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Distance Measurement in Linear Surveying/Numerical Example (Temperature Correction)

Distance Measurement in Linear Surveying

In surveying, we primarily use three methods to measure the distance between two points:
Direct Method: Involves the direct use of a tape or chain.
Optical Method: Uses instruments like a Tacheometer where it is not necessary to physically walk the ground.
EDM Method (Electronic Distance Measurement): A modern method that utilizes laser or infrared waves.

रेखीय सर्वेक्षण (Linear Surveying) में दूरी मापन

Tape Corrections

To standardize the distance measured in the field ( $L$ ), the following corrections are applied:

1. Correction for Absolute Length

When the actual length of the tape is more or less than its designated length:

C_a = \frac{C \cdot L}{l}

Where $C$ is the correction per tape length.

Rule: If the tape is longer than standard, the correction is positive (+). If the tape is shorter, the correction is negative (-).

2. Correction for Temperature

If the temperature at the time of measurement ( $t_m$ ) differs from the standard temperature ( $t_o$ ):

C_t = \alpha(t_m - t_o)L

Where $\alpha$ is the coefficient of thermal expansion of the tape material.

3. Correction for Pull (Tension)

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

Where $P$ is the applied pull and $P_o$ is the standard pull.

4. Correction for Sag

When a tape is suspended in the air between two supports, it sags under its own weight.

C_s = \frac{L(W)^2}{24P^2}

Where $W$ is the total weight of the tape.

Important: Sag correction is always negative (-).

5. Correction for Slope

If the ground is sloping, to convert the measured inclined distance to a horizontal one:

C_{slope} = \frac{h^2}{2L}

Where $h$ is the difference in elevation between the two points.

Important: Slope correction is also always negative (-).

Numerical Example (Temperature Correction)

Question: A distance of 600m was measured between two points using a 30m steel tape. The average temperature during measurement was 35°C, while the tape was standardized at 20°C. The coefficient of thermal expansion ( $\alpha$ ) is $11.5 \times 10^{-6} / ^\circ\text{C}$ . Find the temperature correction and calculate the corrected distance.

Solution:

Given Data:
- Measured Length ( $L$ ) = 600 m
- Field Temperature ( $t_m$ ) = 35°C
- Standard Temperature ( $t_o$ ) = 20°C
- $\alpha = 11.5 \times 10^{-6} / ^\circ\text{C}$
Calculation:
$C_t = 11.5 \times 10^{-6} \times (35 - 20) \times 600$
$C_t = 0.1035 \text{ m}$
Since the field temperature ( $35^\circ\text{C}$ ) is higher than the standard ( $20^\circ\text{C}$ ), the tape has expanded. Therefore, the correction is positive (+ve).
Corrected Distance:
$\text{Corrected Distance} = 600 + 0.1035 = \mathbf{600.1035 \text{ m}}$

Advanced Numerical Example (Sag & Slope Correction)

Question: A 30m steel tape weighs 0.8 kg. It was used to measure distance on ground with a 10% slope. If the measured inclined distance is 300m and a pull of 10 kg was applied, calculate the slope correction, sag correction, and the final corrected horizontal distance.

Solution:

Given Data:
- $L = 300 \text{ m}$
- $W = 0.8 \text{ kg}$ (per 30m tape)
- $P = 10 \text{ kg}$
- Slope = 10% (10m vertical rise for every 100m horizontal)
Slope Correction ( $C_{slope}$ ):
For a 300m distance, the height ( $h$ ) is:
$h = 300 \times \frac{10}{100} = 30 \text{ m}$
$C_{slope} = \frac{30^2}{2 \times 300} = \mathbf{1.5 \text{ m (always -ve)}}$
Sag Correction ( $C_s$ ):
Since we used a 30m tape for 300m, there are 10 spans ( $n=10$ ).
$C_s = \frac{300 \times (0.8)^2}{24 \times 10^2} = \frac{192}{2400} = \mathbf{0.08 \text{ m (always -ve)}}$
Total Corrected Horizontal Distance:
$\text{Total Correction} = (-1.5) + (-0.08) = -1.58 \text{ m}$
$\text{Final Distance} = 300 - 1.58 = \mathbf{2 9 8.42 \text{ m}}$

NTS Study Pro-Tips:

Slope Correction: The steeper the ground, the larger the correction.
Sag Correction: The higher the Pull ( $P$ ), the smaller the sag.
Remember: In the field, measured distance is almost always greater than the actual horizontal distance, which is why these two corrections are always subtracted.

🏗️ 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).

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