Introduction, triangulation, principle and uses of triangulation, triangulation systems and its classification, well-conditioned triangles, strength of figure, selection of triangulation stations and their inter-visibility, stations marks, signals, towers and scaffolds, base line, site selection and base line measurement, tape corrections, the base net, extension of base line, satellite station and reduction to centre.

1. 1
PREPARED BY : ASST. PROF. VATSAL D. PATEL
MAHATMA GANDHI INSTITUTE OF
TECHNICAL EDUCATION &
RESEARCH CENTRE, NAVSARI.

2.  The Plane surveying is that type of the surveying in which
earth surface is consider as a plane and the curvature of the
earth surface is ignored.
 While the geodetic surveying is that type of survey in which
the curvature of the earth is taken into account. It generally
extends over large areas.
2

3. Plane Surveying Geodetic Surveying
The earth surface is considered as
plane.
The earth surface is considered as
curved surface.
The curvature of the earth is ignored. The curvature of the earth is taken in
to account.
Line joining any two station are
considered to be straight line.
Line joining any two station are
considered to be curve line.
The triangle formed are considered as
a plane.
The triangle formed are considered as
a Spherical.
The angle of triangle considered as
plane angle.
The angle of triangle considered as
Spherical angle.
Carried out for small area < 250 m2. Carried out for large area > 250 m2.
3

4.  Horizontal control usually consists of a combination of
traverse and triangulation.
 For a small area, the horizontal control survey may consist of
one or more connecting traverses.
 However, for large area, a horizontal control survey usually
consists of triangulation. A horizontal control survey usually
involves the measurements of horizontal angles and distances.
4

5.  The horizontal control in Geodetic survey is established by
triangulation, trilateration, and precise traversing.
 Of the three, triangulation is the most popular method.
Triangulation is preferred for hills and undulating areas, since
it is easy to establish stations at reasonable distances apart,
with intervisibility. Method of triangulation is more accurate
as accumulation of error in triangulation is less as compared to
that of traversing.
5

6.  Entire survey area is covered by the triangle.
 Three angle and one line is measured.
 The length of the first line is measured is called base line.
6

7.  Marking the horizontal control points for plane and geodetic
survey.
 Mark the points for aerial photography.
 Find out the accurate location of engineering.
 Transfer the control points across the large water bodies.
 For deciding the direction of the movement of clouds.
 Find out the size and the shape of the area.
7

8.  The area of the triangles are known as triangulation stations.
 Whole figure is known as triangulation figure.
 Arrangement of the various triangulation system are known as
the layout of triangulation.
8

9.  Single chain of triangle
 Double chain of triangle
 Braced quadrilaterals in chain
 Centered triangles polygons
 Grid iron system
 Central system
9

10. Single chain of triangle Double chain of triangle
 Narrow strip of land is
covered.
 System is economical and
rapid.
 Cover large area.
 If the width is large so this
method is used.
10

11. Braced quadrilaterals in
chain
Centered triangles &
polygons
 Used for hilly area.
 Four station and two observer
diagonals in each quadrilateral.
 No station at the intersection.
 Its overlapping triangles.
 This method is used to measure
the vast area.
 The centered figures generally
are triangles, quadrilateral
triangles, pentagons or hexagon
with central station.
 Centered station is called vertex to
all triangle.
11

12. Grid iron system Central system
 System is used for the large
area.
 Primary triangulation is laid in
series of the chain.
 Generally run in two
approximately perpendicular
direction, generally east-west
and north south direction.
 Method is used for the survey
area which is extended.
 Whole area is covered by
the net work.
12

13.  The classification of a triangulation is based upon the degree
of accuracy required. It depends upon the extent of the area to
be surveyed, length of the base, length of the sides and
triangular misclosure. On the basis of accuracy and purpose,
triangulation systems are classified as under :
1. First order or Primary triangulation
2. Second order or Secondary triangulation
3. Third order or Tertiary triangulation
13

14.  A first order triangulation is the highest order triangulation and
is carried out either to determine the earth's figure (shape and
size of the earth's surface) or for providing the most precise
control points to which secondary triangulation may be
connected.
14

15.  The lengths of the sides of the triangle are large. The stations
are precisely located 16 km to 150 km apart. Precise
instruments are used for observations and every precaution is
taken in making linear, angular and astronomical observations
and in performing the reductions (calculations).
15

16.  A second order triangulation is employed for running a second
series - of triangles by fixing points at close intervals inside
the primary series of triangles. It provides control points closer
than those of the primary triangulation. It is connected to the
primary triangulation stations at various points.
16

17.  This system of triangulation is used to provide control points
fixed within the framework of secondary triangulation.
 This triangulation gives a set of control points which are
normally used by agencies conducting engineering surveys i.e.
topographic surveys, hydrographic surveys and other such
projects where lower accuracy can be accepted.
17

18.  The length of the sides of the triangle depends upon many
factors. It varies according to the order of the triangulation and
topography of the country.
18

19.  In a system of triangulation, the angles and the base line are
subjected to the errors of measurement. The accuracy achieved
depends upon the shape of the triangle.
 The shape of the triangle should be such that the sides of the
triangle computed with the measured angles are least affected
by any error in the angles such a triangle is then called well-
conditioned triangle. The triangles used in a triangulation
system should be well-conditioned.
19

20.  In any triangle of a triangulation system, the length of one side
is known from the computations of the adjacent triangle. The
error in the other two sides will affect the rest of the triangles.
Due to accumulated errors, the entire triangulation system is
thus affected.
 To ensure that the two computed sides of a triangle are equally
affected, they should be equal in length. This can be attained
by making the triangle isosceles.
20

21.  The strength of the figures in triangulation plays an important
role. It is considered in establishing a triangulation system for
which the computations can be maintained within a desired
degree of precision.
 The accuracy of a triangulation system depends not only on
the methods and precise instruments used in making
observations but also on shapes of figures in the triangulation
network.
21

22.  The strength of the triangulation system may be defined as the
number which gives the least error in the computed length of
the last line of the system due to the shape of triangle and the
composition of the figures.
22

23.  Stations should be intervisible. For this purpose stations are
placed on the highest points of the elevated ground such as hill
tops, house tops, etc.
 Stations should form well-conditioned triangles. In general, no
angle should be less than 30o
or more than 120o
. As far as
possible, the triangles should be isosceles with base angles of
about 56o
or they should be equilateral triangles.
23

24.  Station should be easily accessible. Supplies of food and water
should be available. There should be a suitable place for
camping or nearest suitable accommodation is available.
 Stations should be so selected that the survey lines are not too
long. Small sights lead to inaccurate centring, while long ones
cause inaccurate bisection of the signal.
 Stations should be so selected that the cost of clearing, Cutting
trees and erecting towers is minimum.
24

25.  Stations should be in commanding positions so as to serve as
control for subsidiary triangulation or detailed surveys inside
the network.
 Stations should be selected so that the line of sight do not pass
over crowded localities such as cities, town, factories, etc. to
avoid irregular atmospheric refraction. The line of sight should
not graze ground or other obstruction. It should pass at least 2
to 3 m above the ground.
25

26.  The most essential condition of triangulation is that the
stations should be intervisibility. As stated earlier, the stations
should be chosen on high ground so that they are inter-visible.
 For small distances, intervisibility can be ascertained during
reconnaissance by direct observations with the help of
powerful binoculars either at ground level or from the tops of
trees.
26

27.  The exact positions of the triangulation stations should be
permanently marked so that the theodolite and signal can be
centred accurately over them.
 The object of station marks is to provide a surface mark with a
permanent mark buried below, and a good target. Depending
upon the nature and purpose of triangulation, stations are fixed
and they are permanently marked.
27

28.  It should also include a complete description to enable the
station to be recovered even after many years.
 Each station is also identified by local reference marks which
are the permanent features of that area. The marking is done
on a copper or brass tablet with the station identification
clearly marked. The name of station and the year in which it is
set should be stamped on the tablet.
28

29.  The following points should be considered while marking the
exact position :
 The mark should be distinctive and indestructible. The station
should be marked on a perfectly stable foundation or rock. If
the size of rock is so large, the station mark on a such large
rock is generally preferred so that the theodolite and surveyor
can stand on it.
29

30.  Generally, a hole 10 to 15 cm deep is drilled into the rock and
a copper or iron bolt is fixed in the hole in cement mortar.
 In some area, if rock is not available, a large stone is
embedded about 1 m deep into the ground. A circle and a dot
are cut on it. A second stone with a circle and a dot is placed
vertically above the first stone.
 A G.I. pipe about 25 cm diameter driven vertically into the
ground upto a depth of 1 m can also serve as a station mark.
30

31.  The mark may be set on a concrete monument also. The
station should be marked with a bronze or copper tablet. The
name of the station and the date on which it was set should be
stamped on the tablet.
31

32.  In earth, generally two marks are set, one about 75 cm below
the surface of the ground and the other extending a few
centimetres above the surface of the ground. The underground
mark may consist of a stone with a copper bolt in the centre or
a concrete monument with a tablet mark set on it.
32

33.  The station mark with a vertical pole placed centrally should
be covered with a conical heep of stones placed symmetrically.
The arrangement of marking a station, is known as placing a
cairn.
33

34.  Two or three reference mark similar in material and shape to
the station mark, should be provided around the station mark.
The distances and bearings of these reference marks from the
station mark and from each other should be recorded on them.
If station is disturbed, it is re-established by using these
reference marks.
34

35.  Surrounding the station mark a platform 3 m x 3 m x 0.5 m
should be built up of earth. It provides rigid support for the
instrument and the signal.
 At each station where a tall signal tower is required, an
azimuth mark should be established at some distance away
from the station mark. It should be of the same size and .
character as the reference mark.
35

36.  They are devices erected to define the exact position of an
observed station. Signals are used to define the exact position
of triangulation stations during observation from other
stations. Signals are centred vertically over the station mark.
 The accuracy of triangulation depends to a large extent on the
proper centring of the signals. Therefore, it is very essential
that the signals are truly vertical, and centred exactly over the
station mark.
36

37.  Signals should satisfy the following requirements :
 It should be conspicuous, i.e. clearly visible against any
background.
 It should be capable of being accurately centred over the
station mark.
 It should be of suitable size for accurate bisection.
37

38.  It should be from phase or it should exhibit little phase.
 It should be symmetrical and easy to erect in minimum time.
 It should carry a flag on its top.
38

39.  Signals can be classified into three types :
1. Daylight or opaque (non-luminous) signals
2. Luminous signals
3. Night signals
39

40.  Opaque signals (Non-luminous signals) :
 These are used for triangulation with less accuracy and for
sights not exceeding 30 km.
 They are used during day time observations.
 They consist of various forms of poles, masts and targets.
40

41.  Pole signal :
 If pole is used when the angle of measurement at the station is
not required and the sights are less than 6 km.
 It consists of a round pole pointed black and white in alternate
strips. It is supported vertically over the station mark,
generally on a tripod or quadripod.
41

42.  Target signal :
 A target signal consists of a pole carrying two Square or
rectangular targets placed at right angles to each other.
 The targets are generally made of cloth stretched on wooden
frames. Target signal is suitable upto a distance of 30 km.
42

43.  Pole and brush signal :
 It consists of a straight pole about 2.5 m long with a bunch of
long grass tied symmetrically around its top to form a cross
shape. The signal is erected vertically over the station mark by
heaping a pile of stones, upto 1.7 m round the pole. A coat of
white wash is applied to the signal to make it conspicuous.
43

44.  Stone cairn :
 A heap of stones is placed around the base. A stone cairn is a
conical heap of stones, about 3 m high.
 A cross shape signal is erected over the stone heap.
44

45.  Beacon :
 It consists of red and white cloth tied round the three straight
poles. This can be easily centred over the station mark, It is
very useful for making simultaneous observations.
45

46.  Beacon :
 To make the signal conspicuous, a flag tied to the top of the
Signal. The diameter of the signal is about 1.3D to 1.9D (cm),
where D is the distance in km.
 The height of the signal is about 13.3D (cm), the vertical angle
to the signal being at least 30°. The signal should be dark in
colour for visibility against the sky. In general, opaque signals
are cheaper than luminous signals and are used for distances.
46

47.  Luminous signals :
 Luminous signals are also known as sun signals as they are
based upon the reflection of the sun's rays from a mirror. Such
signals can be used only in day time when the weather is clear.
They can be used for long distances.
 For geodetic work it is a general practice to make observations
on luminous signals. These have the advantage of distinct and
clear visibility even for long distances (more than 30 km).
47

48.  Heliotrope :
 A heliotrope essentially consists of a plane mirror for
reflecting the sun's rays and a line of sight to direct the
reflected rays towards the observer.
 Heliotrope may be simply a sight vane with an aperture and
cross hairs, or it may be telescopic.
48

49.  Heliotrope :
49

50.  Heliotrope :
 There is a small hole at the centre of the mirror, and a sight
vane with an aperture carrying cross hairs. The line of sight
passes from the mirror hole to the centre of cross-hairs.
 The circular mirror can be rotated horizontally as well as
vertically through 360°. The heliotrope is centred over the
station mark, and the line of sight is directed towards the
station of observation.
50

51.  Heliotrope :
 Flashes are sent from the observing station to establish the line
of sight. The mirror should be adjusted every few minutes
since the direction of the sun goes on changing. A form of
heliotrope is the Galton sun signal, used for lines of sight
exceeding 30 km.
51

52.  Heliotrope :
 A telescope is sometimes used instead of the sight vane to
form a telescope line of sight.
 The best time for observation with helios is towards sunset.
The heliotrope reflects a continuous beam of light, whereas a
heliograph reflects periodic beams.
52

53.  The following points should be noted :
 The heliotropes do not give better results compared to the
opaque signals.
 These are useful when the signal station is in flat plane, and
the station of observation is on elevated ground.
 When the distance between the stations exceed 30 km, the
heliotropes become very useful.
53

54.  The following points should be noted :
 These are very cheap and have no running and operating cost.
 But use of these signals for first order triangulation is
restricted since it can be used on sunny days only.
54

55.  Night signals :
 When the observations are required to be made at night, the
night signals may be used. Various type of night signals are :
 Various forms of oil lamps with parabolic reflectors for sights
less than 80 km.
 Acetylene lamps designed by Captain G.T. McCaw for sights
more than 80 km.
55

56.  Night signals :
 Magnesium lamps with parabolic reflectors are used for long
sights.
 Sometimes electric lamps are also used.
56

57.  A tower is erected when it is desired to elevate the instrument
or signal, above the triangulation station, to obtain a line of
sight clear of obstructions.
 Tower is temporary structure constructed for the purpose of
surveying to elevate instrument and signals.
 The height of tower depends upon the character of the terrain
and the length of sight.
57

58.  The structure actually consists of two towers one inside the
other.
58

59.  The-inner structure-supports the instrument only whereas the
outer structure supports the observer and the signal. This is
done to avoid any disturbance to the towers due to the
movement of the survey party.
59

60.  The two towers may be made of masonry, timber or steel. For
small heights, masonry towers are most suitable.
 Timber scaffolds are most commonly used, and have been
constructed to heights over 50 m. For greater heights, steel
towers are commonly used.
 Steel towers made of light sections are very portable and can
be easily erected and dismantled and transported.
60

61.  Bilby towers patented by J.S. Bilby of the U.S. Coast and
Geodetic survey, are popular for heights ranging from 30 to 40
m, with a beacon 3 m higher. Five persons can errect this
tower weighing about 3 tonnes in just 5 hours.
61

62.  Scaffolds :
 For first order. and second order triangulation, occasionally the
scaffolds are used across plain. They are portable and may be
made with steel or timber. These are used for small height,
generally 10 to 15 m.
62

63.  Scaffolds :
 The scaffolds are also made with a double structure similar to
towers. The two towers should be entirely independent of each
other so that the movement of the observer does not disturb
the instrument.
63

64.  Accuracy of any triangular is depend on measurement of the
base line.
 Length of the base line is one-third or two third of the side.
 Primary triangulation system of India, 9 base line of length
varying from 10.30 km to 12.55 km
64

65.  Site should be firm and levelled.
 Site should be free from obstruction.
 Line should be indivisible.
 Selected site should be such that well-condition triangle.
 Take minimum length of the base line.
 Cost of the clearing of the ground should be minimum.
 Base line should pass through the Centre of the area.
65

66.  Base is connected through the triangulation system by the
base net.
 The connection between the base and the main network is
achieved through the small network called base net.
66

67.  Usually length of the base line is much shorter.
 Base line select shorter length by two reasons :
1. Not get possible site for longer base.
2. Difficult to measure long length.
67

68.  Points to be kept in mind for selecting base net :
 Small angle opposite the known sides must be avoided.
 A ratio of the base length and the side length should be at
least 0.5.
 The net should have sufficient redundant line.
 Length of the base line should be long a possible so the
quickest extension by few station.
68

69.  Two ways of connecting the selected base to the triangulation
stations :
69
Base extension by
prolongation
Base extension by
double sighting

70.  Short base is called hunter’s short base by Dr. Hunter who
was director of the survey of the India.
 The short base consist of the four chain and each chain
20.117m long. Each chain support between two stand.
 There are main five stand and in this five stand there are three
stand of the two legged and two main stand are three legged.
 Three legged stand are fixed at the end.
 The end of the chain is fixed at the both end.
70

71.  The weight of 1kg is suspended at the end of the chain so all
the chain are in the tensile form and make chain straight.
 The length of the joints between two chains at intermediate
support are measured .
 To obtain correct length between the centers of the target usual
correction for temperature ,sag, slope, tension, reduction to
MSL. etc. are applied.
71

72.  Marked the station A and B.
 Station A marked with red colour and station B marked with
green colour.
 The stand of A is centered on the marked ground A.
 The end of the base is hooked with the plate A.
 The another end is fixed at station B.
72

73.  At the stand B 1kg of the weight is attached at the end of the
lever.
 Approximate alignment of the base line checked by eye
judgment and finally is done by using a theodolite.
73

74.  The following correction to the base line measurement are
apply to get the correct length of the base line :
74
Correction for
absolute length
Correction for
temperature
Correction for
tension
Correction for
sag
Correction for
slope
Correction for
alignment
Correction for
MSL (mean sea
level)

75.  Nature of the correction are +ve or –ve.
 If the actual length of the tap is not equal to the nominal or
designated length, a correction will be applied to measure the
line.
 If the actual length of the tap is greater than the nominal length
the measured distance is too short and the correction will be
additive.
75

76.  If the actual length of the tap is shorter than the nominal length
the measured distance is too long and the correction will be
negative.
Ca = (L * C) / l
Where , Ca = Correction for actual length
L = Measured length of line
C = Correction per tap length
l = designated length of the tap
76

77.  Nature of the correction are +ve or –ve.
 The length of the is increase or decrease with increase or
decrease in standard temperature.
77

78.  Ct = α (Tm – Ts) L
 Where , Ct = Correction of temperature in m
α = Co-efficient of the thermal expansion
Tm = Mean temperature during measurement
Ts = Standard temp. for tap
L = Length of the tap in m
78

79.  The average value of the thermal expansion for steel 12 x 10-6
and for invar tape 0.9 x 10-6 per degree Celsius.
 Ct will be positive if Tm > Ts and Ct will be negative if Tm < Ts.
79

80.  Nature of the correction are +ve or –ve.
 The correction of the pull is necessary when the pull applied
during measurement differ from that at which tap is
standardized.
80

81.  .
 Where , Cp= Correction of pull
Pm = Pull applied during measurement in N
Ps = Pull at which the tap is standardized in N
L = Length of the tap in m
A = Cross-sectional area of the tap in mm2 or cm2
E = modulus of elasticity of the tape material
81

82.  Where, E may be taken as,
 E = 2.1 X 107 N/cm2 for steel
 E = 1.5 X 107 N/cm2 for invar
 The correction may be positive or negative is according to Pm is
greater or less than Ps .
82

83.  Nature of the correction is +ve or –ve
 When a tap is stretched between two support, it takes the form of sag
which is assumed to be parabolic curve.
 In the sag correction is always –ve.
83

84.  The correction for the slope are required when the point of support
are not at the same level.
84

85.  Generally line is set out as a straight line. But some time necessary to
bent path due to an obstruction. The bent line is composed of a two
straight lines.
 AC = l1 and CB = l2
 Angle BAC = θ1 and AngleABC = θ2
 AB = l1 Cos θ1 + l2 Cos θ2
 The require correction for alignment = Cm
 Cm = (l1 + l2) – (l1 Cos θ1 + l2 Cos θ2)
85
A B
C

86.  The measured length of a line at an altitude of h meter above the
mean sea level will be more as compare to the corresponding line on
the mean sea level.
86

87.  L = measured horizontal distance an altitude of h meter above the
mean sea level.
 D = distance reduced to mean sea level
 h = altitude above the mean sea level
 R = Radius of Earth
 θ = the angle subtended by lineAB
 From the property of the circle L= (R + h) θ, D = R θ
87

88.  From the property of the circle
 L= (R + h) θ
 D = R θ
 From above equations,
OR
88

89.  The altitude correction is given by,
 As h is very small compared to R, it can be neglected in the
denominator.
 Thus, Cr = So, the correction is negative.
89

90.  After the base line measurement the next procedure is to make
the triangle.
 For making the triangle the horizontal angle is required.
 Horizontal angle are also measured with the help of the
electronic theodolite for primary and secondary triangle.
 For the tertiary triangle generally transit theodolite is used.
90

91.  There are main two method is used to find out the
horizontal angle.
1. Method of repetition
2. Method of reiteration
91

92.  In this method the angle are measured in number of time
repeatedly.
 Taking face left and face right reading.
 To measure the angle ABC, make six face left reading and
angle measured in clockwise direction and find the average of
the reading.
 To measure the angle ABC, make six face right reading and
angle measured in anti clockwise direction and find the
average of the reading.
92

93.  The method of the reiteration is used when a number of angle
are to be measured at a triangulation station.
 This method uses the principle of closing of horizon, the
reading should be same as the initial reading.
 If any error seen so error is distributed in all the angle.
 One of the triangulation station, which is likely to be visible
may be selected as a reference point.
93

94.  In this method face left and face right reading are taken in
number of time and then after the average reading we get is the
final reading.
94

95.  For clearly seen the station and make well conditioned
triangle, sometimes high objects like church spire, tower,
temple, etc. are selected as a triangulation station.
 It is impossible to set the instrument exactly over or under the
such station to measure the angle.
95

96.  In this case subsidiary station is selected near the main station
as a instrument station and this subsidiary station are called
satellite or eccentric station.
 Observation are taken to other station from the subsidiary
station.
 The distance between the true station to satellite station is
called satellite distance.
96

97.  The angle of the satellite station are measured same care taken
no any type of the error done for taking reading.
 The operation of applying the correction due to the satellite
station is generally known as reduction to centre.
 Fro each angle at the true station one additional angle at the
satellite station must be measured.
97

98.  Satellite station must be avoided in primary triangulation.
 Fig shows the different cases that can be regarding the position
of the satellite station relative to the true station.
98

99.  Now apply the sine rule for the triangle BAS1
 Now apply the sine rule for the triangle BCS1
99

100.  Multiplied both the side by Sin1’’ for equation 1
 Multiplied both the side by Sin1’’ for equation 2
 From the triangle OAS1 angle
 From the triangle OBC angle
100

101. 10
1