Module 2

Theodolite Traversing and Tacheometry

2.1 Theodolite Traversing

Traversing is a method of establishing control points by measuring angles and distances between them
using surveying instruments.
2.1.1Types of Traverses:
1. Open Traverse – Does not return to the starting point. Used in roads, canals, etc.
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 2. Closed Traverse – Returns to the starting point or connects between two known points. Used
for boundary surveys.
2.2 Methods of Theodolite Traversing:
2.2.1 Traversing By Direct Observation of Angles
In this method, the angles between the lines are directly measured by a theodolite. The method is
therefore most accurate in comparison to the previous three methods. The magnetic bearing of any line
can also be measured (if required) and the magnetic bearing of other lines can be calculated. The angles
measured at different stations may be either (a) included angles or (b) deflection angles.
(i)Traversing by included angle
An included angle at a station is either of the two angles formed by the two survey lines meeting there.
The method consists simply in measuring each angle directly from a backsight on the preceding station.
The angles may also be measured by repetition, if so desired. Both face observations must be taken and
both the vernier should be read. Included angles can be measured either clockwise or counter-clockwise
but it is better to measure all angles clockwise, since the graduations of the theodolite circle increase in
this direction. The angles measured clockwise from the back station may be interior or exterior
depending upon the direction of progress round the survey. Thus, in Fig (a), direction of progress is
counter-clockwise and hence the angles measured clockwise are directly the interior angles. In Fig (b),
the direction of progress around the survey is clockwise and hence angles measured clockwise are
exterior angles.
(ii) Traversing by deflection angles
A deflection angle is the angle which a survey line makes with the prolongation of the preceding line. It
is designed as right (R) or left (L) according as it is measured clockwise or anti-clockwise from the
prolongation of the previous line.
This method of traversing is more suitable for survey of roads, railways, pipe-lines etc. where the
survey lines make small deflection angles. Great care must be taken in recording and plotting whether
it is right deflection angle or left deflection angle. However, except for specialized work in which
deflection angles are required, it is preferable to read the included angles by reading clockwise from the
back station. Lengths of lines are measured precisely using a steel tape.
2.2.2 Measurement of bearing of a traverse leg
In land surveying, the bearing of a traverse leg refers to the horizontal angle between a reference
direction (usually true north, magnetic north, or grid north) and the line connecting two successive
traverse stations. Bearings can be measured using several methods. Two common methods are the
Direct Method and the Back Bearing Method.
(i). Direct Method of Measuring Bearing
Definition:
The direct method involves measuring the bearing of a traverse leg from the starting station to the next
station using a compass or theodolite.
Procedure:
2
  Set up the instrument (compass or theodolite) at the starting point (station A).
 Sight the line to the next point (station B).
 Measure the angle between the reference meridian (e.g., magnetic north) and the line AB.
 The measured value is the bearing of line AB.
(ii). Back Bearing Method
Definition:
The back bearing is the bearing taken in the reverse direction of a line. It is measured by setting up the
instrument at the forward station and sighting back toward the previous station.
Procedure:
 Set up the instrument at station B (the forward point).
 Sight back to station A.
 Measure the angle between the reference meridian and the line BA.
 This gives the back bearing of AB, which ideally should be equal to the forward bearing ± 180°.

2.3 Traverse Computations:

Technical Terms:
 Latitude (L): Projection of a line on the N-S axis.
 Departure (D): Projection on the E-W axis.
 Consecutive Coordinates: Based on a reference point and each traverse leg.
 Independent Coordinates: Coordinates calculated relative to the first point.
Coordinate Computations:
Using angle and distance:

3
2.3.1 Consecutive co-ordinates: latitude and departure

The latitude of a survey line may be defined as its co-ordinate length measured
parallel to an assumed meridian direction (i.e. true north or magnetic north or any other reference
direction). The departure of survey line may be defined as its co-ordinate length measured at
right angles to the meridian direction. The latitude (L) of the line is positive when measured
northward (or upward) and is termed as northing; the latitude is negative when measured
southward (or downward) and is termed as southing. Similarly, the departure (D) of the line is
positive when measured eastward and is termed as easting, the departure is negative when
measured westward and is termed as westing.

D=l sin 𝜃
B
IV I
(+, -) l (+, +)

L=l cos 𝜃
�
�

A
III II
(-, -)
(-, +)

Fig 2.1 Consecutive co-ordinates

4
 Thus in Fig. the latitude and departure of the line AB of length 1 and reduced bearing 𝜃 are

L = + 1 cos 𝜃
given by

D = + 1 sin 𝜃
To calculate the latitudes and departure of the traverse lines, therefore, it is first essential to
reduce the bearing in the quadrantal system. The sign of latitudes and departures will depend
upon the reduced bearing of a line. The following table gives signs of latitudes and departures.

Table 2.1 Quadrant

W.C.B R.B. and Quadrant Sign of Latitude Sign of Departure
N 𝜃 E: I
S 𝜃 E: II
0 0
0 to 90 + +

S 𝜃 W:
900 to 1800 - +
1800 to 2700 - -

N 𝜃 W: IV
2700 to 3600 III + -

Thus, latitude and departure co-ordinates of any point with reference to the preceding point
are equal to the latitude and departure of the line joining the preceding point to the point under
consideration. Such co-ordinates are also known as consecutive co-ordinates or dependent co-
ordinates.

Problem 1: Calculate latitude and departure of the following traverse

Line Length (m) WCD
AB 232 320 12`
BC 148 1380 36`
CD 417 2020 24`
DE 372 2920

Line Length (l) WCB RB (𝜃) L = l cos 𝜃 D = l sin 𝜃

N S E W
AB 232 32012` N 32012` E 196.32 123.63
BC 148 138036` S 41024` E 111.02 97.87
CD 417 202024` S 22024` W 385.54 158.91
DE 372 2920 N 680 W 139.35 344.91

2.3.2 Independent co-ordinate

The co-ordinates of traverse stations can be calculated with respect to a common origin.
The total latitude and departure of any point with respect to a common origin are known as
independent co-ordinates or total co-ordinates of the point. The two reference axes in this case
may be chosen to pass through any of the traverse station but generally a most westerly station is
chosen for this purpose. The independent co-ordinates of any point may be obtained by adding
algebraically the latitudes and the departure of the lines between that point and the origin.

5
 Thus, total latitude (or departure) of end point of a traverse = total latitudes (or departures).
The axes are so chosen that the whole of the survey lines lie in the north east quadrant with
respect to the origin so that the co-ordinates of all the points are positive. To achieve this,
arbitrary values of co-ordinates are assigned to the starting point and co-ordinates of other points
are calculated.

Problem 2: Calculate total coordinate of the following traverse

Line Length WCD
(m)
AB 232 320 12`
BC 148 1380 36`
CD 417 2020 24`
DE 372 2920

Dependent co-ordinates Total co-

L = 𝓁 cos 𝜃 D = 𝓁 sin 𝜃
Stn Line Length WCB RB ordinates
L D
N S E W N E
A 600 700
AB 232 32012` N 32012` E
B 196.32 123.63 796.32 823.63
BC 148 138036` S 41024` E
C 111.02 97.87 685.3 921.5
CD 417 202024` S 22024`W
D 385.54 158.91 299.76 762.59

DE 372 2920 N 680W

E 139.35 344.91 439.11 417.68

6
2.4 Closing error

If a closed traverse is plotted according to the field measurements, the end point of the
traverse will coincide exactly with the starting point, owing to the errors in the field
measurements of angles and distances. Such error is known as closing error.

Fig 2.2 Closing error

In a closed traverse, algebraic sum of the latitudes (i.e. ∑𝐿) should be zero and the

may ascertained by finding ∑𝐿 and ∑𝐷, both of these being the components of error ℯ parallel
algebraic sum of the departures (i.e. ∑𝐷) should be zero. The error of closure for such traverse

and perpendicular to the meridian.

Closing error ℯ = AA' = √(∑𝐿)2 + (∑𝐷)2

The direction of closing error is given by

tan 𝛿 =
Z𝐷

Z𝐿
The sign of ∑𝐿 and ∑𝐷 will thus define the quadrant in which the closing error lies. The
relative error of closure is

𝐸𝑟𝑟𝑜𝑟 𝑜𝑓 𝑐𝑙𝑜𝑠𝑢𝑟𝑒 1
ℯ
= = =
𝑝⁄
𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑒
𝑡𝑟𝑎𝑣𝑒𝑟𝑠𝑒
𝒫

7
 Adjustment of the angular error

Before calculating latitudes and departures, the traverse angles should be adjusted to
satisfy geometric conditions. In a closed traverse, the sum of interior angles should be equal to
(2N – 4) right angles (or the algebraic sum of deflection angles should be 360 0). If the angles are
measured with the same degree of precision, the error in the sum of angles may be distributed
equally to each angle of the traverse. If the angular error is small, it may be arbitrarily distributed
among two or three angles.

Adjustment of bearings

in a closed traverse in which bearings are observed, the closing error in bearing may be

of traverse. Let ℯ be the closing error in bearing of last line of a closed traverse having N sides.
determined by comparing the two bearings of the last line as observed at the first and last stations

We get

Correction for first line = 𝑒

𝑁

𝑁
Correction for second line = 2𝑒

𝑁
Correction for third line = 3𝑒
𝑁𝑒
𝑁
Correction for last line = =e

2.5 Balancing the traverse

The term ‘balancing’ is generally applied to the operation of applying corrections to

latitudes and departures so that ∑𝐿 = 0 and ∑𝐷 = 0. This applies only when the survey forms a
closed polygon.
The following are common methods of adjusting a traverse:
1. Bowditch’s method
2. Transit method
3. Graphical method
4. Axis method

2.5.1 Bowditch’s method

The basis of this method is on the assumptions that the errors in linear measurements are
proportional to √𝑙 and that the errors in angular measurements are inversely proportional to √𝑙
where l is the length of a line. The Bowditch’s rule, also termed as the compass rule, is mostly
used to balance a traverse where linear and angular measurements are of equal precision. The
total error in latitude and in the departure is distributed in proportion to the lengths of the sides.

The Bowditich Rule is:

Correction to latitude (or departure) of any side
𝑙𝑒𝑛g𝑡ℎ 𝑜𝑓 𝑡ℎ𝑎𝑡 𝑠𝑖𝑑𝑒
𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑡𝑟𝑎𝑣𝑒𝑟𝑠𝑒
= Total error in latitude (or departure) x

8
Thus if,
CL = correction to latitude of any side
CD = correction of departure of any side
∑𝐷 = total error in latitude
∑𝐿 = total error in departure
∑𝑙 = length of the
perimeter l = length of any
side
We have, CL = ∑𝐿 x and CD = ∑𝐷 x 𝑙
𝑙 Z𝑙
Z𝑙

2.5.2 Transit
method

The transit rule may be employed where angular measurements are more precise than the
linear measurements. According to this rule, the total error in latitudes and in departures is
distributed in proportion to the latitudes and departures of the sides. It is claimed that the angles
are less affected by corrections applied by transit method than by those by Bowditich’s method.

The transit rule is

Correction to latitude (or departure) of any side =

𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒 (𝑜𝑟 𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒)𝑜𝑓 𝑡ℎ𝑎𝑡 𝑙𝑖𝑛𝑒

𝐴𝑟𝑖𝑡ℎ𝑚𝑒𝑡𝑖𝑐 𝑠𝑢𝑚 𝑜𝑓 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒𝑠 (𝑜𝑟
𝑑𝑒𝑝𝑎𝑟𝑡𝑢𝑟𝑒𝑠)
x

Thus if,
L = latitude of any line
D = departure of any
line
L1 = arithmetic sum of latitudes
D1 = arithmetic sum of departure
and CD = ∑𝐷 x 𝐷
We have, CL = ∑𝐿 x
𝐿
𝐷𝑇
𝐿𝑇

9
2.6 Gales traverse table

Traverse computations are usually done in a tabular form, a more common form being
Gales traverse table. For complete traverse computations, the following steps are usually
necessary:
 right angles and exterior angles (2N + 4) right in the case of a compass traverse, the
bearings are adjusted for local attraction, if any.
 Starting with observed bearings of one line, calculate the bearings of all other lines.
Reduce all bearings to quadrantal system.
 Calculate the consecutive co-ordinates (i.e latitudes and departures).
 Calculate ∑𝐿 and ∑𝐷
 Apply necessary corrections to the latitudes and departures of the lines so that ∑𝐿 = 0
and ∑𝐷 = 0. The corrections may be applied either by transit rule or by compass rule
depending upon the type of traverse.
 Using the corrected consecutive co-ordinates, calculate the independent co-ordinates to
the points so that they are all positive, the whole of the traverse thus lying in the North
east quadrant.

Problem 3: The length and bearing of a closed traverse ABCD, as observed with transit
theodolite, are given below. Prepare a Gale’s traverse table.

Line Length (m) Included Angle WCB

AB 250 < A = 950 24` 860 42`
BC 123 < B = 880 42`
CD 256 < C = 880 12`
DA 108 <D = 880 06`

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Geometric check:

Sum of interior angle = (2N – 4)900

LHS = < A + < B + < C + < D = 360024`0``

RHS = (2N – 4)900 = (2 x 4 – 4)900

N=4 = 3600

∴ error = 360024` – 3600 = 24`

∴ correction = -24`

Correction to each angle = −24` = -6`

4

Reduced bearing from induced angle:

Bearing of any line = [bearing of previous line + measured clockwise angle] ± 1800

: FB of AD = [FB of BA + < A] ± 1800

= [(FB of AB ± 1800) + corrected < A] ± 1800

= [(86042` + 1800) + 95018`] -1800

= 3620 – 1820 = 1820

: FB of DC = [FB of AD + < D] ± 1800

= [1820 + 880] – 1800

= 900

: FB of CB = [FB of DC + < C] ± 1800

= [900 + 88006`] +1800

= 35806`

: FB of BA = [FB of CB + < B] ± 1800

= [35806` + 88036`] -1800

= 266042`
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WCB:
FAB = FBA ± 1800 = 266042` – 1800 = 86042`
Hence check is ok
FBC = FCB ± 1800 = 35806` – 1800 = 17806`
FCD = FDC ± 1800 = 900 + 1800 = 2700
FDA = FAD ± 1800 = 1820 – 1800 = 20

RB:
AB – N 86042`E
BC – S 1054`E
CD – S 900 W
DA – N 20 E

CL = ∑𝐿 x 𝐿
𝐿𝑇

0.61 𝑥 = 0.036
(CL)
14.39AB =
(122.32 +
122.93) = 0.306

0.61 𝑥 =0
(CL) BC =
122.93
(122.32 +
122.93) = 0.268

0.61 𝑥 0
(CL)CD =
(122.32 +
122.93)

0.61 𝑥
(CL) DA =
107.93
(122.32 +
122.93)

CD = ∑𝐷 x 𝐷
𝐷𝑇

1.44 𝑥 249.59
(CD)AB =
12
 (257.44 +
256) = 0.7

1.44 𝑥 = 0.011
(CD)
4.08 BC =
(257.44 +
256) = 0.718

1.44 𝑥 = 0.011
(CD)
256 CD =
(257.44 +
256)

1.44 𝑥
(CD)
3.77 DA =
(257.44 +
256)

13
1 2 3 4 5 6 7 8 9E 10 11 12 13
Sta Li Incl Corr RB Consecutive Correction Corrected Indepe
ti ne ude ected coordinates consecutive ndent
o An d inclu coordinates coordi
n d ang ded nates
L=𝓵 D=𝓵
len le angle
cos 𝜃 sin 𝜃
L D L D L D
gth

N S E W N S E W N S E W N E
A 950241 950181 107. 3.77 +0.2 - 108.1 3.76 300 400
93 68 0.01 98 assumpt
1 ion
A N860421
B E
25
0
B 880421 880361 14.3 249. +0.0 -0.7 14.43 248. 300 +
9 59 36 89 14.43
=
314
.43
B S10541E
C
1
2
3
C 880121 88061 122.9 4.08 - - 122.6 4.07
 3 0.306 0.01 2
1
C N900W
D
2
5
6
D 880061 880 0 256 +0 +0.71 0 256.7
8 2
D N20E
A
1
0
8
Sum 122. 122.9 257. 256
32 3 44
𝚺𝐿 = - 𝚺𝐷 =
0.61 1.44
2.7 Omitted Measurements in Traverse Surveying

In traverse surveying, sometimes field measurements such as lengths or bearings of traverse legs may
be omitted or lost due to errors or practical difficulties. These omitted values must be computed using
the remaining data and traverse adjustment methods such as coordinate geometry (latitude and
departure), trigonometry, and geometric constraints.

Basic Terms
 Bearing (θ): Direction of a line with respect to a reference meridian.
 Length (L): Distance between two traverse stations.
 Latitude (Lat): L × cos(θ)
 Departure (Dep): L × sin(θ)

2.7.1 Common Cases of Omitted Measurements

Case 1: Length of One Leg is Missing

Given:
 All bearings are known.
 One side length (say, AB) is missing.
Method:
1. Compute latitudes and departures for all known sides.
2. Apply ∑Lat = 0 and ∑Dep = 0 (since the traverse is closed).
3. Use the known bearing of the missing side and the residual lat/departure to compute its length.
Formula:

Case 2: Bearing of One Leg is Missing

Given:
16
  All lengths are known.
 One bearing (say, of AB) is missing.
Method:
1. Compute lat/departure for all known sides.
2. Use closure equations: ∑Lat = 0, ∑Dep = 0.
3. From the residual lat and dep, find:

Case 3: Length and Bearing of One Leg are Missing

Given:
 One side (say, AB) has both length and bearing missing.
 Remaining traverse is complete.
Method:
1. Compute lat/departure of known sides.
2. Use closure conditions to find:
o Latitude = -∑(Lat of known sides)
o Departure = -∑(Dep of known sides)
3. Then:
o Length = √(Lat² + Dep²)
o Bearing = tan⁻¹(Dep / Lat)

Case 4: Length of One Leg and Bearing of Another Leg Missing

Given:
 One side (say, AB) has length missing.
 Another side (say, BC) has bearing missing.
Method:
1. Assign variables for unknowns.
2. Use lat/departure expressions and closure conditions.
3. Solve the system of equations simultaneously.
4. Requires more algebraic work or matrix solution.

Case 5: Lengths of Two Adjacent Sides Missing

Given:
 Two consecutive legs (say, AB and BC) have lengths missing.
 All bearings known.
Method:
1. Write lat/dep equations for all known sides.
2. Let missing lengths be x and y.
3. Use closure conditions:

4. Solve the two simultaneous equations to get x and y.

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Case 6: Length and Bearing of Two Legs Missing (Rare and Underdetermined)
Note: If both length and bearing of two sides are missing, and the traverse is not tied to fixed
coordinates or control points, the problem is usually indeterminate and cannot be solved uniquely
without additional constraints.
2.8 Height and Distance in Surveying

Height and distance problems in surveying deal with determining the elevation or horizontal distance
of an object using trigonometric principles and angle measurements (especially vertical angles) taken
from instruments such as the theodolite or total station.

2.8.1 Key Terms

 Vertical Angle (θ): Angle measured in the vertical plane between the line of sight and the
horizontal.
o Angle of Elevation: Line of sight is above the horizontal.
o Angle of Depression: Line of sight is below the horizontal.
 Line of Sight: The imaginary straight line from the instrument to the object.
 Instrument Height (HI): Vertical distance from ground to the instrument’s line of sight.
 Staff Reading / Target Height (HT): Vertical distance from the object’s base to the point
where the line of sight strikes.

2.8.2 Cases Based on Object Accessibility and Instrument Position

Case 1: Base Accessible, Instrument and Object on Same Horizontal Plane

 Setup:
o Vertical angle θ measured to the top of the object.
o Horizontal distance DDD measured using tape or EDM.
o Instrument height hih_ihi known.
Elevation of Top of Object (H): H=hi+D⋅tan(θ)

Case 2: Base Inaccessible, Instrument and Object on Same Horizontal Plane

 Setup:
o Cannot measure horizontal distance directly to base.
o Take two observations from known points at distances D1 and D2.
o Vertical angles θ1 and θ2 taken to top of the object.
.

Case 3: Instrument at Lower Plane Than Object

 θ is an angle of elevation.
H=hi+D⋅tan(θ)
Case 4: Instrument at Higher Plane Than Object
 Use:
18
 H=hi−D⋅tan(θ)
 θ is an angle of depression.

Case 5: Measuring Height Between Two Points on Different Planes

 Measure vertical angles θ1, θ2 to both points.
 Determine respective heights using:
h=D⋅(tanθ1−tanθ2)
 Adjust based on instrument height.

2.9 Measurement of vertical angles

Vertical angle is the angle which the inclined line of sight to an object makes with the horizontal, It
may be an angle of elevation or angle of depression depending upon whether the object is above or
below the horizontal plane passing through the trunnion axis of the instrument. To measure a vertical
angle, the instrument should be levelled with reference to the altitude bubble.
When the altitude bubble is on the index frame, proceed as follows:
(1) Level the instrument with reference to the plate level, as already explained.
(2) Keep the altitude level parallel to any two foot screws and bring the bubble central. Rotate the
telescope through 900 till the altitude bubble is on the third screw. Bring the bubble to the centre with
the third food screw. Repeat the procedure till the bubble is central in both the positions. If the bubble
is in adjustment it will remain central for all pointings of the telescope.
(3) Loose the vertical circle clamp and rotate the telescope in vertical plane to sight the object. Use
vertical circle tangent screw for accurate bisection.
(4) Read both verniers (i.e., C and D) of vertical circle. The mean of the two gives the vertical circle.
Similar observation may be made with another face. The average of the two will give the required
angle. If it is required to measure the vertical angle between two points A and B as subtended at the
trunnion axis, sight first the higher point and take the reading of the vertical circle. Then sight the
lower point and take the reading. The required vertical angle will be equal to the algebraic difference
between the two readings taking angle of elevation as positive and angle of depression as negative.

2.10 Tacheometry

Tacheometry (or Tachymetry) is a rapid surveying method used to determine horizontal distances and
elevations of points indirectly using angular measurements. Instead of physically measuring the
distance with a chain or tape, tacheometric instruments use optical principles (angles and staff
readings) to compute distances and heights.
2.10.1 Applications of Tacheometry
1. Surveying in rough or inaccessible terrain
2. Topographic surveys
3. Hydrological and road surveys
4. Reconnaissance surveys
5. Checking intermediate points during traverses

19
2.10.2 Principle of Tacheometry

The principle is based on the optical geometric method of observing a staff intercept
(difference in staff readings between upper and lower stadia hairs) and multiplying it with a
constant to get the horizontal distance.
Basic Equation:

D=k⋅s+ C
Where:
D = horizontal distance from instrument to staff
s = staff intercept (top hair – bottom hair reading)
k = multiplying constant = fi
C = additive constant = f+df + df+d
f = focal length of the objective lens
i = stadia hair interval
d = distance from the objective lens to the instrument axis
Tacheometric Constants
Multiplying Constant (k):
k=fi
Usually k = 100 in standard instruments.
Additive Constant (C):C=f+dC = f + dC=f+d
Usually between 0 and 30 cm; often neglected if small.
2.10.3. Systems of Tacheometric Measurement
There are two main systems:
A. Stadia System (Fixed Hair Method)
B. Tangential System (Movable Hair Method)
A. Stadia System (Fixed Hair Method)
Principle:
Uses a telescope with three cross hairs: upper, middle, and lower. The difference between the upper
and lower hair readings on the staff gives the staff intercept (s).
Types:
Inclined Line of Sight
Horizontal Line of Sight
Formula for Horizontal Distance (D):
1. For Horizontal Sight (θ = 0):
20
 D=k⋅s+C
R.L.=H.I.+h−s/2
Where:
h = height of instrument above ground
s = staff intercept
2. For Inclined Sight (θ ≠ 0):
Let θ = angle of inclination
Then:
D=k⋅s⋅cos2θ+C⋅cos θ

Advantages of Stadia System:

Quick and convenient
High accuracy for medium distances (up to 600m)
Easy to automate in digital instruments
Disadvantages:
Requires clear visibility of staff
Errors may occur on undulating ground
Less accurate than EDM or total station over long distances

B. Tangential System (Movable Hair Method)

Principle:
Only one crosshair is used. Two vertical angle measurements are taken from the same station:
One to the top of a fixed staff reading (or mark)
One to the bottom of the same object
Let:
hhh = known vertical distance on the staff
θ1,θ2\theta_1, \theta_2θ1,θ2 = vertical angles to upper and lower points

Formulas:
D=htan⁡θ1−tan⁡θ2
Elevation=HI+D⋅tan⁡θ1
Where:
D = horizontal distance
HI= height of instrument
Applications of Tangential Method:
Used when stadia hairs are not available
Used when staff intercepts cannot be easily read
Ideal for high points, inaccessible terrain
21
 Limitations:
Requires precise angle measurements
Accuracy depends heavily on angular reading
More time-consuming than stadia system

2.11 Setting Out Simple Curves

Definition:
Curve setting involves laying out curved alignment between two straight paths, commonly
used in roads and railways.
Types of Curves:
1. Simple Circular Curve: Constant radius
2. Compound Curve: Two or more curves with different radii
3. Reverse Curve: Two curves in opposite directions
4. Transition Curve: Radius varies gradually (not covered in depth)

Fig 2.3 types of curves

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2.11.1 Curve Elements:

fig 2.4 Elements of curves

23
2.11.2 Methods of Curve Setting:

24
 o

Fig 2.5 curve

o

25
26
27
 2.11.3 Transition Curves
Description:
Transition curves provide a gradual introduction from straight to curved path. They're crucial
in highways and railways for safety and comfort.
Types of Transition Curves:
 Clothoid or Spiral: Radius decreases with distance.
 Cubic Parabola: Used where simplicity in calculation is needed.
 Lemniscate: Suitable for sharp turns.
Functions:
 Reduces sudden application of centrifugal force.
 Facilitates gradual superelevation (tilt) of the road surface.
 Enhances driver/passenger comfort and safety.

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 Module 3
ELECTRONIC THEODOLITE AND TOTAL STATION

3.1 Electronic Theodolite

An Electronic Theodolite is an optical instrument integrated with electronic angle
measurement systems used to measure both horizontal and vertical angles with high accuracy.
3.1.1Working Principle:
 Uses a rotating encoder disc with a fine scale marked optically or magnetically.
 Photoelectric sensors detect these markings to measure angles digitally.
 Displays readings on an LCD screen.
3.1.2 Components of an Electronic Theodolite:
1. Telescope – For sighting distant objects.
2. Electronic Angle Measuring System – Uses encoder discs for accurate angle measurement.

29
3. LCD Display – Shows horizontal and vertical angle readings.
4. Battery Pack – Rechargeable power source.
5. Keypad – For user input and instrument control.
6. Tribrach and Levelling Screws – For setting up and adjusting the instrument.
7. Optical Plummet or Laser Plummet – To centre the instrument over the survey station.
3.1.3 Temporary Adjustments:
1. Centering – Placing instrument exactly over the station point.
2. Levelling – Bringing vertical axis to a true vertical using levelling screws and circular bubble.
3. Focusing – Adjusting telescope and crosshairs for sharp image and elimination of parallax.
3.1.4 Advantages:
 Quick and accurate angle measurement.
 Digital display reduces manual reading errors.
 Can store and transfer data to total stations and computers.
3.2 Electromagnetic distance measurement

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 3.2.1 Principal of EDM

Fig 3.1 EDM

3.3 Total Station

Definition:
A Total Station is an integrated surveying instrument that combines:
 Electronic Theodolite
 Electronic Distance Measurement (EDM) device
 Microprocessor, data storage, and display system

31
 3.3.1 Uses:
 Measurement of horizontal and vertical angles.
 Measurement of distances (sloping, horizontal, vertical).
 Coordinate determination (X, Y, Z).
 Topographic and construction surveys.
3.3.2 Components of Total Station:
1. EDM Unit – Measures distances using laser or infrared.
2. Electronic Theodolite – Measures angles digitally.
3. Microprocessor – Computes coordinates and stores data.
4. Data Storage & Display – Internal memory or memory cards to store survey data.
5. Battery – Portable rechargeable power supply.
6. Tribrach – Removable base for instrument setup.
7. Keyboard/Touchpad – Interface for user commands and data entry
3.3.3 Working Principle:
1. The instrument sends a laser/infrared signal to a reflecting prism.
2. Signal bounces back to EDM which calculates time taken.
3. Angle readings are taken simultaneously.
4. Internal processor calculates position and displays coordinates.
3.3.4 Temporary Adjustments:
Same as electronic theodolite:
 Centering
 Levelling
 Focusing
3.3.5 Maintenance of EDM:
 Keep lenses clean and free of dust.
 Avoid exposure to water or direct sunlight.
 Check calibration periodically.
 Properly charge and store batteries.
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 3.4 Traversing Using Total Station
Steps:
1. Setup instrument over a known station and perform temporary adjustments.
2. Backsight to a known station to orient instrument.
3. Sight and measure other stations.
4. Store angle and distance readings.
5. Download and process data using software.
3.4.1 Advantages over Manual Traversing:
 Higher speed and efficiency.
 Greater accuracy.
 Automated error checking.
 Real-time coordinate display.
3.5 Data Gathering and Processing Using Software
Field Data Collection:
 Collected using total station during survey.
 Includes station descriptions, codes, angles, distances.
Data Transfer:
 Using data cable, Bluetooth, USB or modem.
 Modes: prism mode and non-prism mode (uses reflectorless measurement).
Data Processing:
 Software processes raw field data to:
o Compute coordinates.
o Plot traverses and topographic maps.
o Perform error corrections.
o Generate reports and drawings.
Field Coding:
 Symbols or abbreviations used for different features (e.g., trees, poles, buildings).

33
 Helps with automated map generation.
Error Sources and Controls:
 Instrumental Errors: Calibration required.
 Natural Errors: Wind, heat shimmer, poor visibility.
 Human Errors: Incorrect setup, wrong input, observation mistakes.
Error Control Measures:
 Frequent checks and re-measurements.
 Use of control points.
 Regular calibration and maintenance.
Table 3.1 difference between theodolites

Manual Electronic
Feature Total Station
Theodolite Theodolite

Angle
Manual reading Digital Digital
Measurement

Distance Manual Separate EDM Integrated

Measurement (chain/tape) needed EDM

Internal
Data Storage None Limited
memory

Speed Slow Medium Fast

Accuracy Moderate High Very High

Cost Low Medium High

3.6 Application of Total station

34
3.7 Advantages of total station

35
 MODULE 4
REMOTE SENSING, GPS, GIS, AND PHOTOGRAMMETRY

4.1 Remote Sensing

36
 Remote sensing is the science of obtaining information about objects or areas from a distance,
typically from aircraft or satellites. Remote sensing is defined as an art and science of obtaining
information about an object or feature without physically coming in contact with that object or
feature.

Fig 4.1: Remote sensing

Earth observation from space and air
Remote Sensing is a technology to observe objects size, shape and character without
direct contact with them.
The reflected or radiated electromagnetic (EM) waves are received by sensors aboard
platform. The characteristics of reflected or radiated EM waves depend on the type or
condition of the objects. By understanding characteristics of EM response and comparing
observed information, we can know the size, shape and character of the objects.

4.1.1 Advantages of Satellite Observation

o Enables to observe a broad area at a time.
Enables to observe the area for a long period.
o Repeat pass observation (Time series data, Change detection)
o Enables to know the condition without visiting the
area Enables to know invisible information
o Sensors for various electromagnetic
spectrum (Infrared, microwave)
Energy Source or Illumination (A) - The first requirement for remote sensing is to have an
energy source which illuminates or provides electromagnetic energy to the target of interest.

37
 Radiation and the Atmosphere (B) - As the energy travels from its source to the target, it
will come in contact with and interact with the atmosphere it passes through. This interaction
may take place a second time as the energy travels from the target to the sensor.

Interaction with the Target (C) - Once the energy makes its way to the target through the
atmosphere, it interacts with the target depending on the properties of both the target and the
radiation.

Recording of Energy by the Sensor (D) - After the energy has been scattered by, or emitted
from the target, we require a sensor (remote – not in contact with the target) to collect and
record the electromagnetic radiation.

Transmission, Reception, and processing (E) - The energy recorded by the sensor has to be
transmitted, often in electronic form, to a receiving and processing station where the date are
processed into an image (hardcopy and
/ or digital).

Interpretation and Analysis (F) – The processed image is interpreted, visually and / or
digitally or electronically, to extract information about the target which was illuminated.

Application (G) - The final element of the remote sensing process is achieved when we apply
the information that we have been able to extract from the imagery about the target, in order to
better understand it, reveal some new information, or assist in solving a particular problem.

4.1.2 Principles:
 Based on the detection and measurement of radiation (usually reflected sunlight) from Earth’s
surface.
 Sensors onboard satellites or aircraft capture data in different wavelengths (visible, infrared,
microwave, etc.).
4.1.3 Types of Remote Sensing:
1. Passive Remote Sensing: Detects natural radiation emitted or reflected by the object.
o Example: Landsat satellite imagery.
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 2. Active Remote Sensing: Emits its own signal and measures reflection.
o Example: Radar, LIDAR.
4.1.4 Components of Remote Sensing System:
1. Energy Source: Usually the Sun (for passive sensors).
2. Platform: Satellite, aircraft, UAV (drones).
3. Sensor: Device that captures energy reflected/emitted (camera, scanner).
4. Data Processing Unit: Enhances and analyses captured images.
5. Data Users: Engineers, planners, scientists
4.1.5 Applications in Civil Engineering:
 Land use and land cover mapping.
 Route alignment studies.
 Flood zone analysis and disaster management.
 Environmental monitoring.
 Urban planning and development

4.2 Global Positioning System (GPS)

Definition:

39
A GPS is a satellite-based navigation system that provides location and time information anywhere on
Earth using a receiver. Identifying and remembering objects and landmarks as points of reference
were the techniques that the early man used to find his way through jungles and deserts. Leaving
stones, marking trees, and referencing mountains were the early navigational and positional aids in
the Stone Age.
Identifying points of reference was easy on land; but it became a matter of life and survival when man
started to explore the oceans, where the only visible objects were the sun, the moon, and the stars.
Naturally, they became the 'points of reference' and the era of celestial navigation and positioning
began. Celestial navigation and positioning was the first serious solution to the problem of finding
one's position in unknown territories, where the sun, the moon, and stars were used as points of
reference.
The idea of automatic computation of position through measurement of distances to points of
reference became a reality only recently, when radio signals were employed and the age of radio
navigation began. About the middle of the twentieth century, scientists discovered a way to measure
distances using radio signals. The concept was to measure the time taken for special radio signals to
travel from a transmitting station (tower) to a special device designed to receive them. Multiplying the
signal travel time by the speed of the signal gives the distance between the transmitter and the
receiver. The speed of radio signals is the same as the speed of light about 3 x 10 m/s (about 186,500
miles/s). LORAN (Long Range Navigation) is one such radio navigation system that became
operational around 1950.
4.2.1 GPS working principle and satellite ranging
The idea behind GPS is rather simple If the distances from a point on the earth (a GPS receiver)
to three GPS satellite are known along with the satellite locations, then the location of the point
(or receiver) can be determined by simply applying the well-known concept of resection.
GPS satellite continuously transmits a microwave radio signal composed of two carriers, two
codes and a navigation message. When a GPS receiver is switched on, it will pick up the GPS
signal through the receiver antenna. Once the receiver acquires the GPS signal, it will process it
using its built-in software. The partial outcome of the signal processing consists of the distance
to the GPS satellites through the digital codes (known as the pseudoranges) and the satellite
coordinates through the navigation massage.
GPS receivers calculate the position of objects in two dimensional or three dimensional spaces
using a mathematical process called trilateration. Trilateration can be either two-dimensional or
three dimensional. Trilateration is a method of determining the position of an object by
measuring its distance from other objects with known locations.
To determine the location of the receiver, the receiver has to known two things:

40
(i) Where the satellites are (satellites location in the space)
(ii) How far they are (distance between the satellite and the
receiver) Determination of "Where the Satellites are"

The GPS receiver picks up two kinds of coded information from each GPS satellite,
They àre almanac and ephemeris data.The almanac data contains the approximate
positions (location) of the satellite. This data is continuously transmitted and stored in
the memory of the GPS receivers. From the almanac data, the GPS receiver knows the
orbits of the satellites and where, each satellite is supposed to be. The aimanac data
periodically updated with new information as the satellites move around Any satellite
can travel slightly out of its orbits, but the ground monitor station keeps the track or
satellite orbits, altitude, location and speed. The ground station send the orbital data to
the master control station, which in turns send corrected data up to the satellites. This
corrected and exact position data is called the ephemeris data, which is valid for about 4
to 6 hours and is transmitted in the coded information to the GPS receiver.So, by having
received the almanac and ephemeris data, the GPS receiver knows the position (location)
of the satellites all times.
Determination of "How far Away the Satellites are"
Time is the most important parameter to known how far away the satellites are? There is a
simple formula that tells the receiver how far it is from each satellite. The distance from a given
satellite to the Object equals the velocity of the transmitted signal multiplied by the travel time of
radio. Waves transmitted from the satellites to reach the object (transit rime).
In this case the distance is calculated as
Distance = light velocity x travel time of the satellite signal (△t)

41
4.2.2 Components:
1. Space Segment: A constellation of at least 24 satellites orbiting Earth.
2. Control Segment: Ground-based stations that monitor and manage satellite signals.
3. User Segment: GPS receivers that process satellite signals to determine position
Since all of the GNSSS are based on similar concepts, it is not necessary to discuss all
systems in depth. We shall focus on the GPS, the most widely used system, to
understand how a GNSS works. The GPS consists of a space segment (the satellites), a
control segment (the ground stations), and a user segment (users and their GPS
receivers). Let us now consider the three parts of the system and discuss them in more
detail. We shall then have a closer look at how GPS works.

Fig.4.2 Components of GPS

Space segment
The space segment consists of at least 24 satellites (21 active plus 3 operating spares)
and is the heart of the system (Fig.). The satellites are in a 'high orbit’ about 20,200 km
(13,000 miles) above the earth's surface. Operating at such a high altitude allows the
signals to cover a greater area, The satellites are arranged in their orbits so a GPS
receiver on the earth can always receive signals or information from at least four of them
at any given time.

42
 Fig.4.3 GPS space system
The satellites travel at a speed of 3870 m/s which allows them to Circle the earth once
every 12h. They are powered by solar energy and are built to last about 10-12 years. If
the solar energy fails (eclipses and such factors), they have back-up batteries on board to
keep them running. They also have small rocket boosters to keep them flying in the
correct path.
The first GPS satellite was launched into space in 1978. A full constellation of 24
satellites was achieved in 1994, completing the system. The satellites are geostationary
as well as non- geostationary. At any given time, there are 12 satellites on either side of
the hemispheres.
The main functions of a GPS satellite are as follows:
• It receives and stores data from the control segment.
• It maintains a very precise time.
• It transmits coded signals to user receivers through the use of two frequencies, LI
(1575.42 MHz) and L2 (1227.60 MHz). Another additional frequency, L5 (1176.45
MHz), will be used in future.
These satellites transmit the coarse acquisition (C/A) code on LI band and precision or
protected
(P) code on both LI and L2 bands. C/A code is available to the civilians whereas P code
is used by the US military. Therefore the GPS can provide two so-called services: the
standard positioning service (SPS) using C/A code and the precise positioning service

43
(PPS) for high precision positioning using P code.
Each satellite contains at least three high-precision atomic clocks and constantly
transmits radio signals using its own unique identification code The GPS receivers are
designed to receive these signals. The signal travels in the 'line of sight, which implies
that it can pass through clouds, glass, and plastic, but not go through most solid objects
such as buildings and mountains.
Each signal contains pseudorandom codes (a complex pattern of digital code). The main
purpose of these coded signals is to allow for calculation of signal travel- time from the
satellite to the user's receiver) This travel time is also called the time of arrival or
propagation time. The travel time multiplied by the speed of light equals the satellite
range (distance from the satellite to the receiver). The satellite signals are timed using
highly accurate atomic clocks. Because the speed of light is about 3 x 10' m/s (precisely
2.9979246 X 10 m/s), a tiny fraction of error can produce a wrong distance
measurement.

Control Segment
The control segment (also referred to as ground segment) does what its name implies. it
'controls' the GPS satellites by tracking them and then providing them with corrected
orbital and clock (time) information. The GPS control segment consists of a master
control station, and three uploading stations. Six monitor stations are used to carry out
the measurements required for the definition of the data to be uploaded. These monitor
stations are called Operational Control Segment (OCS) monitor stations, Additionally,
10 National Geospatial Agency (NGA) stations for monitoring are also there since
September 2005.One backup master control station has also been established. Figure
gives details of the locations of the GPS ground segment. The main functions of the
ground segments are to
• Monitor the satellites.
• Estimate the on-board clock state and define the corresponding parameters to be
broadcast (with reference to the constellation's master time);
• Define the orbits of each satellite in order to predict the ephemeris (precise
orbital information), together with the almanac (coarse orbital information);
• Determine the attitude (orientation) and location of the satellites in order to
determine the parameters to be sent to the satellites for correcting their orbits; and
• Uploading (sending) the derived clock correction parameters, ephemeris, almanac,

44
and orbit correction commands to the satellites.
Monitor stations track the satellites continuously and provide tracking. information to the
master control station/ In the master control station, the information sent by the monitor
stations is then incorporated into precise satellite orbit and clock correction coefficients
and the master control station forwards them to the upload stations. The upload stations
transmit these data to each satellite at least once in a day. The satellites then send the
orbital information to the GPS receivers over radio signals. Figure illustrates this concept
schematically.

Fig 4.4 control segment

User Segment
The user segment just consists of the user and his GPS receiver. In general, GIS
receivers are composed of an antenna (internal or external), tuned to the frequencies
transmitted by the satellites, receiver-processors, and a highly stable clock (often a
crystal oscillator).
Remember that receiver clocks are not as precise as the satellite atomic clocks.
Generally, receivers also include a display for providing location and other information
to the user. A receiver is often described by its number of channels: this signifies signals
from how many satellites it can process simultaneously. Originally limited to maximum
of four or five, this has progressively increased over the years so that, nowadays,
receivers typically have between 12- 24 channels. However, special types of receiver
may have as many as 48 channels or even more. These special receivers can capture
signals from satellites of more than one constellation (e.g., both GPS and GLONASS).

45
Many GPS receivers can relay the position data to a personal computer or other devices.
Receivers can interface with other devices using methods including a serial connection,
USB, or Bluetooth. The user segment is composed of a great variety of terminals which
includes boaters, pilots, hikers, hunters, the military, and anyone who would wish to
know where they are, where they have been, or where they are going. The major tasks of
a receiver are to:
• Select the satellites in view;
•Acquire the corresponding signals and evaluate their health;
• Carry out the propagation time measurements;
• Calculate the location of the terminal and estimate the error;
• Calculate the speed of the terminal; and
• Provide accurate time.
Therefore, users will have at their disposal a single terminal allowing
localization, time reference, altitude determination, speed indicator, and so on.
Working Principle:
 GPS receivers calculate position by timing the signals sent by multiple satellites.
 At least four satellites are required to determine a 3D position (latitude, longitude,
altitude)
Types of GPS Observations:
 Static GPS: High-precision surveying (long observation time).
 Kinematic GPS: Used for dynamic data collection (e.g., moving vehicles).
 Differential GPS (DGPS): Increases accuracy by correcting errors using a reference
station.
Applications in Surveying:
 Establishing geodetic control points.
 Topographic and cadastral mapping.
 Navigation and tracking in construction sites.
 Monitoring of land movements and subsidence.

4.3 Geographic Information System (GIS)

A geographic information system (GIS) is a computer system for capturing, storing,

querying, analyzing, and displaying geospatial data. Also called geographically

46
referenced data, geospatial data are data that describe both the locations and the
characteristics of spatial features such as roads, land parcels, and vegetation stands on
the Earth's surface. The ability of a GIS to handle and process geospatial data
distinguishes GIS from other information systems. It also establishes GIS as a
technology important to such occupations as market research analysts, environmental
engineers, and urban and regional planners, which are also listed at the U.S. Department
of Labor's website.
4.3.1 Important Applications of GIS
1) Disaster Management: Today well-developed GIS systems are used to protect the
environment. It has become an integrated, well developed and successful tool in disaster
management and mitigation. GIS can help with risk management and analysis by
displaying which areas are likely to be prone to natural or man- made disasters. When
such disasters are identified, preventive measures can be developed.
2) Crime Statistics: GIS is now vital to law enforcement and planning in terms of crime
statistics. Though most police forces in the USA have used them for a long time,
automated and digital mapping of reported crime has made the process much easier,
especially when looking at different types of crime from different departments in larger
cities. The ability to share maps and look for correlations between different types of
crime can give police a much better idea of an overall picture of a wider region. The
study cited here also permitted community leaders and the police to get a better
understanding of each other, facilitating two-way dialogue.
3) Transport: GlS can be used in managing transportation and logistical problems. If
transport department is planning for a new railway or a road route then this can be
performed by adding environmental and topographical data into the GIS platform. This
will easily output the best route for the transportation based on the criteria like fastest
route, least damage to habitats and

least disturbance from local people. GIS can also help in monitoring rail systems and
road conditions. Some other applications are remote sensing applications, solid waste
management, hydrology, Archaeology etc.
4.3.2 Components of a GIS
Like any other information technology, GIS requires the following five components to
work with geospatial data:

47
 Fig 4.5 Components of GIS

 Computer System/Hardware. The computer system includes the computer and

the operating system to run GIS. Typically the choices are PCs that use the
Windows operating system or workstations that use the UNIX or Linux operating
system. Additional equipment may include monitors for display, digitizers and
scanners for spatial data input, GPS receivers and mobile devices for fieldwork,
and printers and plotters for hard-copy data display. The choice of hardware
system ranges from Personal Computers to multi user Super Computers. These
computers should have essentially an efficient processor to run the software and
sufficient memory to store enough information (data).
 GIS Software, The GIS software includes the program and the user interface for
driving the hardware. GIS software provides the functions and tools needed to
store, analyse, and display geographic information. The software available can be
said to be application specific. All GIS software generally fit all these
requirements, but their on screen

appearance (user interface) maybe different. We are currently using ArcGis

software for gis operations. Common user interfaces in GIS are menus, graphical
icons, command lines, and scripts.
 Data. Geographic data and related tabular data are the backbone of GIS. It can
be collected in-House or purchased from a commercial data provider. The digital
map forms the basic data input for GIS. Tabular data related to the map objects
can also be attached to the digital data. A GIS will integrate spatial data with
other data resources and can even use a DBMS. Data consist of various kinds of
inputs that the system takes to produce information.
 People: GIS users range from technical specialists who design and maintain the

48
 system to those who use it to help them perform their everyday work. GIS
operators solve real time spatial problems. They plan, implement and operate to
draw conclusions for decision making.
 Methods: A successful GIS operates according to a well- designed plan, which
are the models and operating practices unique to each task. There are various
techniques used for map creation and further usage for any project. The map
creation can either be automated raster to vector creator or it can be mamually
vectorised using the scanned images. The source of these digital maps can be
either map prepared by any survey agency or satellite imagery.
4.3.4 GIS Functions:
 Data Capture: Digitizing maps, GPS input, satellite imagery.
 Data Storage: Organized in layers (roads, rivers, buildings).
 Data Manipulation: Buffering, overlay analysis.
 Analysis: Distance, area calculation, terrain analysis.
 Presentation: Thematic maps, 3D views, charts.
4.3.5 Applications in Civil Engineering:
 Utility and infrastructure mapping (water, sewer, electric lines).
 Urban and regional planning.
 Site selection for buildings, industries, roads.
 Environmental impact analysis.
 Disaster management planning
4.3.6 Map Definitions

In GIS, maps are visual representations of geographic data. Key terms include:

 Base Map: A background reference map (e.g., satellite imagery, street map).
 Thematic Map: Shows specific information like population density, rainfall, or soil
type.
 Vector Data: Uses points, lines, and polygons to represent features like roads, rivers,
and land parcels.
 Raster Data: A grid of pixels representing spatial data, such as elevation or land
cover.

4.3.7 Map Projections:

 A method of representing the curved surface of the Earth on a flat map.

49
Common types: UTM (Universal Transverse Mercator), Lambert Conformal Conic.
The shape of the Earth is represented as a sphere. It is also modeled more accurately as
an oblate spheroid or an ellipsoid. A globe is a scaled down model of the Earth.
Although they can represent size, shape, distance and directions of the Earth features
with reasonable accuracy, globes are not practical or suitable for many applications.
They are hard to transport and store; for example you cannot stuff a globe in your
backpack while hiking. Globes are not suitable for use at large scales, such as finding
directions in a city or following a hiking route, where a more detailed image is essential.
They are expensive to produce, especially in varying sizes (scales).

On a curved surface, measuring terrain properties is difficult, and it is not possible to see
large portions of the Earth at once.
A map projection is the transformation of Earth's curved surface (or a portion
of) onto a two-dimensional flat surface by means of mathematical equations. During
such transformation, the angular geographic coordinates (latitude, longitude) referencing
positions on the surface of the Earth are converted to Cartesian coordinates (x, y)
representing position of points on a flat map.

4.4 Photogrammetry

 Definition:
 Photogrammetry is the art and science of obtaining reliable measurements by using
photographs, especially for creating maps from aerial or satellite images.

4.4.1 Types:
1. Aerial Photogrammetry: Photographs taken from aircraft.
2. Terrestrial (Ground-based) Photogrammetry: Photographs taken from ground
stations.
Fundamentals:
 Uses the principle of stereoscopy: Viewing overlapping images to perceive depth and
derive 3D information.
 By knowing the camera position and geometry, distances and elevations can be
calculated.

4.4.2 Applications:
 Topographic map preparation.

50
 Contour mapping.
 Earthwork volume estimation.
 Site analysis and land development planning.
 Structural deformation and monitoring studies
4.5 Drone Surveying and GNSS (Introductory)
Drone Surveying:
 Use of UAVs (Unmanned Aerial Vehicles) equipped with cameras or LiDAR to
conduct surveys.
 Advantages: Rapid data collection, access to difficult terrain, high-resolution imagery.

4.6 Global Navigation Satellite System (GNSS):

 Broader term than GPS, includes other satellite systems:
o GPS (USA)
o GLONASS (Russia)
o Galileo (EU)
o BeiDou (China)
 Multi-constellation support improves positioning accuracy and availability.

51