Analysis of Errors in Taping/Chaining

Errors that occur while measuring distances with a tape or chain are generally Systematic. This means the more you use the tape, the more the error accumulates (Cumulative).

1. Correction for Standardization

A tape is only as accurate as its standardization. If a tape is shorter or longer than its Nominal Length, every single measurement will be incorrect.

• Rule: If the tape is longer than its actual length, the measured distance will be less than reality; therefore, the correction is Positive (+).

• Rule: If the tape is shorter than its actual length, the measured distance will be more than reality; therefore, the correction is Negative (-).

2. Correction for Temperature ($C_t$)

Steel tapes are highly sensitive to temperature. As seen in your example, in cold conditions like winter in the UK, a $20^\circ\text{C}$ difference can cause an error of $11.2\text{ mm}$ in a 50m tape.

• Formula:

  $$C_t = \alpha \cdot (T_m - T_o) \cdot L$$

  • $\alpha$ = Coefficient of thermal expansion

  • $T_m$ = Temperature during measurement

  • $T_o$ = Standard temperature (at which the tape was calibrated)

Analysis of Temperature Error:

Ignoring the temperature effect is a major source of error. For instance, at $0^\circ\text{C}$, a 50m tape standardized at $20^\circ\text{C}$ will contract by:

$$11.2 \times 10^{-6} \times 50 \times 20 \approx 11.2\text{ mm per 50m}$$

Even if you measure the temperature, inaccuracies can arise from a faulty thermometer, parts of the tape being in the shade while others are in the sun, or the thermometer recording air/ground temperature rather than the actual tape temperature. While an Invar tape would solve this, they are rarely used on-site due to their high cost and fragility.

The effect of temperature error ($\delta C_t$) can be assessed as:

$$\delta C_t = \alpha \cdot L \cdot \delta(T)$$

If $L = 50\text{m}$ and the temperature error is $\pm 2^\circ\text{C}$, then $\delta C_t = \pm 1.1\text{mm}$. If this error remains constant, it will be proportional to the number of tape lengths. Therefore, every effort should be made to obtain accurate values using a calibrated thermometer.

3. Correction for Pull/Tension ($C_p$)

If a tape is pulled harder than the Standard Pull, it stretches.

• Formula:

  $$C_p = \frac{(P_m - P_o)L}{AE}$$

  • $P_m$ = Pull applied in the field

  • $P_o$ = Standard pull (usually $50\text{ N}$ or $70\text{ N}$)

  • $A$ = Cross-sectional area of the tape

  • $E$ = Modulus of Elasticity (Young's Modulus)

Example:

Consider a 50m tape with a cross-sectional area of $4\text{ mm}^2$, a standard tension of $50\text{ N}$, and $E = 210\text{ kN/mm}^2$. Under a pull of $90\text{ N}$ ($40\text{ N}$ excess), the tape will stretch by:

$$C_p = \frac{40 \times 50,000}{4 \times 210 \times 10^3} \approx 2.4\text{ mm}$$

Since this value is proportional to the number of tape lengths, using a calibrated tensioning device (like a spring balance) is essential for precision.

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NTS Study Pro Tips:

• Tools: For high-precision measurements, always use a Spring Balance (for tension) and a Thermometer (for temperature).

• Invar: A common exam question—"Which tape is least affected by temperature?" Answer: Invar Tape (36% Nickel + 64% Steel).

• Nature of Error: Temperature and tension errors are Cumulative, meaning they grow as the total distance increases.

🏗️ 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

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📚 Quick Revision Resources

• Surveying Top 1-100 One-Liners

• Surveying Advanced (101-200) One-Liners

• Surveying Master Class (Part 1)

• Surveying Master Class (Part 2)

• Quick Revision Guide

• Quick Surveying Formulas

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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.

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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.

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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.

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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).

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5. Modern Surveying (Total Station & GPS)

• IS 16481:2016 – Guidelines for Accuracy and Testing of Total Stations.

• IS 14855:2000 – Terminology and Concepts for GIS and Remote Sensing.

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6. Measurement of Building Works

• IS 1200 (Part 27):1992 – Method of Measurement of Building and Civil Engineering Works (Earthwork & Surveying).