alignment changes
from straight to Curve.
b) Point of tangency or end of curve (E.C): - The point where the curve ends are Called
point of tangency. It is the point where, the alignment changes from curve to straight.
c) Back tangent: - The tangent before starting of curve is called back tangent.
d) forward tangent: - The tangent after ending the curve is called forward tangent.
e) Long chord(L): - The Straight Line Joining the point of curve and point of tangency. is
Called Long Chord.
f) Length of curve (l): - It is the arc length Joining point of curve and point of tangency.
g) point of intersection (IP): - The point where the produced and extended back tangent and
forward tangent meet at a point is called point of intersection.
h) Tangent length: - The distance between point of Curvature and point of intersection or
the distance between point of tangency and point of intersection is called tangent length
i) Mid- Ordinate: - The distance between the midpoint of Curve and midpoint of Long
Chord is called mid ordinate.
j) Apex distance or external distance: - The distance between point of intersection to mid-
point of Curve is called apex distance.

Figure 1.a- 3 Simple circular curve with terminologies

<Operation Procedures of Road Alignment Survey>
 1. Planning
It is first stage of operation which basically
office operation, in this stages, relevant maps
and documents are collected from secondary
sources and a detailed plan for the field
operation is designed. In this stage best feasible
route or alignment is selected on an existing
map.

Factors to be considered while planning the best

route are: Figure 1.a- 4rrr

 Purposed route should pass through more

villages, cities, industrial and religious
areas.
 Route should pass perpendicularly through
river having less breadth.
 Route shouldn’t pass through middle of
religious areas, agricultural areas etc.
 Earth work should be as less as possible.
 Route should be passed through
geologically stable area.
Besides this, following tasks are also managed
 Team leader, Surveyors, Assistants Helpers
Porters, Cooks & others as per the project
requirement,
 Means of transportation (Aircraft, Horses,
Vehicle etc.) Figure 1.a- 5sss
 Instruments and Accessories.
 Tentative camping location.
 . Alternate routes to be examined and tentative
schedule of visiting them.
 List of local offices, representatives,
 knowledgeable persons to be visited.
 Field books and stationary.
 Control point's coordinates & D-cards.

2. Reconnaissance
Reconnaissance survey is conducted to collect the
topographical information between two terminals
for the best route. It is a preliminary examination of
the entire area to select the best route and estimate
the cost of project. Some works in Reconnaissance
survey are as follows:
a. Data of rivers, culverts, subways etc. are
collected.
b. Maximum discharge of river, HFL, breadth of
river etc. are collected.
c. Earthwork, volume and cost of proposed route
should be estimated.
d. For rough estimation of elevation, distance Figure 1.a- 6 Reconnaissance /site visit of area
instruments like altimeter, passometer etc. are
used.
3. Prepare Necessary Equipment
Different instruments are prepared. Tape is
used for distance measurement. Theodolite is
used for measurement of deflection angles.
Compass is used for measuring bearing of a IP
line. Pegs are used for marking the control
stations. Level machine is used for RL transfer
from benchmark nearby, L-section and Cross
section and staffs are used for taking readings
through level machine. Ranging Rods are used
to fix tangent points (PC & PT) from IP. Figure 1.a- 7 Equipment used in Road alignment
Survey
4. Alignment fixing and IP
establishment

 Road alignment selection i.e. IP selection

shall be carried out considering the
obligatory points, permissible gradient,
bridge site, balancing cut and fill, shape of
the valley and cross drainage, lateral slopes,
geometry of horizontal and vertical curves
etc.
 All the Ips should be fixed at the suitable
point on the ground
 If the external deflection angle at the I.P. of
the road is less than 3°, curves need not be
fitted.
 The deflection angle should not be greater Figure 1.a- 8 IP establishment for alignment
than 90 degrees.
 The radius of the curve was chosen such
that it was convenient and safe. The radius
of the curve should not be less than 15 m.
radius must be within the multiple of 5 or
10.
 Two successive curves must not be
overlapped.
 The gradient of the road had to be
maintained below 12 %.
Figure 1.a- 9 Road alignment along with IP
5. Deflection angle measurement
a) The instrument was setup & level
accurately at the station ‘B’
b) Both the plates wear clamped at the ‘B’
level & back sight was taken on the station
point.
c) The upper plate was in the clamped & the
fore sight of the station ‘B’ was taken. The
reading on both Vernier’s were recorded.
d) The lower clamp was unclamped & the
instrument was shifted to the station ‘A’
again. There was no change in the reading
as recorded in step 3 above.
e) The process was repeated & the
instruments was again sighted to ‘C’. The
readings on the both Vernier’s are
recorded.
f) As the deflection angle was doubled
because of the taking both face reading.
The average value of the deflection angle
was obtained by dividing the final reading
Figure 1.a- 10 Deflection angle measurement
by 2.

6. Setting out of curve

Before the setting out of curve, IP Point of
curve (P.C), Point of tangency (P. T) is located
in the field. It is located as shown below.
Chainage of PC= Chainage of IP –Tangent
length
Chainage of PT = Chainage of P.C+ curve
length
After locating P.C and P.T, different methods
can be applied for curve setting out as shown in Figure 1.a- 11 Curve setting out method
fig 1.a-11
 7. Chainaging of alignment
Since distances between IPs are known, and radius and deflection angle is calculated then field book
is filled up.

Line/Leg Chainage
IP to IP Deflection Angle = ± Δ

Station
From To of IP
Distance
IP IP station ± d m s

Radius
Tangent Length IP
Apex Chainage Chainage Chainage
of
Length of Curve, Distance, of BC of MC of EC Remarks
Curve,
TL (m) L (m) E (m) (km) (km) (km)
R (m)

Figure 1.a- 12 Chainaging the alignment along with tangent points .

8. Identification and establishment of control points.
If control point is available nearly our survey site, then control point is investigated with the help of
D –card. Control point is established if necessary and reference sketch is also prepared for TBM and
D-card can be prepared for PBM for future reference.

Figure 1.a- 14 D-Card

9. Transfer RL to the TBM (Fly levelling)

Reduced level (R. L) is transferred to the TBM
from Benchmark nearby (if available) by fly
levelling. Fly levelling is done as shown in the
table below .levelling is closed in (P)BM to the
last steps and permissible error should be within
24√ K
Where k= total circuit distance

Station BS FS HI RL Remarks
PBM
 Figure 1.a- 15 Fly levelling from BM to
TBM alignment

PBM
Table 1.a- 1Field book of Fly levelling
10. Perform L-section and Cross- Section
simultaneously
The operation of leveling carried out to
determine the elevations of the points at
known distances apart and also other salient
features along a given straight line is called
profile leveling. It is also called longitudinal
leveling.
Cross sections are run at perpendicular to the Figure 1.a- 16Profile of a plan
profile leveling and on either side of it for the
purpose of lateral outline of the ground nature.
For x-section there are two different approaches
can be applied
(1) equal interval approach
(2) Change in slope approach.
In equal interval approach the section is taken
perpendicular to the route at a particular interval
Figure 1.a- 17 Cross-section
(chainage) of the center line of the route in a
fixed interval. Where as in change in slope
approach the interval of the distance in the
section is not kept fixed but observations are
taken at the points along the x-section lines,
wherever the slope changes significantly.

L sections and X- sections are done

simultaneously or separately as per the
requirement. Figure 1.a- 18 L-Section & X-section both
Steps:
a) Set up the instruments nearby benchmark
and suitable position from where optimum
distances or readings can be taken.

b) Mark regular intervals along the proposed

alignment of the route. These intervals
typically range from 10,15m, 20m, or
depends upon the purpose or nature of
terrain. In figure, 10m is taken as regular
interval.
c) Cross section line is established
perpendicular to the main alignment (L-
section) at regular intervals or change in Figure 1.a- 21 Marking alignment for L-section
slope approach typically at station points.
d) Level instrument is set up at suitable place
 considering the clear sighting of optimum
cross section as shown in the Figure 1.a- 19
e) Levelling staff is used take staff readings at
regular intervals along the center and cross-
section line. Distances of the staff points
are measured with a tape, left and right of
the center station on the center line Record
Figure 1.a- 22 Instrument set up covering cross
the backsight(BS), intermediate (IS) and
section
foresight (FS) readings for each point as in
the Figure 1.a- 20

f) when it is not possible to read the staff

clearly at a great distance a fore sight is
taken on a relatively permanent point CP
not necessarily on the line of the profile.
Shift the level to another convenient
station sand take a back sight reading on
the change point (CP). Figure 1.a- 23 Taking staff reading(cross-
section)

11. Computation of Survey Data

All data are recorded in field book carefully as shown in the figure below. Calculate the RL of each
point using the formula:
HI = Known RL + BS
RL = HI –IS/FS
Check arithmetically by using formula
ƩBS-ƩFS= Last RL- First RL

Figure 1.a- 24 field book for survey data computation

Computation of survey data for RLs of all points are done as in the figure below.
Station Distance(m) Reading HI RL Remarks
L C R BS IS FS
BM 1.155 501.155 500 0+000 Chainage
0 1.234 499.921
R1 2 2.325 498.83
R2 4 2.222 498.933
R3 6 1.575 499.58
L1 2 2.321 498.834
L2 4 2.325 498.83
 L3 6 3.215 497.94
C 0 1.325 2.255 500.225 498.9 CP
R1 2 2.125 498.1 0+015Chainage
R2 4 2.222 498.003
R3 6 1.565 498.66
L1 2 2.321 497.904
L2 4 2.225 498
L3 6 2.215 498.01
Total ƩBS=2.48 ƩFS=4.47

Arithmetic Check:
ƩBS-ƩFS = Last RL-First RL
or,2.48-4.47=498.01-500
or,-1.99 =-1.99 Checked//

12. Preparation of plan and profiles

a. Preparation of plan.
Since the data of chainaging has been calculated already and deflection angle and radius has been
already determined, we draw the plan in suitable scale as shown in the Figure 1.a- 25 First with the
help of initial bearing, deflection angle and distances between IPs. we draw the lines at suitable scale
shown below in Figure 1.a- 26 Then by using design radius, and deflection angle, tangent length is
calculated and BC,MC.EC are marked as shown in the Figure 1.a- 27

Figure 1.a- 28 Drawing of IPs stations Figure 1.a- 29 Marking tangent points
Figure 1.a- 30 Plan Manually Figure 1.a- Plan through CAD
b. Preparation of profiles (L-section) & X-section
Steps:
i. Define the scale. Generally, the scale is defined as shown below;
Type Horizontal Vertical Remarks
(H) (V)
L-section 1cm=10m i.e. 1:1000 1cm=1m i.e. H= V/10
1:100
Scale
X-section 1cm=1m i.e. 1:100 1cm=1m H=V
i,e.1:100

ii. Horizontal distances are plotted along the horizontal axis to scale defined.
iii. The elevations are plotted along the vertical scale defined.
iv. Each ground point is thus plotted by the two coordinates (chainages and elevations).
 Horizontal distance; x- coordinate
 Vertical distance; y- coordinate
 Origin is assumed as per convenience i.e. below to lowest RL

.
Figure 1.a- 32 Designing X- &Y- axes
Figure 1.a- 33Plotting of profile in graph Figure 1. a- 34Plotting of profile CAD

Figure 1.a- 36 Cross sections at graphs Figure 1.a- Cross section at O+OOO Chainage

Figure 1.a- 37 Cross sections at Ec(End of curve) with chainage 0+057.10

Exercise
1. Plan for Road alignment
2. Reccee the area
3. Establish IPs
4. Chainage the IPs
5. Set out Curve
 6. Perform L-section and X-section
7. Plotting
Main items Sub items Fu Standards Score Remarks
ll
Planning Alignment 1. Study the area :3
fixation 5
2. Consider the factor :2
Reconnaissance 1. Site Visit :3
5
2. Minor relevant data collection:2
Field work IPs 1. Fix IPs:5
establishment 10
2. Chainage Ips:5
Curve Setting 1. Marks BC, MC, EC:5
10
2. Set out curve :5
Data collection 1. Set up instrument:3
2. Marking center line:2
15 3. Marking cross section lines:5
4. Take staff reading
completely::5
Standards

Compute 1. Elevation along center line :3

elevation 5 2. Elevation across center line:2
3. Wrong Calculation:-5
Check 5 1. Arithmetic Check:5
1. H-Scale &V-scale Design:5
Define scale 5
2. In appropriate Scale:-5
X & Y-axes 1. Place horizontal distance:3
5
2. Place elevation Value:2
Plotting Point Marking 1. Point Marks for profile :5
15 2. Point mark for X-Section:10
3. Wrong marking :-5
Join points 1. Join points for profile:5
10
2. Join points for X-section:5
Profile 1. Fill all the data for profile :5
Layout 2. Fill data for X-section :5
10
X-section 3. Wrong filling :-5
4. Damage of drawings:-5
 Hours
Job Name 1.b Water ………………..

8. Understand the road alignment

9. Identify and establish control points
10. Understand the concept of curve setting.
Objectives 11. Perform detailing of route.
12. Perform L-section and x- section survey
13. Compute survey data
14. Prepare plans and profiles
Instruments Safety and
Materials Specification Quantity
1.Set up following
and Tools Caution
-Level - Sheet -Auto Level Level machine-1

2. Hold staff
Machine paper -3 or 5m staff Tripod-1 temporary adjustment.
-Tripod - Pencil -Peg: rigid suitable, Theodolite -1
-Theodolite - Eraser pointed and rigid Staff-2 perfectly vertical.
-Staff - Ink pen type Pegs-2 3.Prevent instruments
-Pegs -Tape:20m or 30m Tape-1 from rainfall or high
-Tape tape Hammer-1 heat.
-Hammer 4. Avoid working
on extreme
weather
conditions.
 Hours
Job Name 2.Bridge Survey

1. Determine the bridge axis

2. Identify and establish control points
3. Understand the concept of Triangulation
4. Apply Reciprocal levelling
Objectives 5. Perform L-section and x- section survey covering upstream & downstream.
6. Find discharge of river.
7. Compute survey data
8. Prepare plans and profiles
Instruments Safety and
Materials Specification Quantity
1.Set up following
and Tools Caution
-Level - Sheet -Auto Level Level machine-1

2. Hold staff
Machine paper -3 or 5m staff Tripod-1 temporary adjustment.
-Tripod - Pencil -Peg: rigid suitable, Theodolite -1
-Theodolite - Eraser pointed and rigid Staff-2 perfectly vertical.
-Staff - Ink pen type Pegs-2 3.Prevent instruments
-Pegs -Tape:20m or 30m Tape-1 from rainfall or high
-Tape tape Hammer-1 heat.
-Hammer 4. Avoid working
on extreme
weather

< Related Knowledge>

conditions.

Bridges are structures that are constructed to

connect places separated by deep valleys or
gorges or rivers and streams. Bridges are
usually the cross drainage and hence a part of
roads making them shorter and hence
economical. For places, where the ground is
uneven and undulated and where the number of Figure 2- 1 Bridge
rivers is large, bridges are the most economic
and efficient way.
Bridge site survey
It provides the preliminary knowledge on
selecting and planning of possible bridge site and
axis for the future construction of the bridge by
collecting the preliminary data about the site such
as normal water flow level, high flow level
geological features of the ground for planning and Figure 2- 2 Bridge Site Survey

designing of the bridge

< Operation procedures>
1. Planning
Planning is very essential steps before
reconnaissance and other essential field work. It
optimizes resources, ensures accuracy, and
delivers high-quality field data. Planning
involves defining the overall strategy for the
bridge survey project. A better planning
symbolizes the good efforts, being pre-alert to
problems and obstacles, this is an office work
which is done before going to the field. It
involves following activities
a. Gathering existing information and relevant
documents Figure 2- 3 Base map study
b. Studying base map and other spatial
information from secondary sources
c. Discussing with local people, stakeholders
and other knowledge us persons
d. Managing team members and other human
resources
e. Analyzing different facilities and scenario of
site
f. Tentative camping location
g. Control point’s coordinates and D-card
h. Miscellaneous
Figure 2- 4 Analyzing existing map for
2. Reconnaissance /site visit
tentative axis location
The preliminary inspection of the area to be
surveyed is called reconnaissance where we go
directly in the field to visit. Tentative bridge
sites are selected by reconnaissance and the
more promising ones are examined in detail.
The selection of a bridge site is governed by
both tactical and technical considerations which
are:
a) Bridge should cross from the river where
span is minimum.
b) Bridge should be made above the high flood
Figure 2- 5 Visit Site
level.
c) Bridge should not be made on turning of the
road.
d) Bridge structure should be according to the
traffic volume and weight of vehicles.
e) The bridge axis & river flow direction
should be at a right angle.
f) Gradient, cut and fill, other aspects are also
considered.
Besides these, control point locations, bridge Figure 2- 6 Tentative bridge axis fixation
axis is tentatively found out and different
information are gathered by GPS/abney level,
passometer, etc.
3. Establishment of control/reference points
a. Brass mark
b. Steel mark
c. Iron Rivet
Normally marks 1 & 2 are used for PBM, but
mark 2 is preferred. Mark 3 is used for
Temporary benchmark. But in practice for very
temporary use wooden pegs has been used.
After establishment of pegs reference sketches Figure 2- 9 Reference points
are also prepared. If it will be required for future
purposes, D-card can be prepared. Special type
of monumentation is followed for permanent
Benchmark(PBM).

4. Reference sketch & D- card preparation

D-card is detailed description for location of
Benchmark so that it can be searched and Figure 2- 10 Reference Sketch Preparation
recovered easily in future. It includes written
description and general sketch as well. Written
description includes
a. District
b. Local level
c. Ward no.
d. Grid sheet no.
e. Type of benchmark
f. Kind of land
g. Land owner

5. Prepare Technical Norms &

Specifications
a) Bridge axis length and control point fixing
is done by triangulation. Triangles are
formed carefully to ensure the angles
between 30° & 120° (Well-conditioned
triangles formation)
b) In triangulation, the distance of baseline
must be measured with an accuracy of
1:1000.
c) Measure all angles with the accuracy of 30”
√ N or 1.5' √ N or any other specifications.
d) Fly levelling should be conducted from the
established TBM to transfer the RL to the
nearest axes point of bridge and also RL was
transferred to the accessible control point by Figure 2- 11 D-card Preparation
this method and permissible error was
checked at all stations with precision of ±25
K mm where k is distance in km.
e) Reciprocal levelling should be conducted to
transfer RL to the another point of bridge
 axes on another bank of river. And fly
levelling should be done to find out the RL
of the station near bridge axes.
f) Detailing of the project area and X-section
and L-section of the river should be
performed by the Total station.
g) Topographic map of project area and bridge
site along with the contour line of contour
interval 1 should be plotted in a suitable
scale. i.e.1:500 Figure 2- 12 Well-Conditioned Triangle
h) To plot the X-section and L-section of river Formation
data should be taken at the chainage of 15 m
about (specified)m upstream and (Specified)
m downstream and all the section should be
plotted in CAD/GIS
6. Prepare necessary Equipment
All essential instruments and equipment are
managed. Missing of any instrument may harm
or delay the field work. Especially following
instruments are carried out.
a) Theodolite Figure 2- 13 Equipment used in Bridge survey
b) Total Station
c) Ranging Rods
d) Measuring Tapes
e) Leveling Staff
f) Pegs & Arrows
g) Marker Pen
h) Compass
i) Prism & Prism Holder
j) Other as per the requirements.

7. Fly levelling from BM to stations

Consider A, B are axis stations & C,D are Figure 2- 14 Fly levelling
reference stations which are formed as well-
conditioned triangle .Fly levelling is done to
transfer RL from benchmark nearby to stations
A as in the Figure 2- 7. It is done again when
RL transfer is to carried out from stations ‘C’ to
D. Data are recorded and RL is calculated in
field book as shown in the Figure 2- 8.
Arithmetic check is done as:
ΣBS-ΣFS= Last RL- First RL

8. Perform Reciprocal levelling

Figure 2- 15 Recording data for Fly levelling

In levelling, BS and FS distances are made
equal by setting up instruments at mid-way.
But, in case of valley, river, we can set up
instrument at the mid- way of two stations.
Steps:
a. Fix staffs at two stations which are at bridge
axis say stations as A & B.
b. Set up the instruments near to station ‘A’,
Follow the temporary adjustment.
c. Hold the staff perfectly vertical at these Figure 2- 16 When Instrument is near to A
station. To check staff verticality, Top,
Middle and bottom staff readings are
checked and compared with mean of these
readings.
d. Take staff readings at these stations. Say
reading be a1&b1 and note the data in field
book and calculate the apparent height
difference as h1 =a1 –b1
e. Shift the instruments near to B.
f. Again set up the instruments following
temporary adjustments
g. Hold the staff perfectly vertical at these
station. To check staff verticality, Top,
Middle and bottom staff readings are Figure 2- 17 When instrument is near to B
checked and compared with mean of these
readings.
h. Take staff readings at these stations. Say
reading be a2 & b2 and note the data in field
book and calculate the apparent height
difference as h1 =a2-b2. Figure 2- 18 RL transfer to opposite bank by
i. Fill all the data in field book and perform Reciprocal levelling
computation as shown in the figure below

Figure 2- 19 Field book of reciprocal levelling

9. Perform Triangulation
A. Measure the length of baseline
The baseline AC and BD are measured either by
tape or EDM as per the project requirement,
budget and accuracy required. It is measured by
both forward and backward distance following
the specification. Generally, precision is 1:2000
for tape and 1:5000 for EDM measurement.
Figure 2- 20 showing baseline and bridge axis
This length of baseline is used further to
calculate the axis length after determining all
angles using sine rule
B. Measure all angles
a. Set up the instrument at station ‘A ‘and temporary adjustment of instrument is followed.
b. Bisect the station ‘C’ and set zero to the reading and record the reading as FL (face left) of C as
O°0’0”
c. Turn telescope clockwise towards B and bisect exactly with the help of tangent screw, note the
reading and record the reading as FL of B
d. Again bisect exactly station D and record the readings as FL of ‘D’
e. Now, transit the instrument and turn clockwise to bisect the target at ‘D’ and record the reading
as FR (face right) of D.
f. Then turn anticlockwise continuously and bisect the station B & C exactly and record the
readings as FR of ‘B’ and FR of ‘C’ respectively.
FL+ FR
g. Calculate the mean angle as
2
h. Repeat the same process by setting 90° instead of 0 degree and the readings and record all data
in the field book as shown in the Figure 2- 21
i. Repeat whole process again by setting up instrument at station ‘C’,’B’ and ‘D’ and measures the
angles in same manner and then ∡ CAB , ∡ CAD , ∡ BADas ∡ BAD=∡CAD−∡ CAB and other
angles also in similar manner.

Figure 2- 22 Triangulation field book for measurement of all angles

C. Calculate the length of bridge axis (AB)

If all angles are measured, then sum of angles is
checked in both the triangles and compared with
angular accuracy. If it is within permissible error
then angles are corrected and entried in Figure 2-
23. Using sine rule, length of AB is calculated
as:
Difference in angle = sum of observed angles Figure 2- 24 Axis length calculation
in a triangle -180°
In triangle ABD,
BD AB
=
sin ∡ DAB sin ∡ ADB

sin ∡ ADB
∴ AB=BD×
sin ∡ DAB

Again in triangle ACB

AC AB
= Figure 2- 25Traverse adjustment for closing
sin ∡ ABC sin ∡ ACB
error
sin ∡ ACB
∴ AB=AC×
sin ∡ ABC
These obtained length of AB is compared with
required precision. In this way length of AB is
determined.

10. Traverse Computation

a. Prepare distance of all line AC, CB, BD,
DA Figure 2- 26 Correcting by Bowditch's rule
b. Measure initial bearing of a line
c. Calculate bearing of all lines with the help
of corrected angles
d. Calculated consecutive coordinates
e. Adjust the traverse by suitable method
 Bowditch’s rule
The Bowditch’s method also termed as
compass
rule is generally used when linear and
angular
Figure 2- 27 Correcting by transit Rule
measurement is of equal precision. The total
error in latitude and departure is distributed in
proportion to lengths of the sides

 Transit rule
The transit rule may be employed where
angular measurements are more precise
than the linear measurements.
According to this rule, total error in latitude
and departure is distributed in proportion to Figure 2- 28 Using Compass to read bearing of
a line
the latitude and departures of the sides.
f. Calculate Independent Coordinates by
filling in Gale’s table as shown in the
Figure 2-29
 Figure 2- 29 Filling Gale’s table for independent Coordinates

11. Measure Discharge

The discharge of a river is the volume of water
which flows through it in a given time. It is
usually measured in cubic meters per second.
Calculation: Cross-sectional area of channel
(m2) X Velocity of the river / water (m/s)
*This gives discharge as the volume (m3/s) or
cumecs. Q=A*V

A. Calculation of velocity(V)
a. Water section is divided into section like
C/S-1 and C/S-2 like in figure
b. The float is released slightly ahead C/S-1,
when the float just crosses the section, the
stop watch is started and when it just
crosses the section C/S-2, the time is
noted. Figure 2- 30 Calculation of velocity
c. This process is repeated several times and
mean time is calculated. Distance of
section is measured. Thus obtained mean
time and distance gives the velocity.

B. Calculation of cross-sectional area(A)

When river is small
a. Two stations or poles are fixed on both
banks of river and rope or tape is stretched
between them .
b. Then the width of river is divided into
different parts by equal distance say ‘d’.
c. The depth of water is measured in each Figure 2- 31 Example of depth measurement
part by staff or sounding rod or cable. Let
depths be ℎ1,,ℎ2,ℎ3 ,ℎ4………. etc.
d. Then area is calculated by using
 trapezoidal

When river is large

river. Two pegs 𝑇1 and 𝑇2 are fixed on AB. Then

The center line AB is taken perpendicular to the

following procedure is adopted

a. At station A, a theodolite is set up and line is
ranged, the width of river is measured by Figure 2- 33 Angle Calculation
stadia method

widths are fixed. Thus the distances 𝐴𝑃1, 𝑃2

b. The width is divided into equal parts; the

𝑃3…. Are fixed

c. Another theodolite is set up at C, so that AC is
perpendicular to AB, the distance AC is

d. Then the angles 𝛼1, 𝛼2, 𝛼3 …. are calculated

measured (say it is equal to D)

Figure 2- 34 Cross-Sectional Area

e. Calculated angles 𝛼1, 𝛼2…. are set out from
as in the figure Figure 2- 32

theodolite at C. Thus the line of sight of

coincide at the points 𝑃1, 𝑃2….

theodolite at A and that of theodolite at C

f. The depth at these points are measured by

suitable instruments
Then the cross –section area is calculated by using
trapezoidal rule
Figure 2- 35 Detailing by Total station
C. Discharge Calculation

A 𝑚2. The mean velocity is measured by any

Let the calculated cross sectional area of water be

suitable method,
Then Discharge Q = A∗V
12. Perform Detailing of a bridge Site
The total station was used for detailing the entire
bridge site. The reading was taken from the
different station set up. The detailing was done
concerning the skeleton formed by triangulation.
Figure 2- 36 Centre line & cross-section line Fixing
The vertices of triangles serve as a control point.
The details were booked, up to (specified)m
upstream and (specified)m downstream with
sections dividing at 10m & left, and the right of
the cross-section at 15m. Tree, structures, spot
height etc. data are taken. Rough skech showing
all details are also prepared so that plotting work
will be very easier and accurate.
13. Cover upstream and downstream
Centre line is fixed and cross-section are also Figure 2- 37 River Section showing details
established where HFL (high flood level)., LFL
(low flood level) WL (water level) data are
collected. Upstream and downstream distances are
specified according to project requirement

14. Data Plotting

a. Collected data are downloaded from Total station and exported to the software CAD and GIS.
b. L-section and cross section of a river are drawn according to chainages interval and width
coverage from center to left and right both.

Figure 2- 38 Data exporting to the CAD Figure 2- 39 Data being exported to

CAD

Figure 2- 40 L-section of a river/bridge site

Figure 2- 41Cross-section of upstream Figure 2- 42Cross-section of downstream

c. Data are exported into GIS
softwares and at suitable
contour interval
topographic map is
prepared.
Exercise
1. Plan about axis selection and Reccee the bridge site.
2. Establish BM with referencing and D-card preparation
3. Transfer RL by fly levelling and Reciprocal levelling
4. Perform Triangulation
5. Perform Detailing, L-section & X-section
6. Measure discharge
7. Export data to the software
8. Prepare L-section, Cross-section and topographic map of bridge site
Main items Sub items Full Standards Score Remarks
Map study & 1.Study the area :3
Planning Discussions 2.Consider the factor :2
/Reconnaissance 10 3.Set criteria for selecting
Visit site bridge axis:3
4.Select the axis:2
BM 1.Select suitable station :2
establishment 10 2. Mark the BM:3
RL transfer 3. prepare complete D-card:5
Levelling 1.Fly lelling:5
10
2.Reciprocal levelling:5
Baseline Measure Baseline:2
5
Standards

measurement Compare precision:3

Angle Instrument set up:5
measurement 15
Triangulation Measure all angles:10
Axis length 1.Correct all the angles:2
10 2.Calculate baseline:5
3.Check accuracy:3
1.Set up instruments:3
Detailing 10
2.Take detailings:7
L-section & 1.Set up sections:3
X-section- 10
2.Take measurements:7
Data collection
Discharge 1.Calculate velocity:3
10 2.Calculate area:5
3.Calculate discharge:2
L-section 1.Prepare L-section:3
2.Prepare X-section:5
Map 10
X-section 3.Prepare Topomap:2
Topomap
 Hours
Job Name 3.Perform Setting out Survey

Objectives

Instruments Safety and

Materials Specification Quantity
1.Set up following
and Tools Caution
-Level - Sheet -Auto Level Level machine-1

2. Hold staff
Machine paper -3 or 5m staff Tripod-1 temporary adjustment.
-Tripod - Pencil -Peg: rigid suitable, Theodolite -1
-Theodolite - Eraser pointed and rigid Staff-2 perfectly vertical.
-Staff - Ink pen type Pegs-2 3.Prevent instruments
-Pegs -Tape:20m or 30m Tape-1 from rainfall or high
-Tape tape Hammer-1 heat.
-Hammer 4. Avoid working
on extreme
weather
conditions.

<Related Knowledge>
 1.Setout Simple Hou
Job rs
Circular
curve 8
1. Understand Elements of
simple circular curve
2. Calculate Chainage of curve
Obj 3. Calculate data for setting
ecti out
ves 4. Understand different
methods of setting out
Simple curve
Inst
rum Safety
Ma
ents Specifi Quan and
ter
and cation tity Cautio
ials
Too n

1.Set
ls
- - S -Auto Level Figure 4- 1 Curve in highway
Leve h Leve machi up
l e l ne-1 followin
Mac e -3 or Tripod g
hine t 5m -1 tempora
- p staff Theod ry
Tripo a -Peg: olite -1 adjustm

2.
d p rigid Staff-2 ent.
- e suita Pegs-2 Figure 4- 2 Simple circular curve
Theo r ble, Tape-1 Hol
dolit - P point Hamm d
e e ed er-1 staf
- n and f
Staff c rigid perf
-Pegs il type ectl
- - E - y
Tape r Tape vert Figure 4- 3Compound Curve
- a :20m ical.
Ham s or 3.Preven
mer e 30m t
r tape instrume
- I nts from
n rainfall
k or high
p heat.
e 4.
n Avo Figure 4- 4 Transition Curve
id
wor
king
on
extr
eme
wea
ther
con
ditio
ns.
<Related Knowledge> Figure 4- 5 Reverse Curve
Curve
Curves are the geometric arcs which are
introduced in order to avoid the abrupt
(sudden) change in direction in both the
horizontal as well as in vertical planes.
Curve is arc of finite radius Introduced when
two straight lines (with different direction)
need to be joined/connected.
Necessity of curve Figure 4- 6 Broken-back Curve
 Make vehicle to move comfortably and
safely, avoiding the sudden change in the
route.
 Whenever the direction of a road or
railway line is to be changed, curves are
provided between the intersecting
straights
Types of curve
a. Simple Circular curve
It connects two intersection straight lines. It Figure 4- 7 Types of curve
Consists of a single arc of a circle i.e. the
curve has constant radius. The curve is
tangential to the connected straight lines at
the joining points
b. Compound Curve
It is combination of two or more simple
circular curves in the same direction with
different radii.
c. Transition Curve
It is introduced between simple circular
curve and straight line or between two simple Figure 4- 8 Simple circular curve
circular curves with varying radius. It
provides a gradual change from straight line
to the circular curve and vice versa It is also
known as easement curve
d. Reverse Curve
It is the combination of two or more simple
circular curves in the opposite direction with
same or different radii. It is also known as
serpentine curve. It is not suitable for
Figure 4- 9 Elements of simple circular curve
highways but suitable for hill roads.
e. Combined Curve
Combination of simple circular curves and
transition curve
f. Broken back curve
It is two circular curves, having centers in the
same side, connected with a tangent.
 Figure 4- 10 Deflection angle measurement
Elements of simple circular Curve
Tangent length(T): It is the distance
between the point of curvature to the point of
intersection; also the distance between the
point of intersection to the point of tangency.
In figure, T1 I or IT2 is tangent distance.
In ∆ T ! IO,
∆ T1I ∆ T ∆
tan = or, tan = ∴ T=R tan
2 O T1 2 R 2
Long Chord(L): Chord of the circular curve
joining the point of curvature(T1) and point of Figure 4- 11 Chainaging of curve(PC,PT)
tangency(T2) In Figure, T1DT2 is long Chord.
In ∆ T ! DO
∆ T1 D ∆
sin = or, T1D=OT1sin
2 OT1 2
∆
∴ T 1 D=R sin
2
∆
L= T1DT2=2 T1D= 2 R sin
2
Mid Ordinate(M): The distance between the Figure 4- 12 Methods of setting out simple
apex of the curve (C) and mid-point (D) of the circular curve
long chord, also known as versine of the curve.
In fig. CD is the Mid ordinate
In ∆ T ! DO
∆ OD ∆
cos = or, OD= OT1cos
2 O T1 2
∆
∴OD = R cos or, CD = OC-OD
2
∆ ∆ Figure 4- 13 perpendicular offsets from tangent
CD= R- R cos ∴ CD=R ¿ cos ) method
2 2
External Distance(E): Distance between the
point of Intersection (I) and apex of the curve
(C), also known as apex distance. In figure
IC is the apex distance.
In ∆ O T ! I
OT 1 R
∆ O T1
cos = or, OI = ∆ = ∆
2 OI cos cos
2 2
R
−R ∆
IC= OI-OC = ∆ = R( sec -1)
cos 2
2
Length of the Curve(l): Total Arc length
between point of curvature and point of
tangency. In figure, T1T2 is length of curve.
By Geometry,
ARC l
Angle= or, ∆= or,l=R∆ (in radian) Figure 4- 14 Calculating Perpendicular offsets
Radius R
 πR ∆ from tangents
l= (in degree)
180°

Chainage of curve
<Operation Procedures>
a. Before setting out the curve P.I., P.C. and
the P.T. are located on the ground
b. After locating the P.I., theodolite is
placed at that point
c. The angle of deflection is measured.
(Telescope is pointed towards one
straight, transited by 180° and swung
Figure 4- 15 Radial Offsets from tangent method
towards other straight)
d. Using this deflection angle, Tangent
length can be computed by:
T = R Tan (Δ/2)
e. This tangent length is measured along IP 0
→ IP 1and IP1→ IP 2 to fix PC and PT.
Then chainage is calculated as:
Chainage of PC= Chainage of IP –Tangent
length
Chainage of PT = Chainage of P.C+ curve
length
Setting out curve
A. Linear method: Only tape/chain is used
for setting out curve.
B. Angular method: Theodolite & tape or
Figure 4- 16 Offsets from long chord method
only theodolite is used to set out curve.
<operation procedures>
A. Linear method
1. Offsets from tangents
i.Perpendicular offsets
Let Ox be the perpendicular offsets to
tangents at D, ‘X’ distance from T1. EE1 is
perpendicular to line T1O.
From derivation, Ox = R−√ (R2− X 2¿ )¿
which gives the value of perpendicular
offsets At different distances from the
tangents.
Steps:
a) Measure equal distances, say, 20 or 30m
along the tangent T1 V from T1. Figure 4- 17 Calculating offsets from long -Chord
method
b) Set out the offsets calculated from
formula perpendicular to T1B at each
distance,
Ox = R−√ (R2− X 2¿ )¿

thus obtaining the required points in the

curve.

c) Continue the process until the apex of the

curve is reached.
d) Set out the remaining half of the curve
from the second tangent

ii.Radial offsets
Let Ox =the Radial offsets for point E at any
point along the tangents =DE
T1D= x (Distance of radial offsets from T1
By Derivation,
Figure 4- 18 Rankine's method of tangential
Radial offsets(OX)= √(R 2+ X 2 ¿)−R ¿ angles
Steps:
a. Erect the ranging rods at T1, V, T2 and O.
b. Measure the distance X along T1V and
fix point D.
c. From point D, a distance equal to the
calculated offsets length OX, along the
line joining the point D and the center of
curve.
d. Similarly locate other points on the first
half of curve.
2. Offsets from long –chord Figure 4- 19 Specimen of data to be set out by
This method is suitable for a curve having Rankine's method
small radius
Let, x be the distance from mid-point of long
chord from which offsets(Ox) are drawn to
find the point on curve. The offsets(Ox) are
calculated as:
√
Ox = (R 2−X 2 ¿ )−√ R2−¿ ¿ ¿
‘x’ is the distance from mid-point of long
chord to either P.C. or PT i.e. if long chord is
40 m then (L/2) =20 m and x can be taken as
0,5,10,15,20 or any other regular interval and Figure 4- 20 using Total deflection angle to be directed
O0, O5, O10, O15, O20 can be calculated.
Steps:
a. Fix the ranging rods at T1, D and T2
b. Divide the long chord T1T2 in equal parts
of suitable length.
c. Calculate the lengths of the offsets
corresponding to the distance (x) from
the origin at D by using the formula
shown above
as:
√
Ox = (R 2−X 2 ¿ )−√ R2−¿ ¿ ¿

d. Erect perpendiculars with the help of an

optical square and measure the calculated Figure 4- 21 Procedures of setting out curve by
offsets of the chord Ox or 3:4:5 rule can deflection angle and chord length(Rankine’s
method)
 be used.

B. Angular method
i. Rankine’s method of tangential angles
In this method, a tape is used for making
linear measurement and a theodolite is used
for making angular measurements
simultaneously.
Here, normal Peg interval =C
First sub-chord =C1 Last sub-chord =Cn
1718.9C 1 1718.9 C 1718.9 C
δ 1= min , δ= min δ n=
R R R
, ( All angles are in min. unit)

∆ 1=δ 1 , ∆ 2=δ 1+ δ 2=∆1 +δ 2=∆ 1+ δ Figure 4- 22 Two theodolite method

δ=δ 2=δ 3=δ 4 =δ n−1
∴ ∆ n=∆ n−1+ δ n
Steps:
a. Prepare a table of deflection angles for
the first sub chord, normal chord and last
sub-chord. Set up the theodolite in the
point of curvature (P.C). With both plates
clamped to zero, direct the theodolite to
bisect the point of intersection (P.I) i.e.
back sight towards the P.I.
b. Release the upper clamp of the theodolite
and set the angle of deflection Δ1 on the
instrument. The line of sight is thus
directed along the chord T1 a
c. With the zero end of the tape pointed at
T1, swing the tape to measure the Figure 4- 23 laying out different points on a curve
distance C1 along the chord T1a until the
ranging rod is bisected by the telescope.
Thus the first point of the curve is fixed.
d. Now set the second deflection angle Δ2
on the instrument so that the line of sight
is in the direction T1 E.
e. With the zero end of the tape pointed at
a, swing the tape to measure the distance
ED=C2 from an until the ranging rod is
bisected by the telescope. Thus the
second point D of the curve is fixed.
f. Repeat the steps until the last point i.e.
point of tangency (P.T) is reached.
g. Repeat steps ‘e’ and ‘f’ till the last point
T2 is reached.

ii.Two theodolite method

This method is suitable when the ground is
not suitable for chaining and is based upon
the assumption that the angle between the
tangent and the chord is equal to the angle
which that chord subtends in the opposite
segment.
Let, E, etc. be the points on the curve The
angle ∆ 1 between the tangent T1B and the
chord T1D is equal to the Chord T1D
subtends in opposite segment i.e. the angle
∠ BT 1 D=∠T 1 T 2 D
Similarly,∠ BT 1 E=∠ T 1 T 2 E
The method is expensive since two
instruments and two surveyors are required.
However, the setting out process is most
accurate.
Steps:
a. Two theodolites are used for setting out
the curve.
b. Set up one theodolite at the point of
curvature (P.C) and the other at the point
of tangency (P.T).
c. Clamp both the plates of each
instruments to zero reading.
d. With the zero reading, direct the line of
sight of the instrument at T1 towards
point of intersection (P.I). Similarly
direct the line of sight of the other
instrument at T2 towards T1 when the
reading is zero.
e. Set the reading of each of the telescopes
to the deflection angle for the first point
A. The line of sight of both the
theodolites are the thus directed towards
A along T1A and T2A respectively.
f. Move a ranging rod or an arrow in such a
way that it is bisected simultaneously by
cross hairs of both the instruments. Thus,
point A is fixed.
g. To fix the second point B, set reading Δ2
on both the instruments and bisect the
ranging rod.
h. Repeat the steps for location of all the
points of the curve
done

.
 Hours
Job Name 2.Perform Construction survey
8
5. Understand Elements of simple circular curve
6. Calculate Chainage of curve
Objectives 7. Calculate data for setting out
8. Understand different methods of setting out Simple curve
Instruments Safety and
Materials Specification Quantity
1. Set up following
and Tools Caution
-Level - Sheet -Auto Level Level machine-1

2. Hold staff
Machine paper -3 or 5m staff Tripod-1 temporary adjustment.
-Tripod - Pencil -Peg: rigid suitable, Theodolite -1
-Theodolite - Eraser pointed and rigid Staff-2 perfectly vertical.
-Staff - Ink pen type Pegs-2 3. Prevent instruments
-Pegs -Tape:20m or 30m Tape-1 from rainfall or high
-Tape tape Hammer-1 heat.
-Hammer 4. Avoid working
on extreme
weather
conditions.
<Related Knowledge>
Construction Survey

Site Survey
It is an inspection of an area where work is proposed ,to gather information for a design or an estimate to
complete the initial tasks required for an outdoor activity.
It can determine a precise location, access, best orientation for the site and location of obstacles

1. Total Stations: A total station is a versatile electronic instrument that combines the functions of a
theodolite and an electronic distance measurement (EDM) device. It allows surveyors to measure
angles and distances with high precision, providing accurate information on the position, elevation,
and alignment of various points on the construction site.
2. GPS/GNSS Receivers: Global Positioning System (GPS) or Global Navigation Satellite System
(GNSS) receivers use satellite signals to determine the precise location and elevation of points on the
earth’s surface. These devices enable surveyors to collect real-time, accurate geospatial data, even in
remote or inaccessible areas, without the need for line-of-sight measurements.
3. Levels: Levels are essential optical instruments used by surveyors to determine the height differences
between points and establish a horizontal plane. There are various types of levels, such as automatic
levels, digital levels, and laser levels, each offering different levels of accuracy and ease of use.
4. 3D Laser Scanners: 3D laser scanners emit laser beams to capture the shape, size, and position of
objects and surfaces within their range. They generate millions of data points, known as point clouds,
which can be processed to create highly detailed and accurate 3D models of the construction site or
structure.
5. Drones/UAVs: Unmanned Aerial Vehicles (UAVs) or drones equipped with high-resolution
cameras or LiDAR sensors have become popular tools for construction surveying. They allow
surveyors to quickly capture aerial images and topographic data, even in challenging terrain or large-
scale projects, reducing the time and effort required for data collection.
6. Data Collectors: Data collectors are handheld devices or tablets that enable surveyors to record, store,
and manage the data obtained from various survey instruments. They often come with built-in
software for data processing, analysis, and visualization, allowing surveyors to generate maps,
reports, and other deliverables on-site.
7. Measuring Tapes and Wheels: While more technologically advanced tools have become prevalent,
measuring tapes and wheels still play a crucial role in construction surveying. They are used for quick
measurements of linear distances, particularly when high precision is not required or when electronic
instruments are not available.
8. Safety Equipment: Construction surveyors work in diverse environments and often encounter
hazards such as heavy machinery, uneven terrain, and adverse weather conditions. Therefore, they
.

°and120°.
vvvvglesareformedcarefullytoensureanglesbetween30
°and12
Bridgeaxislengthandcontrolpointfixingdonebytriangula
tion.Trianglesareformedcarefullytoensureanglesbetwe
en30°and120°.
0°.
 Hours
Job Name Calculate Area
8
1. Understand methods of area finding of field
2. Measure area of regular and irregular figures
Objectives 3. Understand the methods of determining the area from map/plan

Instruments Safety and

Materials Specification Quantity
1. Set up following
and Tools Caution
-Level - Sheet -Auto Level Level machine-1

2. Hold staff
Machine paper -3 or 5m staff Tripod-1 temporary adjustment.
-Tripod - Pencil -Peg: rigid suitable, Theodolite -1
-Theodolite - Eraser pointed and rigid Staff-2 perfectly vertical.
-Staff - Ink pen type Pegs-2 3. Prevent instruments
-Pegs -Tape:20m or 30m Tape-1 from rainfall or high
-Tape tape Hammer-1 heat.
-Hammer 4. Avoid working
on extreme
weather
conditions.

<Related knowledge>
Distance measurement
For instance, lengths, heights, and widths
of geometric figures are distances, as are
the radius, diameter and circumference of a
circle.
Distance is measured in linear units, such
as inches, feet, yards, miles, meters,
centimeters, millimeters and kilometers.
There are many other units of linear
measure, but those listed above are
commonly used.
Basic units of distance measurement in the
English system (inches, feet, yards, miles),
and among the basic units of linear measure
in the metric system (meters, centimeters, Figure 6 - 3 Distance unit conversion table
millimeters, kilometers).
Area Measurement
Generally, area refers to the total regions
being occupied. The term ‘area ‘in the
context of surveying refers to the area of a
tract of a land projected upon the horizontal
plane, and not to the actual area of land
surface. Generally field area may be
expressed in the following units. Figure 6 - 4 Ropani and Bigaha system
i.Square meters
ii.Hectares
iii.Square feet
iv.Acres (1 Acre =4840 sq.= 43560 sq.)
Beside this, in Nepal, the area is expressed
in
Ropoani-aana-Paisa-Dam (in velley)
Bigaha-Katha-Dhur-Kanuwa ( in Terai
region)
One should know conversion mentioned in
Figure 6- 1 during area measurement and
calculation.
Equipment used in distance Figure 6 - 5 Area unit Conversion
measurement:
Chain/tape is used for linear measurement.
Ranging rod is used for distance
measurement by ranging by when distance
is too far. Arrow is used to fix point of
starting or ending point, Dimension of
arrow is shown in figure. If two points are
in slope relative to each other, then distance
measurement by stepping is shown in the
Figure 6 - 6 Correctly horizontal distance
figure Figure 6- 2 measurement and slopping

Different methods of determining area

The area can be measured either by
graphically by calculating using formula or
by directly using instrument e.g. Total
station. Methods are detail mentioned in
Figure 6- 3
Figure 6 - 7 Methods of computation of area
<Operation procedures>
A. Measuring area of regular figures
a. Triangle
Steps:
a.Establish pegs at three stations A, B, C
b.Measure distance horizontally between
AB, BC, CA and record as c, a and b
respectively
c.Be clear and consistent about unit of
measurement.
d.Apply formula, A=
S √ (S−a)(S−b)(S−c )
a+b+ c
Where,S¿ is semiperimeter
2
Figure 6 - 8 Ranging rod,, arrow ,chain & direct
e.Convert area into required unit. ranging in distance measurement

b. Right angled triangles

Steps:
 a.Establish pegs at stations covering area
representing right angled triangle.
b.Measure distance horizontally denoting
as height(h) and base of a right angled
triangle
c.Apply formula for calculating area A=
1 Figure 6 - 9 Triangles and dividing land into
b×h
2 triangles
d.Convert area into required unit.
e.Sum the area if region is divided into
number of triangles as shown in the
Figure 6 - 1

Figure 6 - 10 Right angled Triangle & Rectangle

c. 3. Rectangle
d. Steps:
a. Establish pegs at stations covering area
representing rectangle.
b. Measure distance horizontally denoting
as length(l)=32m and breadth (b) =20m
as shown in the figure.
c. Apply formula for calculating area A=
Figure 6 - 11 Square and trapezoid
l×b
d. Convert area into required unit.
e. Sum the area for total area if the region
is divided into the number of a
rectangle.

1. Square Figure 6 - 12 Dividing into geometrical figures.

Steps:
a. Establish pegs at stations covering area
representing square.
b. Measure distance horizontally denoting
as length(l)=700ft
c. Apply formula for calculating area A=l2
d. Convert area into required unit
e. Sum the area for total area if the region
is divided into the number of a square.

2. Trapezoid
Steps:
a. Establish pegs at stations covering area
representing trapezoid.
b. Measure distance horizontally denoting
as a.b,h as shown in the Figure 6 - 2 Figure 6 - 13 Area calculation for different shape
of land
a+b
c. Apply formula for area A= ×h
2
d. Convert area into required unit
e. Sum the area for total area if the region
 is divided into the number of
trapezoids.

B. Measuring area of irregular figures

1. Mid-ordinate rule
Steps:
a. Divide the region into chain line and irregular
boundary as in the Figure 6 - 14 Figure 6 - 17 Mid-ordinate Rule
b. Measure the ordinate O1, O2...... perpendicular
to chain line at regular interval ‘d’.
O +O
c. Find the all mid ordinate as h1= 1 2 ,
2
Figure 6 - 18 Taking ordinates by Mid
d. Apply the formula: A=d (h1+h2+…+hn)
ordinate rule
e. Convert into required unit.

2. Average Ordinate rule:

Steps:
a. Divide the region into chain line and irregular
boundary as in the Figure 6 - 15
b. Measure the ordinate O1, O2...... perpendicular
to chain line at regular interval ‘d’.
O +O +..+On
c. Apply formula ,A= 1 2 ×l Figure 6 - 19 Calculating area by mid-
no . of ordinates
ordinate rule
d. Convert into required unit.

3. Trapezoidal rule
While applying the trapezoidal rule, boundaries
between the ends of ordinates are assumed to be
straight. Figure 6 - 20 Average ordinate rule
a. Divide the region into number of trapezoids.
b. Measure the ordinate O1, O2...... perpendicular
to chain line at regular interval ‘d
c. Apply formula to calculate area of entire
region,

d. Convert into required unit.

Figure 6 - 21 Area calculation by trapezoidal

4. Simpson’s rule
rule
In this rule, boundaries between ends of ordinates
are assumed to form an arc of parabola. So, it is
also called the parabolic rule.
Steps:
a.Divide the region into chain line and irregular
boundary as Figure 6 - 16
b.Measure the ordinate O1, O2...... perpendicular
 to chain line at regular interval ‘d
c.Separate ordinates as first ordinates, even
ordinates, odd ordinates and last ordinates.
d.Separate odd no of ordinates for Simpson’s rule

Figure 6 - 22 Simpson's Rule

e.apply trapezoidal rule to second last and last

ordinates and add this area to area of
remaining ordinates by Sampson’s rule as in
the figure as Simpson’s rule is applicable
when there is no of ordinates odd.
f. Apply Simpson’s rule by applying formula

Figure 6 - 18 Calculating area by Simpson’s

Rule for even no of ordinates

g.Convert into required unit.

5. Coordinate Method
a. Set up total station covering area of interest
b. Set prism to all corner A, B, C & D.
c. Measure coordinate and note down as
A(x1,y1), B(x2,y2), C(x3,y3) and D(x4,y4)
d. Apply the formula coordinate method of
calculating area shown below Repeat the first
Figure 6 – 19 Coordinate measurement by
coordinate in last too. Total station

A = |(x₁y₂ - y₁x₂) + (x₂y₃ - y₂x₃) + ... + (x n-

1yn - yn-1 xn) + (xn y₁ - ynx₁)| / 2
e. Convert into required units. Figure 6 – 20 Coordinates represented by
Graph
C. Measurement of map/plan
The entire area is divided into regions of a
convenient shape, and calculated as follows:
1. Dividing the area into triangles
a. Draw the triangles as to equalize the irregular
boundary line.
b. Then determine the bases and altitudes of the
triangles according to the scale to which the
plan was drawn.
c. After this, calculate the areas of these
triangles (area = 1/2 x base x altitude). Then
add areas to obtain the total area
2. By dividing the area into squares
a. In this method, squares of equal size are ruled

Figure 6 - 21 Dividing into Triangles

out on a piece of tracing paper. Each square

represents a unit area, which could be 1 cm² or 1
m².
b. Place the tracing paper over the plan
c. Count the number of full squares.
d. Calculate total area by multiplying the
number of squares by the unit area of each
square
3. By drawing parallel lines and converting
them to rectangles Figure 6 - 22 Dividing into Squares
a. In this method, draw a series of equidistant
parallel lines on a tracing paper The constant
distance represents a meter or centimeter.
b. Place the tracing paper over the plan in such
a way that the area is enclosed between the
two parallel lines at the top and bottom. Thus
the area is divided into a number of strips.
c. Replace the curved ends of the strips by
perpendicular lines (by give and taken
principle) and a number of rectangles are
formed.
d. Calculate the sum of the lengths of the Figure 6 - 23 Parallel line method
rectangles
e. Required area =∑length of rectangles x
constant distance
If a large square or rectangle is formed within
the area in the plan. Then ordinates are drawn at
regular intervals from the side of the square to
the curved boundary. The middle area is
calculated in the usual way. The boundary area is
calculated by any of the formula of calculating
area of irregular geometry.
4. Area by planimeter
a. In the first step anchor point is to be fixed at one point. If the given plan area is small, then
anchor point is placed outside the plan.
b. Similarly, if the given plan area is large then it is placed inside the plan.
c. After placing the anchor point, place the tracing point on the outline of the given plan using
tracing arm. Mark the tracing point and note down the reading on Vernier as initial reading A.
d. Now move the tracing needle carefully over the outline of the given plan till the first point is
reached. The movement of tracing needle should be in clockwise direction.
e. Note down the reading on Vernier after reaching the first point and it is the final reading B.
f. Now the area of the plan which boundary is traced by the planimeter is determined from the
below formula. Area = M (B – A + 10N + C)

Where, A = initial reading B = final reading N = no.

of completed revolutions of wheel during one
complete tracing. N is positive if dial passes index
in clockwise, N is negative if dial rotates in anti-
clock wise direction. M and C = constants which
Figure 6 - 24 Planimeter
values are provided on the planimeter.
 Hours
Job Name Calculate Volume
6
a. Understand Elements of simple circular curve
b. Calculate Chainage of curve
Objectives c. Calculate data for setting out
d. Understand different methods of setting out Simple curve
Instrument
Material Safety and
s Specification Quantity
s Caution
1. Set up following
and Tools
-Level - Sheet -Auto Level Level machine-1

2. Hold staff
Machine paper -3 or 5m staff Tripod-1 temporary adjustment.
-Tripod - Pencil -Peg: rigid Theodolite -1
-Theodolite - Eraser suitable, pointed Staff-2 perfectly vertical.
-Staff - Ink pen and rigid type Pegs-2 3. Prevent instruments
-Pegs -Tape:20m or 30m Tape-1 from rainfall or high
-Tape tape Hammer-1 heat.
-Hammer 4. Avoid working
on extreme
weather
conditions.
<Related Knowledge>
Volume
The volume of an object is the amount of space occupied by the object or shape, which is in
three-dimensional space. It is usually measured in terms of cubic units. In other words, the
volume of any object or container is the capacity of the container to hold the amount of fluid (gas
or liquid).
Volume for different Solid shapes
1. Cube
The volume of a cube can be easily found out by just knowing the
length of the edge of the cube. If the length of the cube is s, then the
formula to calculate the volume of a cube is:
Volume of the cube V =S 3 where 's is the length of the side of the
Figure 7- 1 Cube
cube.
2. Cuboid:
The volume of a cuboid is the space occupied by a cuboid. The volume of
the cuboid is equal to the product of the base area (area of the rectangular
face) and height. Volume = (Length × width) × Height Figure 7- 2 Cuboid
3. Sphere
The volume here depends on the diameter or radius of
the sphere since if we take the cross-section of the sphere, it is
a circle. The surface area of sphere is the area or region of its outer
surface. To calculate the sphere volume, whose radius is ‘r’ we
have the below formula: Volume of a sphere(V) = 4/3 πr3 Figure 7- 3 Sphere
4. Cone
The volume of a cone is the space occupied by the cone. The formula to find
the volume of a cone, whose radius is 'r' and height is 'h' is given as, Volume =
(1/3) πr2h cubic units.
Figure 7- 4 Cone
1. Cylinder
The volume of a cylinder is the amount of space there is inside a cylinder. In
order to find the volume of a cylinder we first need to find the circular area of
the base. The formula for calculating the area of a circle is: Area=πr2 We then
multiply the area of the circular base by the height (or length) of the
cylinder.
The formula for the volume of a cylinder is:
d
Volume(V)=πr2h where r =
2
Conversion of Volume into quantity
1 m3=1000 liter
If a rectangular tank has dimensions 9’×9’×2’. Then amount/quantity
of water that can be inside tank is calculated as:

162
Volume(V) = 9×9×2 =162 cube feet =
3.2808∗3.2808∗3.2808
m3=4.5875litre

Methods of measuring Volume

1. From Cross Section
2. From spot heights
3. From contours
1. From Cross-section
For computation of the volume of earthwork, the sectional areas of the cross-section which are taken
transverse to the longitudinal section during profile levelling are first calculated. Cross-section may
be of different types. They are: level section, two-level section, Three-level Section, multi-level
section etc. After calculating cross-sectional areas, the volume of earthwork is calculated.

But, as per the course of study, we only practice cases of Level section. In this case width of
embankment is denoted by ‘b’, height is denoted by ‘h’ and Side
slope is denoted as S:1, Then
b+ b+2 sh
Cross Sectional Area ( A ) = ∗h=( b+ sh ) h
2
Earthwork estimation
Earthwork estimation refers determination of the quantity(volume) of earth material (soil, rock, etc.)
that needs to be excavated or added at a construction site. This estimation is very essential for
planning and budgeting purposes in construction projects.
<Procedures>
a. after the centerline has been staked, ground profiles
called cross sections are taken (at right angles to the
centerline), usually at intervals of full or half stations if
the English system of units is being used, or at perhaps
10, 20, 30, or 40 m if the metric system is being
employed.
b. Cross-sectioning consists of observing ground
elevations and their corresponding distances left and
right perpendicular to the centerline.
c. Readings must be taken at the centerline, at high and
 low points, and at locations where slope changes occur to determine the ground profile
accurately.
d. This can be done in the field using a level, level rod, and tape
Different methods can be used in earthwork estimation.We
can apply following methods for calculation.
A. Mean Sectional Area Method
B. Trapezoidal Rule
C. Prismoidal Rule

A. Mean sectional area method

Steps:
a. Consider the cross sectional areas of earth work at two given
sections as A1 & A2 which are at a distance ‘L’ apart.
A +A
b. Compute the mean area by A= 1 2
2
A1+ A2
c. Calculate volume of earth work between the two sections by volume (V) = A×L= ∗L
2

B. Trapezoidal rule
It is extended form of mean area method i.e. it is used when there are more than two sections,
Steps:
a. Consider different sections as A1, A2,
A3……An which are separated by common
distance ‘d’
b. Then compute the total volume of earth work
along the given section from the relation. Figure 7- 12 Trapezoidal rule
D
V= *(A0+An+2(A1+A2+A3+……..+An-1)
2
C. Prismoidal Rule
The volume V of a prismoid can be found using the prismoidal formula. The Prismoidal formula is
applicable when there are odd number of sections. If the number of sections are even, the end
section is treated separately and the area is calculated according to the trapezoidal rule. The volume
of the remaining section is calculated in the usual manner by the prismoidal formula. Then both the
result is added to obtain the total volume.
Steps:
a. Consider Ao and A1 as the areas of the faces in the two
parallel planes,
b. Take Am as the area of the intersection of the prismoid
with the plane parallel to the two planes and midway
between them. If h denotes the distance between the planes
with areas Ao and A1,
h
c. Calculates Volume V= ¿ 0+4Am+A1)
6
d. Convert into required unit.
e. If there are no of cross –sections separated by a common Figure 7- 13 Prismoidal Rule
distance D, then
D
V= [first area + last area + 4 ∑ Even area + 2 ∑ odd areas].
3
D
∴V= [A1 +An + 4(A2+ A4+..+An-1)+2(A3+A5+…+An-2)].
3
If there are 7 Croo-sections,then Figure 7- 14Applying Prismoidal Rule
D
V= [A1 +A7 + 4(A2+ A4+A6)+2(A3+A5)]
3
Prismoidal Correction:
a) The volume by the prismoidal formula is more accurate than any other method.
b) But the trapezoidal method is more often used for calculating the volume of earthwork in the field.
c) The difference between the volume computed by the trapezoidal formula and the prismoidal formula is
known as a prismoidal correction.
d) since the trapezoidal formula always overestimates the volume, the prismoidal correction is always
subtractive in nature is usually more than calculated by the prismoidal formula, therefore the prismoidal
correction is generally subtractive.
e) Volume by prismoidal formula = volume by the trapezoidal formula - prismoidal correction

2. From spot heights

Before diving into the calculations, it's essential to understand what spot levels are. They are the
elevations of specific points on the ground surface, usually determined through surveying. These
points are often evenly spaced for accurate volume calculations.
This method is commonly used for calculating volumes of excavations for basements, tanks, or other
areas where the sides and base are planes but the surface is irregular.
<Procedures>
a. Divide the whole area into a number of rectangles or triangles as shown in the figure below.
b. Set up instruments at suitable positions so that all corner station can set up with levelling staffs.
c. Take staff readings and calculate elevations of corner points before and also after excavation.
The depth of excavation at each corner point is measured. Then for each simple figure (rectangle
or triangle).

d. Measure the area of triangles or rectangle as

per the division of grid
e. Record the elevation value taking either
triangle or rectangles into consideration.
f. Interpolate value of elevation to find out
elevation value of exactly grid corner.
g. Average the elevation value for each grid/box
by applying formula as shown in the figure.
h. Add the average of all elevation value for
respective grid.

It may be noted that in Fig. total volume calculations Figure 7- 18 Using spot height for
depth of some corners appear once, some twice, some of volume
them 3 times and some 4 times. If

∑h1 = some of depths used once ∑h2 = sum of depths used twice
∑h3 = sum of depths used thrice ∑h4 = sum of depths used four times.
A
i. Then calculate the volume as V= (∑h1+2∑h2+3∑h3+4∑h4) for rectangular spot height grid.
4
For triangular spot height grid depth of some corners appear once, some twice, some of them 3
A
times and some 6 times so V= V= (∑h1+2∑h2+3∑h3+4∑h6)
3
j. Alternative method of calculation earthwork is shown in figure below.
j.1 Triangular grid
j.2 Rectangular grid

Figure 7- 19 Triangular grid spot height using for earthwork calculation

Figure 7- 20 Rectangular gular grid spot height using for earthwork calculation
3. From Contours
Contour is an imaginary line connection point of
equal elevation. The vertical distance between two
consecutive contour is called contour interval.
Contour interval is kept small for flat area whereas it is
kept large for sloppy areas. Horizontal distance
between two consecutive contour is horizontal equivalent. It is not constant It varies according to
terrain or sloppiness of the ground
The measurement of volume can be made by contour map. But volume computed by this method is
approximate as the full ground irregularities are not predicted by contours and contour intervals are
not small, Volume computed from this method is likely to be approximate. To compute volume
from this method general recommendation of the contour interval is max.2m for regular ground and
0.5m for irregular topography.
<Procedures>
a) Identify Contour Lines: Start by identifying the contour lines on the topographic map. Each
line represents a specific elevation level.
b) Determine Contour Interval: The contour interval is the vertical distance between two
consecutive contour lines. It is recommended to use a maximum interval of 2 meters for regular
ground surfaces and 0.5 meters for more detailed areas.
c) Divide the Area: Divide the area into sections or regular shapes (e.g., trapezoids or rectangles)
based on the contour lines. This helps in simplifying the volume calculation.
d) Calculate Area of Each Section: For each section, calculate the area based on the contour lines.
The area can be estimated using geometric formulas depending on the shape of the section.
e) Calculate Volume: The volume can be estimated by multiplying the average area of each
section by the contour interval. The formula for volume V between two contour lines can be
expressed as:
V=Area ×Contour Interval
f. Sum the Volumes: Add the volumes of all sections to get the total volume of the area being
analyzed.

If contour interval is constant, then it can be calculated as:

If we have to calculate volume from starting of the data collection to contour formation then,
Steps:
Figure 7- 24 Dividing the area into grid

a) Divide the region of interest into square or rectangular grid as

shown in the Figure 7- 25
b) Set up Total station or level machine at suitable position so
that all grid corners can be measured.
c) Hold prism or staff at grid corner perfectly vertical.
d) Collect the data and record it and plot the contour as in the
e) Find out the area of respective contour
f) Find the volume by either prismoidal or trapezoidal rule as in
the example below

Construction of mass-haul diagram

The mass haul diagram is a curve plotted on a distance base, the ordinate at any point of which
represents the algebraic sum up to that point of the volumes of cuttings and embankments from the
start of the project or from any arbitrary point. In obtaining the algebraic sum, cuttings are

considered positive and embankments

negative. Earth work consists of the

following four operations
 Cutting
 Loading
 Hauling
 Filling
The haulage cost depends on the weight
as well as the distance from the place of
excavation to the place of fill So a diagram, known as mass-haul diagram, is plotted to estimate this
task
Mass-haul diagram is a plot between the cumulative volume of earthwork and distance; ordinate
represents the volume and the abscissa represents the distance
Characteristics
 The mass-haul diagram rises in the case of cutting and
falls in the case of fillings
 The peak occurring at the end of an excavation is known as maxima point where as the peak
occurring at the end of the embankment is known as minima point
 The vertical distance between a maximum point and the next minimum point represents the total
volume of filling
 The vertical distance between a minimum point and the next maximum point represents the total
volume of cutting
 The vertical distance between two points on the curve represents the volume of earthwork (cut or
fill) between their chainage, provided there is no maximum or minimum point between them
 If the diagram cuts the base line at any two points in succession, the volume of cuttings between
the two points is equal to the volume of fillings, as the algebraic sum of the volume is zero
 The length of the base line intercepted by a loop of the diagram represents the maximum haul
distance in that section
 The area bounded by a loop of the diagram and the base line is known as the haul in that section
Cutting
The process of excavating earth material from a work location to
achieve the desired topography.
Filling
The process of moving the excavated material or additional
earth material to a work location to achieve the desired
topography
Haul: A haul refers to the transportation of your project’s
excavated materials. The haul includes the movement of
material from the position where you excavated it to the disposal
area or a specified location. A haul is also sometimes referred to as an authorized haul.
Overhaul: When you get authorization to haul material farther than the original free-haul distance,
the transportation of said material is called an overhaul.
Free haul: A free project’s average haul is referred to as a free haul.
Average haul: You can find the average haul using the mass diagram. The average haul is a specific
area in a mass diagram. It represents how many cubic yard stations are between balance points
divided by the ordinate of mass that the yardage gets hauled.
<Procedures>
a. Divide the length of the road (or railway) in separate reaches.
b. Compute the volume of earthwork for each reach.
c. Plot a L-section of each reach on a suitable scale.
d. Determine the accumulated volumes at various points taking the volume of starting point as 0.
e. Generally mass haul diagram is drawn below the L-section.
f. Plot the cumulative volumes as ordinates and the distance as abscissa.
g. Join the ends of the adjacent ordinates by a smooth curve.
Figure 7- 30 Construction of Mass-haul diagram for Earthwork calculation

Exercise