Measurement of Vertical Distances (Leveling)

Measurement of Vertical Distances

Vertical distance is the elevation difference between points. Leveling is the process of finding elevations or establishing points at a given elevation.

Methods of Leveling

1. Differential Leveling: Using a level (dumpy, tilting, automatic) and a graduated rod.
2. Profile Leveling: Determining elevations along a specific line (e.g., centerline of a road).
3. Trigonometric Leveling: Measuring vertical angles and horizontal distances to compute elevation.
4. Barometric Leveling: Using atmospheric pressure differences.

Differential Leveling Concepts

Standard Leveling Formulas

$HI = \text{Elev}_{BM} + BS$ $\text{Elev}_{TP} = HI - FS$

Curvature and Refraction ($h_{cr}$)

Due to the earth's curvature and atmospheric refraction, the line of sight is not truly horizontal.

1. Curvature ($h_c$): The earth curves away from the tangent line. $h_c = 0.0785 K^2$ (Where $K$ is distance in km, $h_c$ in meters).

2. Refraction ($h_r$): Light bends downward due to atmospheric density. $h_r = 0.0110 K^2$ (Where $K$ is distance in km, $h_r$ in meters).

3. Combined Correction ($h_{cr}$): $h_{cr} = h_c - h_r = 0.0675 K^2$ (Where $K$ is distance in km, $h_{cr}$ in meters).

Sign:

• Curvature makes objects appear lower.
• Refraction makes objects appear higher.
• Combined effect makes objects appear lower than they are. Add correction to rod reading.

Solved Problems