Home
Surveying
Errors and Corrections in Chain Surveying

Errors and Corrections in Chain Surveying

The inaccuracies that occur during linear measurement are primarily divided into three categories:

1. Personal Errors (Mistakes)

These errors are caused by the negligence of the surveyor or human error.

Examples: Reading a 20-meter chain as 30 meters, or failing to stretch the chain perfectly straight.
Prevention: Always verify the 'Zero' point and have a teammate double-check the data while recording.
Remedy: Cross-check every measurement twice and pay close attention to the zero marks.

2. Compensating Errors

These are random errors that tend to cancel each other out over time.

Concept: Also known as 'Random Errors', they may sometimes increase the measurement and other times decrease it, neutralizing the overall effect.
Principle: They follow the law of probability, expressed as $E \propto \sqrt{L}$ (where $E$ is the error and $L$ is the total length measured). This means if you increase the distance 100 times, the error only increases by 10 times.
Causes: Mud stuck in the links or links not opening fully.

3. Cumulative Errors

These are the most dangerous errors because they accumulate in one direction at every step.

Positive (+ve) Error: When the measured distance is greater than the actual distance (e.g., the chain is too short).
Negative (-ve) Error: When the measured distance is less than the actual distance (e.g., the chain is longer than the standard length).

Classification and Corrections:

Type of Error	Nature of Error (+ve / -ve)	Nature of Correction
Chain is longer than standard	Negative (-ve)	Positive (+ve)
Chain is shorter than standard	Positive (+ve)	Negative (-ve)
Slope	Always Positive (+ve)	Always Negative (-ve)
Sag (Slack)	Always Positive (+ve)	Always Negative (-ve)

Important Technical Problems

A. Slope Error

On undulating or sloping ground, we measure the slope distance (hypotenuse), which is always greater than the horizontal distance.

Correction Formula: $C_{slope} = \frac{h^2}{2L}$ (where $h$ is the difference in elevation).

B. Sag Error

When a chain is suspended in the air between two points, it sags in the middle due to its own weight. This makes the measured distance appear longer than it actually is.

Correction: This is always subtractive (-ve). To minimize this, a standard Pull must be applied.

Key Correction Formulas

Correction for Absolute Length:
Use this if your 20m or 30m chain is inaccurate:
$L = \left( \frac{l'}{l} \right) \times L'$
- $L$ : True length of the line.
- $l'$ : Actual length of the chain used.
- $l$ : Standard length of the chain (e.g., 20m).
- $L'$ : Measured length in the field.
Correction for Slope:
To find the horizontal distance on sloping ground, the correction is always negative:
$C_{slope} = \frac{h^2}{2L}$
Correction for Pull:
If the pull applied ( $P$ ) differs from the standard pull ( $P_s$ ):
$C_p = \frac{(P - P_s) \times L}{A \times E}$
- $A$ : Cross-sectional area of the tape/chain.
- $E$ : Modulus of Elasticity.
Correction for Temperature:
If the field temperature ( $T_m$ ) differs from the standard temperature ( $T_o$ ):
$C_t = \alpha \times (T_m - T_o) \times L$
- $\alpha$ : Coefficient of thermal expansion.
Correction for Sag:
When the chain is suspended, this correction is always subtracted:
$C_{sag} = \frac{W^2 \times L}{24 \times P^2}$
- $W$ : Total weight of the chain.

Summary Table: Nature of Corrections

Source of Error	Nature of Correction
Slope	Always Negative (-ve)
Sag	Always Negative (-ve)
Chain is too short	Negative (-ve)
Chain is too long	Positive (+ve)

NTS Study Tips:
Before starting a survey, always verify your 20m or 30m chain against a Steel Tape.
In the field, no chain is 100% accurate; adjustments are expected.
"For a Civil Engineer, measuring the distance is only half the job; identifying and mathematically correcting hidden errors is where true engineering lies."

🏗️ 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).

NTS STUDY