📚 CTEVT | Fundamental of Surveying & Geomatics – Chapter 6: Linear Measurements
(Full Notes + Examples + Practice Questions + Free PDF)
Linear Measurement is one of the most essential and practical components of surveying.
Every survey — whether cadastral, engineering, topographic, or construction — involves measuring distance.
Chapter 6 explains the principles, methods, obstacles, errors, and plotting techniques involved in distance measurement.
This chapter forms the basis for chain survey, tape survey, EDM, optical measurement, and total station work.
🧩 Chapter Overview: Linear Measurements
Linear measurement = Determining the distance between two points.
This chapter covers:
✔️ Principles of linear measurement
✔️ Slope, horizontal & vertical distances
✔️ Direct & indirect measurement methods
✔️ Optical & Electronic Distance Measurement (EDM)
✔️ Field procedures & plotting
✔️ Obstacles & solutions
✔️ Errors in linear measurement
Highly important for practical exam & fieldwork.
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🔍 6.1 Introduction & Principles
Linear measurement determines the shortest distance between two survey points.
⭐ Instruments Used
✔️ Chain
✔️ Tape (Steel, Fiber, Linen)
✔️ Ranging rod
✔️ Arrows
✔️ EDM instruments
✔️ Optical devices (Odometer, Pedometer)
⭐ Principles
✔️ Measure along a straight line
✔️ Convert slope distance → horizontal distance
✔️ Use tension, temperature & alignment correction when needed
✔️ Ensure accuracy with proper field procedure
🔍 6.2 Slope, Horizontal & Vertical Distances
⭐ Slope Distance
Distance measured along the inclined ground.
⭐ Horizontal Distance
True distance used for plotting & calculations.
Calculated from slope distance:
If θ = angle of slope
Horizontal Distance (H) = Slope Distance × cos(θ)
⭐ Vertical Distance
Difference in height between two points.
Used in leveling, contouring, and design.
🔍 6.3 Direct & Indirect Methods of Linear Measurement
⭐ A. Direct Methods
Actual measurement with instruments.
✔️ 1. Chain Measurement
Using 20 m or 30 m chain.
Used in simple, small-area surveys.
✔️ 2. Tape Measurement
More accurate than chain.
Used in engineering surveys.
✔️ 3. Pacing
Used for rough estimation.
Accuracy: ±1/50
⭐ B. Indirect Methods
Distance is computed rather than physically measured.
✔️ 1. Optical Methods
Using optical instruments such as:
- Tachometer
- Rangefinder
- Odometer
✔️ 2. Triangulation
Distance found using trigonometry.
✔️ 3. EDM
Electronic measurement using electromagnetic waves.
Indirect methods are more useful in rough terrain, long distances & inaccessible locations.
🔍 6.4 Optical Distance Measurement
Used when distance cannot be physically measured.
⭐ Common Optical Methods
✔️ Pedometer
Used for walking distance.
✔️ Odometer Wheel
Measures distance by wheel rotation.
✔️ Rangefinder
Simple optical tool for quick estimation.
✔️ Tacheometry
Distance computed using tacheometric formula:
D = KS + C
Where,
K = multiplying constant
S = staff intercept
C = additive constant
Optical methods are fast but less accurate than EDM.
🔍 6.5 Electronic Distance Measurement (EDM)
EDM uses electromagnetic waves (light or radio) to measure distance very accurately.
⭐ Working Principle
EDM measures distance using the time taken by waves to travel to the target and return.
⭐ Advantages
✔️ High accuracy
✔️ Very fast
✔️ Can measure long distances (up to 5 km+)
✔️ Useful in difficult terrain
✔️ Eliminates chaining errors
⭐ EDM Instruments
✔️ Total Station
✔️ Distomat
✔️ Microdist
✔️ Laser Distance Meter
EDM is widely used in modern surveying.
🔍 6.6 Linear Survey
Survey conducted for measuring distances and locating features.
⭐ Steps
1️⃣ Reconnaissance
2️⃣ Ranging
3️⃣ Marking stations
4️⃣ Chaining/taping
5️⃣ Recording measurements
6️⃣ Plotting in field book
🔍 6.7 Field Procedure & Plotting
⭐ Ranging
Aligning two points in a straight line using:
✔️ Ranging rods
✔️ Line ranger
✔️ Optical square
⭐ Recording
Field book is used to record field measurements.
⭐ Plotting
✔️ Plot measured distances
✔️ Plot offsets
✔️ Draw features (buildings, roads, boundaries)
Plotting requires accuracy and understanding of scale.
🔍 6.8 Obstacles in Linear Survey & Solutions
Two types of obstacles:
⭐ A. Obstacle to Measurement
When the line cannot be measured directly.
Examples:
✔️ River
✔️ Wall
✔️ Pond
✔️ Forest/bush
✔️ Solutions
- Triangulation
- Indirect measurement
- Reciprocal chaining
⭐ B. Obstacle to Line of Sight
When two points cannot see each other.
Examples:
✔️ Hill
✔️ Building
✔️ Trees
✔️ Solutions
- Set intermediate stations
- Use line ranger
- Use mirrors
🔍 6.9 Errors in Linear Measurement
Errors reduce accuracy. They are of three types:
⭐ 1️⃣ Gross Errors
Big mistakes
✔️ Wrong reading
✔️ Wrong recording
✔️ Wrong instrument use
⭐ 2️⃣ Systematic Errors
Occur due to predictable causes
✔️ Temperature variation
✔️ Incorrect tape length
✔️ Sag
✔️ Lack of tension
Corrections must be applied.
⭐ 3️⃣ Random Errors
Small, accidental errors
✔️ Irregular pull
✔️ Unstable hand
✔️ Slight reading error
🧪 Practical Utility of This Chapter
Used in:
📌 Chain/Tape Survey
📌 Compass Survey
📌 Triangulation
📌 Theodolite Traverse
📌 EDM & Total Station Survey
📌 Road, canal, pipeline layout
📌 Plotting & field book preparation
Linear measurement is the core of all surveying work.
📝 Short Questions
1️⃣ Define linear measurement.
2️⃣ Write two direct methods of measuring distance.
3️⃣ What is slope distance?
4️⃣ Write the formula for horizontal distance.
5️⃣ What is an EDM?
6️⃣ Name two obstacles in linear measurement.
7️⃣ What is ranging?
8️⃣ Write any two sources of systematic error.
📝 Long Questions
1️⃣ Explain direct and indirect methods of distance measurement.
2️⃣ Describe EDM and its advantages.
3️⃣ Discuss obstacles in linear measurement and their solutions.
4️⃣ Explain slope, horizontal & vertical distances with a neat diagram.
5️⃣ Describe the field procedure and plotting of a linear survey.
6️⃣ Write notes on tacheometric distance measurement.
🎯 Key Takeaways
✔️ Linear measurement is fundamental to all surveying.
✔️ Distances can be measured directly or indirectly.
✔️ EDM provides fast and accurate distance measurement.
✔️ Obstacles require special techniques.
✔️ Errors must be understood and corrected.
📂 Download Free PDF Notes – Chapter 6
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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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