Question Bank • QB_SWCE_ADV_135 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Surveying and Levelling

Subtopic: Types of levelling

Question Statement:

A levelling staff is held vertically at a distance of $d = 2.40\text{ km}$ from a level instrument. The staff reading observed through the telescope is $3.250\text{ m}$. Accounting for both Earth's curvature and atmospheric refraction, the true staff reading in meters is ________ (round off to two decimal places).

Answer Key:

2.86

Step-by-Step Solution & Explanation

**Method 1: Combined Curvature and Refraction Formulation** 1. Combined correction $C$ for distance $d$ in kilometers: $C = -0.0673 \cdot d^2\text{ meters}$ For $d = 2.40\text{ km}$: $C = -0.0673 \times (2.40)^2 = -0.0673 \times 5.76 = -0.38765\text{ m}$ 2. Corrected true staff reading: $\text{True Reading} = \text{Observed Reading} + C = 3.250 - 0.38765 = 2.86235\text{ m} \approx 2.86\text{ m}$ **Method 2: Separate Curvature and Refraction Components** - Curvature correction: $C_c = -0.0785 \times (2.4)^2 = -0.0785 \times 5.76 = -0.45216\text{ m}$ - Refraction correction: $C_r = +0.0112 \times (2.4)^2 = +0.0112 \times 5.76 = +0.06451\text{ m}$ - Net combined correction: $C = C_c + C_r = -0.45216 + 0.06451 = -0.38765\text{ m}$ - True reading $= 3.250 - 0.38765 = 2.862\text{ m} \approx 2.86\text{ m}$
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