📚 CTEVT | Fundamental of Surveying & Geomatics – Chapter 7: Angular Measurements
(Full Notes + Examples + Practice Questions + Free PDF)
Angular measurement is the heart of surveying instruments like compass, theodolite, total station, plane table, and traversing.
Without accurate angles, no map, traverse, or coordinate calculation is possible.
Chapter 7 dives deep into bearings, angles, direction measurement, magnetic variation, local attraction, compass survey, and full theodolite operation.
Super important for exam + lab + real survey field.
🧩 Chapter Overview: Angular Measurements
This chapter explains:
✔️ Types of angles
✔️ Bearings & direction systems
✔️ Compass surveying
✔️ Local attraction & corrections
✔️ Magnetic variation
✔️ Theodolite parts, uses & field procedures
✔️ Angular adjustments
✔️ Plotting & traverse correction
One of the most scoring & practical chapters of the subject.
📥 Download the Full Chapter 7 Notes (Free PDF)
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🔍 7.1 Principle of Direction Measurement
Surveyors define direction by angles.
Direction is always measured clockwise or anticlockwise from a reference line.
⭐ Common reference lines
✔️ True Meridian
✔️ Magnetic Meridian
✔️ Arbitrary line
✔️ Survey line (for interior angle)
⭐ Tools used
- Compass
- Theodolite
- Total Station
Angular measurement ensures:
✔️ Accurate traverse
✔️ Proper plotting
✔️ Orientation of survey
✔️ Coordinate computation
🔍 7.2 Angles and Bearings
⭐ Types of Angles
✔️ Horizontal angle – angle in a horizontal plane
✔️ Vertical angle – angle above or below horizontal
✔️ Zenith angle – measured from vertical downward
✔️ Included angle – between two survey lines
⭐ Bearings
Bearing = angle made by a line with a meridian.
✔️ Types of Bearings
1️⃣ Whole Circle Bearing (WCB)
Measured clockwise from North (0° to 360°)
Example:
• 60°
• 245°
2️⃣ Quadrantal Bearing (QB)
Measured from North or South toward East or West.
Example:
• N 30° E
• S 45° W
⭐ Conversion
WCB ↔ QB
QB ↔ included angle
Included angle ↔ bearings
Exam always asks 1 numerical from conversion!
🔍 7.3 Terminologies in Compass Surveying
✔️ Fore bearing (FB) – bearing from start to end
✔️ Back bearing (BB) – opposite direction of FB
✔️ Magnetic meridian – line shown by magnetic needle
✔️ Dip – needle tilts vertically due to magnetism
✔️ Declination – angle between true north & magnetic north
🔍 7.4 Computation of Included Angles
Included angle = difference between bearings
Used in traverse survey.
⭐ Rules
- If turning right, subtract
- If turning left, add
- Add 360° if angle comes negative
Very important in the exam + plotting.
🔍 7.5 Magnetic Variation & Declination
Magnetic north ≠ true north.
⭐ Types of declination
✔️ East declination
✔️ West declination
⭐ Changes in magnetic declination
✔️ Secular variation (long-term)
✔️ Annual variation (yearly)
✔️ Daily variation (sunlight effect)
✔️ Local attraction influence
Surveyor must correct declination to obtain true bearing.
🔍 7.6 Horizontal & Vertical Angles
Measured using:
✔️ Compass → horizontal angles
✔️ Theodolite → both horizontal & vertical
✔️ Total station → all angles + distances
🔍 7.7 Local Attraction & Its Solution
Local attraction occurs when magnetic needle is disturbed by:
✔️ Electric poles
✔️ Iron pipes
✔️ Railway lines
✔️ Vehicles
✔️ Buildings with steel
⭐ Detection
Compare FB and BB:
If FB − BB ≠ 180°, local attraction exists.
⭐ Correction Steps
1️⃣ Identify unaffected station
2️⃣ Apply correction to all affected stations
3️⃣ Adjust bearings systematically
This is a guaranteed exam question!
🔍 7.8 Compass Survey – Field Procedure
⭐ Steps
1️⃣ Fix stations
2️⃣ Mark station with pegs
3️⃣ Set compass
4️⃣ Take FB & BB
5️⃣ Measure lengths (chain/tape)
6️⃣ Enter data in field book
7️⃣ Apply corrections
8️⃣ Prepare traverse
⭐ Instruments
- Prismatic compass
- Surveyor’s compass
- Chain/tape
- Ranging rods
🔍 7.9 Plotting & Adjustment of Compass Traverse
⭐ Plotting
✔️ Use protractor or angle plotting
✔️ Use scale for distances
✔️ Draw offsets & details
⭐ Adjustment Methods
✔️ Bowditch method
✔️ Transit rule
✔️ Graphical adjustment
Used to correct closing error in traverse.
🔍 7.10 Theodolite Survey
The most important part of this chapter.
⭐ Theodolite: Introduction
A precision instrument to measure horizontal & vertical angles.
⭐ Parts of Theodolite
✔️ Telescope
✔️ Vertical circle
✔️ Horizontal circle
✔️ Level tubes
✔️ Plumb bob
✔️ Focusing screw
✔️ Trunnion axis
✔️ Line of sight
🔍 7.11 Basic Axes & Their Relations
Three main axes:
1️⃣ Vertical axis
2️⃣ Horizontal axis
3️⃣ Line of collimation
⭐ Conditions for accuracy
✔️ Line of sight ⟂ horizontal axis
✔️ Horizontal axis ⟂ vertical axis
✔️ Vertical circle aligned properly
These are tested during theodolite adjustment.
🔍 7.12 Field Procedure for Angular Measurement
⭐ Setting up theodolite
1️⃣ Centering
2️⃣ Leveling
3️⃣ Focusing
4️⃣ Zero setting
⭐ Measuring horizontal angle
- Repetition method
- Reiteration method
⭐ Measuring vertical angle
- Sight staff
- Take readings
- Apply corrections
🔍 7.13 Test & Adjustments of Theodolite
Surveyors perform tests to ensure accuracy:
✔️ Plate level test
✔️ Telescope axis test
✔️ Collimation test
✔️ Horizontal axis test
✔️ Vertical circle index error test
Important for practical + viva.
📝 Short Questions
1️⃣ Define bearing.
2️⃣ What is magnetic declination?
3️⃣ Write two types of compass used in surveying.
4️⃣ Define local attraction.
5️⃣ What is a horizontal angle?
6️⃣ Name two parts of a theodolite.
7️⃣ What is a fore bearing?
8️⃣ Give one cause of needle dip.
📝 Long Questions
1️⃣ Explain different types of bearings with examples.
2️⃣ What is local attraction? How is it detected and corrected?
3️⃣ Describe magnetic declination and its variations.
4️⃣ Explain theodolite parts and uses in detail.
5️⃣ Explain the field procedure of compass traverse.
6️⃣ What are included angles? Write steps to compute them from bearings.
🎯 Key Takeaways
✔️ Angular measurement is essential for direction & traverse.
✔️ Bearings form the basis of compass surveying.
✔️ Magnetic declination and local attraction must be corrected.
✔️ Theodolite is the most accurate tool for angle measurement.
✔️ Proper field procedures ensure accuracy in plotting.
📂 Download Free PDF Notes – Chapter 7
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📘 Explore More from Fundamental of Survey and Geomatics
📘 SYLLABUS – Download PDF
📘 Unit 1: Historical Background – Download PDF
📘 Unit 2: Introduction to Surveying – Download PDF
📘 Unit 3: Principles & Classifications – Download PDF
📘 Unit 4: Measurement Units – Download PDF
📘 Unit 5: Map Scale –Download PDF
📘 Unit 6: Linear Measurements – Download PDF
📘 Unit 7: Angular Measurements – Download PDF
📘 Unit 8: Map Reading – Download PDF
📘 Unit 9: Measurement Errors – Download PDF
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