Home
Civil Engineering Notes
Surveying
Surveying Master Class Part 1:All Topic Cover in One Place

Surveying Master Class Part 1 : All Topic Cover in One Place

Surveying ek aisi art hai jisme kisi fixed point ke sapeksh (with respect to) dusre points ki relative position nirdharit ki jati hai. Iske liye distances aur angles ko mapa jata hai. Civil engineering exams mein iska weightage lagbhag 7-8% hota hai.

Surveying Master Class Part 1: Comprehensive Topic Coverage

Surveying is an art used to determine the relative positions of points with respect to a fixed point. This is achieved by measuring distances and angles. In civil engineering exams, it typically carries a weightage of 7-8%.

Primary Types of Surveying

Surveying is categorized based on whether the Earth's curvature is considered:

Plane Surveying: Curvature is neglected; the surface is treated as a flat plane. Used for small areas (Area < 260 $km^2$ ).
Geodetic Surveying: Curvature is considered for high precision. Used for large areas (Area > 260 $km^2$ ).

Key Technical Language:

Linear Difference: For a 12 km line, the difference between the arc (Geodetic) and chord (Plane) is only 1 cm.
Spherical Excess: For a spherical triangle of 195.5 $km^2$ , the sum of interior angles is 180° 0' 1".
Angle Sum: In plane surveying, the sum of a triangle's angles is exactly 180°.
Units: 1° = 60 minutes; 1 minute = 60 seconds.

Classification of Surveys

Topographic Survey: To map natural and man-made features (rivers, mountains, buildings).
Cadastral Survey: To determine property lines and boundaries.
City Survey: For urban infrastructure planning (roads, sewers).
Hydrographic Survey: To map features within water bodies.
Astronomical Survey: To determine the position of celestial bodies.

Understanding Scale

Scale is the ratio of map distance to ground distance.

Representative Fraction (R.F.): If 1 cm on a map = 10 m on ground, R.F. = 1/1000.
Area Scale: $S^2 = \frac{\text{Map Area}}{\text{Ground Area}}$

Shrunk Scale and Shrinkage Factor:

Shrinkage Factor (S.F.) = $\frac{\text{Shrunk length}}{\text{Actual (original) length}}$
Shrunk Scale = S.F. $\times$ Old R.F.

Vernier Scales: An Introduction

A Vernier scale is an auxiliary scale used to read fractional parts of the smallest division of the main scale.

Types of Vernier Scales:

Feature	Direct Vernier	Retrograde Vernier
Calibration	Same direction as main scale	Opposite direction to main scale
Division Relation	$(n-1)$ main divisions = $n$ vernier divisions	$(n+1)$ main divisions = $n$ vernier divisions
Division Size	Main scale ( $s$ ) > Vernier ( $v$ )	Vernier ( $v$ ) > Main scale ( $s$ )

Least Count (L.C.) = $s/n$

Principles of Surveying

Working from Whole to Part: The area is divided into large parts, then subdivided. This localizes errors and prevents them from accumulating.
Relative Position: Locating a new point by taking at least two measurements from fixed reference points.

Chain Surveying

Base Line: The longest and most important line dividing the area.
Tie Line: Used for detailing features.
Check Line: Used to verify accuracy.
Offsets: Perpendicular (90°) or Oblique (any other angle).

Common Instruments:

Angle Measurement (90°): Cross Staff, Optical Square (works on Double Reflection, mirrors at 45°).
Slope: Clinometer.

Types of Chains:

Metric: 20 m (100 links) or 30 m (150 links).
Gunter's: 66 ft (100 links).
Engineer's: 100 ft (100 links).
Revenue: 33 ft (16 links).

Tapes:

Invar Tape: Alloy of Nickel (36%) and Steel. It has a very low thermal expansion coefficient ( $\alpha$ ), making it ideal for measuring Base Lines.

Error and Correction Principles

Correction (C) = True Value - Measured Value
Error (E) = Measured Value - True Value ( $E = -C$ )

Corrections in Chaining/Taping:

Length Correction: $L \times l = L' \times l'$ (True length $\times$ True Tape = Measured length $\times$ Incorrect Tape).
Slope Correction ( $C_s$ ): $-\frac{h^2}{2l'}$ . Always Negative.
Temperature Correction ( $C_{Temp}$ ): $L \alpha (T_m - T_0)$ . Positive if $T_m > T_0$ .
Pull Correction ( $C_{pull}$ ): $\frac{(P_m - P_0)L}{AE}$ . Positive if $P_m > P_0$ .
Sag Correction ( $C_{sag}$ ): $-\frac{W^2L}{24P_m^2}$ . Always Negative.
Normal Tension: The pull at which pull correction and sag correction cancel each other out.

Bearing and Meridian

Bearing: Horizontal angle measured with respect to a fixed direction (Meridian).

Systems of Bearing:

Whole Circle Bearing (WCB): Measured clockwise from North (0° to 360°).
Reduced Bearing (RB) / Quadrantal Bearing: Measured from North or South (whichever is closer). Range is 0° to 90°. Written as $N\theta E, S\theta W$ , etc.

Conversion Examples (WCB to RB):

$95^\circ$ (SE Quadrant) $\rightarrow 180^\circ - 95^\circ = S~85^\circ~E$ .
$272^\circ$ (NW Quadrant) $\rightarrow 360^\circ - 272^\circ = N~88^\circ~W$ .
$351^\circ$ (NW Quadrant) $\rightarrow 360^\circ - 351^\circ = N~9^\circ~W$ .

Conversion Examples (RB to WCB):

$S~10^\circ~E \rightarrow 180^\circ - 10^\circ = 170^\circ$ .
$S~79^\circ~W \rightarrow 180^\circ + 79^\circ = 259^\circ$ .
$N~81^\circ~W \rightarrow 360^\circ - 81^\circ = 279^\circ$ .

Types of Meridians

In surveying, two main meridians are used as references:

True Meridian: A line passing through the Earth's True North and True South.
Magnetic Meridian: A line passing through the Magnetic North and Magnetic South, following the direction of the Earth's magnetic flux.

Magnetic Declination and Variations

Magnetic Declination is the horizontal angle between the True Meridian and the Magnetic Meridian. Since the Magnetic Meridian is constantly shifting, the declination is not constant. Changes in declination are called Variations:

Diurnal Variation: Daily changes.
Yearly Variation: Changes occurring over one year.
Secular Variation: Changes occurring over an interval of approximately 150 years.
Irregular Variation: Sudden changes caused by natural disasters like earthquakes or tsunamis.

Types of Declination and Calculations

When performing calculations, Declination is divided into two parts:

1. Eastern Declination (Positive)

When Magnetic North is toward the East of True North, it is considered positive.

Formula:

TB = MB + \delta_E

(Where $TB$ = True Bearing, $MB$ = Magnetic Bearing, and $\delta_E$ = Eastern Declination)

2. Western Declination (Negative)

When Magnetic North is toward the West of True North, it is considered negative.

Formula:

TB = MB - \delta_W

(Where $\delta_W$ = Western Declination)

Note: Both formulas are always used in the Whole Circle Bearing (WCB) system.

Examples of Magnetic Declination

In a compass survey, True Bearing ( $TB$ ) is calculated using Magnetic Bearing ( $MB$ ) and Declination ( $\delta$ ):

Question 1: If the Magnetic Bearing of a line is $S~70^\circ~W$ and the Declination is $6^\circ~West$ , what will be the True Bearing?
- Calculation: First, convert $MB$ to $WCB$ : $180^\circ + 70^\circ = 250^\circ$ .
- Formula: $TB = MB - \delta_W = 250^\circ - 6^\circ = 244^\circ$ .
- Result: Converting back to $RB$ gives $S~64^\circ~W$ .
Question 2: If $TB = 140^\circ$ and $MB = 172^\circ$ , what is the Declination?
- Calculation: The difference between the two is $172^\circ - 140^\circ = 32^\circ$ .
- Result: Since $MB > TB$ , the Declination is $32^\circ~West$ .

Angle of Dip

The Angle of Dip is the vertical angle between the direction of magnetic flux and the horizontal plane.

At the Equator, the value of Dip is $0^\circ$ .
At the Poles, the value of Dip is $90^\circ$ .

Fore Bearing (FB) and Back Bearing (BB)

Bearings are divided into two parts according to the direction of the survey:

Fore Bearing (FB): The bearing taken from a point toward the next point in the direction of the survey.
Back Bearing (BB): The bearing taken from a point toward the previous point, opposite to the direction of the survey.

Line	Fore Bearing (FB)	Back Bearing (BB)
AB	Measured at Point A $(\theta_A)$	Measured at Point B $(\theta_B)$

Note: In the WCB system, the difference between FB and BB is always $180^\circ$ .

Relationship between FB and BB

For any single line, the difference between its Fore Bearing and Back Bearing is always $180^\circ$ .

Formula: $|FB - BB| = 180^\circ$ .

Rules for Calculating BB

In the Whole Circle Bearing (WCB) system, the following rules are used to find the BB:

Rule 1: If the value of FB is less than $180^\circ$ ( $FB < 180^\circ$ ), then $BB = FB + 180^\circ$ .
Rule 2: If the value of FB is more than $180^\circ$ ( $FB > 180^\circ$ ), then $BB = FB - 180^\circ$ .

Internal and External Angles

At any station, the difference between the Back Bearing (BB) of the previous line and the Fore Bearing (FB) of the next line determines the internal or external angle.

Numerical Examples

Question 1: If the FB of line AB is $290^\circ$ , what will be the BB?
- Solution: Since $290^\circ > 180^\circ$ , then $290^\circ - 180^\circ = 110^\circ$ .
Question 2: If the FB of line BA is $60^\circ$ , what will be the FB of line AB?
- Hint: The FB of line BA is actually the BB of line AB.
- Solution: $60^\circ + 180^\circ = 240^\circ$ .

Bearing Conversion (RB System)

In the Reduced Bearing (RB) system, finding the Back Bearing (BB) from the Fore Bearing (FB) is very simple. Only the cardinal directions ( $N, S, E, W$ ) are changed, while the numerical value remains the same.

Rule: Change $N$ to $S$ , $S$ to $N$ , $E$ to $W$ , and $W$ to $E$ .
Example: If the FB is $S~30^\circ~E$ , then the BB will be $N~30^\circ~W$ .

Formula for Calculating Internal Angle

To find the internal angle between two lines at any station:

Internal Angle = FB of next line - BB of previous line

Local Attraction

Local Attraction is an error that occurs in the magnetic needle when a local magnetic object (such as electric poles, steel buildings, or iron tools) is present in the survey area.

Detection: If the difference between the FB and BB of a line is not $180^\circ$ ( $|FB - BB| \neq 180^\circ$ ), it means the stations are affected by local attraction.
Clean Station: If $|FB - BB| = 180^\circ$ , both readings are correct, and the stations are free from local attraction.

Impact of Local Attraction

Even if stations are affected by local attraction, the internal or external angle between them remains correct. This is because local attraction changes both readings by the same amount, and the error cancels out during subtraction.

Latitude and Departure

In traversing, the coordinates of a line are divided into Latitude and Departure:

Latitude (L): The projection of a line on the North-South axis.
- Formula: $L = l \cos \theta$ (Positive toward North, Negative toward South).
Departure (D): The projection of a line on the East-West axis.
- Formula: $D = l \sin \theta$ (Positive toward East, Negative toward West).

Rules for a Closed Traverse

For a perfect closed traverse:

The sum of all Latitudes must be zero: $\Sigma L = 0$ .
The sum of all Departures must be zero: $\Sigma D = 0$ .

Closing Error ( $e$ )

If the sums of $L$ and $D$ are not zero, there is a "Closing Error" in the traverse.

Formula: $e = \sqrt{(\Sigma L)^2 + (\Sigma D)^2}$

Methods for Correcting Closing Error

There are four main methods to correct the closing error in a traverse:

Bowditch Method
Transit Method
Graphical Method
Axis Method

Comparison between Bowditch and Transit Methods

Feature	Bowditch Method	Transit Method
Precision	Linear and angular measurements are taken with equal precision.	Angular measurement is more precise than linear measurement.
Latitude Correction ( $C_L$ )	$C_L = - (\frac{\text{length of side}}{\text{perimeter}}) \times \Sigma L$	$C_L = - (\frac{\text{latitude of line}}{\sum
Departure Correction ( $C_D$ )	$C_D = - (\frac{\text{length of side}}{\text{perimeter}}) \times \Sigma D$	$C_D = - (\frac{\text{departure of line}}{\sum

Read in details:-

🏗️ Surveying: Complete Study Guide & Index

📔 Part 1: Fundamentals of Surveying

Surveying: A Bird's Eye View – Meaning and significance of land surveying.
Fundamental Principles – Classification and types of surveying.
Primary Division – Understanding Plane vs. Geodetic Surveying.
Representative Fraction (RF) – Utilization of scales and reduction factors.

📏 Part 2: Linear Measurement & Chain Survey

Chain Surveying – Basic procedures and workflow.
Errors & Adjustments in Chaining – Deficiencies in measurement and their remedies.
Distance Measurement Methods – Detailed discussion on linear surveying tools.
Tape Corrections – Adjustments for Sag, Temperature, and Pull.

🧭 Part 3: Angular & Instrumental Survey

Compass Surveying – Magnetic bearing survey and its applications.
Plane Table Surveying – Equipment used and graphical methods.
Theodolite Surveying – Horizontal and vertical angle measurement.
Total Station – Components, features, and modern digital use.

🏔️ Part 4: Levelling & Elevation

Need for Levelling – Why vertical measurement is vital in civil engineering.
Key Concepts: RL & Datum – Definitions of Reduced Level, Datum, and Benchmarks.
Operating Levelling Instruments – Handling Auto Level and Tilting Level.

🛰️ Part 5: Modern Technologies

Remote Sensing – Information on INSAT and IRS Series satellites.
GIS & LIS Systems – Geographic data management and functionality.
Laser Scanning – Advanced application and control.
Geoid & Ellipsoid – Understanding the mathematical shape of the Earth.

📝 Part 6: Practice & Quizzes (MCQs)

Surveying Quiz 1 (01-25) – GPS, Remote Sensing, and Photogrammetry.
Surveying Quiz 2 (26-50) – Ranging, EDM, and Tacheometry.
Surveying Quiz 3 (51-75) – Contouring and HI Method Levelling.
Surveying Quiz 4 (76-100) – Transition Curves and Bowditch Rule.
Surveying Quiz 5 (101-125) – Plane table and Compass
Surveying Quiz 6 (125-150) – Theodolite Surveying and Levelling
Surveying Quiz 7 (151-175) – Tacheometry, Curves, Modern Surveying Instruments (EDM/GPS)
Surveying Quiz 8 (175-200) – Area & Volume Calculation, Minor Instruments

📚 Quick Revision Resources

Surveying IS Codes with Latest Revision Years

1. General Surveying & Instruments

IS 1491:1959 – Specification for Prismatic Compass (Liquid and Non-liquid).
IS 1963:1981 – Specification for Bubbles for Surveying Instruments.
IS 2988:1995 – Glossary of Terms Relating to Surveying Instruments.
IS 1634:1992 – Code of Practice for Design and Construction of Storage for Surveying Instruments.

2. Chain and Tape Surveying

IS 1492:1970 – Specification for Metric Surveying Chains.
IS 1269 (Part 1):1997 – Material and Construction of Steel Tapes.
IS 1269 (Part 2):1997 – Woven Metallic and Glass Fibre Tapes.
IS 1659:2006 – Specification for Invar Tapes for High Precision Measurement.

3. Theodolite and Tacheometry

IS 8002:1976 – Specification for Surveying Chain Vertical Vernier Theodolite.
IS 8330:1976 – Specification for Tilting Levels (Optical).
IS 8636:1977 – Specification for Tacheometers.

4. Leveling and Contouring

IS 9128:1992 – Specification for Tilting Levels.
IS 9573:1980 – Specification for Automatic Levels.
IS 1779:1961 – Specification for 4-metre Leveling Staff (Folding Type).